Structure, Fluctuation, and Relaxation in Solutions

studies in physical and theoretical chemistry 83

STRUCTURE, FLUCTUATION, AND RELAXATION IN SOLUTIONS

This Page Intentionally Left Blank

studies in physical and theoretical chemistry 83

STRUCTURE, FLUCTUATION, AND RELAXATION IN SOLUTIONS Proceedings of t h e Y a m a d a C o n f e r e n c e X X X X l l , held at N a g o y a , J a p a n , 11 - 15 D e c e m b e r 1994

Edited by HIROYASU NOMURA

and F U M I O K A W A I Z U M I

Department of Chemical Engineering, School of Engineering, Nagoya University, Nagoya 464-01, Japan and JACK YARWOOD

Materials Research Institute, Sheffield Hal/am University, Pond Street, Sheffield $1 1WB, United Kingdom Reprinted from the Journal of Molocular Liquids, Volumes 65 and 66

A m s t e r d a m - L a u s a n n e - N e w York - O x f o r d

ELSEVIER - S h a n n o n - T o k y o 1995

ELSEVIER SCIENCE B.V. Sara Burgerhartstraat 25 P.O. Box 211, 1000 AE Amsterdam, The Netherlands

ISBN 0-444-82384-0 9Elsevier Science Publicatiosl and Yamada Science Foundation, 1995. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without the prior written permission from the publisher. Published by Elsevier Science B.V., Sara Burgerhartstraat 25, P.O. Box 211, 1000 AE Amsterdam, The Netherlands Special regulations for readers in the U.S.A.- This publication has been registered with the Copyright Clearance Center Inc. (CCC), 222 Rosewood Drive, Danvers MA 01923. Information can be obtained from the CCC about conditions under which photocopies of parts of this publication may be made in the U.S.A. All other copyright questions, including photocopying outside of the U.S.A., should be referred to the copyright owners, Elsevier Science B.V. and Yamada Science Fondation, unless otherwise specified. No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. This book is printed on acid-free paper. Printed in The Netherlands

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vi

z
/N, which describes the time evolution of the spacial correlation of an atom (self) and a pair of atoms (distinct). Multiplying F-~I.(6) by ~p(-k,0) and taking ensemble average, we have the diffusion equation for F(k,t), -

0F(k,t) = _ k 2 D(k) pdp(k)F(k,t) (9) (gt Taking the Fourier-Laplace transform of Eq. (9), the dynamic structure factor can be obtained

as, S(k,s) =[st+ kZD(k){co(k) -l - oc(k) } ~ ~F(k,t =0)

(10)

where I denotes the n-by-n unit matrix. Eq. (1 0) can be inversely transformed to give, F(k,t) ffi L(k,t)F(k, tffiO) where L(k,0 is defined by, 1

"

L( k,t) ffi - ~ t _ ~ .

+ A(k) l-i e*'ds

(11) (12)

and A(k) is defined as, A(k)--- k 2D(k)[to(k) -' - pc(k)]. The integral in Eq. (12) can be performed to lead for the (a,l~)-element of the matrix L, ~j (-1)p+a A ~ (sj)e*/ L~ = .

H,i.j)(s~ = s , )

(13) '

where {si} are the eigen values of the matrix sI+A, and A(xl3denotes the minor of the (a,l~)element of the determinant IIsI+AII.It is worthwhile to note that Fcttl(k,t) is a superposition of a number of exponentials with different time constants. In the following section, we will observe some interesting consequence of the multiexponential behavior of solvent dynamics, which is manifested in the solvation dynamics of ions. 1 0"9l~

0.8 ~ 0.7 ~i\ 0.6i ~ o.4i

Co)

o.~ ~

",,.',, S +) and the opposite process (S + >SO).While the second component begins after about 1/4 of the energy is relaxed in the S~ + process, it begins after almost 100 percent of the energy is relaxed in the S + E > S 0 process. Our current theory does not distinguish the two process due to the symmetric ~ of Eq. (19). Also noteworthy in the simulation result is that the nonequilibrium results in short time resemble the linear response results averaged over the equilibrium ensemble at the initial state, while those in later time come close to the linear response results at the final state. Our result shows closer resemblance to the linear response results sampled from the equilibrium ensemble prepared with SOthe neutral solute, which turns out to be similar to the non-equilibrium result for the S+E>SO process in overall behavior. This can be understood by considering the fact that our treatment uses the pure solvent dynamics at equilibrium although the solute pemtrbation is taken into aca~unt at the initial and the final states. The equilibrium ensemble prepared at the S O state has less perturbation to the solvent, and thereby it is closer to our theoretical model. Although the time constant for the second component of the S+-->S 0 process is not explicitly given in the literature, it would be much longer than - 1 ps, and would be closer to our result. Methyl chloride shows a similar hiexponential decay with acetonitrile with time constants, 0.21 and 82 ps. Methyl chloride shows the slower initial decay than acetonitrile despite of its less bulky strucUtre. This may be because the temperature of MeCI is significantly lower. Nonetheless, the general feature of the relaxation behavior for both solutes is almost identical in harmony with the simulation re$ults. 18 Water STCF for water features a bi-exponential behavior with very fast initial decay characteriz~ by the time constant 0.01 ps and a slow decay of time constant 36 ps. The fast decay can be assigned to the rotational relaxation of water molecules in the first coordination shell from their initial orientation to the final state in which the hydrogen atom points toward the chloride ion. The following slow decay can be attributed to the reorganization of water molecules in the second and further shells in order to adapt the new situation. A similar behavior in the initial decay has been found in the simulation study by Maroncelli and Flemingl7 except for the pronounced oscillation observed in the simulation. The oscillation is caused by a combination of the two factors, the inertial motion and restoring force due to the hydrogen-bonded structure. The theory does not reproduce the oscillation because it does not include the inertia term although it does take account for the hydrogen-bonded structure. 3 2.5

/

S 1.5

5 4

31 0..5

I

2

//'i

21 11

r

~

~

Fig.4(a) Solvent-sitedistributionaround CIwithout charge.CI-O (~); CI-Me (...);CI-H (--)

o.L

1

3

4

~

6

r

Fig.4(b) Solvent-site distribution around CI- ion. CI-O (--); CI-Me(...); CI-H (--)

Of more interest is the much faster decay compared to acetonitrile. A possible explanation for the phenomena is that water molecules are spherical in shape and thereby the friction due to collision is very small for the rotational motion. Recently, Nakahara and coworkers have measured the rotational diffusion rate of a single water molecule in a variety of solvent based on NMR relaxation time and have observed no-correlation between the rate and the viscosity of solvent. 19 Instead they have found a quite good correlation between the rate a n d the interaction between the solute (water) and solven~ The observation implies that as long as the rotational motion of water molecules is concerned friction due to the collision is less important. Methanol STCF for methanol is characterizedby a tri-exponential decay. Although fu~her study including the molecular dynamics simulation is required in order to clarify the detailed mechanism of each decay, we give here a speculative interpretation regarding a possible mechanism which gives rise to the tri-exponential decay. In Fig. 4, the radial distributions of atoms around chloride ion in equilibrium before and after the abrupt production of the charge on the solute are shown. Before the change, the solute is primarily coordinated either by the methyl group or by the oxygen site. After the change, the solute is predominantly coordinated by the hydrogen site. The first decay c h a r a c ~ by the time constant 0.03 ps is attributed to the initial rotation which brings the methyl group in the first coordination shell, which has a positive partial charge, into the intermediate position to form a weak Coulombic bond with C1-. This tm3cess will be quick because the solute was already well coordinated by the methyl group before the change. The solvent molecules in the first coordination shell further rotate to brmg the hydrogen atom into the final equilibrium position in which the hydrogen atom and the ion are 'bonded' by the strong electrostatic interaction. This process gives the second decay with the time constant 1.69 ps in the lnZ(t) plot- After the solvent molecules in the first coordination shell settled down in the final orientation, the molecules in the second and timber shells must be reorganized cooperatively to adapt themselves in the new equilibrium state. The prtx3ess will be very slow since it involves the relaxation of many molecules. The third decay characterized by the time constant 61.2 ps is assigned to that reorganization process. If the mechanism stated above is correct, the behavior should be different when the solute is a cation instead of an anion, because in that case, the primarily coordination site of the solvent after the abrupt change in charge state of the solute, is the oxygen atom. There is no such intermediate coordination structure as in the case of CI-. The behavior of lnZ(t) for Na + in fact shows essentially biexponential decay as shown in Fig.5. The different behavior in lnZ(t) between the CI-->CI- and Nam>Na + suggests that the multi-exponential behavior is caused not only by the solvent dynamics itself (Fjj'(k,t)) but also by the solute-solvent coupling represented by Bjj'(k) in Eq. (20). O

o%'I 0.15 T1

MeCI

MeCN MeOH Water

.

0.03 0.01

T2

T3

.0

34.6 1.69 36.3

.

.

.

,-6 ""

61.2

.

2

Table 1. Relaxation Times.

~= -10 - -12 ! -14~

.............

-16 -18

-2

~

lb 1'5 2'o 23 3'o 3'5 ~ 4'5 t/ps Fig. 5 in Z(t) for Na -->Na + and Clm>Clprocesses in MeOH; Cl, (m); Na, (--). Concluding R e m a r k s We have presented a method of describing the dynamics of liquids and the solvation dynamics based on the interaction-site model. The method has exhibited its ability to account for the diversity in the relaxation behavior of solvent, such as the multi-exvonential decay.

22 observed in the polar and hydrogen-bonded solvents. An important implication of the results is that the detailed microscopic description of solvent structure and the solute-solvent coupling is essential for studying the solvation dynamics. The results presented here are still preliminary in quantitative sense. The problem which can be easily recognized is the much faster initial decay in every case than what is observed in the experiments (or simulations). Two remedies for the problem are under investigation: (1) replacing the translational diffusion constant by more elaborated model for the single particle dynamics which explicitly includes the rigid body rotation, and (2) inclusion of the nonlinearity in the density field in the SSSV equation.

Acknowledgment Authors ate gateful to the refen~es for invaluable comments on the manuscript.

References 1. Dynamics and Mechanics of Photoinduced Electron Transfer and Related Phenomena, Proceedings of Yamada Conference XXIX, N. Mataga, eds., Elsevier Science Publication and Yamada Science Foundation, 1992. 2. F. O. Raineri, Y. Zhou, H. L. Friedman, Chem. Phys., 152, 201 (1991). 3. F. tFuma, J. Chem. Phys., 96, 4619 (1992). 4. F. O. Raineri, H. Resat, B-C Perng, F. Hirata and H. L. Friedman, J. Chem. Phys. 100. 1477-1491(1994). 5. H. L. Friedman, F. O. Raineri, F. Hirata and B-C Pemg, J. Star. Mech., 78, No 1/2, 239 (1995). 6. H. Mori, Prog. Theor. Phys., 33, 423 (1965). 7. D. Chandler and H. C. Andersen, J. Chem. Phys., 57, 1930 (1972). 8. F. Hirata and P. J. Rossky, Chem. Phys. Leg., 83, 329 (1981); F. Hirata, P. J. Rossky, and B. M. Pettitt, J. Chem. Phys., 78, 4133 (1983). 9. F. Hiram and T. Munakata, in preparation. 10. T. Munakata, J. Phys. Soc. Jptt, 58, 2434 (1989). 11. D. Chandler, J.D. McCoy and SJ. Singer, J. Chem. Phys., 85, 5971(1986); 85, 5977(1986). 12. S. Okazaki, Y. Miyamoto, and I. Okada, Phys. Rev., 1145, 2055 (1992). 13. B. Bigot, B. J. Costa-Cabral and J. L. Riv'~l, J. Chem. Phys., 83,3083 (1985). 14. D. M. Edwards, P. A. Madden, and I. R. McDonald, Mol. Phys., 1141 (1984). 15. H. J. C. Berendsen, J.P.M. Postma, W.F. van Gunsteren, and J. Hermans, in Intermolecular Forces, ed. B. Pullman (Reidel, Dordrecht, 1981). 16. W. L. Jorgensen, J. Am. Chem. Soc., 103, 335 (1981); J. Chandrasekhar, D. C. Sellmeyer, W. L. Jorgensen, J. Am. Chem. Soc., 106, 903 (1984). 17. M. MaronceUi and G. R. Fleming, J. Chem. Phys., 89, 5044 (1988). 18. M. Maroncelli, J. Chem. Phys., 94, 2084 (1991). 19. M. Nakahara and C. Wakai, Chem. Left., 809 (1992); J. Chem. Phys., 97,4413 (1992).

journal of

~IOLECULAR

LIQUIDS Journal of Molecular Liquids, 65/66 (1995) 23-30

ELSEVIER

The Interplay of Dielectric and Mechanical Relaxation in Soivation Dynamics Benjamin J. Schwartz and Peter J. Rossky Department of Chemistry and Biochemistry University of Texas at Austin Austin, TX 78712-1167 USA Abstract Quantum molecular dynamics simulations are used to explore the possible coupling between dielectric solvation, the response of the solvent to a change in charge distribution of the solute, and mechanical solvation, the response of the solvent to a change in solute size or shape. The hydrated electron is chosen as a solvation probe, due to its large increase in spatial extent upon photoexcitation and significant contraction in size upon non-adiabatic relaxation. The strong displacement of translational solvent modes upon excitation hampers the effectiveness of individual solvent molecule rotations in providing relaxation, decreasing the relative amplitude of the inertial response. Following non-adiabatic relaxation, solvent molecules can freely translate and reorient, leading to rapid, effective initial solvation. These results suggest that in many situations where solutes undergo changes in both charge distribution and size, solvation can become rate-limited by the relatively slow viscoelastic solvent response.

I. Introduction Whenever the electronic states of a solute are coupled strongly to the surrounding environment, the dynamics of the solvent can play a critical role in determining the fate of condensed phase chemical species. Indeed, solvent fluctuations define the reaction coordinate for electron transfer and many other types of chemical reactions, l This has prompted an explosion of recent interest in solvation dynamics: the study of the relaxation of the solvent following a sudden perturbation due to a change in the solute. 2 At the heart of the issue are the specific solvent motions that lead to relaxation. When the solvent rearranges to accommodate the change in the solute, are the motions of individual solvent molecules important or should the response be viewed as inherently collective? In polar solutions, are reorientational or translational motions of the solvent molecules more effective in lowering the energy of the perturbed solute? Are there different types of solvent responses to changes in solute charge distribution versus changes in solute size and shape? A great deal of progress has been made recently in answering these questions for dielectric relaxation, that is, the response of the solvent accompanying a change in charge distribution of the solute. 2 Theory predicts that the earliest time motions of the solvent relaxing th e perturbed solute are inertial in character. 3 This inertial relaxation has now been observed in many simulations and by experiment, which are approaching generally good agreement. 4 Simulations have established that this early time relaxation can be ascribed to individual molecular behavior, 5 and theoretical developments have linked these motions to an instantaneous normal mode description of the solvent. 6 Less well examined, however, are the molecular details for the solvent mechanical response, that is, 0167-7322/95/$09.50 91995 Elsevier Science B.V. All rights reserved. SSDi 0167-7322 (95) 00841-1

24 the relaxation of the solvent accompanying a change in solute size and/or shape. Transient hole-burning experiments using non-polar solutes have established that the mechanical relaxation of the solvent behaves in a manner qualitatively similar to the dielectric response. 7 Molecular dynamics simulations changing the dispersion interaction between the solute and the solvent also show similar behavior. 8 Since real chemical solutes undergo changes in both size and shape and charge distribution upon photoexcitation or chemical relaxation, it is imperative to study the potential interplay between these mechanical and dielectric solvent responses. In this paper, we present the results of quantum molecular dynamics simulations aimed at a preliminary exploration of the coupling between mechanical and dielectric solvation dynamics. We have chosen the hydrated electron as our solute probe, since the hydrated electron is known to undergo large changes in both size and shape and charge distribution upon photoexcitation, and since experimental results are available for direct comparison. We find that translational motions of the solvent are of key importance in accommodating the change in size of the solute, and that relaxation by solvent rotational motions may in fact be significantly altered by coupling to the mechanically-induced solvent translations. II. Methodology The non-adiabatic quantum simulation procedures 9 we employ have been well described previously in the literature, 10 so we describe them only briefly here. The model system consists of 200 classical SPC flexible water molecules, II and one quantum mechanical electron interacting with the water molecules via a pseudopotential. 12 The equations of motion were integrated using the Verlet algorithm with a 1 fs time step in the microcanonical ensemble, and the adiabatic eigenstates at each time step were calculated with an iterative and block Lanczos scheme. 9 Periodic boundary conditions were employed using a cubic simulation box of side 18.17/~ (water density 0.997 g/ml). Twenty configurations from a 35 ps ground state adiabatic trajectory, chosen to be on resonance with the laser bandwidth corresponding to the experiments, were selected as the starting points for non-adiabatic excited state trajectories, lo A corresponding set of trajectories was run in D20, with a model identical in all respects to the work described previously except that the mass of the H atom was changed from 1 to 2 amu, and preliminary results of the behavior in D20 are included here. III. Results Figure 1 presents the dynamical history of the 2 lowest adiabatic eigenstates of the hydrated electron for a typical trajectory. At times before t=0, the electron resides in its nearly spherical s-like ground state, with the first p-like excited state lying -2.2 eV to higher energies. Solvent fluctuations modulate the energies of these states, and the strength of the coupling is readily manifest in the large changes in energy (nearly an eV on time scales of tens of femtoseconds). Previous work has established that size and shape fluctuations of the solvent environment have different effects on the quantum energy levels. 13,14 Upon promotion to the first excited state, the electron grows in size by a factor o f - 2 along the axial lobes of the p-like wavefunction, but remains unchanged in diameter in the other two dimensions, l0 The surrounding solvent cavity takes on a peanut shape to accommodate this change, and the net result is that the energy of the unoccupied nodeless ground state is raised while the energy of the occupied p-like state remains mostly unchanged. The electron eventually makes a non-adiabatic transition back to the ground state (which happens near t=200 fs for the trajectory shown, before the excited state equilibrium is attained). After the transition, the eigenenergy of the s-like state rapidly drops so the ground state equilibrium energy gap is quickly recovered, and

0-

'

~-l~

-100

0

100

Time

200

300

400

(fs)

Figure 1. Adiabaticeigenstatesof the hydrated electron for a typical trajectory. Solid and dashed lines denote the ground and first excited states, respectively. Diamondsmark the occupied state. the electronic density quickly becomes localized in one half of the peanut shaped cavity, creating a void in the solvent. As discussed elsewhere, 10 the behavior of the quantum energy levels upon excitation is in good agreement with previous simulations using a different model of the hydrated electron, 15 and the rapid re-establishment of equilibrium following radiationless relaxation is consistent with older, adiabatic calculations. 14 Since the hydrated electron experiences a substantial change in charge distribution upon quantum transition, undergoes a large increase in spatial extent upon photoexcitation, and experiences a corresponding collapse in size upon non-adiabatic relaxation, it serves as an outstanding quantum mechanical probe of the coupling between the mechanical and dielectric solvent responses. To better understand the behavior of the quantum eigenstates following photoexcitation and non-adiabatic relaxation, we have computed non-equilibrium ensemble averages of the quantum energy levels, shown in Figure 2. The left panel shows the response of the adiabatic eigenstates following photoexcitation (the "up" ensemble average); it is an ensemble average that only includes configurations in which the electron still occupies the excited state. Thus, the data at early times contain contributions from all 20 trajectories, but the statistics get poorer at later times as electrons make the radiationless transition to the ground state and are removed from the ensemble. The data clearly show that following photoexcitation, the excited state energy remains essentially unchanged while the ground state energy is raised on two time scales: a rapid increase which takes place in the first 30 fs, and a slower response which takes several hundred femtoseconds. At equilibrium, it is apparent that the gap has decreased from its initial value o f - 2 . 2 eV to 0.5-0.6 eV. The fight-hand portion of Figure 2 shows the change in the quantum energy levels following the non-adiabatic transition (the "down" ensemble average); in constructing this average, we have defined t=0 to be the point at which the non-adiabatic transition occurs for each trajectory. This is a fairly unusual kind of ensemble average: many of the initial configurations start after radiationless transition from the equilibrated excited state, but some initial configurations result from excited state trajectories in which the solvation response is not yet complete (such as the -200 fs point shown in Figure 1). Since all the excited trajectories undergo non-adiabatic relaxation at some point, the traces presented here are averaged over all twenty runs, resulting in good statistics over the entire time period displayed. After radiationless decay over an average gap size of -0.6 eV, solvent relaxation rapidly lowers the energy of the occupied ground state, with most of the response completed within 25 fs. There is evidence for slower relaxation of the ground state on longer time scales, but any slower component of the response plays a much smaller role than that following photoexcitation. Like the upwards transition, the first electronic excited state undergoes little change in energy in response to non-adiabatic

26

.

>

@

@

m

-2

0

I t I I I 300 600 900 1200 0 50 100 150 200 250 Time After Ph0toexcitation (fs) Time After Non-Adiabatic Transition (fs)

Figure 2. Non-equilibriumensemble averages of the lowest 2 adiabatic eigenstates of the hydrated electron. Solid line denotes the ground state, dashed line the first excited state. The left panel shows the response of the energy levels following promotion via photoexcitation; the right panel shows the response following the radiationless transition to the ground state. See text for details. relaxation. Within a few hundred fs of the non-adiabatic transition, the equilibrium structure of the hydrated electron is already re-established, with the gap enlarging to its original value o f - 2 . 2 eV. This rapid evolution to equilibrium once the ground state becomes occupied is in agreement with both the results of previous calculations 15 and the observed dependence of the different elements of the calculated ultrafast transient spectroscopy compared to experiment. 16 One interesting feature of the downwards ensemble average lies in the smoothness of the traces present in the right-hand plot of Figure 2. The energy levels of the individual trajectories (cf. Fig. 1) fluctuate by - 1 eV on a rapid time scale due to coupling with various modes of the solvent. The fact that these large fluctuations are washed out in the ensemble average following relaxation to the ground state indicates that there is no preferred phase of a particular solvent motion that drives the non-adiabatic transition. If, for example, particular configurations of water molecules characterized by being at the turning point of a collective librational mode were more favorable for non-adiabatic relaxation, then some of the oscillations observed in the individual trajectories would add coherently and hence be enhanced in the ensemble average. The lack of large amplitude oscillations in the average indicate that no special water configurations are responsible for driving the non-adiabatic dynamics. It is also interesting to note the small recurrence in dae response between 25 and 30 fs after the downward transition. This oscillation is most likely due to an underdamped librational mode of the solvent, and has been observed in previous aqueous molecular dynamics simulations. 17 IV. D i s c u s s i o n

The effects of mechanical and dielectric solvent fluctuations on the quantum energy gap of a solute are described by the equilibrium solvent response function: C(t) = (~SU(0) 8U(t))/((~SU) 2 ) where U(t) is the value of the quantum gap at time t and 5U(t) = U ( t ) - (U) represents the deviation of the gap from its average value. For small

27 perturbations, the regression of fluctuations due to a non-equilibrium perturbation should decay in the same manner as those present in equilibrium. Thus, in the limit of linear response, the non-equilibrium correlation function S(t) = (U(t) - U(oo))/(U(O) - O(oo)) (1) where the overbar denotes a non-equilibrium average quantity, should be identical to the equilibrium response, C(t). We note that the typical time-dependent Stokes shift experiment which investigates the solvent dielectric response or the transient holeburning experiment used to explore mechanical solvation measure the non-equilibrium solvent response function S(t). Figure 3 presents a comparison of the non-equilibrium solvent response functions, Eq (I), for both the photoexcitation ("up") and non-adiabatic ("down") transitions (cf. Fig. 2). The two traces are markedly different: the inertial component for the downwards transition is faster and accounts for a much larger total percentage of the total solvation response than that following photoexcitation. The solvent molecular motions underlying the upwards dynamics have been explored in detail in previous work, where it was also determined that the solvent response falls within the linear regime, i~ Unfortunately, the relatively small amount of time the electron spends in the excited state prevents the calculation of the equilibrium excited state solvent response function due to poor statistics, leaving the matter of linear response for the downwards S(t) unresolved. Whether the radiationless transition obeys linear response or not, it is clear that the upward and downwards solvation response behave very differently, due in part to the very different equilibrium solvation structures of the ground and excited state species. Interestingly, the downwards S(t), with its much larger inertial component, resembles the aqueous solvation response computed in other simulation studies, 17 and bears a striking similarity to that recently determined in experimental work based on a combination of depolarized Raman and optical Kerr effect data. 18 While the difference in the upwards and downwards solvent responses presented in Figure 3 is striking, this is not the first time that variations in solvation dynamics for the same solvent have been observed. Experimental studies have shown differences in solvation response for different probe molecules in the same solvent.2 This is a direct indication that probe molecules which have different excited state charge distributions and different mechanical interactions with the solvent produce differing relaxation dynamics. Computersimulations have also observed differing solvation dynamics for the forward and reverse transitions of the sudden appearance of charge, indicative of a solutedependent solvent response.17 Moreover, theoretical work has shown that dielectric solvation dynamics is sensitive to the shape of a solute,19 and that solute size is intimately connected to viscoelastic relaxation.2~ It is these effects which are manifest in the

\

0

- - -

100 Time (fs)

Down

200

Figure 3. Photoexcitation (up) and non-adiabatic relaxation (down) solvent responses (Eq. 1)

28 difference between the upwards and downwards solvent responses for the hydrated electron. The size, shape and charge distribution of the electron change continuously (on the time scale of the solvent response) following photoexcitation, creating a situation where the solvent dynamics polarize the solute which then alters the solvent dynamics. The solvent response is determined by both the dynamically changing charge distribution and the mechanical forces of the growing electron pushing on the first solvent shell during its initial expansion. Upon the non-adiabatic relaxation, the electronic density quickly localizes to a shape about that of the final equilibrium ground state. The solvent response to this rapid change in charge distribution is also affected mechanically by the presence of the large void recently occupied by one lobe of the excited state electron. These microscopic differences in the upwards and downwards transitions have profound implications for the coupling of viscoelastic and dielectric solvation dynamics and the nature of the solvent response. Previous work examining dielectric solvation has ascribed the initial relaxation to rotational motions of individual solvent molecules (i.e., polar solvent molecules inertially reorient to create a more favorable dipole interaction with the new charge distribution of the solute). 4,5 The rapid expansion of the hydrated electron upon photoexcitation, however, displaces predominantly translational modes of the solvent. Water molecules in the first solvation shell are simply pushed back by the Pauli repulsion (mechanical) forces as the electron expands. Thus, much of the initial relaxation of the solvent is the launching of an acoustic wave following this sudden expansion of the solute: the relaxation is predominantly viscoelastic in character. There are three major pieces of evidence pointing towards the strong translational nature of the initial response. First, time-dependent pair distribution functions show large solvent molecule displacements relative to the solute center of mass on the inertial time scale. 10 Second, computed ultrafast transient spectroscopic traces show ringing at frequencies corresponding to intermolecular H-bond stretching and bending motions. 16 Finally, deuteration changes the time scale of the initial relaxation by < 10%, a value in accord with motion involving translation of an entire water molecule whose mass has increased from 18 to 20 amu (the corresponding change in moment of inertia if the initial dynamics were predominantly rotational in nature would be 2 !/2, resulting in a --40% increase in the inertial time scale). This isotope effect is illustrated in Figure 4. This idea of predominantly displacing translational solvent modes upon excitation leads to an appealing microscopic picture for the coupling of the mechanical and dielectric solvent response. Upon photoexcitation, the free energy will be lowered by both solvent molecule translations, accommodating the new solute size and shape, and solvent molecule rotations, creating favorable electrostatic interactions with the new

08 ~

1_ ~ x

H20

0.6

0.4? 0.2 0

I ~,, 50 100 T i m e (fs)

150

Figure 4. Solvent response following hydrated electron photoexcitation (Eq. 1) for H20 and I)20

29 solute charge distribution. With a continuously expanding solute like the newly excited hydrated electron, the effectiveness of rotational motions of solvent molecules in the first shell will be hindered due to the overwhelming Pauli repulsion forces driving these molecules translationally. This leads to a kind of "dielectric frustration", where the electrostatic relaxation accomplished through solvent rotations is rate-limited by the overall translational rearrangement which accompanies the viscoelastic relaxation. This idea has support in recent experimental work examining the solvent response of the polar solvent propylene carbonate to photoexcitation of a completely non-polar solute, stetrazine. 21 In this work, the solvent response function near room temperature, which is well fit by a simple analytic theory incorporating only viscoelastic relaxation, 20 is virtually identical to that observed using the polar dye molecule coumarin 152 as a probe. 22 This opens up the possibility that in the latter work, the dye molecule undergoes a change in size and shape as well as dipole moment, and that the observed dielectric solvent response is actually rate-limited by the mechanical relaxation, producing the remarkable agreement between the two very different experiments. The relatively small amplitude of the inertial component of the upwards solvent response may also be the result of this mechanical-dielectric solvation coupling. While the motion of the first shell molecules is inertial in the sense that the solvent-solvent forces play little role in the dynamics, the pressure on these molecules due to the expanding solute hinders their rotational motion. Thus, the decreased effectiveness of these initial ballistic motions can also explain the differences in inertial component amplitude observed in Figure 3 (40%) and in previous aqueous simulation work 17 (8090%) where only the charge but not the size of the solute was varied. The downward solvent response for the hydrated electron also fits nicely into this picture. The effective size of the ground state electron in one lobe of the excited state peanut-shaped cavity does not significantly change upon non-adiabatic collapse. Molecules in the first solvation shell along the lobe into which the electron localizes do not need to significantly translate to accommodate the newly formed ground state electron. Molecules along the newly vacant lobe can freely translate into the void unhindered, providing rapid solvation. This picture is in accord with the agreement between the downward S(t) and that determined experimentally from the Raman-OKE data; the Raman-OKE experiments are not sensitive to relaxation by solvent translations, and show this same type of dominant rapid inertial response. 18 V. Conclusions In summary, we have used quantum molecular dynamics simulations of the hydrated electron to investigate the coupling between the mechanical and dielectric solvent responses. The solvation dynamics following photoexcitation shows a strong degree of translational character, because the increase in size of the hydrated electron provides mechanical pressure on the first solvation shell. This mechanical displacement hampers the effectiveness of solvent molecule rotations in providing relaxation, and results in a smaller amplitude of the inertial response. Following non-adiabatic relaxation, molecules in the first solvation shell are either displaced very little, or can freely translate through the newly created void in the solvent, providing for rapid and highly effective solvation. These results suggest that there is strong interplay between the dielectric and mechanical solvent responses, and that in certain cases, "dielectric frustration" can occur in which dielectric relaxation may be altered or even rate-limited by the viscoelastic response of the solvent.

Acknowledgments This work was supported by the National Science Foundation. BJS thanks Dave Vanden Bout for many stimulating discussions. BJS gratefully acknowledges the support of a National Science Foundation Postdoctoral Fellowship in Chemistry, and the allocation of computational resources from the San Diego Supercomputing Center.

References 1. see, e . g . J . T . Hynes in Ultrafast Dynamics of Chemical Systems, edited by J. D. Simon, p. 345 (Kluwer, Dordrecht, 1994). 2. M. Maroncelli, J. Mol. Liq. 57, 1 (1993). 3. M. Maroncelli, P. V. Kumar, A. Papazyan, M. L. Horng, S. J. Rosenthal and G. R. Fleming, in Ultrafast Reaction Dynamics and Solvent Effects, edited by Y. Gauduel and P. J. Rossky, AIP Conf. Proc. 298, p. 310 (AIP Press, New York, 1994); E. A. Carter and J. T. Hynes, J. Chem. Phys. 94, 5961 (1991). 4. S.J. Rosenthal, X. Xie, M Du and G. R. Fleming, J. Chem. Phys. 95, 4715 (1991); R. Jimenez, G. R. Fleming, P. V. Kumar and M. Maroncelli, Nature, 369, 471 (1994). 5. see, e . g . M . Maroncelli, J. Chem. Phys. 94, 2084 (1991); L. Perera and M. L. Berkowitz, J. Chem. Phys. 96, 3092 (1992); Ibid. 97, 5253 (1992). 6. R.M. Stratt and M. Cho, J. Chem. Phys. 100, 6700 (1994). 7. J.T. Fourkas and M. Berg, J. Chem. Phys. 98, 7773 (1993); J. T. Fourkas, A. Benigno and M. Berg, J. Chem. Phys. 99, 8852 (1993). 8. J.G. Saven andJ. L. Skinner, J. Chem. Phys. 99, 4391 (1993). 9. F. A. Webster, P. J. Rossky and R. A. Friesner, Comput. Phys. Commun. 63, 494 (1991); F. A. Webster, E. T. Wang, P. J. Rossky and R. A. Friesner, J. Chem. Phys. 100, 4835 (1994). 10. B.J. Schwartz and P. J. Rossky, J. Chem. Phys. 101, 6902 (1994); Ibid., p. 6917. 11. K. Toukan and A. Rahman, Phys. Rev. B 31, 2643 (1985). 12. J. Schnitker and P. J. Rossky, J. Chem. Phys. 86, 3462 (1987). 13. B.J. Schwartz and P. J. Rossky, Phys. Rev. Lett. 72, 3282 (1994). 14 J. Schnitker and P. J. Rossky, J. Phys. Chem. 92, 4277 (1988). 15. R.B. Barnett, U. Landman and A. Nitzan, J. Chem. Phys. 90, 4413 (1989). 16. B. J. Schwartz and P. J. Rossky, J. Phys. Chem. 98, 4489 (1994); Y. Kimuar, J. C. Alfano, P. K. Walhout and P. F. Barbara, J. Phys. Chem. 98, 3450 (1994). 17. see, e.g., M. Maroncelli and G. R. Fleming, J. Chem. Phys. 89, 5044 (1988). 18. E. W. Castner Jr., Y. J. Chang, Y. C. Chu and G. E. Walrafen, J. Chem. Phys., in press; Y. J. Chang and E. W. Castner Jr., J. Chem. Phys. 99, 7289 (1993). 19. see, e.g.E.W. Castner Jr., G. R. Fleming and B. Bacghi, Chem. Phys. Lett. 143, 270 (1988). 20. M. Berg, Chem. Phys. Lett. 228, 317 (1994); B. Bagchi, J. Chem. Phys. 100, 6658 (1994). 21. J. Ma, D. Vanden Bout and M. Berg, private communication. 22. M. A. Kahlow, W. Jarzeba, T. J. Kang and P. F. Barbara, J. Chem. Phys. 90, 151 (1989).

journal o f

~IOLECULAR

LIQUIDS ELSEVIER

Journ',d of Molecular Liquids, 65/66 (1995) 3 I--40

Fluctuating Charge Force Fields for Aqueous Solutions Steven W. Rick, Steven J. Stuart, Joel S. Bader, and B.J. B e r n e D e p a r t m e n t of C h e m i s t r y and Center for Biomolecular Simulation C o l u m b i a University, NY 10027

Abstract

A new molecular dynamics model in which the point charges on atomic sites are allowed to fluctuate in response to the environment has been developed in a previous work (J. Chem. Phys., 101:6151 (1994)). The model and its application to liquid water are briefly reviewed. Various properties of the model are calculated, with emphasis on the bonding characteristics. The water model is also used to investigate the aqueous solvation of formaldehyde.

1

Introduction

In simple molecular force fields the intramolecular electronic structure is often modeled by point charges fixed on well-defined sites in the molecular frame. The charges are constant and thus cannot respond to changing electrostatic fields which arise from movement of the atoms during the simulation. In reality, molecular electronic structure can be strongly influenced by the external environment. Charge induction effects are not pair-wise additive and improved models must go beyond pair potentials. A new simulation method in which the charges are responsive to environmental changes, presented in a recent paper[l], combines the electronegativity equalization (EE) method for determining atomic charges[2, 3, 4, 5, 6, 7] and the extended Lagrangian method for treating fictitious degrees of freedom as dynamical variables [8, 9, 10, 11]. This approach treats charges on the molecular sites as dynamical variables by introducing fictitious kinetic energy terms and selfenergy terms for these charges into the Lagrangian for the system, along with Lagrange constraints ensuring electroneutrality. In this extended Lagrangian approach the charges are propagated according to Newtonian mechanics in a similar way to the atomic degrees of freedom. An application of this model to liquid water and comparisons to wen-known water potentials are given in P~ef. [1]. In this paper we briefly review the fluctuating charge method, and describe its application to both liquid water and a dilute aqueous solution of formaldehyde.

2

Dynamical Fluctuating Charge Models

In an isolated atom the energy of creating a partial charge, QA, can be expanded to second order

E(QA) = ~~

lr0

,a2

+ -~AA~A,

0167-7322/95/$09.50 r 1995 Elsevier Science B.V. All rights reserved. SSDi 0167-7322 (95) 00842-X

(2.1)

32 where )~4 and J~4A are parameters dependent on the atom type. The parameter ~ is the Mulliken electronegativity of the isolated atom (per electronic charge lel) and J~4A is twice the atom's hardness. For a molecule, the polarization energy to create a set of partial charges is a sum of these atomic self-energies and intramolecular Coulomb interactions, Job(r), or E p~

1

Y~fr176 + "~Y~ Y]~ Qi~Qi/3Ja~(rio,iz)- E~p, cr

a

(2.2)

/3

rio,iZ is Iria - ri/31 and E~ p is the gas-phase energy of molecule i. The total energy for Nmoler molecules includes this polarization energy plus the usual Lennard-Jones and intermolecular

where

Coulomb terms,

The electronegativity per unit charge of atom A is given by XA = (OU/OQA). The charges, by the EE principle, are those for which the electronegativities are equal. This is equivalent to minimizing the energy subject to a charge neutrality constraint. Since the potential is quadratic in the charges, the minimization will lead to a set of coupled linear equations for the charge. The charges are not independent variables since there is a charge conservation constraint. In the following we constrain each molecule to be neutral, ~ a Qia = O. We treat the charges as independent and use the method of undetermined multipliers to enforce the constraint. T h e Lagrangian is then Nmolec N . . . .

Nmolec Natom

lrno§ + E i=1

c):l

E

i--1

Nmolec

1M'"O.~ - U({Q}, {r}) - E

~:1

i=1

Na.tom

~' E

Qi~,

(2.4)

o--1

where mo is the mass of atom c~ and Mio is a fictitious charge "mass", with units of energy • time 2/charge 2, and the ,~i are Lagrange multipliers. The nuclear degrees of freedom evolve according to Newton's equation and the set of charges evolve in time according to Mi.Qi,~

= _OU({Q}, {r}) _ )~i = -;~i,~ - ~ . OQi.

(2.5)

If the total charge of molecule i is a constant of the motion, then it can be shown that )q is the negative of the average electronegativity on molecule i. The force on the charge is simply the difference between the average electronegativity and the instantaneous electronegativity at that site. The charge mass, Mia, a fictitious quantity, should be chosen to be small enough to guarantee that the charges readjust very rapidly to changes in the nuclear degrees of freedom[l]. The Coulomb interaction, Ji/(r), for intramolecular pairs is taken to be the Coulomb overlap integral between Slater orbitals centered on each atomic site, with each orbital characterized by a principal quantum number, ni, and an exponent (i[6].

Table 1: Properties for potentials with the TIP4P geometry: the fixed-charge TIP4P and the flexible charge TIP4P-FQ models. Properties listed are the the gas-phase dipole moment, the dipole polarizabilities, c~ii (the y and z directions lie in the plane of the molecule, with the z-axis along the C2 axis), the energy of the dimer in its minimum energy configuration, the distance between oxygen atoms for the minimum dimer configuration, and properties of the liquid as indicated.

Gas-phase dipole moment (Debye)

~zz (h3) %~ (A 3) ~ (h 3)

TIP4P ~ 2.18

TIP4P- FQ 1.85

0 0 o

0.82

2.55 o

experimental 1.85c 1.468+0.003 d 1.5284-0.013 a 1.4154-0.013 d -5.44-0.7 9 2.98 e

Dimer energy (kcal/mole) -6.3 -4.5 Dimer O-O length (~) 2.75 2.92 Liquid state properties (7'=298 K, p=l.0 g/cm a) Energy (kcal/mole) -10.1 a -9.9 -9.9 a 0.0 b -0.16-1-0.03 0.0 Pressure (kbar) Dipole moment (Debye) 2.18 2.62 53+21 79-1-8 78~ ~0 1 1.5925=0.003 1.79g Diffusion constant(10 -9 m2/s) ' 3.6+0.2 ~ 1.9+0.1 2.30 h 1.44-0.2b 2.1-t-0.1 2.1 / r#M. (ps) 74-2b 84-2 8.274-0.02J To (ps)

a) Ref. [13], b) Ref. [14], c) Ref. [15], d) Ref. [16], e) Ref. [17], f) Ref. [181, g) Ref. [19], h)

l~ef. [20],i)Ref. [21],j)Ref. [22]

3

Results

P u r e w a t e r . The fluctuating-charge method (fluc-q) has been applied to two commonly used models of water[l], the simple point charge model (SPC)[12] and the 4-point transferable intermolecular potential model (TIP4P)[13]. Here we focus on the fluc-q version of the T I P 4 P model ( T I P 4 P - F Q ) . Systems of 256 TIP4P-FQ or TIP4P water molecules have been simulated in the NVE ensemble at an average temperature of 298 K and a density of 1 g/cm 3, using Ewald summation for the long-ranged interactions. For more detailed discussion of the model parametrization and simulation methodology, the reader is referred to our previous work[l]. The properties of the TIP4P and T I P 4 P - F Q models for the water monomer, water dimer, and liquid water are listed in Table 1. The T I P 4 P - F Q electrostatic parameters are chosen to give the correct gas phase dipole moment for the monomer. The dimer properties listed in Table 1 are the energy of the minimum energy configuration and the oxygen-oxygen distance of this configuration. Pair potentials, such as SPC and TIP4P, are parametrized to give the experimental liquid state energies and radial distribution functions and tend to overestimate the gas phase water dimer energy. The fluctuating charge potentials predict an oxygen-oxygen separation closer to the experimental value but underestimate the dimer energy.

34 We have calculated both static and dynamical properties of liquid water at a temperature 298 K and a density of 1 g/cm 3. The parameters for both fluc-q models are chosen to give a binding energy of-9.9 kcal/mol. This energy includes the self polarization energy, which is the difference between the self-energy in the liquid phase and the gas phase (see Eq. 2.2). The average self-polarization energy is 5.7 kcal/mol, which represents a large contribution to the total energy. Pair correlation functions give detailed information about the structure of the liquid. The TIP4P-FQ model gives pair correlation functions that are in good agreement with the neutron diffraction results of Soper and Phillips[23]. For details see Ref. [1]. The static dielectric constant, e0, is calculated from the fluctuations in M , the total dipole of the central simulation box, by (4~p~ eo = %0 + \ 3kT ]

( M ~ -- (___M)2] Nmolec J "

(3.1)

For the TIP4P-FQ model, a 1 ns simulation gave e0 = 79-/-8, in good agreement with experiment. This is consistent with earlier findings that models with a dipole moment of 2.6 D have a dielectric constant near 80[24, 14, 25]. The value obtained for the optical dielectric constant, coo, is 1.59, close to the experimental value of 1.79119], and is underestimated because the perpendicular polarizability, axx, is zero. The frequency dependent dielectric constant, e(w), for the TIP4P-FQ model is shown in Figure 1. The agreement with the experimental results[22, 26, 27] is very good. The close agreement in the low-frequency microwave range is due to the accurate T I P 4 P - F Q values of ~0 and the Debye relaxation time, rD (the exponential decay constant for the autocorrelation function of the total system dipole, M ) . The features at frequencies higher than 300 ps -1 are due to bond stretches and bends absent in the rigid geometry models used here. The highest frequency feature given by the TIP4P-FQ model is the librational mode, which shows a peak in e" at 130 ps -1. The experimental peak is at 90 ps-1127]. The feature at 25 ps -1 has been interpreted as a translational vibration of a water molecule in its cage of nearest neighbors[28], and is not present in the spectrum for non-polarizable water models such as TIP4P[18] or Matsuoka-Clementi-Yoshimine (MCY)[29]. As argued by Neumann, this translational motion will not change the system's dipole moment much for non-polarizable models, but for polarizable models, the translational motion will induce a change in the dipole moment[18]. Therefore this feature only exists in polarizable models. We have investigated the differences in bonding between the fluc-q and fixed-charge models by examining the distributions of pair energies, solvation energies, and residence times. In a molecular model with fixed charges, the pair energy Eij is easily defined as the sum of all pairwise interactions between molecules i and j. For many-body potentials, however, there is no unique definition of a pair energy; the sum of the pair energies Etj does not add up to the total system energy because the self-polarization energy is not included. There are several reasonable ways to distribute a molecule's polarization energy among the pairwise interactions in which it participates, each leading to a different definition of the pair energy. We have defined a normalized pair energy /~ij by including a portion of each participating molecule's polarization energy proportional to the strength of the pair energy,

E'i = E'.i +

Eij E~j AEyOl+ AZpOi. ~ k # i Eik ~kCj Ekj

(3.2)

This weighting reflects that the polarization energy varies as the magnitude of the induced dipole, and that large dipoles will be induced in pairs with strong interactions.

35 A distribution of pair energies is shown in Figure 2 for both TIP4P-FQ and TIP4P. The large peak centered near zero consists of the many distant, weakly interacting pairs in the liquid. The much smaller peak at low energies represents the strongly-bound close neighbors. A convenient definition of a hydrogen bond is any pair bound more strongly than the minimum in this distribution (-2.7 kcal/mol for TIP4P,-2.6 kcal/mol for TIP4P-FQ). Integrating up to this threshold gives 3.1 hydrogen bonds for both models. (Other authors have reported larger hydrogen bonding numbers, but used a different cutoff for the hydrogen bond energy[13].) The longer tail on the T I P 4 P - F Q distribution demonstrates the ability of fluc-q methods to allow for cooperativity in bonding; TIP4P water has a fixed lower limit of-6.2 kcal/mol on any pair interaction, while T I P 4 P - F Q waters have

100

10

~g'

1

t:

0.1

ir, il 0.01 0.01

-------L----

0.1

1

10

100

1000

w/ps -1 Figure 1: Real(top) and imaginary (bottom) parts of the frequency dependent dielectric constant for the TIP4P-FQ model (solid lines), compared to experiment (dotted lines).

36 no such restriction and can form much stronger bonds when other neighbors are oriented favorably. The average strength of a hydrogen bond for TIP4P-FQ waters is 4.38 kcal/mol, compared to 4.32 kcal/mol for TIP4P. Cooperativity can also hinder bonding, and will generally serve to broaden the bonding distribution. Although the high-energy (weakly bound) tail of the H-bond distribution is lost in the zero-energy peak, the broadening can also be seen in the total bonding energy between one molecule and the rest of the simulation cell (obtained by summing Eq. 3.2 over a single index). The distribution of these values is centered at -20 kcal/mot for both models (twice the solvation energy per molecule) but the widths differ. The full width at half-maximum is 8.2 kcal/mol for TIP4P, and 10.1 kcal/mol for TIP4P-FQ. Another way of examining the hydrogen bonding character of the liquid is to determine the first passage time of neighbors out of the first coordination shell, a sphere of radius equal to the first minimum in the oxygen-oxygen pair correlation function (3.3/~ for both T I P 4 P and TIP4P-FQ). A distribution of first-crossing times shows that the TIP4P-FQ molecules are more labile than TIP4P waters at times shorter than 0.3 ps, with a probability of escaping from the first shell increased by 8% over TIP4P waters. But at times between 0.5 and 4 ps, the TIP4P waters leave more readily, with an 18% higher escape probability. This suggests that the fluc-q waters are more fickle in forming hydrogen bonds, breaking away from unfavorable interactions more easily. But once a bond has been formed, it tends to last longer. After 4 ps, the number of molecules who have not left the first solvation shell decays exponentially, with the same decay constant for both models. A survival probability can also be defined by allowing for multiple recrossings[30], but this obscures the short-time behavior which illustrates an important difference between the two models.

i

I

!

i

1.4 1.2

if j

/

]

11

",,

,

',,

!

0.8

/ ',, 9 "", ....

II

I

I

iI ,,/

N(E)

0.6 0.4 0.2 J

0

-8

/I I

-6

!

-4

,

I

1

-2

0

2

4

E (kcal/mol)

Figure 2: Pair energy distributions for TIP4P (dashed line) and TIP4P-FQ (solid line).

37 In general, however, the flexible charge models have slower translational and rotational timescales than the fixed-charge models, primarily due to the stronger electrostatic interactions from the higher charges. The self-diffusion constant, D, is smaller than the fixed-charge models and closer to the experimental value (see Table 1). Rotational time constants for both molecular and system dipole reorientation (rNMR and rD) are also slower and in good agreement with experiment. F o r m a l d e h y d e . Fluctuating charge models for water can also provide insight regarding the structuraJ, energetic, and dynamic aspects of hydrogen bond formation between a water molecule and a solute. One expects that polarizable water molecules next to a solute molecule more polar than bulk water will have a dipole moment enhanced over the bulk value. We have studied the enhancement of the induced dipole on water molecules around a polar solute. As we will show below, the magnitude of the induced dipole on a water molecule next to a solute is strongly correlated with certain aspects of the solvation structure. The system we studied consisted of 209 TIP4P-FQ water molecules and one formaldehyde molecule in a cubic box 18.6/~ on a side. The formaldehyde solute was based on a model of Levy and coworkers [31, 32]. The rigid, planar formaldehyde molecule has a CO bond length of 1.184/~, a CH bond length of 1.093 ~, and an OCtt angle of 122.3 ~ The charges on 0, C, and tt are -0.577, 0.331, and 0.123 lel respectively; the Lennard-Jones a parameters are 2.85, 3.296, and 2.744 ~'; and the Lennard-Jones e parameters are 0.20, 0.12, and 0.01 kcal/mol. Standard combining rules were used to obtain the Lennard-Jones parameters for the interactions between formaldehyde sites and the oxygen site of TIP4P-FQ water. This model for formaldehyde yields a dipole moment of 3.9 D, which is 50% larger than the mean dipole moment of a TIP4P-FQ water molecule in bulk water. The results we present in Figure 3 are from a 20 ps run in the NVE ensemble with an average temperature of 300 K. In the top panel of Figure 3, the mean dipole moment of a water molecule is shown as a function of the distance between the water oxygen and the formaldehyde oxygen. Waters closer than 3 are seen to have a dipole moment enhanced over the bulk dipole moment by as much as 0.3 D. Past 4 ~, the water dipoles rapidly approach the value of 2.62 D characteristic of the bulk liquid. It is interesting to note the dip in the dipole moment of water molecules about 3/~ away from the formaldehyde molecule. Waters in this region are caught between the first and second solvation shell. These water molecules presumably lack the opportunity to form a strong hydrogen bond with either the formaldehyde or a neighboring water molecule. Consequently a smaller dipole moment is induced on these water molecules than the mean dipole induced on bulk water. The bottom panel of Figure 3 shows the strong angular correlations exhibited by water molecules between the first and second solvation shells. The cosine of the OHO angle formed by the formaldehyde oxygen and the H O of a water molecule is nearly 1 for water molecules closer than 3 /?k, indicative of a strong linear hydrogen bond. There is a precipitous drop at 3 /~, signaling the breaking of the hydrogen bond as the water molecule leaves the first solvation shell. Other angular correlations do not show nearly as sharp a jump between the first and second solvation shells. The dashed line, for instance, depicts the cosine of the angle made by the formaldehyde CO and a water oxygen. This angle tends to be more linear for waters closer to the formaldehyde, and angular correlation is lost slowly as the water moves away. The cosine of the angle between the symmetry axes of formaldehyde and water is shown in the dotted line. This angular correlation is also weak compared with the dramatic behavior of the OHO angle.

38

2.9

(,.,o>

I

I

I

I

I

2.8

(Debye) 2.7 2.6 2.5

2

0.75

0.5

(cos(0)) 0.25

i

i

i

i

i

i

i

2.5

3

3.5

4

4.5

5

5.5

I

I

I

I

I

I

~ "'""......

~

9

~

f

~

.'-..

QIIO '..'"'"....-......." - - . 7 - " = (

-0.25

f

~...

6

-

,, -.-.~. 0, the spectral shapes given by the terms [A]+[C] and [B] are reduced to

[A]+[C]-exp[-t/Vo]~r-eexp[-Aoge/0,e]exp[-Ao92/2 0,2 ], [ B ] - e x p [ - t / v 0 ] 0 , -2 exp[-Aw 2/G2]exp[-(Ao92 + 2aQ 2 + 2 b q 2 ) 2 / G 2 ] ,

(4) (5)

apart from the unimportant factor. The spectral shapes corresponding to the term [A]+[C] and [B] are coincident with those of the stationary absorption and fluorescence spectra, respectively. Then the hole spectrum is expected to be expressed by the sum of the steady state

43 absorption and fluorescence spectra. Under this condition, we can obtain the term [D] in eq (3), the Sn~--S1 absorption spectrum of the solute molecule, subtracting [A]+[C] and [B] from the hole spectrum. According to eq (3) the time dependences of the hole spectrum on the excitation energy are as follows. When we excite the dye solution at the center of the absorption band, a hole is created around the peak of the ground state population, while an excited state population created by the light irradiation shows a considerable deviation from the energy minimum of the adiabatic potential curve. The subsequent relaxation process causes a time dependent shift in position for the excited state population, while the ground state hole only broadens with time. Consequently, the fluorescence spectrum shows a time shift. The transient absorption spectrum also shifts toward the low energy side with broadening. However, this shift is caused mainly by the time dependent shift of the excited state population. Contrary to this, the case where the excitation is chosen at the tail of the low energy side of the absorption band is completely different. In this case, a hole is created at the tail of the ground state population and then shifts gradually to the peak of the initial population, while in the excited state the population is created almost at the bottom of the potential curve and hence does not show the time dependent shift. Therefore, the shift of the hole spectrum is caused mainly by the time dependent shift in the ground state population, and the shift in this case occurs toward the higher energy side. It is well known that the fluctuational behavior of the solvent molecules is characterized by the normalized time correlation function of the fluctuation, p,, (t), which is expressed as a following equation using observed time resolved fluorescence spectra,

p.(t)- v[(t)- ~1(oo), ~ (0) - r (~)

(6)

where ~;r(0), vr(t), and ~;i(o0) denote the peak energy of the fluorescence spectrum at t

=

0,

t, and oo, respectively. Fluorescence Stokes shift, i.e., ~5.(0)- vi(t), is usually explained as the dielectric dispersion of the surrounding medium and interaction of the solute dipole with the reaction field, in which the energy shift in the fluorescence spectrum is proportional to the square of the difference of the dipole moments between the ground and excited states of the solute molecule. On the other hand, the spectral width is linearly related with the difference of the dipole moment under the assumption included in eqs (1) and (2). Then p,, (t) is expressed using spectral widths as,

[,~(t)'- _,~(o~),~1~9m (t) ~ , V ' ~ 2

--. C~'(00) 2

(7)

where &(t) is the half width of the spectrum at time t. In this paper we investigate the time dependent ground state hole spectrum of cresyl violet in polar solvents by means of subpicosecond transient absorption spectroscopy. The time correlation function expressed by eq (7) showed large difference in time profiles compared with the reported one expressed by eq (6). Possible mechanisms will be discussed.

Experimental Time resolved hole burning spectra were measured by means of a femtosecond transient absorption spectrometer system. A second harmonics of a mode locked cw Nd 3+:YAG laser (Quantronix, 82MHz) was used for a pumping source. A synchronously pumped rhodamine 6G dye laser with a saturable absorber dye jet (DODCI/DQOCI) and dispersion compensating prisms in the cavity was used. The output of the dye laser (100fs fwhm, 600pJ/pulse) was

44 amplified up to ca. 400 p J/pulse by 4-stage dye amplifier excited by a regenerative YAG amplifier (Continuum) with 50Hz. The optical arrangement of the spectrometer is illustrated in Fig. 1. The amplified laser pulse was divided into two by a beam splitter; one was used as a pump pulse collimated to a 2mm sample cell, the other was focused into a quartz cell containing I)20 to produce a continuum probe pulse which was used for the absorption measurement employing the combination of a spectrograph and a multichannel photodiode array. A small part of the probe pulse was used as a reference employing another spectrograph/detector combination. The time resolution of this system was about 150fs. Dispersion effect of the probe pulse was corrected automatically using calibration table obtained from the measurements of a cross-correlation between pump pulse and continuum probe pulse or of a rise curve at each wavelength of a broad band Sn*--S 1 absorption spectrum such as chrysene and porphyrins. Cresyl violet (Exiton) was used as received. Spectrograde acetonitrile, methanol and ethanol were used without further purification. Two or three samples of each solvent with different dye concentration in the order of 10-5M were used for the measurements. No concentration effect on the time correlation function was observed. ,,

I

I~

H2

0

H2

cresyl violet

CPU

PC

^i.,

V, ~ j L P ~ ' f

s,.a.

\

M aS

M

I" O C ~ (DO)

]

"~:.-,.S..

,a f .......

~,

L .......

"

(c)

i

~'--'

E~L 7L

fromDyek'~. FIG. 1. The optical arrangement of the spectrometer. L:lens, BS:beam splitter, M:mirror, D:depolarizer, F:filter, PC:spectrograph, S:shutter, MCPD:multichannel photodiode array detector, CPU: computer,

Results

4OO

~) 6O0 wavelengthInm

700

FIG. 2. Steady state absoption and stimulated fluorescence spectra of cresyl violet in acetonitrile (a), methanol (b), and ethanol (c) at room temperature. Exciting wavelength is indicated by the arrow.

and Discussion

Normalized steady state absorption and stimulated fluorescence spectra of cresyl violet in polar solvents are shown in Fig. 2. Stimulated spectra were calculated from the fluorescence spectra divided by the square of the wavenumber. Exciting wavelengths in each solvent used for the measurements are also indicated in the figure by arrows. Mirror image relation between

45 absorption and fluorescence specWa was observed in each solvent and the amounts of Stokes shift were about 800em "1 in acetonitrile and methanol, and 700crn -1 in ethanol, indicating that the difference of the dipole moment of cresyl violet between the ground and fluorescent states is rather small, and that the equal curvature of their potential curves assumed in the model discussed in the previous chapter may be acceptable in this system. The exciting wavelengths used here correspond to the 0-0 transition of the molecule according to the literature9.

9

9

9

9

9

9

",...

(2 4ee

,~e

9 see

sse

~/

9 .;

O#

4) 6ee

6~

"tee

Toe

~e

o

0

.....

5

. . . .

,

10'

'

t i m e / ps

wavelength / rn

FIG. 3. Estimation of the Sn5), the solvation dyna~cs observed follows the predictions simple models based on the solvent's bulk dielectric response. For a number of "non-dipolar" solvents such as dioxane and benzene, for which e o ) of the various response functions. These data show that the SC prediction for the response to a charge perturbation (#1) is too fast compared to the observed dynamics by a factor of approximately two. (The SC prediction for a dipole jump is sinfilar to that for a charge jump.) The DMSA prediction for a charge jump (#2; "DMSAi") is very close to the observed dynamics whereas the DMSA prediction for a change in solute dipole CDMSAd") is more than two-fold slower than the observed response. These observations concerning the performance of the various theories are quite general, as we will show presently. However, before doing so, we must make an important point regarding the use of dielectric data in such comparisons. The solvent response measured in time-resolved emission studies involves all solvent motion occurring on time scales slower than that of the electronic transition itself, i.e. slower than optical frequencies. Dielectric data, even those from recent experiments that, as in the case of DMSO [20], extend to the 100 GHz range, do not include all relevant nuclear motions of the solvent. For example, the dielectric data for DMSO used in Fig. 3 was reported to follow a Davidson-Cole distribution with parameters ao--46.40 ande..--4.16. The fact that some of the nuclear polarizability of the solvent is missed by this parameterization is indicated by the fact that at optical frequencies eop,--nv2=2.19. The difference e . . - nv2=1.97 reflects the contributions of nuclear responses in the FIR CPoley absorption") and IR regions (intramolecular vibrations) not captured in the dielectric data. Although this neglected part may seem small compared to the total polarizability of E0--46.40, the effect of these contributions on the computed solvation dynamics can be considerable, as illustrated by curve #4 in Fig. 3. This curve is a SC (ion) calculation which ignores such

54 contributions. The t~, and < ~ > times are slower than the same SC calculations that include these effects by factors of 9 and 5 respectively[ Although DMSO is an extreme example (in most solvents e . - no 2 is smaller than in DMSO), the difference is an important one, and proper comparisons must include the fast part of the nuclear response not directly observed in dielectric measurements. In the calculations described here we have treated this contribution as if it were a single relaxation m r m with a longitudinal time constant of 0.1 ps. This particular form of the time-dependence is arbitrary and is certainly an over simplification of the real dynamics. Luckily however, as long as the term describing the unobserved part of s is assumed reasonably rapid, its particular form and time scale do not appreciably affect the calculated values of t~, and < 1:>.

m 102

te

Figure 4. Comparison of ob~rv~ solvation times to predictions of the SC and DMSA theorics. The points show the comparison between the DMSA theory for an ionic solute with polar aprotic solvents denoted by circles and associated solvents by squares. For clarity,

j " ~ - - " .....--'" ........Q ...-'" .......

101 ._E~v i 0 ~ ~

. ~

..

the SC and DMSAd comparisons are only shown

E--

-o

I03

"~

I0 2 101

.j~ ~ '

I

t~'

L~ i 0 o

lO-t 10-1

10 ~

Observed

101 Time

102

103

as the linear fits to the log-log data with the SC predictions being the lower dashed line and the DMSAd the uPl~ dashed line. The solvents represented here are, in order of ~ i n g tie: acetonitrile, acetone, tetmhydrofuran, dimethylformamide, dimethylsulfoxide, propylene carbonate, dimethyl carbonate, chloroform, and benzonitrile (circles) and water [16], formamide, methanol, ethylene glycol, ethanol, l-prolmnol, l-peatanol, and l-decanol (squares).

(ps)

Figure 4 compares the characteristic times observed with C153 in a wide range of polar solvents to the predictions of the diele,ctric theories just described. As in Fig. 3, one finds good agreement between the times predicted by the DMSA theory for the response to a charge jump CDMSAi") and the observed dynamics. In contrast, the predictions of the simple continuum (ion) and DMSA calculations for a dipole change in the solute CDMSAd ~176 are r c s ~ v e l y too fast and too slow compared to experiment. The agreement between the observed dynamics and the DMSAi predictions also extends to the shapes of the response functions, as illustrated in the comparisons provided in Figs. 2 and 3. This is rather remarkable agreement, given that it extends over a wide variety of polar solvents, both associawxi and non-associated, whose solvation times span more than 3 orders of magnitude. It demonstrates the basic soundness of theories that link polar solvation dynamics to the solvent's dielectric response. However, it must be recognized that the DMSA theow is not a complete theory for the observed dynamics. If it were, one would expect to find agreement with predictions of the DMSA theory meant to model dipole jumps CDMSAd') rather than

55 with the ion version CDMSAi"), since the lowest-order multipole of the solute that changes upon electronic excitation is its dipole moment, not its charge. Indeed, calculations show that charge distributions of polyatomic molecules such as C153 and their change upon excitation are likely to be more quadrupolar in nature than dipolar [21]. Thus, one would expect that the observed dynamics should be even slower than that predicted by the DMSAd theory. The fact that the observed dynamics is in actuality faster is an indication that some aspect of the real system's dynamics is not properly captured by the DMSA theory. Simulations of lattice solvents [22] demonstrate that the DMSA theory does accurately predict the dynanfics of both charge and dipole jumps when (as assumed by the theory) the solvent dynamics involves only rotational motion of point dipole particles. What is neglected in the DMSA theory is: i) that solvent molecules translate in addition to rotate and ii) that the solute does not really see a nearby solvent molecule as a point dipole but rather as an extended charge distribution. The effect of translational motions, which contribute an additional relaxation channel for solvation via "polarization diffusion" [2,23] is clearly to speed up the response relative to the DMSA predictions. The effect of the extended charge distribution of solvent molecules is more subtle to gauge but, at least in some cases, this difference has also been shown to hasten the response [24]. We can summarize these results in the following way. The SC model provides useful first estimates for the solvation dynamics observed with a polar solute such as C153. However, due to its complete neglect of molecular aspects of solvation, it predicts response times that are uniformly too rapid. The DMSA approach, when properly applied (i.e. the DMSAd model), predicts too slow a solvation response. This latter model includes some important effects of solvent molecularity which serve to increase the response time compared to the SC predictions, while it neglects certain others that happen to act in the opposite direction. Thus, the agreement between the dynamics observed with the solute C153 and those pwxiicted by the "inappropriate" DMSAi theory should be regarded as partly fortuitous. Nevertheless, the surprising accuracy of the DMSAi predictions makes this simple model of considerable practical value. DYNAMICS IN NON-DIPOLAR SOLVENTS The success of dielectric models in describing the solvation of C153 in polar solvents is quite remarkable. Although, as just discussed, certain aspects of the dynamics are still not quantitatively described by theory, it is fair to say that the basic features of solvation dynamics in polar solvents are well understood. We would like to conclude by observing that the same cannot be claimed for the dynamics in non-dipolar solvents. Figure 5 shows that in the nominally "nonpolar" solvents dioxane and benzene, C153 undergoes time-dependent shifts that are in all respects analogous to the dynamics observed in weakly polar solvents such as chloroform [8]. However, theories of the sort described above, relying as they do on e(co), are inadequate to describe apparently similar solvation dynamics taking place in these latter solvents. Because they lack significant dipole moments, the solvation response predicted on the basis of their dielectric properties (i.e. by e0) is very small [6]. The fact that these and similar non-dipolar solvents we have examined do solvate C153 strongly is a consequence of the large quadrupole and higher-order electrostatic moments these molecules possess. At the short ranges relevant for molecular solvation, these higher moments (or alternatively the

56 charged groups or dipolar bonds) of the solvent molecules are as effective in solvating C153 as are the dipoles of weakly polar solvents. But the long-range dipolar correlations measured by the bulk property E(ca) are virtually absent in these solvents. Thus, to describe the dynamics observed in such solvents one does not have empirical information of the sort contained in e(o~) or an equivalent of the benchmark SC approach available for dipolar solvents. Furthermore, since the range of the interactions between the solvent and solute is shorter in such solvents, one expects that the details of the solvation structure and the effects of wanslational motion should be of much greater importance to the dynamics than in the dipolar solvent case. Thus, we anticipate that these types of solvents should provide a challenging testing ground for the future development of molecular models of solvation and solvation dynamics. l~gare5. Trine-resolvedspeclra of C153 in dioxane and benzene (connected points). The times shown are 0, 0.1, 0.5, 1, 2, and 10 ps from right to left. The dashed curves are the steady-state emission (red curve) and the speclrum expected prior to any solvent relaxation (blue curve; see Ref. 17).

i

3

0 16.

18.

Frequency

20.

22.

24.

(10 3 c m -I )

ACKNOWLEDGMENTS This research was supported by funds from the Office of Basic Energy Sciences of the US Department of Energy and by the Office of Naval Research. REFERENCES 1. See the reviews: J. T. Hynes, in Ultrafast Dynamics of Chemical Systems, I. D. Simon, Ed. (Klewer, Dordrecht, 1994), pp. 345-381; H. Heitele, Angew. Chem. Int. Ed. Engl. 32, 359 (1993). 2. Reviews of the experimental literature are provided in: M. Maroncelli, J. Mol. Liq. 57, 1 (1993); and P. F. Barbara and W. Jarzeba, Adv. Photochem. 15, 1 (1990); W. Jarzcba, G. C. Walker, A. E. Johnson, P. F. Barbara, Chem. Phys. 152, 57 (1991). 3. Reviews of theoretical and simulation studies can be found in Ref. 1 and B. Bagchi and A. Chandra, Adv. Chem. Phys. 80, 1 (1991); and F. O. Raineri, Y. Zhou, H. L. Friedman, Chem. Phys. 152, 201 (1991). Some of the most recent theoretical developments are described in: F. O. Raineri, H. Resat, B.-C. Perng, F. Hirata~ H. L. Friedman, J. Chem. Phys. 100, 1477 (1994); and B. M. Ladanyi and R. M. Stratt, J. Chem. Phys. (1995).

4. B. Bagchi, J. Chem. Phys. I00, 6658 (1994); Svaen and J. L. Skinner, J. Chem. Phys. 99, 4391 (1993) and luther work in progress. 5. M. Berg, "Comparison of a ViscoelasticTheory of Solvation Dynamics to Tune-Resolved Experiments in a Nonpolar Solution," Chem. Phys. Lett.,in press. 6 J.T. Fourkas, A. Benigno, M. Berg, J. Chem. Phys. 99, 8552 (1993); J. T. Fourkas and M. Berg, J. Chem. Phys. 98, 7773 (1993). 7. See, for example, E. T. J. Nibbering, D. A. Wiersma, K. Duppen, J. Chem. Phys. 183, 167 (1994); S. Y. Goldberg, E. Bart, A. Meltsin, B. D. Fainberg, D. Huppert, J. Chem. Phys. 183, 217 (1994); T. Joo, Y. Jia, G. R. Fleming, "Ultrafast Liquid Dynamics Studied by Thrid and Fifth Order Three Pulse Photon Echoes," preprint (1995). 8. A more complete account of these studies is cunently in preparation. (M. L. Homg, J. Gardecki, and M. Maroncelli, "Sub-Picosecond Measurements of the Solvation Dynmrdcs of Coumain 153," to be submitted to J. Chem. Phys.) 9. M. Maroncelli and G. R. Fleming, J. Chem. Phys. 86, 6221 (1987); M. Maroncelli and G. R. Fleming, J. Chem. Phys. 86, 3251 (1990). 10. P. K. McCarthy and G. J. Blanchard, J. Phys. Chem. 97, 12205 (1993); W. Baumann and Z. Nagy, Pure Appl. Chem. 65, 1729 (1993). 11. M. Maroncelli, P. V. Kumar, A. Papazyan, M. L. Homg, S. J. Rosenthal, G. R. Fleming, in Ultrafast Reaction Dynamics and Solvent Effects, Y. Gauduel and P. J. Rossky, Eds. (American Institute of Physics, New York, 1994), pp. 310-333. 12. M. Maroncelli and G. R. Fleming, J. Chem. Phys. 89, 5044 (1988); J. S. Bader and D. Chandler, Chem. Phys. Lett 157, 501 (1989). 13. M. Maroncelli, J. Chem. Phys. 94, 2084 (1991). 14. A. E. Carter and J. T. Hynes, J. Chem. Phys. 94, 5961 (1991). 15. S. J. Rosenthal, X. Xie, M. Du, G. R. Fleming, J. Chem. Phys. 95, 4715 (1991); S. J. Rosenthal, R. Jimenez, G. R. Fleming, P. V. Kumar, M. Maroncelli, J. Mol. Liq. 60, 25 (1994). 16. R. Jimenez, G. R. Fleming, P. V. Kumar, M. Maroncelli, Nature 369, 471 (1994). 17. R. S. Fee and M. Maroncelli, Chem. Phys. 183, 235 (1994). 18. B. Bagchi, D. W. Oxtoby, G. R. Fleming, Chem. Phys. 86, 257 (1984); G. van der Zwan and J. T. Hynes, J. Phys. Chem. 89, 4181 (1985). 19. I. Rips, J. Klafter, J. Jormer, J. Chem. Phys. 88, 3246 (1988); I. Rips, J. Klafter, J. Jormer, J. Chem. Phys. 89, 4288 (1988); A. L. Nichols HI and D. F. Calef, J. Chem. Phys. 89, 3783 (1988); see also M. Maroncelli and G. R. Fleming, J. Chem. Phys. 89, 875 (1988). 20. J. Barthel, IC Bachhuber, R. Buchner, J. B. Gill, and M. Kleebauer, Chem. Phys. Lett. 167, 62 (1990). 21. C. F. Chapman, R. S. Fee, and M. Maroncelli, "Measurements of the Solute Dependence of Solvation Dynamics in 1-Propanol: The Role of Specific Hydrogen Bonding Interactions," submitted to Chem. Phys. Lett. 22. H. X. Zhou, B. Bagchi, A. Papazyan, M. Maronceili, J. Chem. Phys. 97, 9311 (1992); A. Papazyan and M. Maroncelli, "Rotational Dielectric Friction and Dipole Solvation: Tests of Theory Based on Simulations of Simple Model Solutions," J. Chem. Phys., in press. 23. G. van der Zwan and J. T. Hynes, Physica 121A, 227 (1983). 24. F. O. Rained, Y. Zhou, H. L. Friedman, Chem. Phys. 152, 201 (1991).

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journal of

~IOLECULAR

LIQUIDS ELSEVIER

Journal of MolecularLiquids,65/66 (1995) 59-64

Solvent and Nuclear Dynamic Effects on Intermolecular Electron Transfer Keitaro Yoshihara, 1, 2 Yutaka Nagasawa, 2 Arkadiy Yartsev, 1, + Alan E. Johnson,l,$ and Keisuke Tominaga 1 llnstitute for Molecular Science, Myodaiji, Okazaki 444, Japan 2The Graduate University for Advanced Studies, Myodaiji, Okazaki 444, Japan

Abstract An ultra_fast intermolecular electron transfer (ET) from electron donating solvent to an excited dye molecule was found. A temperature-dependent non-exponential time dependence was observed in aniline, and a temperature-independent single exponential process for Nile blue (160 fs) and oxazine 1 (260 fs) was observed in N,N-dimethylaniline. The solvation times of solvent anilines were obtained by dynamic Stokes shift measurements. The rate of ET in some systems was observed to be much greater than the solvation time of anilines. The dynamic behavior was simulated by the 2-dimensional potential energy surface for reaction, taking into account of the effects of both solvent reorientation and nuclear motion of reactants.

I. Introduction The universality of intermolecular electron transfer (ET) makes the mechanism one of the central questions to be solved in chemistry and biology. ET is strongly influenced by the nature of solvent and its dynamics in solution. Dynamical solvent effects on the course of reaction have recently studied both theoretically [1-5] and experimentally [6-15]. For ET with a rate comparable to the solvent fluctuation rate, the motion and structure of the solvent can determine the rate of ET and it becomes the "solvent-controlled" reaction [2,3, 6-9]. Most recently we have investigated ultrafast ET (as fast as ca. 1013 s-1) between excited dye and weakly polar electron-donating solvent molecules [10-14]. These systems have several interesting features. (1) The electron donor and acceptor are in contact and there is no translational diffusion to induce ET. (2) Non-equilibrium reaction caused by solvent dynamics can be observed. (3) Some systems have a rate of ET much faster than that of solvent relaxation. In this case the reaction is mainly due to the nuclear dynamics and is independent of solvent dynamics. (4) A clear substituent effect of electron acceptor molecules on the rates of ET is observed. The time scale of ET observed in these systems falls into the time scale of solvent relaxation and of nuclear motions and the reaction will be severely influenced by these dynamics. It is also the aim of the present study to investigate the role of intermolecular interaction, namely, solvent effects to the reaction as well as the effects of inter- and intramolecular dynamics. The oxazine dyes are Nile blue A perchlorate (NB) and oxazine 1 perchlorate (OX1), which are ionic dyes, and coumarin 102 is chosen as a fluorescent probe molecule in the dynamic Stokes shift measurements. The electron donating solvents are aniline (AN) and N,N-dimethylaniline (DMA).

II. Experimental Ultrafast fluorescence quenching dynamics were studied by the fluorescence-upconversion method with femtosecond mode-locked laser systems. For the studies of oxazine dyes, a synchronously pumped hybrid mode-locked dye laser with group velocity 0167-7322/95/509.50

91995 ElsevierScience B.V. All rights reserved.

SSDI 0167-7322 (95) 00910-8

60 compensation prisms was made to generate optical pulses at different wavelengths at 76 MHz. Using a combination of Rh-6G and DODCI/DQOCI and spatial filters between the second prism and end mirror, 70 fs pulses were generated at 615 nm. With a combination of sulforhodamine 101 and DQTCI generation of 50 fs pulses at 675 nm was achieved. For the studies of fluorescence dynamics of coumarins, we used the second-harmonic of a modelocked Ti: sapphire laser, at 395nm, to excite the sample. The remaining fundamental at 790nm was used to up-convert the fluorescence from the sample.

IH. Results and Discussion A. Solvent relaxation times of electron donating solvents W e observed ultrafastE T in the subpicosecond timescale which was thought to be much faster than the diffusive solvent relaxation process [I]. To confirm this the measurement of solvent relaxation time is carried out. The dynamic fluorescence Stokes shift is used to determine solvent relaxation times of the donor solvents ( D M A and AN). W h e n a probe dye molecule is photo-excited, the dipole moment increases instantaneously. The polarization of the surrounding solvent molecule responds to this change and startsto reorganize. Therefore, the energy relaxation process, caused by the solvent reorganization, shiftsthe fluorescence spectrum to longer wavelengths. To extract dynamical information of solvent relaxation process, the normalized spectral shiftcorrelation function C(O is measured [16],

C(t) = v(t)- v(..)

v(O)- v(..)

(1)

where v(t), v(,,), and v(O) are the fluorescence peak frequencies at times, t, ,0, and 0, respectively. For this method, a probe molecule which undergoes a large instantaneous change of dipole moment upon photo-excitation has to be chosen. Coumarin dyes are often used as probe molecules for this type of experiment [17-19]. Coumarin 102 (C102), which has a lifetime of 2.8 ns in DMA and 1.4 ns in AN, is the choice for this experiment. Figure 1 shows fluorescence decays of C102 observed at different wavelengths. At shorter wavelengths there is a fast decay and at longer wavelengths there is a concurrent rise. This implies that the fluorescence spectrum of C102 is shifting towards red with time. Time-resolved fluorescence spectra would illustrate this red shift. We have used the spectral reconstruction method to obtain a time-resolved fluorescence spectrum [13] When the fluorescence up-conversion method is used, the relative intensity between each wavelength becomes uncertain because the angle of the nonlinear crystal has to be tuned at each wavelength of observation. However, the intensity of the fluorescence l(/q,, t), at a given time t and wavelength ;I,, can be obtained from the normalized fitted decay series D(t ,;t) and intensity of the steady-state fluorescence 10()0;

l(/q;, t) = D(t,~) Io(~)

D(t, ~) dt

(2)

Figure 2 shows the reconstructed spectrum. The symbols correspond to the intensities of the fluorescence at the measured wavelength at a given time t. The lines are the least-square-fits to the points using a log-normal function. The log-normal function describes an asymmetric line shape and is often used to fit broad featureless absorption or fluorescence spectra. As expected from examinations of the individual fluorescence transients, the peak of the reconstructed spectrum shifts to red with time. In Figure 3, the spectral shift correlation functions C(t) are shown with the results of bi-exponential fitting. The observed solvent relaxation times are 7.9 ps (19 %) and 18.7 ps (81%) for DMA and 6.7 ps (81%) and 13.3 ps (19 %) for AN. These are much longer than the fluorescence lifetimes of NB, i.e., 0.1 ps

61

I (a)

497 nm

20 ps

Idl/// ~ll

(a)

I 16p~

Izr

;1111 o

'

(b)

~'

'~

. . . . .. . .

'

_ . ~ . , ~ ' ~ " *~ ~'~'~

~

.

.

~

.

~

a;

-

y

~o

.....

Time / ps

;o

.

.

.

.

.

.

.

.

!

500

....

16 ps

484 nm

9

o . . . . .

450

/ ' ~

....

497 nm ~

,,i .

400

~,

Figure 1. Fluorescence decays of C 102 (a) in DMA and (b) in AN, measured at various wavelengths.

/,P//

4~1

_'t,W/o~

1 ...... 500

5~}

I

6OO

Wavelength / n m

Figure 2. Reconstructed time-resolved fluorescence spectra of C 102 in (a) DMA and (b) AN. The dots are the data experimentally obtained, and the curves are the log-normal fits to the dots.

(95 %) and 2.5 ps (5 %) in DMA, and 0.4 ps (56 %) and 2.5 ps (44 %) in AN. Therefore, our previous prediction is confirmed; the ET occurs much faster than the diffusive solvation process. B. Temperature dependence of electron transfer The fluorescence of OX 1 in anilines is severely (ca. 103 times) quenched by ET, and, therefore, its dynamics reveal the ET dynamics. The temperature dependence of fluorescence decays of OX1 in anilines is shown in Figure 4. The ultrafast single exponential decay (280 fs) of OXI in DMA does not show any temperature dependence from 280 K (7 ~ to 373 K (100 ~ In AN, however, a clear temperature dependence was observed in its non-exponential decay. As the temperature increases from 283 K (10 ~ to 353 K (80 ~ the decay becomes faster. A tri-exponential fitting is performed at different temperatures. The first component (-430 fs) does not show temperature dependence, but the second component shows dependence which gives an activation energy of 1.0 kcal/mol. C. Effect of solvent dynamics on electron transfer and Sumi-Marcus two-dimensional model It is clear in the present system that ET occurs much faster than the diffusive solvation process. To explain exponential and non-exponential kinetics of ET, the idea of Sumi-Marcus two-dimensional reaction coordinate is used. In this treatment, instead of the usual one dimensional reaction coordinate (solvent coordinate), two coordinates are used, i.e., the solvent coordinate and the vibrational nuclear coordinate. A free energy surface is drawn in a two-dimensional plane spanned by the solvent coordinate, X, and the nuclear coordinate, q.

62 The Sumi-Marcus model treats both the solvent and intramolecular mode classically. However, the actual system should have not only the classical modes but also quantum mechanical high-frequency modes. Jortner and Bixon have developed an ET model which introduces the effect of the quantum mechanical high-frequency modes [4]. In this model, the reactant surface crosses not only with the vibrational ground state of the product but also with vibrationally excited states of the product. The reaction of oxazines in DMA is activationless, which means that the reaction is not in the inverted region but very close to it. We use a hybrid model of Sumi-Marcus and Jortner-Bixon developed by Walker et al. [15]. In this model, the intramolecular vibration is separated into the quantum mechanical highfrequency mode and classical low-frequency mode;

~p(X, t) = D ~ (9 + 1 dV(X) ] p(X, t)- ~, k(n, X) p(X, t) n ~t ~ [ 3t kBT dX

(3)

where p(X, t) is the population of the reactant at X and t, and k(n, X) is the reaction rate between the vibrational ground state of the reactant and vibrational state n of the product. The non-adiabatic formula is used for k(n, X) 9

(4)

k(n, X) =~ V~l2 (4ZCXlkBT)I/2exp( - AG*(n,X) ) kBT

,t

~

-:os

=o< +s2ll-2+3-4>+...)g(a,A)-(ll>+sll-2+3> +s211 - 2 + 3 - 4 + 5 > + . . . ) J ( a , A) -

H(x - xo)(ll>o + sll - 2 + 3>0

+8211 -- 2 + 3 - - 4 + 5 > 0 + ...)

J(x,~)

=

-s(]-l>+s]-l+2-3>+s

(13)

2]-l+2-3+4-5>+...)g(a,A)+(l+s]-l+2>

+s2l - 1 + 2 - 3 + 4 > +...)J(a,)Q +

H(x - xo)(1 + s I - 1 + 2>0

+s2l - 1 + 2 - 3 + 4>0 + ...)

(14)

where we have employed bra ket notation through the following definition: [1 - 2 + 3... > .

.

.

JO"

J~

.

exp {[V(xl) - V(x2) + V(x3) - . . . ] / k B T }

dxldx2dx3...

(15)

and I...>o stands for the above integral on replacing the lower limit, a by x0. We are interested in the domain of reaction time, that is the barrier heights are sufficiently high in comparison with the thermal energy and the long time-behaviour of the dynamics. As a first general example, we shall consider the case where the potential heights at x = ul and x = u2 are infinitively high so t h a t

J(ul, A) =0

J(u~, )~) =0

These boundary conditions together with Eqs. (11) and (12) lead after taking the limit of s --, 0 to the following expression valid for the long time:

p(x,t.) _.exp[-V(x)/kBT] [ 1 - e x p ( - < _ l + 2 _ 3 >-

DE)]

(16)

where < ... > represents the integral in Eq.(15) with the upper and lower limits of us and ul, respectively. This shows explicitly the long time dynamical processes reaching the final Boltzmann equilibrium distribution. By separating the reaction coordinate into ul _ r >_ oc from the beginning whereas we have introduced the absorbing boundary first at an finite distance, r = R and let it go to infinity in finding Eq. (29), because we know the integral in Eq. (28) does not differ considerably from that in large finite value of R. In other words, we were concerned with Brownian motion in confined space while Hong and Noolandi treated that in unconfined infinite space whose physics must be different. This is the very reason why the dyna~nics of our model has been expressed by a function of s only, whereas that of the latter needed v/~ in addition to s. For example, our case of p(r,t) decays exponentially as expressed by Eq. (19) whereas that of Hong and Noolandi decreases with e x p ( r c / ( r ~ ) .

83

I would like to record that results on irreversible and reversible reactions under square-well potentials are partly due to Mr. Satoshi Suzuki. References [I] H. A. Kramers, Physica 7, 284 (1940) [2] N. G. van Kampen, Stochastic Processes in Physics and Chemistry, North-Holland, Amsterdam (1992) [3] S. A. Rice, Di1~usion-Limited Reactions, Elsevier, Amsterdam (1985) [4] A. Morita,Phys. Rev. E, 4 9 , 3 6 9 7 (1994) [5] S. Suzuki and A. Morita to be published [6] E. Wong, Proc. Syrup. Appl. Math. 16, 264 (1964) [7] K. M. Hong and J. Noolandi, J. Chem. Phys.,68, 5163 (1978) [8] H. Risken, The Fokker-Planck Equation, Springer-Verlag, Berlin (1984)

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journal of

MOLECULAR

LIQUIDS ELSEVIER

Journal of Molecular Liquids, 65/66 (1995) 85-90

STRUCTURAL CHARACTERISTICS OF HYDROGEN-BONDED N E T W O R K S IN WATER AND ICE SYSTEMS

J C Dore and D M Blakey s

Laboratory, University of Kent, Canterbury, Kent, ~

7 N , UK.)

Abstract The molecular configurations of water molecules in the disordered condensed state are investigated by neutron diffraction. The results provide evidence for the interplay of hydrogen-bond goemetry with thermal disorder, leading to a sensitive response to external variables and local influences.

1)

Introduction

R is well known that liquid water exhibits a number of properties that are distinct from those of other molecular liquids.These characteristics are attributed specifically to the effects of a strong hydrogen-bonding interaction which leads to stmcaual ordering on a molecular scale. The tetrahedral nature of the interaction tends towards the creation of a space-filling network but the thermal disorder causes the static geometrical features to be modified. As a result, the water structure is extremely sensitive to the influence of thermophysical variables such as temperature and pressure and also to the presence of other molecules and ions, either in the form of solute entities in solution or due to the effects of a neighbouring interface. The importance of water in physical, chemical and biological sciences provides a compelling reason to study the microstrucmral and dynamical features in some detail. However, it becomes clear that the characteristics are rather subtle and although considerable advances have been made, particularly in the last decade, there are many fundamental questions that remain, at best, partially answered. The present paper provides a short critical review of current issues on the structural properties of pure water in the normal and under-cooled phases as studied by neutron diffraction incorporating information from studies of amorphous ice.

2)

Neutron diffraction techniques

a)

Structural characteristics at room temperature

Neutron diffraction measurements yield the liquid strucan~ factor Sin(Q) which contains information on the spatial correlations at an atomic scale. In the ease of water where the molecules comprise two atomic species, three independent measurements on H20/D20 mixtures of varying composition are required to determine the three pair correlation functions, goo(r), goD(r) and gDD(r) based on the assumption that hydrogen and deuterium occupy equivalent sites. The most frequently quoted results of Soper and Phillips [ 1] were based on reactor measurements with three sample compositions. Similar measurements for a different composition range have also been made by Garawi, Dote and Bellissent-Funel [2]but a detailed report has not been made of these datase~ as the five independent measurements revealed the possibility of minor differences in the hydrogen and deuterium characteristics. However, the data can be used to derive two of the partial functions and Fig 1 shows a comparison between the results of the two experiments. The consistency in the overall features is encouraging as the measurements are technically demanding but the shift in the peak position at low-r may have some significance in terms of detailed interpretation of the results. 0167-7322/95/509.50 91995 Elsevier Science B.V. All fights reserved. SSDi 0167-7322 (95) 00845-4

86

1.6

goo(r)

...

0.6

0.~

-0.2

1

2

3

4

S

(I

1

8

--0.~

1

2

3

4

5

6

r/A Fig 1: A comparison of gOD(0 and gDD(r) for water at 20oC from data of Garawi et al [2], (solid line) and Soper and Phillips [ 1] (dashed line). A full analysis of the systematic behaviour for the five d a t a s ~ has been delayed (by manpower resources) but seems to suggest that there may be small variations in the distribution of H and D atoms in the various mixtures. A further factor was also app.arent in the behaviour of the goo(r) curve where it was clear that the first peak at 2.8A was over-estimated in the Soper and Phillips data. The d~_a displayed in Fig 1 can be readily understood in terms of the local configurations of water molecules since the peak position are simply related to the distances of a hydrogen-bonded pair as shown in the insets. Most molecular dynamics studies using a range of interaction potentials are able to reproduce these featmes quite well on a qualitative basis. More recently, Soper and Finney [3] have used pulsed neutron techniques and obtained similar data for the goD(r) and gDD(r) functions but now have a goo(r) curve with a smaller peak height that is in beaer agreement with the results obtained from X-ray diffraction studies. The present situation is much beue~ than a decade ago when several groups had widely differing results [4] but a detailed examination of the s y s ~ c errors in the data treatment and a critical comparison of the various measurements has not yet been made. It therefore a p ~ that a definitive set of partial pair correlation functions has not yet been achieved for liquid water at room temperature. Although the present information is sufficiently accurate to give a clear indication of the inter-molecular features, it does not provide a sufficiently precise distribution to discriminate between the various forms proposed for the interaction potential. More recent approaches to the interpretation of either simulation or experimental results have now begun to emphasise the orientational characteristics rather than the site-site correlation [5]. Fig 2 shows a contour plot of the oxygen distribution function around a fixed water molecule by Svischev [6] using a SPC potential, and Soper has obtained a similar representation in a spherical harmonic (SHARM) analysis of neutron datao This relatively new approach should provide a greater insight into the way the basic tetrahedral order is disrupted by the thermal motion at 300 K.

7

r/,~

87

Fig 2: The orientational correlation of oxygen atoms around a water molecule shown as a contour plot from computer calculations of Svishev [6]. b)

Temperature variation studies

Temperature variation studies are based on a fast order difference technique, such that ADm(Q,AT) = Sm(Q,T2) - Sm(Q,T1) defines the change in the diffraction pattern for a temperature change AT = T2 - TI. Due to the density maximum (1 loc in D20), it is possible to choose pairs of temperatures either side of the maximum where the density is constant. This method defines the isochoric temperature derivative [7] which can be transformed to give the real-space function AdL(r,AT) where oo

AdL(r~T) = 41rrpA~(r) = 2 IQ ADm(Q,AT) sin Qr dQ 7r6 The results for two pairs of temperatures are shown in Fig 3 and reveal several interesting features. The two curves are in remarkable quantative agreement except at the low-r peak position corresponding the OD hydrogen-bond distance. It therefore seems that the local variation in the molecular correlations changes systematically across the density maximum. Furthermore, the re-arrangement is not restricted to the fast neighbour but extends to 8A, involving second and third-neighbour molecules. This result emphasises that the important characteristics of the structure are not simply dependent on adjacent molecules but are influenced by longer range effects arising from ring closure within the local network Of H-bonds. The significance of this observation becomes clearer at lower temperatures.

88

0.008

AT

0

----

-0.008

-

4

-

8

2 / 2 4 *C -o

e

se

*c

1;,

r/J, Fig 3: The isochoric temperature derivative for liquid water from Sufl et al [7] showing systematic variation over the density maximum. c)

The under-cooled liquid and amorphous ice

The structural correlations are strongly enhanced in the under-cooled state as the temperature is reduced towards the metastable limit of -40~ (for D20) and various thermophysical properties exhibit diverged behaviour [81. The exact nature of this anomaly is still the subject of some controversy. However, the diffraction pattern indicates that the structure is evolving towards that of amorphous ice which is characterised as a continuous random network of tetrahedral hydrogen-bonds [9]. Recent neutron measurements on amorphous ice [ 10] have re-inforced the earlier conjectures and shown that the structure is similar to that of hyper-quenehed glassy water produced by rapid cooling of micron-sized water droplets. It can now be realised that the CRN model for the disordered phase of ice is effectively the limiting structure of water at low temperatures. i

I

i

i

ii

i

i

]

2

4

6

8 r/A

10

12

14

16

Fig 4: The spatial function d(r) for a single single molecule form-factor fit and after removal of the cluster contribution for a-ice. The latest data has been analysed by a novel use of a cluster form-factor to fit the data in the high-Q region. The inter-molecular correlations within the tetrahedral network are evaluated up to a range of second nearest neighbour molecules. The transformation to a real-space representation in Fig 4, shows how well the local structure is represented by this approach and conf'ums that the four-bonded network gives excellent results.

89

d)

Argon/a-ice co-deposits

The presence of apolar solute molecules in liquid water is know to affect the local hydrogen-bond geometry and leads to the hydrophobic interaction. Isotopic techniques using natAr/36Ar difference measurements are feasible but difficult due to the low solubility of argon in water. Neutron results for this case have recently been given by Broadbent et al[ 111 using a pressure cell. d ~

i

,

,

,

|

i

!

2

4

6

8

10

|

,

12

14

I

g

2000

m

i

0

91A '

1.2

I

I

I

I

I

I

0.6

i5

......

o

-0.6

,

0

I

I

I

I

I

!

2

4

6

8 dA

10

12

,

I

14

16

Fig 5: a) Diffraction measurements for argon/a-ice co-deposit using Ar isotopes. b) The partial pair correlation function, dAr(r) obtained from the difference technique. An altemative approach to this question is to investigate the effect in the disordered solid phase where the spatial correlations are more pronounced and higher argon concentrations can be achieved. Fig 5a shows the two curves for a sample of codeposited amorphous ice with 8 atomic per cent of argon. A difference analysis yields a composite pair correlation function in the form 0.259gAro(r) + 0.595 gArD (r) + 0.146 gArAr(r)

90

which is shown in Fig 5b. The highly-structured curve shows that there is a wellformed cage of water molecules around the argon atoms which is very similar to the computer predictions for the liquid phase made by Guillot et al [12]. The plane of the water molecules is approximately tangentialto the Ar-O vector so that a localised clathrateg c o m c ~ is created. A doaflcd analysisof thisgeometry has yet to be made but further work is in progress. This type of measurement opens up many possibilities for further studies and is complementary to work currently being pursued by Soper, Finney and collaborators [ 131. 3)

Conclusions

The present work has shown that neutron diffractionhas an important role to play in the study of water structurein the normal and super-cooled liquid phases and also through the investigation of amorphous ice systems. The high sensitivity to minor permd3ations is seen to be due to the specificbchaviour of the hydrogen-bond geometry either through temperature change or proximity of solute particles. In the former case there is a systematic change resultingfrom a delicatebalance between the ordering effectsof the H-bond geometry and the disordering effectsof thermal motion. In the second case, the presence of the argon atoms effectivelycreates void volumes within the material and resultsin network modification such thatthe hydrogen-bond connectivity is preserved by forming cage-like structuresaround the apolar region.

The basic principles seem to be well established for the low t e m ~ regime although a full quantitative description has yet to be developed. The increased spatial correlations are important in providing clear indications of local structure but it remains to be seem whether this information can be extrapolated to predict the behaviour of water systems at ambient conditions. 4)

Acknowledgements

We would like to acknowledge many people who have contributed to this work over the last decade and would particularly like to mention Pierre Chieux (ILL) and Marie-Oaire Bellissent-Funel (LLB). It is also a great pleasure for one of us (JCD) to achknowledge the Yamada Foundation and the conference organisers for the invitation to the meeting and an enjoyable fast visit to Japan. References

1) 2) 3)

4)

5) 6) 7)

8) 9) lO) 11) 12) 13)

A K Soper and M G Phillips, Chem Phys 107, 47 (1985) M S Garawi, Thesis, University of Kent, (1987); M Garawi, J C Dore and M C Bellissent-Funel, in preparation. A K Soper and J L Finney, private communication J C Dore, p3 in Water Science Reviews' Vol 1, F Franks (ed), Cambridge (pub) 1985. 1994 A K Soper p97 in 'Hydrogen Bond Networks', NATO ASI Series Vo1435, I M Svischev and P G Kusalik, J Chem Phys 99, 3049 (1994). P A Egelstaff et al, Phys Rev Lett 47, 1722 (1981), M A M Sufi, Thesis, University of Kent, 1986; M A M Sufi and J C Bore, in preparation. A Angeil, Chap 1 in 'Water : a comprehensive treatise', Vol 7, F Franks (ed), Plenum (pub), 1982. (1984) M R Chowdhury, J C Dore and J T W enzel, J Non Cryst Solids, 53, 247 D M Blakey, p381 in 'Hydrogen Bond Networks', NATO ASI Series Vo1435, M C Bellissent-Funel and J C Dore (eds), Kluwer (pub), 1994. R D Broadbent and G W Neilson, J Chem Phys 100, 5743 (1994). B Guillot et al, J Chem Phys 95, 3643 (1991 ) A K Soper and J L Finney, Phys Rev Letts, 71, 4346 (1993).

journal of

MOLECULAR

LIQUIDS ELSEVIER

Journal of Molecular Liquids, 65166 (1995) 91-98

S t r u c t u r e and D y n a m i c s of S u p e r c o o l e d and Glassy A q u e o u s I o n i c S o l u t i o n s Toshio Y a m a g u c h i , ~'* M o t o y u k i Y a m a g a m i , ~ H i s a n o b u W a k i t a , ~ a n d Alan K. Soper b ~ D e p a r t m e n t of C h e m i s t r y , Faculty of Science, F u k u o k a University, F u k u o k a 814-80, J a p a n bISIS Facility, R u t h e r f o r d A p p l e t o n L a b o r a t o r y , D i d c o t , Oxon, O X l l 0QX, U.K.

Abstract X-ray diffraction, neutron diffraction isotopic substitution(NDIS), and quasi-elastic neutron scattering(QENS) measurements have been made on concentrated aqueous solutions of lithium halides LiX (X=C1, Br, and I) in a temperature range covering the room-temperature liquid, the supercooled liquid, and the glassy state. X-ray radial distribution functions have revealed that the hydration shell of the halide ions is gradually structured with lowering temperature. Another interesting feature is the evolution of water-water interactions centered at 4.3 and 6.9 ~ independent of the halide ions, due probably to reinforced hydrogen bonds at low temperatures. The NDIS radial distribution functions related to Li + and C1- have demonstrated that the orientational correlation of bound water molecules for C1- is more strongly temperature-dependent than that for Li +. At low temperature the formation of a second hydration shell of Li + and C1- has been established. The QENS data have shown that the translational motion of water molecules in the LiC1 solution is more hindered with lowering temperature. The structural and dynamic characteristics of the supercooled and glassy solutions are discussed in connection with nucleation of ice, isotropic reorientational motion of water, and the partial recovery of hydrogen bonds in these solutions. I. I n t r o d u c t i o n The microscopic structure and dynamic properties of supercooled aqueous solutions have recently attracted much attention in various aspects such as nucleation of ice, crystallization of solutions, glass transition, hydrogen-bonded specificity, and ionic hydration. Lithium halides are very hygroscopic, and their concentrated solutions easily form glassy solutions at low temperatures. The physico-chemical properties of supercooled and glassy aqueous lithium halide solutions have been measured by various techniques such as thermal analysis (DTA and DSC), Rayleigh, Brillouin, and Raman scatterings) ,2 All of these data are, however, limited to qualitative features of the supercooled and glassy solutions. The structural information at an atomic level is essential for understanding the various properties of supercooled and glassy solutions. X-ray and neutron diffraction enables us to obtain direct structure information (bond distance and coordination number) of ionic solutions in terms of the radial distribution function. In the case of aqueous lithium halide solutions, X-ray diffraction data are dominated by halide-oxygen, halideoxygen, and oxygen-oxygen interactions. On the contrary, neutron isotopic substitution

0167-7322/95/$09.50 91995ElsevierScience B.V. All rightsreserved. 0167-7322(95)00896-9

SSDi

92

data with respect of Li and C1 give us the information related mostly to Li-O, Li-D, C1-O, and C1-D interactions. In addition to the static structure of the ionic solutions, their dynamic properties are also needed to explain various phenomena of the supercooled and glassy solutions. One of the available methods for this purpose is the quasi-elastic neutron scattering technique. In the present study, we have made X-ray diffraction, neutron diffraction with isotopic substitution, and quasi-elastic neutron scattering measurements on highly concentrated aqueous solutions of lithium halides in a wide temperature range from room temperature to below glass transition temperature, from which the microscopic behaviors of the static structure and dynamic properties of the solutions are revealed with lowering temperature. The results obtained are discussed in connection with ice nucleation, anisotropic motion of water, crystallization, and the partial recovery of hydrogen bonds. II. E x p e r i m e n t a l X - r a y Diffraction The sample solutions were prepared by dissolving anhydrous lithium halides into distilled water to the [H20]/[LiX] molar ratios of 5.22 (10.6 m, m=mol kg -1) and 12.1 (4.60 m, LiC1), 4.98 (11.2 m, LiSr), and 5.00 (11.1 m, LiI). X-ray scattering data were collected in reflection geometry with a 0 - 0 diffractometer (RIGAKU), except for the 5.22 m aqueous solution where a rapid liquid X-ray diffractometer with an imaging plate (Mac Science) was used in transmission geometry. Mo Ka radiation (A=0.7107 A), monochromatized by a LiF crystal for the former diffractometer and by a graphite crystal for the latter, was used for the measurements. For low temperature measurements, a cryostat described in ref. 3 was used for the 0 - 0 diffractometer, whereas cold N2 gas was used for the imaging-plate diffractometer. The scattering angle (20) covered for both diffractometer is 0,,,140 ~ corresponding to the scattering vector q=4rA -1 sin 0 of 0~16.8 A -1. The details of the X-ray measurements and the diffractometers have been described elsewhere. 4'5 The X-ray diffraction data were corrected for background, polarization, absorption, multiple scattering, and incoherent scattering with the usual procedures. 4'5 The structure functions i(q) were obtained by I(q)- Ex,f~(q) where I(q)is the observed X-ray intensities, xi and fi(q) are the mole fraction and the form factor of species i. The X-ray radial distribution function was obtained from eq. (1).

D(r) = 47rr2po+ (2r/r) f qi(q)M(q)sin(rq)dq

(I)

where p0(= [Zx,fi(O)]2/V) denotes the average scattering density of water and V is the stoichiometric volume (/~3) per halide ion. A modification function M(q) of the form [Y]xif2(O)/~xif2(q)] exp(-O.Olq 2) was used. Neutron Diffraction Sample solutions were prepared by dissolving into D20 ~ (a null mixture of 6Li and ZLi) and ZLi~tC1 for Li-enriched solutions, and ZLi3SC1 and ZLi3ZCl for C1enriched solutions. The sample solution was sealed into a Ti-Zr null alloy cell with inner diameter of 8 mm. Pulsed neutron diffraction measurements were made with HIT at KENS, Japan, and with SANDALS at ISIS, UK. Neutron scattering measurements were also made for background, an empty can, and a vanadium rod. The observed neutron

93 data were corrected for absorption, multiple scattering, and incoherent scattering, and scaled to absolute units by using the vanadium data as have previously been described. 6 The first-order difference function A.(q) between the two total structure factors for isotopic ions a and c~' is given by A,~(q) = A s . o ( q ) + Bs~D(q) + C s . ~ ( q ) + D s . , , ( q ) + E A = 2cacobo(b. - bt,,), B = 2C•CDbD(b. -- b~,) C = 2cac~b~(ba - b~,), D = %2(b~ - b~,),E = - ( A + B + C + D)

(2)

where sii(q) is the partial structure factor of atom pair i - j, c~ is the atomic fraction of atom i, and bi is its scattering length. The important parameter values are given in Table 1. The A a ( q ) is Fourier transformed to give the radial distribution function G~(r) represented by Ga(r) = Agao(r) + BgaD(r) + C g ~ ( r ) + Dg=~(r) + E

(3)

Table 1. Experimental data for the sample solutions" scattering lengths b (10 -12 cm), concentrations m (mol kg-Z), molar ratios R ( - [D20]/[LiC1]), densities p (g cm -a) at 298 K, and coefficients A , B , C and D (10 -27 cm -2) in Eq. (2) in the text. Solution ~ 7Lin~tC1 0Lir~tc1 7Linatc1 7Li35C1 'Li37C1

bLi -0.009 -0.222 0.011 -0.222 -0.222 -0.222

ba 0.958 0.958 0.958 0.958 1.163 0.345

m 4.96 4.98 9.32 9.41 9.61 9.42

R 10.0 10.0 5.36 5.30 5.20 5.30

p 1.20 1.20 1.27 1.27 1.27 1.28

A 2.40

B C D 5 . 5 1 0.'40 -0.05

4.41

1 0 . 1 1.36

-0.15

15.8

36.0

3.92

-1.15

Quasi-Elastic N e u t r o n S c a t t e r i n g The aqueous LiC1 solution with the composition of LiC1.6.0H20 was prepared in the same way as described for the X-ray samples. In the aqueous solution the proton (ZH) has a very large incoherent scattering cross section; the observed differential scattering cross section can be approximated to the incoherent dynamic structure factor through (d2aldFLdw) = (k/ko)[< b2 > - < b >2]Si"C(q,w)

(4)

Since water molecules are involved in translational, rotational, and vibrational motions, the incoherent dynamical structure factor may be described as a convolution of the three terms as

s~"~

~) = S'(q,~)

9S'(q,~)

9S~(q,~)

(5)

Here, the scattering law for the translational motion is expressed by the Lorentzian function as S t ( q , w ) = ( 1 / r ) [ D s q 2 / ( D ~ q 4 + w2)] (6) where DH is the translational diffusion coefficient of the proton.

The neutron quasi-elastic scattering measurements have been made from room temperature to glassy transition temperature on LAM-40 spectrometer at KENS. The details of the spectrometer and the data analysis have been described elsewhere/ III. R e s u l t s and D i s c u s s i o n

X - r a y Diffraction Figure l(a), (b), and (c) show the X-ray radial distribution functions (RDF) for the 10.6 m LiC1, 11.2 m LiBr, and 11.1 rn LiI aqueous solutions, respectively, at the various temperatures. The first prominent peak observed at 3.1 - 3.6 ~ in the RDFs corresponds mainly to the halide-water interactions due to the halide hydration. The contribution of the water-water interactions within the primary hydration shell of Li + also falls within this range. A characteristic feature of the RDFs with temperature is an appearance of a new peak centered at 4.3 /~. The position of the peak does not depend on the halide ions; the peak is gradually enhanced with lowering temperature. We have previously assigned this peak mainly to water-water interactions for the 11 m aqueous LiC1 solution, s The quantitative analysis has been made by a least-squares fitting procedure, and the important structural parameter values finally obtained are summarized in Table 2. The evolution of the 4.3 A peak with lowering temperature is clearly seen in Fig. 6

_

|

|

i

,

|

,

|

|

0

!

=,98 K

.k

:< s

4,

29.:

~

2.~

0

~'1

S

0 -61-

41 . . . . . . . . .

.'
/ < n(q)n(-q) > .

(19)

135

with n(q,t)=_ f dr { n ( r , t ) - nL } e x p ( - - i q - r ) / N 1/2. Fourier-transformation of (18) and the FD theorem (9) yield

On(q, t)/Ot = -7(q)n(q,t) + Ek V(q, k)n(k,t)n(q - k,t) + r = - 2 D q . q'6(t - t') {6q+q,,0 + n(q + q',t)/NX/2},

(21)

where 7(q) = Dq2/s(q), with s(q) denoting the static structure factor, c(q) = 1 - 1/s(q), and V(q,k) =

Dc(k)q. k / N ~/2. If we neglect effects of both nonlinearity in(20) and the multiplicativeness of the noise, n(q,t) becomes a simple Ornstein -Uhlenbeck process ~1 and G(q,t) and the dynamic structure factor G"(q,w) = (1/2) f dtG(q,t)exp(iwt) are given by Go(q,t) = exp(-v(q)t) and Gg(q, w) = 7(q)/[v(q) 2 + w2],

(22)

respectively, where the subscript 0 on G means that we regard it as the zeroth aproximation to G.

In

calculating G(q,t) based on (20) and (21) we follow a nonlinear theory of fluctuations by Mori and Fujisaka. xr

Numerical calculation is performed for a hard sphere system characterized by a packing

fraction p = r~3nL/6, is Percus-Yevick approximation is used to supply the structural information. As p becomes large we observe narrowing of the central peak, reflecting slowing down of the density fluctuations due to nonlinear coupling in (20). At p = 0.53 a dynamic 'instability' occured where an effective diffusion constant crosses zero. As is well known the hard sphere system freezes at p ~_ 0.5 and the D F T in its various version has been applied to study the transition. 19 It is interesting to note that the interaction part of the free-energy(4) gives rise to the equilibrium transition on the one hand and it also gives rise to the instability through the nonlinear coupling in the L-D equation (20). Before leaving this section it is noted that if we take the free-energy functional (6) for an S-component mixture we have a set of L-D equations for S density fields ni(r,t)(i = 1,... ,S), which lead to

On,(r,t)/Ot=D, [ V 2 n , ( r , t ) - V

.n,(v,t)V { E j / d , ' c , ~ ( l r -

r'l)6nj(r', t)}]-

V . in,,

(23)

Furthermore if we take the free-energy functional as given by Chandler et hi. 5 for molecular(polyatomic) liquids, we obtain from (11) a L-D equation for each of the atomic species constituting the molecules, which is very similar to (20). After liniarization as done in (22), we obtain a linear diffusion equation, which was used by Hirata lr to investigate the dynamic structure factors of water.

(B) Some Transport Coefficients In this subsection we put a particle at an origin in a velocity field u ( r ) and study effects of flow on a stationary density profile n,t(r). When there is no flow u(r) = o, n,t(r) is obviously given by nLg(r), with g(r) a radial distribution function. Due to the flow u(r), this equilibrium distribution is distorted and from the distortion we can calculate some transport coefficients, like viscosity 7] and friction constant ~, as we show below. We consider a one-component system and neglect random current JR in (18) to obtain

8n(r,t)lbt = - V - j , ( r , t ) ,

(24)

136

j,(v,t) = DVn - a D ~ V t f dr'v~]] (Jr - r ' l ) , ( r ' , t ) + r where v,/l(r ) = -kBTc(r) and r

+ nu,

(25)

two-body interaction, represents effects of the particle fixed at

r = o. The last term on the rhs of (25) represents particle flow due to the velocity field, u ( r ) . We are interested in a stationary density profile n , t ( r ) around the fixed particle. First we consider the equilibrium solution n , q ( r ) when u = 0. In this case the particle flow j0 = o and from (25) we readily obtain ln[gCr)] __

ln[-,,C.)/-L] = -~ f dr'v,ss(l~ -

v'l)nL[g(r')

-

1] -- flr

(26)

where the boundary condition n,q(r) --* nL as r ---,oo is taken into account. From the relation (5) between h and c, we observe immediately that (26) is equivalent to the H N C equation to determine g(r). Thus our theory, when applied to anequilibrium situation, g!ves the H N C

result for g(r).z

Now let us turn to effects of the flow field u(r) on nat(r). We consider, to be concrete, shear flow

u(r) = 7yeffi where ez denotes a unit vector in the x-direction. In this case we assume a solution of the form n , i ( r ) - nLg(r)[1 4- w(r)7/D -t- o(7)]

(27)

where o(7)/~ --+ 0 as 7 ~ 0. Inserting (27) into (24) with i)n/Ot - O, we obtain

gV2w--nLgV2 i dr'c(Ir-r'l)g(r')w(r')+Vg.Vw-nLVg.V

i dr'c(Ir-r'l)g(r')w(,')

zyg'(r)/7. (28)

with use of Fourier transformation it is seen that (28) has a solution of the form w(r) = z y a ( r )

(29)

and a(r) satisfies a complicated integro-differential equation, which we do not write down here. The final step to obtain shear viscosity 71 is to calculate the xy component of the stress tensor axy, which is expressed, on the one hand, in terms of ,7 and 7 as =! =

'7")'

(30)

and also microscopically as T

ffxy = where r

(nLI2) ] drno,(r)xyr

(31)

- de~dr and we have neglected the kinetic contribution, which is very small at a liquid

density. Use of the solution (29) together with (30) and (31) gives

r] = (n2L/2D) / dr(xy)~ g(r)r

(32)

If we fix a particle in a uniform flow u ( r ) = uoe~, we can calculate the friction constant ( from a stationary force on a fixed particle by following similar lines of reasoning as above. Our preliminary results for shear viscosity r / o f a soft-core system with r

= e ( a / r ) 12 shows that

main contributions in the integrand in (32) come from the region r ~_ (V/N) ~/a (of course in the highdensity state) and that r/increases sharply as a function of p. =_ (elkBT)I/4(Nvra/V). Although detailed

137

analysis of 77 and ~ based on our TD-DFT needs some time to be completed, it seems that our approach is promising in view of the fact that we have at the moment nearly no (microscopic) theory for r/and (, especially for dense complex systems like water.

V. S o m e R e m a r k s a n d S u m m a r y

In this paper we gave a dynamic extension of the DFT, by deriving a L-D equation (11) with the /

fluctuation-dissipation theorem (9). We showed that the stochastic equation correctly samples the density field according to the probability exp {-/~F[n]},(17), based on the second H-theorem (16). At this point we note however that our TD-DFT is phenomenological and it is desirable to have a first-principle dynamics generalization of DFT. As applications of TD-DFT, we considered density fluctuations in liquids and transport coefficients. We are currently trying to solve the L-D equation in a real space-time to study slow dynamics in supercooled liquids. This study may be considered to be a dynamic counterpart of the work by Dasgupta and Ramaswamy is and as a similar attempt we mention the work by Lust and Valls 2~ We expect that our L-D equation has many fields of application. One example is dynamics in molecular liquids, as noted at the end of subsection IV(A), which is a very important field in connection with chemical reactions in solutions but, at the same time, is very complex to deal with from first principles.

References 1 R.Evans, Adv.Phys. 28 143(1979). 2 A.D.J.Haymet, Ann.Rev.Phys.Chem. 38 89(1987). 3 D.W.Oxtoby, In 'Liquid, Freezing, and the Glass Transition', (Eds. J.P.Hansen,D.Levesque and J.Zinn-Justin) (Elsevier:New York,1990) 4 Y.Singh, Phys.Rep. 207 351(1991). 5 D.Chandler, J.D.McCoy, and S.J.Singer, J.Chem.Phys. 85 5971;5977(1986). 6 T.V.Ramakrishnan, and M.Yussouff, Phys.Rev. B19 2775(1979). 7 J.P.Hansen, and I.R.McDonald.' Theory of Simple Liquid s'(Academic, New York, 1986). 8 T.Munakata, J.Phys.Soc.Jpn. 58 2434(1989). 9 T.Munakata, Phys.Rev.E(1994) to appear 10 T.R.Kirkpatrick and P.G.Wolynes, Phys.Rev. A35 3072(1987). 11 C.W.Gardiner ' Handbook od Stochastic Methods' (Springer, Berlin,1982) 12 A.S.Mikhailov, Phys.Rep. 84 307(1989).

13 C.Dasgupta and S.C.Ramaswamy, Physica A186 314(1992). 14 T.Munakata, J.Phys.Soc.Jpn. 43 1723(1977). 15 B.Bagchi, Physica 145 A 273(1987). 16 D.F.Calefand P.G.Wolynes, J.Chem.Phys. 78 4145(1983).

17 F.Hirata, J.Chem.Phys. 96 4619(1992). 18 H.Mori and H.Fujisaka, Prog.Theor.Phys. 49 764(1973). 19 T.Munakata, J.Phys.Soc.Jpn. 59 1299(1990). 20 A.D.J.ttaymet and D.W.Oxtoby, J.Chem.Phys. 84 1769(1986). 21 L.M.Lust and V.Valls, Phys.Rev.E 48 1787(1993).

journal of

~IOLECULAR

LIQUIDS ELSEVIER

Journal of Molecular Liquids, 65/66 (1995) 139-147

Dissociation and Solvation in W a t e r and A q u e o u s Solutions A.D.J. H a y m e t School of Chemistry, University of Sydney, N S W 2006 Australia Abstract Recently the properties of both charged and un-charged solutes in aqueous solution have been elucidated by computer simulations and approximate integral equation theories. While answering some questions, others are raised. In particular the structure of water next to a charged surface (or a very large charged solute) is a challenge. Approximate integral equation theories can address this challenge.

I.

Introduction

Water plays an important role in the chemistry and physics of bulk solutions and interfaces, including electrochemistry and macromolecules in solution. Usually the water is treated as a structureless, dielectric continuum, such as in the Debye-Hiickle approximation 1 for electrolytes, the Gouy-Chapman-Stern 2-4 (GCS) approximation for the electrical 'double layer' and the DLVO 5'6 approximation for colloids. Properties sensitive to the molecular nature of water cannot be determined by these theories. Recently we have published integral equation predictions for a flexible model of water next to a planar interface. T Experimental motivation for this work includes electrochemical experiments on ultra-pure (O2-free) water, s'9 surface EXAFS studies of the oxygenmetal distance for water at an electrode, 1~ and the tunnel junction device measurements of Porter and Zinn. 11 Vossen and Forstmann ~2 have published a related calculation using a different model of water and a different approximation for the bulk water bridge functions. Below we compare the input to the two calculations. First we review some results in bulk water and solutions of non-polar solutes.

II.

A m o d e l of water

We have studied via molecular dynamics computer simulation a number of properties of so-called CF1 central force model of water, 13'14 although our methods may be applied to any model of water with a unified Hamiltonian for intra- and inter-molecular degrees of freedom. The CF1 model is a slight variant of the central force (CF) model of Stillinger and Rahman, is which allows the water molecules to vibrate and even dissociate. 13,~6 Central force models view water as a 'molten salt' of two fractionally charged species, hydrogen and oxygen. MD simulations show that the static dielectric constant and pH of the CF1 model at 25~ and 1.000 g cm -a are in good agreement with experiment. Such properties 0167-7322/95/$09.50 91995 Elsevier Science B.V. All rights reserved. SSD! 0167-7322 (95) 00848-9

140

are important for models of water which are to be used in electrolyte theory and other solution phase studies. We have also determined a number of physical properties of the CF1 model using integral equation methods. We conclude from these studies that the CF1 model is a valuable addition to the family of classical models of water. The output from this calculation is used in theories of inhomogeneous solutions. 7 The revised central force (CF) potentials of Stillinger and Rahman 15 are defined by

uoo(r)

=

144.538 { 26758.2C1 - 0 . 2 5 e -4(r-3"4)2 - 0 25e -1"5(r-4"5)2 r

7.8.8591

UHH(r) -- 36.1345 ~18 r 1 + e 4~176 72.269 UOH(7")

:

r

,

"

'

-- 17e-762177('-1"45251)2

6.23403

10

r 9"19912

1 -l- e 4 0 ( r - I ' 0 5 )

4 -

I

-I- e 5"49305(r-2"2)

'

(:)

where the values of the constants are C1 = C2 = 1. The distances are measured i n / ~ and energies in kcal tool -1. At the temperature 25~ and a mass density of 1.000 g cm -3, this model predicts a pressure of 3.54 kbar, thousands of times greater than atmospheric pressure of approximately 1 bar. 1T'ls By changing the constants slightly to C1 - 0.9 and C2 - 1/1.025, it was found that the pressure could be reduced to a more acceptable value of 120 bar. 13 We call this model of water the CF1 model. For both CF1 and CF water, each hydrogen species is assigned a partial charge of qH -- 0.32998e where e is the proton charge, while the oxygen species each carry a charge of qo - -2qH to ensure electroneutrality of individual H20 molecules. This fractional charge should not be regarded as a defect of the model, 19 but instead as arising from the 'screening' induced by integration over polarisation terms, three- and higher-body potentials, etc., to obtain the effective pairwise additive potential energies displayed in Equation (1). III.

Hydrophobicity

In 1993 Blokzijl and Engberts 2~ published an important review article on hydrophobic effects. In 1992, Smith, Zhang and Haymet 21'22 showed that hydrophobic association of uncharged solutes in water is almost entirely an entropy effect. Haymet 2a went on to point out that experimental data show that methane "likes" water about as well as it "likes" any other solvent from the point of view of enthalpy. This view is underlined by the experimentally high solubility of water in cryogenic solvents such as liquid methane. Hydrophobicity in fact arises from the entropy penalty incurred by the water. The methane is not hydrophobic: the water is 'methophobic'. Very recently Guillot 24 has performed a beautiful series of simulations using faithful models of rare gases and water, and determined solubilities along the liquid-gas coexistence line. These new contributions revise substantially the traditional view of hydrophobicity.

141

IV.

Ionic

Association

and

Dissociation

The potential of mean force (PMF) for sodium chloride in water has been simulated by numerous investigators for many different models. Smith and Haymet is noted that to dissociate a model sodium ion and chloride ion at room temperature and pressure, two free energy barriers appear to have to be surmounted. The first barrier is associated with the formation of a 'shared' layer of water molecules between the ions, now constituting a so-called 'solvent separated ion pair', and the second barrier associated with the final unlinking of the solvations shells of the two ions. Very recently, Cui and Harris 25 have evaluated the P MF for sodium ion and chloride ion in a model of supercritical water. They decompose the PMF into enthalpy and entropy contributions, as did Smith and Haymet for uncharged solutes, 21 and find that, at least in supercritical water, the entropy effect is dominant, just as for uncharged solutes at room temperature and pressure. The dissociation of a single water molecule has been studied, for the CF1 model, by our group, la'14 By calculating the PMF for separating a single water molecule into two ionic fragments, an upper bound to the pH of the CF1 model was predicted to be 8.4. Future work will involve calculating the relative concentration of H(aq) , + H30~-a.~,( ~, ..., HgO+(aq) and related OH~-,q) species. V.

Properties

of bulk

water

from

an integral

equation

The results summarised here are for pure water at the temperature 25~ and the density 1.000 g cm -3, and are obtained by solving numerically the Ornstein-Zernike (OZ) equation for the pair correlation functions, using a closure that supplements the hypernetted chain (HNC) approximation with a bridge function. The bridge function is determined from computer simulations as described below. The numerical method for solving the OZ equation is described by Ichiye and Haymet 26'27 and by Duh and Haymet. 2s For a liquid mixture of u species at temperature T and volume V. The potential energy Uab(rl:) between particles of species a and b, separated by a distance rl: - Irl - r21, is spherically symmetric and pairwise additive. The (iirect correlation function C~b(r12) is defined by the OZ equation:

hab(r12) -- Cab(r12) + ~-~.ps /v dra cas(rla)hsb(r32) ,

(2)

s--1

where hab(rl2) = gab(rl2)- 1 is the total correlation function and ps is the density of species s. The pair potential is separated into short- and long-range contributions: U~b = u~b + l which leads to a decomposition of the direct and total correlation functions into Uab, ._. 8 8 Cab Cab ~ (~ab and 'hab = hab + qab, where the long range parts of Cab and hab a r e defined to be r = --~U~b and q~b = &~b + ~ = 1 P~ ( ~ * %b, where ~-1 = k T , k is the Boltzmann constant, and 9denotes the convolution integral as in Equation (2). The long-range part of the potential is chosen to be the Coulombic interaction and Cab(r) = --/3q~qb/47r~o~r, where q, is the charge on species a. We retain the symbol e to display the formal similarity

142

with standard theories of electrolytes. Of course, for the present case of CF1 water, E = 1. The function qab is the (negative, dimensionless) Debye-Hiickel (DH) potential of mean force, qab(r) = --~qaq_______~bexp (--~r)

(3)

4~rEo~r

where a is the Debye inverse length defined by ~2 = f l ( e o e ) - i ~ a paq~. For the CF1 model at 25~ and 1.000 g cm -a, a-1 _ 12.402/1,, so this is a DH "strongly interacting" case. To solve the OZ equation, we use the exact closure which may be derived directly from the partition function: hab -I- 1 = exp(--flUab + hab -- Cab ~- Bab) ,

(4)

where Bab is the bridge function. 29 In the HNC approximation, Bab = 0 for all distances. The bridge functions used in this work are discussed below. The above equation becomes C~b -- exp(--~U~b + Tab + qab + Sab) -- 1 -- Tab - qab ,

(5)

where Tab = h~b -- C~b, which is the renormalized closure. The OZ equation and equation 3

g~

2

1 0 2

go.

1 0

i_.

4 3

gHH

2 1 0

0

2

4

6

r/A

Figure 1" Pair correlation functions gab(r) from experimental data of Soper31(thick solid line), and for CF1 water (solid line) and the VF model (dashed line). (5) are solved iteratively to obtain Tab and C~b. Since (I)ab and qab are determined once the potential has been separated into short- and long-range contributions, Cab and hab may be calculated from their definitions. Further details of the integral equation method may be found in the references. 2a-2s For central force models of water, the bridge function is essential for accurate solutions of the integral equations. Thuraisingham and Friedman 3~ found that at room temperature the HNC [Bab(r) -- 0] approximation for the CF model was in very poor agreement with

143

$

COO

-50 -100

,

i

,

i

,

CSoH -50

s

CHH

......i.......i........i....... -50 8

Figure 2: Short-range direct correlation functions c~b for CF1 water (solid line) and the VF model (dashed line). "exact" results from computer simulations. In 1988 Ichiye and Haymet ~~ showed that hard sphere bridge functions can be used to improve the quality of the solutions. We have determined these bridge functions by a numerical method. 16 The pair correlation function gab(r) obtained by solving the OZ equation with these bridge functions is shown in Figure 1, together with the experimental data for water by Soper. al Our integral equation calculation agrees to within the thinkness of the line with MD simulation of the same Hamiltonian. Also shown are the pair correlation functions for bulk water predicted by Vossen and Forstmann12(VF). They use the original CF model of water, together with a bridge function based on the original hard sphere bridge functions of Ichiye and Haymet, 26 augmented with an empirical hydrogen-hydrogen bridge function. The agreement between experiment and the VF calculation is not as good as our calculation, due in part to the CF model of water, and in part to the much more approximate bridge function. The pressure of the bulk VF water, calculated from these pair correlation functions, is approximately -48,000 bar. A full range of properties (including the dielectric constant) arising from our calculation are available. 16 The dielectric constant of CF1 water has been determined by molecular dynamics simulation to be 69 • 11.13 These calculations can also be compared with the perturbation calculations on CF water by Holovko and collaborators, a2 The difference between the two calculation is displayed more dramatically in Figure 2, where the short-range direct correlation functions arising from the two calculations are plotted. They differ markedly. As show below, a convenient theory of the wall - solution interface uses moments of these functions as input into the calculation of the structure and properties of the inhomogeneous system. Not shown in Figures 1 and 2 are the predictions of the well-known HNC approximation, which yields unacceptable CF1 pair correlation functions.

14,4,

VI.

Theory

for the

Interface

To predict the normalized probability g~i(z) for finding an oxygen (i = O) or hydrogen (i = H) atom of a water molecule at a distance z perpendicular to the planar interface ('wall'), we use the 'singlet' theory version of the Ornstein-Zernike equation due to Henderson, Abraham and Barker a3-3S and Percus. 36 We have also used this level of theory to study soft-core primitive model electrolytes next to charged interfaces. 3r The input to the calculation is: (i) the structure of the bulk model water, obtained above, contained in the direct correlation functions cij(r) for all distinct pairs of species, ij = OO, OH and HH, separated by a distance r; (ii) the bulk water density pB and temperature T; (iii) the short-range potential energy between the wall and the oxygen and hydrogen atoms, r i = O, H; and (iv) the surface potential r The normalized density profile g~i(z) is related to the absolute density profile p~i(z) via pwi(z)/p~ - g~i(z) - [ 1 + h~i(z)] , (6) where h~i(z) is the total wall-species correlation function. At fixed surface potential r the total correlation function and the surface charge density a are obtained from the equations ln[1 + h~i(z)] = - f ~ r

+ 2r ~_, pj

~qir

and

j=O,H

zfO)(z) - f(i])(z)

Loo

o

=

E qJp~ dthw,(t),

-

(8)

j=O,H

where e - 4tee0, e0 is the permittivity of free space, and e = 1 is the 'relative permittivity'. The bulk quantities f[~')(z) - f ~ drr"ci~(r ) are the moments of the short-ranged bulk direct correlation functions, c~j(r) = cij(r) + ~qiqj/(er). The mean electrostatic potential, experienced by a test charge at a distance z from the surface, is obtained from r

= (4r/e) ~

j=O,H

qj p3B

L dt(z-t)hwj(t).

(9)

Differentiating ~p(z) with respect to z, and using the charge neutrality constraint of Equation (8), yields at z = 0 de(z)

dz

I

z=o

_

4__~_~~

e j=O,H

qJ pB

/o=

dt t hwj (t) _

4na ~

(10)

Thus the surface charge density is proportional to the negative slope of the mean electrostatic potential at z - 0. In fact, the initial shape of the mean electrostatic potential is necessarily linear with slope - 4 r a / e .

145

The potential energy between the charged, planar wall and the oxygen and hydrogen species may be divided into two parts: a short-range contribution r due to any specific interactions between the oxygen and hydrogen species with the interface (including softbetween the charged wall and core repulsions); and the Coulombic interactions r the partially charged oxygen and hydrogen species. The total potential energy u~i(z) , may be expressed as a sum of these two contributions u~i(z) = r + r where (I)~i(z) = - q i E z and E = 4 r a / e is the electric field strength at the wall. The Coulombic interactions are specified implicitly in Equation (7) through the value of the surface potential. The properties of our charged, planar interface are determined solely by the short-range potentials r and r and the surface potential Co. For our choice of the short-range interactions, at zero surface potential, by construction the wall shows no preference for either oxygen or hydrogen. The oxygen and hydrogen atoms of the water molecules may approach the interface equally. We observe that hydrogen prefers to be slightly closer to the wall than oxygen. Thus water molecules in the contact layer are oriented predominantly with both hydrogens directed towards the interface. The effect of the inhomogeneity created by the wall extends approximately 15/~ into the bulk of the liquid, equivalent to about four layers of water molecules, after which the water attains it bulk properties, as the normalized profiles approach unity asymptotically. An interesting feature of the normalized wall-oxygen profile is that in the region between approximately 2.4 and 3.7/~ from the wall there is very low probability for finding an oxygen atom. Similar behavior is not observed in gwn(Z). Therefore it is unlikely to find another oxygen atom near that of the one in the contact layer of water, due to both the favorable electrostatic interaction between hydrogen and oxygen and the unfavorable oxygen-oxygen interaction. Thus oxygen is largely excluded from this region. Outside the contact layer some structure continues in both profiles, but it is less well defined. The decaying oscillations in the oxygen and hydrogen profiles are approximately in phase outside the region within 5/~ from the wall. A useful way to see this fact is to plot the charge profile q(z) -- --qOP~[gwg(Z) -- gwO(Z)] shown in Figure 3. For this choice of wall-water potentials, the oxygen centres of the water molecules sit in layers at approximately 1.6 /~ and 4.3 /~ from the wall, with high probability of hydrogen species located at certain distances. As the surface charge on the wall is made increasingly negative, the positive end of the water molecule- the hydrogen - is attracted to the wall, and the oxygen end is repelled, as expected. The calculations performed to date suggest that (i) the details of the short-range wall-water potentials dominate the average orientation of the contact layer of water (in combination with the strong water-water and charged wall-water interactions); and (ii) beyond the first layer the structure is insensitive to these details. The layered solvent structure extends approximately 15/~ into the bulk of the liquid, representing about 4 layers of water molecules, a distance remarkably similar to that found in earlier simulations of an ice / water interface. 3s The potential of zero charge is calculated 7 to be -32 inV. The differential capacitance can be calculated, as discussed by Booth et al. 7 Our calculations are being extended to to incorporate the 'pair' theory. 34'39 Higher order correlation functions, such as the inhomogeneous pair correlation function g~ij(R; zl, z2)

146

q(z)

s

-10 -15

2

,

6_ Z

8

,0

/A

Figure 3" For the case of a wall with surface potentials: -1000,-750, -500, -250, 0, 250, 500, 600. 750 and 1000 mV the charge profile q(z) = --qOP~[g~g(Z) -- gwo(Z)] in units of 109 C cm -3 as a function of distance z from the wall. which appear in the pair theory, should provide a more detailed description of this region, particularly in terms of additional information on orientational correlations. Ions will be added to the water to yield a fully molecular description of the 'double layer:. A c k n o w l e d g e m e n t s : This research is supported by the Australian Research Council (ARC) (Grant No. A29530010). I thank Dr. D.-M. Duh, M. Booth and A. Eaton.

References 1p. Debye and E. Hfickel, Phys. Z. 24, 305 (1923). 2G. Gouy, J. Phys. (Paris) 9, 457 (1910). aD. L. Chapman, Phil. Mag. 25, 475 (1913). 40. Stern, Z. Elektro. Chem. 30, 508 (1924). 5B. Derjaguin and L. Landau, Acta Physiochem. 14, 633 (1941). 6E. J. W. Verwey and J. T. G. Overbeek, Theory of the Stability of L yophobic Colloids (Elsevier, Amsterdam, 1948). 7M. J. Booth. D.-M. Duh. and A. D. J. Havmer, J. Chem. Phys. 101. 7925 (1994). 8M. Heyrovsk~ and S. Vavricka, J. Electroanal. Chem. 353, 335 (1993). ~M. Hevrovsk~ and F. Pllcciarelli, J. Heyrovsk~ Memorial Congress on Polarography II. 65 (I 980). tow. Schmickler, D. Henderson, and O. R. Melroy, Chem. Phys. Letts. 216, 424 (1993). 11j. D. Porter and A. S. Zinn, J. "Phys. Chem. 97, 1190 (1993).

147

I2M. Vossen and F. Forstmann, Journal of Chemical Physics 101, 2379 (1994). I3A. Nyberg, D. Smith, L. Zhang, and A. Haymet, J. Chem. Phys. (1994), submitted. I4A. Nyberg and A. D. J. Haymet, in Structure and Reactivity in Aqueous Solution, edited by D. Trular and C. Kramer (American Chemical Society, New York, 1994). 15F. H. Stillinger and A. Rahman, J. Chem. Phys. 68(2), 666 (1978). 16D.-M. Duh, D. N. Perera, and A. D. J. Haymet, J. Chem. Phys. 102, 3736 (1995). IVT. A. Andrea, W. C. Swope, and H. C. Andersen, J. Chem. Phys. 79, 4576 (1983). ISD. E. Smith and A. D. J. Haymet, J. Chem. Phys. 96, 8450 (1992). tgj. W. Halley, J. R. Rustad, and A. Rahman, J. Chem. Phys 98, 4110 (1993). soW. Blokzijl and J. B. F. N. Engberts, Angew. Chem. Int. Ed. Engl. 32, 154 (1993). 21D. Smith, L. Zhang, and A. Haymet, J. Am. Chem. Soc. 114, 5875 (1992). 22D. Smith and A. Haymet, J. Chem. Phys. 98, 6445 (1993). 23A. Haymet, Annals of the New York Academy of Sciences 715, 146 (1994). 24B. Guillot, 12th International Conference on the properties of Water and Steam (1995). 25S. Cui and J. G. Harris, 12th International Conference on the properties of Water and Steam in press (1995). 26T. Ichiye and A. D. J. Haymet, J. Chem. Phys. 89, 4315 (1988). 27T. Ichiye and A. D. J. Haymet, J. Chem. Phys. 93, 8954 (1990). 2SD.-M. Duh and A. D. J. Haymet, J. Chem. Phys. 97, 7716 (1992). 29R. O. Watts, Statistical Mechanics (The Chemical Society, London, 1973), Vol. 1. 3~ A. Thuraisingham and H. L. Friedman, J. Chem. Phys. 78, 5772 (1983). 31A. K. Soper, Chem. Phys. 107, 61 (1986). 32A. D. Trokhymchuk, M. F. Holovko, E. Spohr, and K. Heinzinger, Mol. Phys 77, 903 (1992). 33D. Henderson, F. F. Abraham, and J. A. Barker, Mol. Phys. 31, 1291 (1976).

34D. Henderson and M. Plischke, J. Phys. Chem. 92, 7177 (1988). 35j. Quintana, D. Henderson, and A. D. J. Haymet, J. Chem. Phys. 98, 1486 (1993). 36j. K. Percus, J. Stat. Phys. 15, 1772 (1976). 37M. J. Booth, A. Eaton, and A. D. J. Haymet, J. Chem. Phys. 103(1), in press (1995). 38B. B. Laird and A. D. J. Haymet, Chemical Reviews 92, 1819 (1992). 39R. Kjellander and S. Mar~elja, Chem. Phys. Lett. 127, 402 (1986).

This Page Intentionally Left Blank

journal o f

~OLECULAR

LIQUIDS ELSEVIER

Journal of MolecularLiquids,65166(1995) 149-155

Effect of Solvent, Temperature, and Pressure on Hydrogen Bonding and Reorientation of Water Molecules Masaru Nakahara and Chihiro Wakai Institute for Chemical Research, Kyoto University, Uji-city, Kyoto 611, Japan Abstract On the basis of the study of the solvent, temperature, and pressure effects, we show how the NMR rotational correlation times %21~for a heavy water molecule in neat liquid and organic solvents arc correlated with the strength of solute-solvent interactions, in particular, H bonds. At room temperature (30 "C), the correlation time is 2.1 ps in the random H-bond network in heavy water, whereas it is as small as 0.1 ps in such an apolar, hydrophobic solvent as carbon tetrachloride because of the absence of the H bonds between water molecules. Pressure distorts H bonds and accelerates the orientational motion of water molecules in neat liquid. Firm evidence is collected for the limitations of the Stokes-Einstein-Debye (SED) law in solution. I. I N T R O D U C T I O N Water is one of the most important H-bonding substances for the living. For a better understanding of reaction dynamics in aqueous systems, it becomes more important to investigate how the water dynamics are controlled by intermolecular interactions (density) as well as kinetic energies (temperature). Anomalous properties of water originate from attractive anisotropic interactions called H bonds, in sharp contrast to simple liquids whose equilibrium structure and transport properties are considered to be dominated by repulsive interactions; recall the van der Waals picture and the SED continuum model or its modifications through boundary conditions. There remains unsolved a nontrivial problem as to how the dynamics of water is controlled by the fluctuating H bonding structures. Here, we examine how the rotational correlation times for a water molecule in neat liquid and solutions are influenced by the H bonding between water molecules and between a solute water and organic solvent molecules. It is interesting to see how water responds to perturbations provided more or less selectively by the potential and momentum terms in the Hamiltonian through pressure, temperature, and solvent. In view of the anisotropic nature of H bonds, the rotational properties are of greater interest than those dominated by the radial distribution function. Nuclear magnetic resonance (NMR) spectroscopy has become one of the most powerful tools for studying the rotational dynamics as well as structure of water and aqueous solution under such extreme conditions as high and low temperatures and high pressures, t,2 Our newly developed multi-purpose NMR spectrometer has been successfully applied to the dynamical study of solutions under such extreme conditions as low and high temperatures, 3-5 high pressures, 6 and low concentration. 3-5,7 We have examined the role of H bonds in determining single-body water rotation dynamics in water and aqueous solution by changing or breaking H bonds through temperattm~, pressure, and organic solvents. II. E X P E R I M E N T A L 0167-7322/95/$09.50 91995ElsevierScienceB.V.All rightsreserved. SSDi 0167-7322(95) 0(}849-7

15o

To carry out high temperature experiment on water with a commercially available standard NMR probe (JEOL), we need to use a capillary in a normal glass sample tube (Wilmad) of 5-10 mm diameter. When a long glass sample tube with a normal size is used, the sample liquid contained vaporizes from a heated portion of liquid, condenses near the top of the tube, and falls down to the original liquid. The circulation prevents the efficient and homogeneous heating of the whole sample. A short capillary immersed in a temperature-transmitting medium (Demnum S-65, Daikin) can be employed at high (superheating) and low (supercooling) temperatures. In the case of dilute aqueous solution, the integrated capillary method5 is useful for avoiding the reduction of the signal intensity due to a low concentration. Glass capillaries can stand relatively high pressures; Yamada's method.l The high resolution can be attained by the capillary method at the expense of the sensitivity. We employed the high-sensitivity, high-resolution, high pressure NMR probe where a sample tube of 8 mm diameter can be introduced into a high pressure vessel made of a titanium alloy.2,6 The spin-lattice relaxation times T1 arc measured by the inversion-recovery method. By the capillary method, we have measured the spin-lattice relaxation times T 1 for heavy water (D20) over a wide range of temperature. The results are in good agreement with those given by Hindman and co-workers s,9 within the experimental uncertainties; our and their uncertainties arc +1% and +7%, r e s t i v e l y . The uncertainty of temperature is i-0.1 "C in the present work. IlL REDUCTION OF Tl TO ~2R The spin-lattice relaxation times T 1 due to the quadrupole interaction mechanism can be convened to the rotational correlation times X2R in a simple manner. In the extreme narrowing limit attained by rapid molecular rotational motions, the spin-lattice relaxation rate 1/T t for the 2I-1nucleus with the spin I--1 is expressed by T1-

2

1 +

X2R,

(1)

where e2qQ~ is the quadrupole coupling constant (QCC), ~ is the asymmetric factor for the electric field gradient, and x2a is the correlation time (the area of the time integral) of the time autocorrelation function of the second-order rotation of a bond or principal axis specified by q.6 In the application of Eq. (1) to water, assumptions are required for evaluating ~, QCC, and x2R. Now we can take QCC as 256 kHz and neglect the small ~ value according to a recent quantum mechanical and molecular dynamic study on liquid heavy water between 260 and 359 K. 10 In organic solvents, a gas-phase value of 308 kHz is used because of very weak H bonds between a water molecule and solvent molecules.4 Furthermore, we assume isotropic rotation Table 1. The rotational correlation times X2Rfor pure 1:)20 (99.8% D) T('C) -24 -22 -20 -18 -16 - 14 -12 -10 -5 0

x~8 (ps) 23.7 19.9 16.9 14.5 12.7 11.2 9.91 8.79 6.84 5.43

T('C) 1 5 10 15 20 25 30 35 40 45

X~l~(ps) 5.26 4.49 3.76 3.20 2.78 2.37 2.08 1.86 1.66 1.47

T('C) 50 55 60 65 70 75 80 100 105 110

x~8 (ps) 1.34 1.23 1.10 1.02 0.944 0.881 0.802 0.606 0.566 0.539

T('C) 115 120 125 130 135 140 145 150 155 160

x~8 (ps) 0.507 0.483 0.456 0.433 0.416 0.393 0.377 0.360 0.344 0.329

151

of a water molecule in the neat liquid and solution for the reasons described elsewhere. 6 In this case, the water rotational relaxation is described in terms of a single correlation time x2s. The value of ~2Rfor pure D20 has been determined over a wider temperature range than before, and the results are summarized in Table 1. IV. T E M P E R A T U R E EFFECT ON 't2R FOR

D20

The water molecule is characterized by the extremely small moments of inertia, the relatively small mass, and the large charge separation causing H bonds. The moments of inertia are so small that equilibrium angular velocities of water molecules distribute over a wide range according to the Maxwell-Boltzmann law. To what extent are the molecular characteristics reflected on the rotational correlation time? Is the H bonding between water molecules more impcmant than these molecular characteristics? To answer these questions, we plot the logarithmic values of x2s for pure D20 in Table 1 and those in the previous world on solutions in various organic solvents against inverse temperature in Figure 1. First, compare the X2Rvalues at 30 "C to see how the correlation time depends on the I

,,,

I

,,

I

,,,,

I

,,,

,

I m

l

41~ (CH3)2CO

j 2-1

A = ClIa

/

x C6H6 N

. f ~

. . P

cc14

1

Jo

~

,

-1

-2 I

I

2.5

3.0

i

3.5 1/T (10 -3 K -1)

Figure 1. Plots of In ~2R against 1/T for D20 in various solvents.

I

I

4.0

4.5

152

molecular environments of a water molecule. This is in the sequence, CC14 (0.10, 0.85) < C6I-I6 (0.22, 0.56) < CHC13 (0.23, 0.51)


/ 7 m site

t2

.s/

1,3 t la'~'

Figure 1. A Liouville space Feynman diagram for CARS process. Each wavy line denotes the molecule-radiation field interaction. This diagram represents the time evolution of the intermolecular coherence between two molecules at g and m sites in the CARS process. Figure 1 shows the Liouville space Feynman diagram representing the time development of the intermolecular coherence between molecules at site g and m in the time-resolved CARS process. The two upper lines show the time development of intramolecular coherence of molecules at g. The two lower lines show the time development of intramolecular coherence of molecules at m, respectively. The upper and lower lines are connected through the incident laser fields(I, II, and III) indicated by wavy lines. In the ordinary pump-probe type time-resolved CARS experiments, the time duration from t3 to t4 corresponds to the pump-probe time x, and the intermolecular coherence time for pair molecules. In other words, it is the time dependence of the coherence between the Raman transition a j and i' j' vibrational Raman transitions is expressed in terms of the population decay constant from each state and intermolecular pure dephasing constant as 13 tm 1 e e t g t~rn(d) r'ji, i,j,:ji.i,j,-~(r'ii:ii + Fjj:jj + Fi,i,:i,i , + I"j.j,:j,j,)+ I"ji.i,j':ji.i'j', (15)

e where l"ii:ii is the population decay constant from state i of the molecule at site ~, and trn(d)

F ji.i'j':ji.i'j' the intermolecular pure dephasing constant. The population decay constant is defined as t 2g (16) F i i : i i - h2 Z X X P i # 42 ~(~tJmfB, iis) 9 iB fs met and the intermolecular pure dephasing constant is defined as s 2~ r j i , i'j':ji,i'j' -- h2

i~B '~afB piBl(<j, iBI lqeBIj, fB>-')

- ( < j ' , iBI lqmBIj', f B > - < i ', iBI lqmBli ', fB>)P 5(C0iB.fB) 9 (17) Here lqeB(lqmB) represents the interaction Hamiltonian between the molecule at site e(m) and the heat bath mode. From the general structure of the intermolecular pure dephasing constant, the intermolecular dephasing constant for the transition i jat e and i ,-->j at site m is expressed as ~m 1 t r'ji, ij:ji,ij -- 2 ( F i i : i i

~ m m + F j j . j j + Fii:ii + F j j : j j )

,

(18)

that is, there are no intramolecular and intermolecular pure dephasing terms. For Raman transitions i jat site g and i k(j ,:k)at site m, the dephasing constant is expressed as gm 1 e t m m gm(d) m ._ l"ji, ik'ji,ik -- 2(l"ii:ii + 1-'jj:jj + l"ii:ii + Fkk:kk) + l"ji, ik:ji.ik. (19) When the heat bath modes are different between sites g and m, these molecules are uncorrelated. In this case, the intermolecular dephasing constant consists of the sum of the intramolecular dephasing constants at the two sites, em e m Fji, ik: ji,ik = l"ji: ji + I ~ ki: ki. (20) When the molecules at different sites are correlated through heat bath modes, the intermolecular dephasing constant is not given by the sum of the intramolecular dephasing constants at the two sites. In this case it is given as em e m 1-'ji, ik:ji,ik = F j i : j i + I " k i : k i -

gm l'~ji, ik:ji,ik,

(21)

174 where I~ji,ik:ji,ik denotes the interference term between the two Raman transitions due to a common heat bath mode. At this poi.nt, a brief discussion about the site-dependence of the intermolecular dephasing constants is worthwhile. The population decay constant, and intramolecular dephasing constant are independent of the sites of the molecules in ordinary systems such as neat liquids. The magnitude of the intermolecular dephasing constant associated with i(--)j and i(---)k Raman transitions at different sites, on the other hand, do depend on the site when molecules are correlated through a common heat bath mode. The site-dependent intermolecular dephasing constant can be evaluated by using a multi-spherical-layer model. 9, l0 In this model the intermolecular dephasing constant is assumed to have the same magnitude within the same spherical layer. Under this assumption, the summation over sites ~ and m in Eq.(10) are carried out easily. 111. Intermolecular rovibratlonai interference m e c h a n i s m Okamoto and Yoshihara I l have reported a decay component of 0.39 ps in addition to a slow component of 2.4 ps in time-resolved CARS profiles of neat benzene at room temperature. This sub-pi~nd decay component is not attributed to the intermolecular vibrational dephasing effects discussed in the preceding section or to the effects of the pulsed lasers used. This is because the decay component has a Gaussian form and a photon polarization dependence. The slow component of 2.4 ps is identified with reorientational motions perpendicular to the C6 symmetry axis. Ultrafast intermolecular dynamics of benzene liquids has also been investigated by several groups using different nonlinear-coherent techniques. 14-18 The 0.39 ps dephasing time is explained in terms of interferences between rovibrational Raman transition amplitudes at different sites in this paper. To explain the origin of the 0.39 ps decay component on the basis of a rovibrational interference mechanism, we assume that the radius of the spot irradiated by the pump laser is much larger than an average correlation length between benzene molecules interacting through the heat bath modes. Further, the observation for the time-resolved CARS is performed in the direction of Ak=0. In this case, the molecules interact independently with the heat bath modes. The CARS intensity is proportional to the absolute square of the third-order nonlinear polarization, averaged over the heat bath mode and the distribution of rotational energy in the initial state. The rotational motion is treated quantum mechanically. For simplicity, rotational motions were treated within a free rotor approximation. This approximation is crude one in treating molecular librations in condensed phases and is only valid for high temperature limits in which the thermal energy is larger than an averaged librational bamer height. Photon polarization- dependence is taken into account by assuming that the geometry of benzene is that of a symmetric-top. Under the polarization condition [Z, X, Z, X] only anisotropic Raman transition contributes to the CARS process. The lime profile IZXZX(%)is given as 19 ZXZX

I

(x) oc I ~zxzx(%)12,

(22)

where

(2) X RJKN exp{-iB[N(N+ l)+2NJ]x}exp[-(i~fi+7 fi)x].

(23)

In Eq.(23), J and K are the rotational quantum numbers for the total angular momentum and the component projected to the molecular principal axis, ~ is the anisotropy of the Raman polarization tensor, pj is the thermal rotational distribution function in the initial state, and N specifies the selection rule of the rotational Raman transitions. ~(J)=0 if J / V (fii, dipole moment of particle i; V, volume of the sample)

< P~'Ct)e.(o)> P~/(O)" >

F~" = < P~'(o)-"

f

oF;,. e x p ( - 2 r i v t ) d t

; eCt,) = [~" - eoo] ( - - - ~ )

(3a, b)

which completely determines ~(v) 13, see eq. (3 b); e" = e'(0) is the permittivity at low frequencies (v ~ o), eoo is the permittivity at frequency too (generally in the FIR region) at which polarization p~r is attenuated to zero by the incapability of the dipole molecules to follow the polarity changes of the external field. Aprotic solvents, such as PC or AN, generally reveal a single relaxation process, with a more or less broad relaxation time distribution hiding the particular rotational diffusion processes around the molecular axes. Dimethyl formamide (DMF) represents a case where two of the particular processes are separable on behalf of a sufficiently large difference in relaxation times .18 Protic solvents show two (1120, formamide FA) or three (alcohols ROH, N-methylformamide NMF) structural relaxation processes, each one with a characteristic relaxation time ri. 18,19 Eqs. 3 can be easily extended to this situation. 13,17 The dispersion and absorption curves of the pure solvents undergo drastic changes when an electrolyte is added, the most important being the superposition of conductivity shown in the absorption curve r/"(v) of fig. 5 a and in the Argand diagram 7?" = f(r of fig. 5 b. Reduction of r/"(v) to r is executed with the help of measured static conductivities a. Two relaxation processes are corroborated by two inflexion points of r two maxima

181

of ~"(v) and two regions in the Argand diagram r corresponding to the relaxation of AN molecules and the ion pairs IP of LiC104. The dispersion curve ~'(v) and the Argand diagram ~"(~') of pure acetonitrile are given for comparison (broken lines), cf. fig. 4. For the sake of clearness the absorption curve of pure AN is not shown; it would be very near to the boundary line of the shaded part AN of the absorption curve of the electrolyte solution. 50

4O g*

40 30 30 20 u 0

g' 10

20

10

0 0.1

0.5 1

5 10

50

0

~l~lv g~l

GHz

g

P

Figure 5: (a) Dispersion (e') and absorption (r/" and ~") curves and (b) Argand diagrams (r/" = f ( d ) and d' = f(~')) of a 0.389 M solution of NaCI04 in AN (25 ~ For explanations see the text.

IV. I n f o r m a t i o n on ion-solvent interactions from high f r e q u e n c y p e r m i t tivity s p e c t r a Free ions do not yield relaxation processes because of lacking proper dipole moments, but they orientate their neighbouring solvent molecules by their strong electrical fields against the external field, thus diminuishing the dispersion amplitude (~* -~oo) of the pure solvent to (~ool~(c) -~oo) where g,ol~(c) may be understood as the permittivity of the solvent in the electrolyte solution. The ion pairs in the solution, and also other polar aggregates capable to relax in the external field, contribute their dispersion amplitudes (eoot(C)- ~,o,,(c)) to the total dispersion amplitude (e,oi(C)- eoo), ~,ol(C) being the static permittivity of the electrolyte solution, see fig. 5. Hence the permittivity of the electrolyte solution e,o~ may be larger than that of the pure solvent when ion-association takes place, whereas the permittivity of the solvent e,ol, in the solution always decreases. The nonlinear decrease is commonly fitted to a polynomial of the type e,o1.(c) = e" - ~ c + ~ c " ; n = 1.5 or 2

(4)

182

Dipolar aprotic solvents such as AN and PC are much less affected than the liquids forruing hydrogen bonded chains, e. g. MeOH and NMF. 13 Values for 6, and ~/~ are reported in ref. 21. The dielectric depression, A~,o~, = ~~ - c*, is caused by three effects, a volume effect (r due to the dilution of the polar solvent by the apolar ions (~ ~, 2), irrotational bonding (IB) of solvent molecules to the ions caused by electrostatic interactions, and kinetic depolarization (KD) resulting from the movement of the ion against the direction into which the solvent dipoles are orientated. 22 (r and (IB) are equilibrium properties reflecting the structure of the solution and yielding solvation numbers, (KD) is dynamic in origin. Actually no unifying theory exists incorporating these three effects into the dielectric depression Ae~ in a consistent way and which can be applied to finite electrolyte concentrations. In our experience it is possible to analyse the experimental decrements 8, 13 (5a, b, c) The depolarization factor ~ is estimated with the help of the continum model of Hubbard and Onsager 22 for ion transport under stick or slip hydrodynamic boundary conditions. Recent MD simulations and theoretical considerations suggest that ~,ol~(c) might depend only on equilibrium properties, i. e. ~ = 0. 23 A decision about these contradictory theoretical statements is not possible with the restricted number of the existing experimental data. The separation of the measured effect into ionic contributions requires assumptions on reference ions depending on the nature of the solvent. 9, 24 For acetonitrile solutions, a attern of consistent solvation numbers is obtained at negligible kinetic depolarization for Li+(4),Na+(4),Br-(2),Bu4N+(O),I-(O),CI04(O)in agreement with those from FTIR measurements for Li +, Na + and CI04. Reasonable solvation numbers are found for Na + ions in FA and DMF both for ~ = 0(6) or ~ # 0(4). 25 Independent of the choice of ~, Na + ions in NMF show large solvation numbers (~ 10), just like in methanol solutions 26, 27, indicating that solvent association in chains produces ion solvation beyond the first solvation shell. The solvation numbers of aqueous solutions based on the assumption that the Cl- ion is the reference are in favour of ~ # 0 and slip boundary conditions. 24

~

Aqueous tetra~lkylammonium salts show a peculiar behaviour due to hydrophobic interaction of the cation with water. It is known that Me4N + ions (Me: methyl), as well as the larger alkali metal ions disorganize water structure in their immediate vicinity and yield negative temperature coefiicients of the Walden product, whereas Pr4N + ions and higher homologs behave just in the opposite manner. 28 Figure 6 shows how MW data reflect the "structure making" effect of Btt4NBr by the comparison of aqueous solutions of Et4NCl and an aqueous solution of Bu4NBr. 29 The Argand diagram of the 2.2 M solution of Et4NCl shows three relaxation processes typical for aqueous electrolyte solutions: (1)ion-pair relaxation (r(1) = rxp), (2)low frequency relaxation (r,(o21),,~ 8 ps) of water, (3) high frequency relaxation (r~o3)~~ 1 ps) of water, in contrast to that of the 2 M solution of B u 4 N B r where the relaxation process (2) splits up into two processes. Figure 7 shows the concentration dependence of the

183

~.(2.) and 'ool,,.,.(2b) corresponding relaxation times 'ool,,

50

30

,•eo

40

20

3O s., o 20 , q4

10

~,ee

10 !

10

20

30

p

8

3

40

'

8oll

=-

r

.

2

10

20

It

40

~.~. zo

0

1

2

3

e

tool

elm"s

Figure 6: Argand diagrams of aqueous solutions (25 ~ of (a) tetraethylammonium chloride (2.23 M Et4NCI) and (b) tetrabutylammonium bromide (2.00 M Bu4NBr). For explanations see the text. Figure 7: Frequency dependence of the low frequency relaxation time ',o1~'(2)of water in Et4NCl solutions (curve 3) and splitting of ',o1~-(2)in Bu4NBr solutions into .(2~) '~ol~ (curve ~.(~b) (curve 2), c. f. fig. 6. 1) and '.o.., Beginning at the relaxation time of 8.3 ps of pure water at electrolyte concentration zero the addition of Btt,NBr produces a relaxation process with the expected almost ~(2b) concentration-independent water relaxation time ',ol~ ~ 8.5 ps (bulk water), the other (2~) with a strongly increasing relaxation time r~ol~ indicating a water structure relaxing at much lower frequency, whereas Et4NCI exhibits no split of the water relaxation time .(2) ' solv"

184

V. I n f o r m a t i o n on ion cluster f o r m a t i o n f r o m high f r e q u e n c y p e r m i t t i vity s p e c t r a The ion-pair relaxation process, found at the low frequency side of the spectra is the consequence of the reorientation of ion pairs behaving like dipole molecules. However, the frequency window of ion-pair reorientation generally comprises the frequency range of the kinetic relaxation process of ion-pair formation and dissociation 14 k12 C+ + A-

~

IP

(6)

h, The overall time constant of the orientational relaxation process r ~ and the kinetic process r~i~'~ - [k21 + 2k12(c- cip)] -1 is given by the relation 1

rip

1

1

T~p i" ~IP

1

~r~P "~ ~21 "~" 2 ~12 (C

CIp )

(7)

permitting the determination of k,2 and [(r~)-'-t-k21]from the linear plot ri"~ vs. (c-cap). O n the other hand, the concentration dependent association constant Kc - kl2/k2x can be determined from the dispersion amplitude e~ ~,o~(c) of the ion-pair relaxation process, so that finally r~,k~2 and k21 are known. In ar~tonitrile LiBr (Ka =148 dm3/mol) and B u 4 N B r (Ka = 17 dm3/mol) form contact ion pairs. The association constants are in agreement with those determined with the help of other methods. However, M W measurements reveal a significant difference between the ion-pairs of Li+ and Bu4N + ions in A N due to their stabilities. For B u 4 N B r the rate constants kl2 = 8 9109 d m 3 tool-I s-l and k21 - 0.35 910 z s-l are in the range of diffusion controlled reactions, whereas no kinetic process can be observed for LiBr.9 Ion-pair formation data from high frequency permittivity measurements are also known for aqueous solutions of 1.1, 2.1 and 2.2 electrolytes 30, 31, M e O H 21, FA, N M F , D M F 21,25-and DMSO (dimethyl sulfoxide) 21 solutions. Charged ion pairs [M2+CIO~] + have been investigated by MW methods in aqueous solutions; CdCl2 forms the inner sphere complex [Cd(H20)sCl] + as can be concluded from the effective volume V~ of dipole rotation available from the analysis of the ion-pair relaxation times, eq. (7), in combination with the Stokes-Einstein-Debye equation 31

3 V~ OT ~'iP = ~ r /

(8)

The study of the effective volume of dipole rotation has proved to be a valuable tool for clearing up the structure of ionic aggregates in electrolyte solutions 9, 14,31,32, as well as the investigation of the effective dipole moments of the aggregates revealing the transition from solvent separated to contact ion pairs, e. g. NaCl04 solutions in AN at increasing electrolyte concentration, where LiBr reveals contact ion pairs down to the lowest measured concentrations. 9

18.5 References

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21 22 23 24 25 26 27

28 29 30 31 32

J . F . Coetzee and W. It. Sharpe, J. Solution Chem. 1, 77 (1972). I.S. Perelygin and M. A. Klimchuk, Russ. J. Phys. Chem. 47, 1138 (1973). D.E. Irish and M. H. Brooker, in It. H. Clark and It. E. Hesters (eds.), Advances in Infraredand Raman Spectroscopy, Vol. 2, Heyden, London 1976, p. 212. J. Barthel and It. Deser, J. Solution Chem., in press. J. Barthel and It. Deser, J. Mol. Liq., in press. I.S. Perelygin and M. A. Klimchuk, Russ. J. Phys. Chem. 51, 838 (1977). J.P. Toth, G. Ritzhaupt and J. P. Devlin, J. Phys. Chem. 85, 1387 (1981). P.G. Glugla, J. H. Byon, and C. A. Eckert, J. Chem. Eng. Data 26, 80 (1981). J. Barthel, M. Kleebauer, and It. Buchner, J. Solution Chem., in press. L. Klein, Diplomarbeit, Regensburg 1988. F. Accascina, G. Pistoia, and S. Schiavo, Itic. Sci. 35, 560 (1966). G. Pistoia, A. M. Polcaro, and S. Schiavo,/tic. Sci. 37, 309 (1967). J. Barthel and 1t. Buclmer, Chem. Soc. Itev. 21,263 (1992). It. Buchner and J. Barthel, J. Mol. Liq., in press. J. Barthel, M. Mfinsterer, and It. Buchner, in preparation. J. Barthel, K. Bachhuber, It. Buchner, H. Hetzenauer, and M. Kleebauer, Ber. Bunsenges. Phys. Chem. 95, 853 (1991). J. Barthel, It. Buchner, and M. Mfinsterer, Electrolyte Data Collection, Parts 2 and 2 a, in: G. Kreysa (ed.) DECHEMA Chemistry Data Series Vol. XII, DECHEMA, will be published 1995. J. Barthel, K. Bachhuber, It. Buchner, J. B. Gill, and M. Kleebauer, Chem. Phys. Lett. 167, 62 (1990). J. Barthel, K. Bachhuber, It. Buchner, and H. Hetzenauer, Chem. Phys. Lett. 165, 369 (1990). J. Barthel, R. Buchner, K. Bachhuber, H. Hetzenauer, M. Kleebauer, and H. Oft maier, Pure Appl. Chem. 62, 2287 (1990). J. Barthel and R. Buchner, Pure Appl. Chem. 63, 1473 (1991). J.B. Hubbard, P. Colonomos, and P. G. Wolynes, J. Chem. Phys. 71, 2652 (1979). A. Chandra, D. Wei, and G. N. Patey, J. Chem. Phys. 98, 4959 (1993). J. Barthel, H. Hetzenauer, and R. Buchner, Ber. Bunsenges. Phys. Chem. 96, 988 (1992). J. Barthel, K. Bachhuber, and It. Buchner, Z. Naturwiss., in press. J. Barthel and It. Buchner, Pure Appl. Chem. 58, 1077 (1986). J.-P. Badiali, H. Cachet, and J.-C. Lestrade, J. Chim. Phys. Physico-Chim. Biol. 25, 1350 (1967). D.F. Evans and T. L. Broadwater, J. Phys. Chem. 72, 1037 (1968). J. Barthel, R. Buchner, M. Mfinsterer, and J. Stauber, 4th EurAsiaConference on Chemical Sciences, Kuala Lumpur 1994. It. Buchner, G. Hefter, and J. Barthel, J. Chem. Soc. Faraday Trans. 90, 2475 (1994). J. Barthel, H. Hetzenauer, and It. Buchner, Ber. Bunsenges. Phys. Chem. 96, 1424 (1992). J. Barthel and M. Kleebauer, J. Solution Chem. 20, 977 (i991).

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journal of

MOLECULAR

LIQUIDS ELSEVIER

Journal of MolecularLiquids.65/66(1995) 187-194

Dynamical Aspects of Water by Low-frequency Raman Scattering Yasunori Tominaga, Yan Wang, Aiko Fujiwara and Kohji Mizoguchi* Department of Physics, Ochanomizu University, Otsuka, Bunkyo.ku, Tokyo 112, Japan *Department of Applied Physics, Osaka University, Yamadaoka, Suita, Osaka 565, Japan Abstract Depolarized Raman spectra below 250 cm "1 in liquid water (H20, D 2 0 and H2180), aqueous electrolyte solutions (LiC1, NaCI, KC1, RbCI, MgCI2 and CaC12), D-glucose solution and ascorbic acid isomerism solutions (L-xylo and D-arabo) were investigated. The Raman spectra below 250 cm "1 in these liquids are interpreted with a superposition of two damped harmonic oscillators and one Debye type relaxation mode (liquid water) or one Cole-Cole type relaxation mode (aqueous solutions). (1) With increasing temperature the half width of half maximum of the central component gl in 1-120 has a small bend at about 20 *C. (2) For aqueous electrolyte solutions, with increasing salt concentration the ratio of relaxation time "r/~rwater shows just the same behavior as the ratio of viscosity 0/r/water. (3) In glucose solution the characteristic frequencies of two oscillator modes do not show any change. This means that the glucose can just embed in the dynamical structure of water. (4) The effect of L-xylo ascorbic acid (Vitamin C) on the dynamical structure of water is different from the effect of D-arabo ascorbic acid.

I. Introduction Water is one of the most familiar material in our life and is indispensable to all living things. In contrast to its apparently simple molecular structure, water shows many anomalous properties from both macroscopic and microscopic points of view. 1-2 However, the basic physical property of water, for example the dynamical structure of water, has not yet been fully clarified. To understand the dynamical aspect of water structure and its significant role in life, it is essential to clarify not only the dynamics of water molecules themselves but also the dynamics of water in the aqueous solutions. Raman spectroscopy has been usually employed to investigate the dynamical structure of water and aqueous solutions for a long time. In the high-frequency spectral region above 300 c m l , intramolecular vibration spectra of water molecule are measured and these spectra are analyzed and discussed by many researchers. 3-9 On the other hand in the low-frequency region intermolecular fluctuation bands which are due to the interaction between water molecules through the hydrogen-bond and/or the dipole-dipole interaction are observed. 9-19 In this low frequency region two broad bands around 190 cm -1 and 70 cm -1 have been observed and assigned to the restricted translational vibrations of the hydrogen bonds between water molecules based on a five-molecules cluster model. 9 The spectral profiles of these modes in aqueous solutions have been widely reported. 20-26 Recently it has been found that besides the above two broad bands one relaxation mode appears as a central component below 50 cm-1.10,17-19,27 This relaxation mode is due to the creation and annihilation process of hydrogen bond among water clusters. From the change of this spectral profile as well as the two broad bands in water and aqueous solutions we can obtain the dynamical aspect of water. 0167-7322/95/$09.50 91995ElsevierScienceB.V.All rightsreservgd. SSD! 0167-7322(95) 0085I-9

188 II. Experimental Raman scattering spectra were obtained by a four-slit double-grating spectrometer (Jobin-Yvon HG-2000M). The exciting light source was a NEC At-ion laser operating at 488 nm with a power from 100 to 300 mW. An apparent local heating due to the laser light was not observed. A right-angle-scattering geometry is always adopted in the present light-scattering experiments. The depolarized Raman spectra were measured with the configurations of X(VH)Y, where the XY plane is horizontal and X denotes the direction of incident light and Y denotes the direction of scattered light. The typical spectral resolution was 1.5 cm "1 - 2.0 cm "1 for the spectral region from -50 cm "1 to 50 cm "1 and 3.0 cm "1 for the spectral region from -250 cm "l to 250 cm "l. The scattered light signals were detected by a photo-multiplier in conjunction with photon-counting electronics. The samples of liquid water were 99.9% D20, natural H20 which was de-ionized and distilled and H2180 which was purchased from Isotec Inc., Japan. Solutes of LiCI, NaCI, KC1, RbCI, MgCI 2 and CaCI 2 arc extra-pure grade, which were purchased from Wake Pure Chemical Industries, Co. Ltd. The aqueous solution was prepared by dissolving solute into deionized distilled water. The concentration range of aqueous electrolyte solution is from 0.00 (water) to 0.11 molar ratio. The molar ratio is the mole number of solute against the mole number of water, which is written as nx/nwatcr in the present paper. The D-glucose was purchased from Wake Pure Chemical Industries Co. Ltd., Japan. Water we used as a solvent was de-ionized and distilled water. The concentrations of the D-glucose aqueous solutions arc from 0.005 to 0.04 molar ratio. The ascorbic acid aqueous solutions were prepared by dissolving L-xylo ascorbic acid or D-arabo ascorbic acid into the de-ionized and distilled water. The concentrations of ascorbic acid aqueous solutions are from 0.0025 to 0.03 molar ratio. The L-xylo ascorbic acid is a well-known vitamin C and the D-arabo ascorbic acid has very litde physiological activity although they arc isomeric with each other. All the samples were further purified by removing dust particles through 0.2 gm Millipore filter and sealed in fused silica cells or Pyrex cells. The sample cell was embedded in a specially designed home-made cryostat or furnace. The temperatures were measured with a chromcl-constantan thermocouple closely attached to a cell. The accuracy of the temperature control is within :1.-0.1 K. The thermocouples were prepared at Chemical Thermodynamics Laboratory, Osaka University. III. Results First we show in Fig.1 a high frequency (VV) and (VII) Raman spectral pattern of water at 295 K. The high frequency spectral pattern characterizes the internal molecular vibrations. Fig.1 shows raw spectra which are not calibrated by the spectrometer efficiency. However this spectral pattern has a typical characteristic of the tetrahedral-like C2v structure although the spectral line shapes arc very broad. In other words, between 1600 cm -1 and 4000 cm -1 essentially four kinds of molecular vibrations (el, v2, v3, v4) exist. This tetrahedral characteristic is consistent with the later discussion of the dynamical aspect of the water structure obtained by the low frequency Raman spectra.

189

Innnnlnnnnlnnnnlnllll qi[WATER (295K)I, If:' .

v,,vo

---"i.'

J .... J :

..........

:

!

~- . . . . . . .

~ :

: . . . . .

---8-

. . . .

-4----. ,

__i..._?_. -,..~ .... (vv)-.-~

~ li

" ~ /

-.4_~.... .

~

i

'I

i ~

"

-

.~L ....... i-~t---

v4

i

--

s

............. -/..4 .... -

-i/(vm

_

7

uuunlUnUUlUUnUlUUUu -200

2000 4000 RamanFrequency (cm"1)

0

0

200

RamanFrequency (cm"l)

Fig.l. High frequency Raman spectralpattern Fig.2L o w frequency reduced Raman spectrum in liquid water at 295 K. Four kinds of internal at 295 K. Solid curve is a best fitcurve and vibration modes from 1600 cm -l to 4000 cm -I. dottedcurves are components of three modes.

8

~-6

I.

ti.

,

I

i

I

,

I

i n

~5 >

~4 ~3 ~ 2 1 0

-200 0 200 Raman Frequency (cm"l) Fig.3 Reduced Raman spectra of various electrolytic solutions. (1):RbCI, (2):KCI (3):NaCI, (4):LiCI, (5):CAC12, (6):MgCI2.

0.00

0.04

0.08

0.12

n x / nw=er(molar ratio) Fig.4 Concentration dependence of the ratio of relaxation time (markers) and the ratio of viscosity (solid curves).

190 To clarify the spectral profile in the low frequency region, we reduced the Raman spectralintensityI(~') into the imaginary part of the complex dynamical susceptibilityX(V).27 The Z"(v) is given by

X"(~) = K (vi -~)--4[n(P)+ 1]-11(~),

(1)

where n(~')+l is Bose-Einstein thermal factor with n(~')=[exp(hcP/kT)-l] -l. The P is the Raman frequency shiftin cm -I,and the vi is the frequency of incident laser fight. The K is an instrumental constant. Fig. 2 shows the X"(V) spectrum of water at 295 K. Fig. 3 shows the typicalX"(V) spectra of various electrolytesolutions of 0.07 molar ratioat 303 K. The central components within :k20 cm-I vary with ion species. Since the reduced spectrum X"(v) clearly shows the low-frequency Raman modes, we introduced a simple model to analyze the spectral profile of Z"(v') for obtaining the quantitative information. The model is composed of two damped harmonic oscillatormodes and one Debye type relaxation mode (liquid water)27 or one Cole-Cole type relaxation mode (aqueous solution).28 Cole-Cole type relaxation is usually adopted in analyzing the dielectric relaxation. The formula of Cole-Cole type relaxationis represented as31

1

Z(to) = 1 + (,~)"'an;"/3'

(2)

where to = 2gc V and c = I/(2gcgl). The to is an angular frequency, c is the relaxation time, and the parameter fl (0> 1 were used As a result, only solutions where the alcohol concentrauon was vaned and surfactant concentrauon was kept constant were used. Plots of 1/1;1 vs Cm/cmc were, for the most part, linear and the deviations from linearity probably reflect the crude method used to obtain an approximate value of ~AS. The values of the kinetic parameters and statistical results are shown in Table II. 9

.A

*

.

Table II. Kinetic Parameters for Aqueous Solutions of D T A B Alcohol Systems Derived from the Aniansson Model.

and D T A B

+

9,.i 1010s oS AV1, AV2, Kc kis 108 k+b~I "1 k2"1010 ~A . . cm3mol-I cm3tool -1 mol-ldm3 noned 4.5 3.0 10 4.4 n-C3H7OH 2.2 1.4 -+0.1 2.4 4.9:t:2 12:t3 4.2 _+0.3 29"2-_2 3.5:k0.3 0.49 n-C4H9OH 1.7 1.1 s 5.6 3.5:t:1 15:1:8 3.1_+0.4 30-+9 2.9+0.2 1.6 n-C5H11OH 1.5 0.95+0.3 8.3 1.7"1-0.4 17-1-102.5-t-0.5 24-1-4 2.4-+0.5 4.9 CaHo(EO)OH 5.1 3.1 -+0.7 2.5 2.2_+0.6 16"3:10 !3_+5 4.3-+0.8 1.2 Reprinted with permission from J. Phys. Chem. 1992, 96, 6811. Copyright f992 American Chemical Society. a Calculated using the cmc in the absence of alcohol where k'~ = k [/cmc. b Calculated from the relationship Ka = k~/k~, c Obtained from conductivitymeasurements, d Obtained using the data of ref. 8. alcohol

k~'a"1109s M "1

l

Values of the average volume change associated with the exchange of both surfactant (AV1) and the alcohol (AV2) can be calculated, according to the Aniansson model, from the following expressions

201 l.tmaxl = (Alfrl u) / 2 = [xAV? / 2RT]F(cmc) / [K:s(I+F)]

(11)

A 2 = 1.18x10 -7 AV 2 C m k~ 1;2

(12)

and

where ~tmaxl is the absorption maximum per wavelength, u is the speed of sound, and 1" = t~22/n)(Cm/cmc) 9 The slopes of graphs of ~tmaxl vs F(cmc)/[r,S(1 + 1")] and A2 vs Cm k -2 x 22 . were analyzed to obtmn estimates of AV1 and AV2, respectively, the results of which are shown in Table II. The volume changes associated with the surfactant are large and comparable for all systems. The rather large values of the exchange volume of DTAB with the mixed micelle, compared to the value of 4.4 cm 3 mo1-1 for this process in a regular mieelle, is puzzling. However, estimates of this property from the data using the model developed by Hall (see below) also show large values. We have speculated [2] that small fragments of alcohol and surfactant may break off from the micelle. A similar conclusion was drawn from the results of time correlated fluorescence measurements of pyrene in mixed alcohol-surfactant micelle systems [9]. On balance, further studies are required to confirm the exchange volume data for the surfactant and the tentative explanation for its magnitude. The volume changes associated with the exchange of the alcohol are much smaller and decrease with increasing chain length of the alcohol. This is contrary to the thermodynamic estimate of AV2 which increases with increasing alcohol chain length [ 10, 11]. Table III shows the values for the kinetic and statistical parameters obtained by analyzing the data for all ternary systems according to the phenomenological model of Hall [5]. A comparison of the values of the various parameters (cf. Table II and Table 111) obtained from analyses employing these two models show, generally, that larger values are obtained with the Hall model; however, the trends in the derived parameters are similar. The values of the rate constants for the alcohol exchange process in the Hall model were obtained by extrapolating CAf --->0 to avoid any concentration dependence of k~. Using the extrapolated value of k~, it was shown [5] that k~ is given by k ~ = n ~ k 2 (Cr~ / C f C~ ) Table III.

(13)

Kinetic P a r a m e t e r s for A q u e o u s Solutions of D T A B and DTAB + Alcohol Systems Derived f r o m the Hall Model.

alcohol

k~,a 109 ki ' 108 k+ b 1010 k~, ib8 t~S AV2, Kc M-1 s-1 s-1 ~-1 s-1 s-1 cm3 mol-1 mol-1dm3 noned 3.8 2.3 10 n-C3H7OH 3.6 2.2 + 0.5 1.6 80 + 6 6.4 + 3 4.9 + 1 0.49 n-C4H9OH 2.9 1.8 + 0.5 0.41 6.5 + 1 5.2 + 2 4.5 + 1 1.6 n-CSHllOH 2.4 1.5 + 0.4 1.6 9.2 + 1 4.0 + 1 3.3+ 1 4.5 C4H9(EO)OH 6.2 3.8 + 0.5 4.4 10 + 5 5.2 + 1 1.2 Reprinted with permission from J. Phys. Chem. 1992, 96, 6811. Copyright 1992 American Chemical Society. a Calculated using the cmc in the absence of alcohol where k~ = k~/cmc, b Calculated using eq. 13. c Obtained by extrapolating to the limit C~ --> 0. d Obtained using the data of ref. 8. where n ~ is the aggregation number of DTAB in the absence of alcohol. In the Aniansson model k~ = K k~. The difference in the values of k~ obtained from the two models is greater for the shorter chain alcohols. There is good agreement in the values of k~ and k i-

202 obtained from analyses of the data using the two models. The term in the Hall model which accounts for the ionic character of the surfactant narrows the range of values for k~" and k ifor the various alcohol-DTAB systems, yielding values closer to those obtained in the absence of any alcohol. From eq 8 one can obtain estimates of AV2 from the slope of a plot of I.tmax2 vs CAf C ~/~SCA. The values of the exchange volume of an alcohol between the mixed micelle and bulk phase are larger using the Hall model. However, both models predict the value of AV2 decreases with increasing chain length of the alcohol. The model developed by Hall does not enable a value of AV1 to be estimated although this parameter has been related [5] to the quantity (~gVI~A2 as follows

(~v~ / ~)A2 = av~~ + av2 (ck c~ / cAc~)

(14)

where AVy is the volume change for the surfactant in the absence of any alcohol. At high alcohol and surfactant concentrations, (0V 1/0~)A2 plateaus at a value of ca. 30 cm 3 mo1-1, similar to the value of AV 1 derived from use of the Aniansson model. If, as mentioned above, this large value were thought to be the volume change associated with the exchange of a fragment, then given that the exchange volume of an alcohol is ca. 5 cm3 mo1-1, the stoichiometric ratio of alcohol to surfactant in such a fragment would be ca. 5:1. As previously mentioned, this interpretation is tentative in the light of our more broadly based understanding of micelles. The data in Tables II and HI show that the exit rate of the monomer surfactant decreases in a linear manner with increasing chain length of the n-alcohol in the mixed micelle. It is also evident from the rate constant data in these tables that the value of k i" for the DTAB-BE system does not readily fit into the above trend. In fact k i- has a value near to that for the exit rate of a monomer surfactant from regular micelles of DTAB. At the same time the magnitude of the exit rate of BE from the mixed miceUes is between the values for Bu and Pc. To explain these results it is important to recall that micelle aggregates exist by virtue of a delicate balance of intermolecular forces. On the one hand, there are the stabilizing contributions arising from the presence of counterions near the head groups and the hydrophobic interactions in the micelle interior. On the other hand, there is the destabilizing, repulsive forces that result from the charged head groups of the ionic surfactant monomers when they are in proximity to one another in the micelle. The degree of solvation of the counterions and of the head groups may also play a role in the balance between stabilizing and destabilizing forces in this outer region of the micelles. The decrease in the magnitude of kiand k~ in mixed micelles containing the n-alcohols, as the hydrocarbon chain length of the alcohol increases, can be explained by increased hydrophobic interactions. There does not appear to be a significant change in the balance of intermolecular forces in the head group region when the hydrophilic moiety of the n-alcohol replaces water. However, in the case of BE it appears that there is a change in the balance of intermolecular forces in this region of the mixed micelles. The data in Table III indicate that the magnitude of k~ for BE is approximately in the range of values for Bu and Pc. This suggests that the butyl segment of BE is embedded in the mixed micelle. However, the magnitude of the exit rate constant for DTAB from mixed

203 micelles containing BE is greater than for mixed micelles containing normal alcohols and for regular micelles of DTAB. We have shown [ 12] that the surface charge density of DTAB-BE mixed micelles is generally greater than that of DTAB-n-alcohol systems. As a result, the increase in repulsive forces in the head group region in the presence of BE appears to cause a more rapid exit rate of the surfactant. It is of interest to speculate about the role of BE in the head group region of the mixed micelle. If the CH2-CH2-O- segment of BE locates on the surface of the micelle or just outside this surface, then it must displace solvent (H20) molecules. As a consequence, solvent of a higher dielectric constant is replaced by solvent of a lower dielectric constant which is less effective in decreasing the repulsive force between head group charges. Also, if ion-solvent dipole interactions play some role, then relatively stronger ion-solvent dipole interactions in the presence of water are replaced by weaker-ion EO dipole interactions. Of the twenty five sterically possible conformers of the EO segment, a large majority of them have small or no dipole moments [ 13]. It is also probable that, when the butyl group of BE enters the micelle, these relatively nonpolar conformations are favoured. This qualitative picture provides an explanation for the different behaviour of BE compared to the n-alcohol series. It is also consistent with a report [14] that the Gibbs energy of transfer of a homologous series of alcohols having the general formula, C4(EO)xOH where 0 ___X ~_ 4, from the bulk to the cationic micellar phase is independent of the number of EO segments in the alcohol. If we exclude the results for BE and assume for the other alcohols that the forward rate constant k~ is diffusion controlled and approximately constant, the decrease in the exit rate of the surfactant represents a measure of the Gibbs energy of stabilization per CH2 group of the alcohol. From AGs = RT din (ki-)/dn c, AGs = -450 J mo1-1 per CH2. A similar calculation using data derived from the Hall model gives an estimate of AGs = -220 J mol-I per CH2. The values of (~A and t~s reported in Table II for the n-alcohols show that the addition of alcohols of increasing hydrocarbon chain length to DTAB micelles decreases the value of aS and increases the value of OA. The increase in (~A probably reflects increased binding of the alcohol in the mixed micelle with increasing alcohol hydrocarbon chain length. This appears to lead to greater polydispersity of alcohols in the mixed micelle, i.e., more of the mixed micelles contain a broader range of alcohols. From the perspective of the surfactant it would appear that there is a reduced polydispersity as the surfactant aggregation number decreases [ 11]. The interesting behaviour observed for aggregate systems of surfactant and BE requires a broader investigation. Systematic thermodynamic and ultrasonic absorption studies of systems where the number of EO units in the alcohol is increased are currently in progress. The information obtained should be of benefit in extending the commercial application of these surfactant-cosurfactant systems.

Acknowledgement We thank the Natural Sciences and Engineering Research Council of Canada for financial support.

204 References

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

Eggers, F.; Funck, Th. J. Acoust. Soc. Am. 1975, 57, 331. Aicart, E.; Jobe, D.J.; Skalski, B.; VerraU, R.E.J. Phys. Chem. 1992, 96, 2348. Jobe, D.J.; Verrall, R.E.; Skalski, B.; Aicart, E. J. Phys. Chem. 1992, 96, 6811. Aniansson, G.E.A. In Techniques and Applications of Fast Reactions in Solution; Gettins, W.J., Wyn-Jones, E., Eds.; Reidel; Holland, 1979; p. 249. Hall, D.G.J. Chem. Soc. Faraday Trans. 2 1981, 77, 1973. Abu-Hamdiyyah, M.; Kumari, K. J. Phys. Chem. 1990, 94, 2518. Evans, C.H.J. Chem. Soc. 1956, 579. Kato, S.; Nomura, H.; Honda, H.; Zielinski, R.; Ikeda, S. J. Phys. Chem. 1988, 92, 2305. Malliaris, A.; Lang, J.; Sturm, J.; Zana, R. J. Phys. Chem. 1987, 91, 1475. De Lisi, R.; Milioto, S.; Triolo, R. J. Solution Chem. 1988, 17, 673. Desnoyers, J.E.; H~tu, D.; Perron, G. J. Solution Chem. 1983, 12, 427. Jobr D.J.; Verrall, R.E.; Skalski, B.D. Langmuir, 1993, 9, 2814. Karlstrtm, G. J. Phys., Chem. 1985, 89, 4962; Karlstrtm, G.; Carlsson, A.; Lindman, B. J. Phys. Chem. 1990, 94, 5005. Marangoni, D.G.; Kwak, LC.T. Langmuir 1991, 7, 2083.

journal of

MOLECULAR

LIQUIDS ELSEVIER

Journal of MolecularLiquids.65/66(1995) 205-212

Organometallic Free Radicals in Solution James H. Espenson Ames Laboratory and Department of Chemistry, Iowa State University, Ames Iowa 50011, USA Abstract Laser flash photolysis of [CpM(CO)3] 2 (M = W, Mo, and Cr) provides a convenient source of CpM(CO)3 ~ an organometallic free radical with 17 valence electrons. It is a transient and highly reactive spedes. D e p e n d i n g on the circumstances and the other reagents present, the radical will dimerize, u n d e r g o halogen and h y d r o g e n atom abstraction reactions, and electron transfer reactions. With t e t r a m e t h y l - p h e n y l e n e d i a m i n e , there is a cyclic process of electron transfer steps, the net result of which is the catalyzed disproportionation of the metal radical. I. Introduction Organometallic compounds of the transition metals with carbonyl and other ~ - a d d ligands are generally constrained to 18 electron configurations, if they are to be stable. Compounds with only 17e are the subject of this paper. Because such species are one electron short of a closed shell, they react like free radicals. The 17e compounds are generally transient entities, except for those cases w h e r e the steric bulk of some of the ligands p r e v e n t s their coupling. The transient entities are typified by the c o m p o u n d s that are the subject of this study, (rl5-C5H5)M(CO)3 . (M = Cr, Mo, W) To achieve stability, these reactive entities may u n d e r g o any n u m b e r of reactions. The purpose here is to enumerate what these reactions are and the mechanisms by which they occur. Moreover, an a t t e m p t is m a d e to show how the organometallic free radicals are analogous to organic radicals, which are in general more familiar. The 17e organometallic species are isolobal with alkyl radicals which are 7e species, also one electron shy of a closed shell. II. Reactions of an OrganometaUic Free Radical To outline the processes the reactive o r g a n o m e t a l l i c radical m a y undergo, we consider the following: (a) dimerization, so as to regenerate the stable dimer from which they were formed by photohomolysis; (b) halogen abstraction from alkyl halides; (c) halogen abstraction from transition metal halides; (d) O H g r o u p abstraction from peroxides; (e) h y d r o g e n atom 0167-7322/95/$09.50 91995ElsevierScienceB.V. All fightsreserved. 0167-7322(95) 00853-5

SSD!

206 abstraction from certain metal hydrides; (f) addition of 30 2 and subsequent reaction; (g) ligand-catalyzed disproportionation; (h) electron-transfer reduction; (i) electron-transfer oxidation, before or after ligand addition; and (j) electron-transfer induced disproportionation. These reactions are outlined in Scheme I. The occurrences and mechanisms of these transformations will be dealt with here.

Scheme I CpW(CO) 3- + CpW(CO)3PPh3 + ~ h CpW(CO)3 L+ ~

(

3P

(a~,, ~ o ~cpw(co)3

(i) CpW(CO)3-

1

~

30 CpW(CO)3OO'~f

[CpW(CO)3]2

\ (h)

OC /

CO

i CO

(b) ~-C p W (CO)3X+ R~ RX

[ ~ ) ~ " (ZpW(CO)3X,M"

(eC~pM ~(e (CO)3H ROOH ~

M = Rh(dmg~2PPh 3) CpW(CO)3OH + RO ~

CpW(CO)3H

III. Experimental Procedures The chemistry of the CpM(CO)3 ~ radicals occurs on the microsecond time scale, and flash photolysis with optical detection is the technique most generally applicable. The radical is created by the photohomolysis of the stable dimer, [CpM(CO)3] 2, available commercially for M = Mo and W. The excitation sources used were Nd-YAG (~'exc 532 nm) and flashlamp-pumped dye lasers (~'exc 490-525 nm). When shorter wavelengths are used, the desired process in accompanied by increasing amounts of CO loss; this is in general undesirable because it introduces other transients into the system. The methods of generation of the radical and of analysis of different types of kinetic data have been referred to. ~-6 Optical detection of species was made, primarily of the parent dimer itself or of certain products referred to later.

20? IV.

Results

Radical recombination. The results p e r t a i n i n g to m a n y of the reactions in S c h e m e I will n o w be presented, starting with (a). W h e n a solution of the metal dimer is subjected to a laser flash, -25% of the d i m e r is dissociated; in a typical experiment a 20 ~M solution of [CpM(CO)3] 2 (M = Mo, W) yields about 25 ~M of the dimer. A slightly different p r o c e d u r e was u s e d for M = Cr, but with comparable results. 7 The recombination of the radicals occurs o v e r about 300 I~s a n d follows s e c o n d - o r d e r kinetics. A typical e x p e r i m e n t for the m o l y b d e n u m radical and the fit to s e c o n d - o r d e r kinetics is s h o w n in Figure 1. The rate constants (k/109 L mol d s -1) in acetonitrile at 23 ~ are: Cr: 0.27, Mo: 2.16, and W: 4.7. In other organic solvents the rate constants are c o m p a r a b l e to these, reflecting the relatively small differences in viscosity. In a q u e o u s solution (CsH4CO2-)Mo(CO)~" has k/109 L mol -I s "I = 3.0.

Absorbance

i

0

0

1 10-4 2 104 Time/s

Figmre 1. The results of a laser flash photolysis experiment, showing the combination reaction of CpMo(CO)3", as monitored by the recovery of the dimer at its 384 run maximum. The smooth curve through the points shows the fit to second-order kinetics. On closer inspection, the c o m b i n a t i o n rate constants are a b o u t 1 / 4 of the estimated diffusion-controlled rate constant. For acetonitrile, for example, kdc .- 2.9 x 1010 L mol "1 s -1 from the y o n S m o l u c h o w s k i e q u a t i o n 8 with a diffusion coefficient from a modified version of the Stokes-Einstein relation, D - . kT/4xTlr. 9,10 O w i n g to the restriction to singlet state recombination, an experimental rate constant 1 / 4 of kdc is quite reasonable. O n the other hand, for these h e a v y metals, the spin restriction m a y not apply, in which case one w o u l d a r g u e that the geometrical a n d o r i e n t a t i o n a l r e q u i r e m e n t s of these large species c o u l d well give r e c o m b i n a t i o n rates s o m e w h a t b e l o w the theoretical m a x i m u m .

208

Halogen atom abstraction. The metal radicals react with alkyl and aralkyl halides (RX, X = C1, Br, I) to yield CpM(CO)3X and R ~ The metal halide p r o d u c t is a species k n o w n i n d e p e n d e n t l y , and its f o r m a t i o n in these reactions was verified by IR. The organic free radicals w e r e not detected directly, but were inferred from the final organic products determined by GC; these products were consistent with those k n o w n to be f o r m e d when R ~ undergoes dimerization and disproportionation reactions. A large n u m b e r of rate constants for organic halides have been reported. 2 A small selection will be presented here. First, the trend with the group R, and then with X, using data for CpW(CO)3": Alkyl group trends

I XUrl: .22 •

[ Bu': 6.0 •

Halide trends AUyl, CH2CHCH2-X Trichloromethyl, C13C-X

k/L mol "1 s "1

Pr': 3.0 •

! Pr":

•

[M,, < 6 •

I

k/L mol "1 s -1 X = I: 1.22 x 108 X = Br: 5.3 x 108

X = Br: 5.4 x 104 X = CI: 2.92 x 104

These results suggest that the transition state features an incipient free radical (note the trends with R), and that the metal atom has begun to make a b o n d to the halogen of appreciable strength. The t r e n d with halogen substitution is a particularly pronounced one, since the trends in BDE(R-X) and BDE(M-X) are in the opposite direction (that is, the low-valent metal center is a soft acid). H a l o g e n atom abstraction occurs also with m e t a l halides, both ( N H 3 ) s C o l I I - x 2+ and X-RhIII(dmgH)2PPh3 having been studied. For the latter, kcl = 9.2 x 107 and kBr = 1.57 x 108 L mo1-1 s -1 for the reactions of C p W ( C O ) 3 ~ The i m m e d i a t e p r o d u c t of the r h o d i u m reaction is the i n d e p e n d e n t l y - k n o w n r h o d i u m radical, RhIl(dmgH)2PPh3 ~ a 17e species. It in turn dimerizes to yield the stable dimer, [Rh(dmgH)2PPh3] 2. Both of these p r o c e s s e s can be m o n i t o r e d d i r e c t l y , the b u i l d u p a n d decay of RhII(dmgH)2PPh3 ~ at 580 nm and the formation of the r h o d i u m dimer at 452 nm. The mechanistic discussion concerning the alkyl halides is pertinent here as well; the rhodium system allowed the direct detection of the radical product, which had only been inferred in the organic reactions.

Hydrogen atom transfer also occurs, as represented in one instance by the reaction of CpW(CO)3 ~ with CpMo(CO)3-H, a process driven by the higher bond energy of the tungsten hydride. 11 The atom transfer process is

209 not to be confused with proton transfer; the reaction of CpMo(CO) 3- with CpMo(CO)3-H is also known.

Reduction of the metal radicals. The anionic complexes CpM(CO) 3- are well k n o w n species; they are stable entities with 18 valence electrons. The standard reduction potential for the CpMo(CO)3~ - couple is -0.08 V vs SSCE. 12 The m o l y b d e n u m radical is thus a mild oxidizing agent; with suitable electron donors it can be reduced to the anion. For example, the radical oxidizes Fe(T15-CsMes)2 with a rate constant of 2.2 x 108 L mo1-1 s "1 in acetonitri]e at 23 ~ 6 Application of the Marcus equation for electron transfer affords the electron exchange rate of the molybdenum radical/anion couple. The value is kee = 3 x 107 L mo1-1 s-1. The high value argues that very little nuclear reorganization is needed to add an electron to the SOMO of the 17e radical. Oxidation of the metal radicals. The cationic d e r i v a t i v e s of these o r g a n o m e t a l l i c c o m p o u n d s contain an a d d i t i o n a l ligand. For example, CpM(CO)3PPh3 + and CpM(CO)3NCCH3 + are readily obtained; the latter can be g e n e r a t e d electrochemically in acetonitrile. The C p M o ( C O ) 3 N C C H 3 +CpMo(CO)3 ~ couple has a standard electrode potential of-0.50 V vs SSCE. 12, which shows that the metal radical is a strong reducing agent. For example, Fe(TIS-CsHs)2 + reacts with CpW(CO)3 ~ with a rate constant of 1.9 x 107 L mol d s "1 in acetonitrile at 23 ~ 6 As large as this this value is, it corresponds to an electron exchange rate between CpMo(CO)3NCCH3 + and CpM(CO)3 ~ of only -10 -12 L mol d s -1. The small value signals a large inner-shell reorganization; the two species differ by one coordinated molecule of solvent. Ligand-catalyzed disproportionation; the role of 19e radicals. There is now considerable evidence for the association of a 17e radical and Lewis bases, such as phosphines, pyridine, and even acetonitrile. The resulting species has the formula CpM(CO)3 L~ and is often referred to as a 19e radical. It is probably just that, but it might instead represent a species with a "slipped" Cp ring, T!3CsH 5. In any event, the 19e species is a much stronger electron donor than C p M ( C O ) 3 L itself. The complex CpW(CO)3PPh3 ~ which has a formation constant of 6 L mol d, reacts at a diffusion-controlled rate with CpW(CO)3 ~ The products are those of the pure electron transfer steps that occur without solvent or ligand redistribution and without W - W b o n d formation. The occurrence of electron transfer alone is the feature that m a k e s the reaction so efficient. The diagram in Scheme II details the various reactions

210 and it presents the electron count for the various species. The electron count is the guide to reactivity.

S c h e m e II:

A t o m Transfer vs Electron Transfer: Electron C o u n t s +L

CpMo(CO)3 ~

~

~-~

C p M o ( C O ) 3 L ~ FeCp2+ ~

CpMo(CO)3 L+

p2§ CpMo(CO)sX + R ~ CpMo(CO)3 + CpMo(CO)3NCCH3 +

Radical disproportionation induced by electron transfer. Several interesting and interrelated p h e n o m e n a occur when N,N,N',N'-tetramethyl1,4-phenylenediamine (TMPD) is a d d e d to the solution of [CpM(CO)3] 2 prior to the laser flash. As expectedfrom the electrode potential of TMPD ~ 0.16 V vs SSCE in acetonitrile, the first event is the rapid growth of the intense absorption band of the amine radical cation centered at 613 nm (e = 1.2 x 104 L mol "1 cm-l). This absorption then fades fairly rapidly. The fading was quite u n e x p e c t e d , since TMPD ~ n o r m a l l y persists indefinitely. This phenomenon is illustrated in Figure 2. Indeed, when independently-prepared T M P D ~ was injected into the cuvette after the laser flash its blue color persisted indefinitely. Clearly, the disappearance of TMPD ~ signals that some intermediate in the system is causing its destruction. Tests based on the kinetics and on the addition of CpMo(CO) 3- and CpMo(CO)3NCCH3 + to the reaction mixture and to samples of TMPD and TMPD ~ have revealed the sequence of chemical events. 4 The reaction occurs by a catalytic cycle of electron transfer events. The net result is the disproportionation of CpMo(CO)3 ~ Scheme III shows the catalytic cycle.

211

0.08

9

,

,

,

,

[Mo'l/gM a 40.5 b 28.4 c 9.76 d 4.43

0.06 ~ a ~ }b\\ 0.04 J \ \ 0.02 0.00 I 010 o

I

I

I

I

1 104

2 10-4

i

3 104

Time/s

Figure 2. Experimental absorbance changes following [TMPD~ at 613 nm in a series of experiments with different initial concentrations of [CpMo(CO)3]2. In each, [TMPD]0 --- 5.00 mM. (Mo~ = CpMo(CO)3"). The fitting to the model in Scheme III is shown by smooth curves.

S c h e m e III

CpMo(CO)3 +

CpMo(CO)3 ~/

CpMo(CO)3 ~

\

~

~, CpMo(CO) 3-

The t h e r m o c h e m i s t r y of this system, discussed intermittently in w h a t has c o m e before, can be s u m m a r i z e d here. D i s p r o p o r t i o n a t i o n is less favorable t h e r m o d y n a m i c a l l y than recombination; the e q u i l i b r i u m constant is 10 7 as c o m p a r e d to 1016. Nonetheless, disproportionation can be m a d e to be the more i m p o r t a n t reaction, even the nearly exclusive one, by virtue of the c o n t r o l e x e r c i s e d by t h e c o n c e n t r a t i o n of T M P D . T h e p r o d u c t s of disproportionation, M o - a n d M o - A N +, do n o t react r e a d i l y . The disproportionation products are " t r a p p e d " as such. In other words, the metal radicals are c a p t u r e d into an electron transfer cycle w h i c h p r e v e n t s their falling to the most stable products, the dimer. The energetics of this system are depicted in Figure 3.

212 Electron-Transfer Catalysis to the Disfavored Product 1:

~

.... 7--Yi

/

F

AG~= 32.1kJ

....... \

- '

\

,

Figure 3. The reaction coordinate diagram comparing the dimerization (left) and electron transfer (right) processes. Note that the ionic products of disproportionation, the products of photolysis in the presence of TMPD, are very slow to yield dimer. One should note that the light energy provided by the initial laser flash has thus been "trapped" in part in the form of the chemical energy of the ionic pair relative to the dimer. They lie in a free energy well above the thermodynamic product, the Mo 2 dimer, but do not rapidly revert to it.

Acknowledgment. This work was supported by the U. S. Department of Energy, Office of Basic Energy Sciences, Chemical Sciences Division under contract W-7405-Eng-82. The author is grateful to many individuals for their assistance: J. Balla, A. Bakac, W-J. Chen, O. Pestovsky, S. Scott, T-J. Won, Q. Yao, and Z. Zhu, and to the Yamada Foundation for sponsoring the conference for which this paper was presented. References (1) Scott, S. L.; Espenson, J. H. Organomet. 1993,12, 4077. (2) Scott, S. L.; Espenson, J. H.; Zhu, Z. J. Am. Chem. Soc. 1993,115, 1789. (3) Scott, S. L.; Bakac, A.; Espenson, J. H. Organomet. 1993, 12, 1044. (4) Balla, J.; Bakac, A.; Espenson, J. H. Organomet. 1994, 13, 1073-1074. (5) Zhu, Z.; Espenson, J. H. Organomet. 1994, 13, 1893-1989. (6) Scott, S. L.; Espenson, J. H.; Chen, W.-J. Organomet. 1993, 12, 4077. (7) Yao, Q.; Bakac, A.; Espenson, J. H. Organomet. 1993, 12, 2010. (8) vonSmoluchowski, M. Z. Phys. Chem. 1917, 92, 129. (9) Edward, J. T. J. Chem. Educ. 1970, 47, 261-270. (10) Beckwith, A. L. J.; Bowry, V. W.; Ingold, K. U. J. Am. Chem. Soc. 1992, 114, 4983-4992. (11) Pestovsky, O.; Espenson, J. H. unpublished results (12) Pugh, R. J.; Meyer, T. J. J. Am. Chem. Soc. 1992, 114, 3784.

joumal of

MOLECULAR

LIQUIDS ELSEVIER

Journal of Molecular Liquids, 65/66 (1995) 2 ! 3-219

The Structure of Metal Complexes of Small Models of Glycoproteins in Aqueous Solution

K._l~_urg~, L. Nagy and B. Gyurcsik

Department of Inorganic and Analytical Chemistry, A. J6zsef University, Szeged, Hungary

Abstract The combination of potentiometric equilibrium measurements and NMR, EPR, CD, EXAFS and M6ssbauer structural studies of metal complexes of small models of the moiety of glycoproteins which connects the protein and carbohydrate parts of the macromoleeule permitted determination of the composition and structure of the coordination sphere of the metal in equilibrium species in solution. Introduction Natural and synthetic compounds with biological activity exert their biological effects only in solution. Simple relationships between the solid-state structures of such compounds and their biological activities can not be expected, since dissolution of the substances in water may change their structure and composition dramatically. For kinetieally labile metal complexes, the presence of several species in equilibdurn with one another in the same solution makes the picture even more complicated. This is why the equilibrium study of complex formation in biologically active systems has to be complemented by structural investigations. To model the moiety of glycoproteins which connects the protein and carbohydrate parts of the molecule, amino acid - carbohydrate adducts (e.g. N-D-gluconylamino acids, 1 thiazolidine-4-carboxylic acid derivatives of carbohydrates, 2"4 D-fructose amino acid derivates, 5 etc.) have been synthetized. The protonation and metal ion (Cu2+, Ni 2+, Co2+, Zn2+ and Et2Sn2+) coordination equilibria of these model compounds have been studied by means of potentiometric equilibrium measurements. 1-5 CD, EPR, NMR, EXAFS and M6ssbauer investigations (the latter in frozen solutions) have been used to determine the structure and symmetry of the coordination sphere of the complexes.l'5, 6 Some typical examples are shown below. Copper(II) complexes of N-D-gluconylamino acids N-D-Gluconylglycine, a pseudopeptide derivative of D-glucono-5-1actone and glycine, was prepared according to ref. 7. The equilibrium constants of its copper coordination, determined according to ref. 1 (Table 1), were used to calculate the concentration distribution curves in Fig. 1, which show the compositions and protonation states of the different species in solutions of different pH. 0167-7322/95/$09.50 9199.5 Elsevier Science B.V. All rights reserved. SSD1 0167-7322 (95) 00854-3

214

100.

.,=.,.=.,,..=

M

MLH_3 ML

MU-L2

03

,

2

i

4

i

6

8

J

10

\

pH Figure 1. Concentration distribution curves of the system coppcKII) - N=D-gluconylglycinc at a metal to ligand ratio of 1:8, [Cu 2+] = 5.0x10 .3 mol rim-3.

13C.NMR relaxation measurements in solution of pH ~ 8.6 suggested the participation of carboxylate, deprotonated amide and deprotonated alcoholic OH groups in the chelate ring of the copper(II) complex formed in the physiological pH range. Since the complex in which this ligand is coordinated only by carboxylate-O and amideN atoms would not be optically active, CD spectroscopy was used to confirm the coordination of the alcoholic OH group on C(2) of the sugar moiety to copper(II), resulting in the formation of a second chelate ring, beside that between the carboxylate-O and amide-N donor atoms. Similar extra stabilization was observed in complexes of carbohydrate derivatives of thiazolidine-4carboxylic acid.2, 3 This effect was shown to depend on the conformation of the sugar moiety. EPR spectra recorded for solutions of different pH were simulated on the basis of the assumption of coordination spheres with different compositions and structures. These measurements indicated the coordination of one N donor atom to copper(II) at pH > 6 in MLH.2, and dimerization of the complex between pH 6 and 10 (M2L2H. 4, M2L2H_3). The EPR spectra also reflected the decomposition of the dimeric species at pH > 10, i.e. the formation of MLH. 3. In general, the amino acid residues of these organic ligands dominate as the primary binding site in metal ion coordination. Therefore, variation in this part may result in complexes with completely different stabilities and structures. Among the amino acids with weakly or noncoordinating side-chains, oc- and 13-amino acid-containing ligands are expected to show the largest differences in chemical behaviour. This appears, for instance, in the ligand excess needed to keep copper(II) ions in solution. However, in spite of the increased distance between the

215

carboxylate and other donor groups in comparison with the a-amino acid derivatives according to both CD and EPR investigations, the species MLH_ 1 and MLH. 2 proved to have analogous structures in the copper(II) complexes of tz- and 13-amino acid-containing ligands. The only difference in the two systems is the higher pK 2 of MLH. 2 (Table 1).

Table 1. Overall formation constants (log 13) for the complexes and pK values for deprotonation processes in the systems copper(II) - N-D-glueonylamino acid (T = 298 K, I = 0.1 mol dm -3, NaCIO4)

Composition HL CuL CuL2.' . CuLH. 1 CuLH. 2 . CuI~.H. 3 Cu2L2H-3 Cu2L2H-4

'

,,,

iii

.

pK1 pK2 _ p8 3

N-])-gluconyl-13-al~e 4.24(1) 2.84(6) 4.87(10) . -2.86(8) -9.45(10) . -20.54(1 O) -8.70(7) -16.78(16) 5.70 " 6'.5'9 .

.

.

.

11.09

N-D-gluc0nylglycine* 3.39 1.94 3.51 -3.82 ._-...... -9.63 ... '-20.0 ] -10.20 -16.63 5.76 5.81 10.38

i

i i

ill

9

i

9

Standard deviations in parenthesis * from ref. 1

EXAFS measurements 6 provided information on the coordination number of the copper, and on the Cu-O/Nequ, Cu-Oax bond lengths and Cu.-.C and Cu...Cu nonbonding distances for the N-D-glueonylglycine complexes in aqueous solution at two different metal:ligand ratios (Table 2). The data distinguished between equatorial Cu-O/Neq u and axial Cu-Oax bond lengths. The latter was found to be significantly shorter than that expected for coordinated water molecules, indicating that the axial donor O atoms are coordinated more strongly than water. NMR and CD measurements indicated that these are OH O atoms of the ligand. 1 Change of the metal:ligand concentration ratio from 1:10 to 1:100 did not cause significant changes in the CuO,Nequ, Cu-Oax and C...C distances, but increase of the ligand excess prevented dimerization (Cu...Cu interaction) in the complex.

216

Table 2. Structure parameters of the copper(II) complexes of N-D-gluconylglycine in aqueous

solution

Metal:ligand ratio 1"10

Coordination number

4 1

4

1"100

Atomic distances

pm

Cu-O/Nequ Cu-Oax Cu...C Cu...Cu Cu-O/Nequ Cu-Oax Cu...C

190 215 270 298 193 218 272

The structures of the species suggested on the basis of the complex investigations outlined above are given in Fig. 2. o

o

0

c ----~ O'l,C),=

0 ....

H.~

:

c~o"

. .OH,

\

(H,C)~--- N"

~ O"

OH

:/

c ---~, CH

!\

o~

!\ [~R,J~.,II

0

Y \ ?"-"

o

/

~c),,

c--o'\ Cu"' o:,,

~.~/\ //

....HO" ! ~ O (c~. ,, _. cu~..... / i ~cx.i " o~c o

o

\

O.~c),~-- N- /

:

~Or --"

o.~C~ \

o~c

\\ o

o

~t~ Figure 2. Structures of the species formed in the equilibrium system in the physiological and basic pH range

217

Diethyitin(IV) complexes of NoD-gluconylamino acids A similar series of complex investigations was performed on diethyltin([V) complexes of N-D-gluconylamino acid ligands. 8 The potentiometrie equilibrium measurements led to the concentration distribution curves in Fig. 3.

100 A

~" o .w

~.

eo ~,

6o

i_

"i

~

,,o

o

ffl

3

4

5

6

8

9

10

pH

Figure 3. Concentration distribution curves of the system diethyltin(IV) - N-D-gluconylglycine at a metal to ligand ratio of 1:10, [Et2Sn2+ ] = 1.0xl0 -1 mol dm-3. 13C-NMR investigations revealed which donor atoms participate in the complexation process. As a result of the very slow ligand exchange in comparison with the NMR time scale, the 13C signals of the bound and the free ligands were observed separately in the 13C-NMR spectrum of the complex MLH_ 2 of diethyltin(IV)-N-D-gluconylglycine. The significant shifts of the -CH2_, -COO- and -CONH- C signals of the ligand (the latter two were distinguished via the proton-coupled 13C-NMR spectra) suggested coordination of the carboxylate group and the deprotonated peptide-N. Shifts observed in the C signals of the polyhydroxyalkyl chain indicated that the alcoholic OH groups are also involved in the coordination. The shift of one of latter signals is significantly larger than that of the others, suggesting the stronger interaction of this specific (and therefore presumably deprotonated) alcoholic OH group, assigned to C(2), with the metal ion. The 13C-NMR spectnun of the N-D-gluconyl-13-alanine complex, soluble in water at pH ~ 10, reflected a different structure. The differences in the chemical shifts of the ligand C atoms in the presence and absence of diethyltin(IV) are small, but the signals of the carboxylate and three other C atoms (C(3), C(4) and C(5)) which carry alcoholic OH groups are broadened, which is characteristic of complexes with an intermediate ligand exchange rate. The above

218

observations suggested coordination of the carboxylate and deprotonated alcoholic OH groups to the organotin(IV) cation. Neither a noticeable shift nor line broadening was observed for the amide and methylene C signals, excluding deprotonation and consequently coordination of the amide-N. Mtssbauer study of quick-frozen solutions of the diethyltin(IV)-N-D-gluconylglycine complexes permitted determination of the geometry of the species in solutions of different pH. The Mtssbauer spectra recorded for the system at pH ~ 4 indicated the presence of two overlapping doublets (Fig. 4), in good agreement with the equilibrium analysis, due to the presence of species ML and MLH. 1 in the same solution. A comparison of the experimental quadrupole splitting (QS) values with those calculated on the basis of the partial quadrupole splitting (PQS) concept 9"10 revealed that the complex ML contains a pentacoordinated, trigonal bipyramidal central tin(IV) atom, while MLH. 1 contains a hexacoordinated, distorted octahedral one. The Mtssbauer spectra recorded for systems at pH between 6 and 9 reflected the presence of only one species, which was shown by equilibrium measurements to be MLH_2. PQS treatment of the data indicated a penta-coordinated central tin(IV) atom in latter complex.

..... .._..---~-_.. ~..

~ -.'..-.... ,\9":..'~ '~ ',. ', I'.'.

:..-- ~::---

.'. i.

I .... ~ . . . . .

-0

-4

..

~]1

'"J

.~,

\~

-q

0

"..,

,

4~

~.[

_0 v ( ~ / s )

Figure 4. 119Ti n Mtssbauer spectrum of the system diethyltin(IV) - N-D-gluconylglycine at a metal to ligand ratio of 1"10, [Et2Sn2+ ] = 0.1 mol dm "3, pH ~ 4, at liquid nitrogen temperature Conclusions

The combined application of equilibrium and structural studies in solution led to the following main conclusions on the studied systems: 1. Equilibrium investigations permitted determination of the compositions and concentrations of successively formed metal complex species in solution. The concentration

219 distribution curves of the species in solution permitted the assignment of independent experimental structural data to the single species in solution. 2. NMR spectroscopy could be used to determine which donor atoms of the polyfunctional ambidentate ligands participate in the coordination processes. 3. The symmetry of the coordination sphere of the complexes could be determined by M6ssbauer measurements on quick-frozen solutions; even the differences in structure of coordination isomers in different protonation states could be demonstrated. 4. The effects exerted by the configuration of the ligand on the complexation process could be determined by means of CD studies.

Acknowledgement The present work was supported by the Hungarian Research Foundation (Grants OTKA 84/1991 and BO11045)

References .

2. 3. ~

10.

B. Gyuresik, T. Gajda, L. Nagy, and K. Burger, d. Chem. Soc. Dalton Trans., 1992, 2787 T. Gajda, L. Nagy, and K. Burger, J.. Chem. Soc Dalton Trans., 1990, 3155 T. Gajda, L. Nagy, N. Rozlosnik, L. Korecz, and K. Burger, d. Chem. Soc. Dalton Trans., 1992, 475 N. Buzz, B. Gyurcsik, L. Nagy, Ying-xia Zhang, L. Koreez, and K. Burger, lnorg. Chim. Acta, 218, 65 (1994) B. Gyurcsik, T. Gajda, L. Nagy, K. Burger, A. Rockenbauer, and L. Korecz, lnorg. Chim. Acta, 214, 57 (1993) L. Nagy, T. Yamaguchi, T. Mitsunaga, B. Gyurcsik and H. Wakita, to be published F. Schneider and H. U. Geyer, Hoppe Seyler's Z Physiol Chem., 330, 182, 189 (1963) B. Gyurcsik, N,. Buzz, T. Gajda, L. :Nagy, E. Kuzmann, A. V6rtes, and K. Burger: Z Naturforschung, to be published G. M. Bancroft: Mi~ssbauer Spectroscopy: An Introduction for Inorganic Chemists and Geochemists, McGraw-Hill Book Company, U.K. (1973) G. M. Bancroft, V. G. Kumar Das, T. K. Sham, and M. G. Clark, J. Chem. Soc. Dalton Trans., 1976, 643

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journal of MOLECULAR

LIQUIDS ELSEVIER

Journal of Molecular Liquids, 65/66 (1995) 221-228

Kinetic Evidence for Short-Lived Intermediates in Metailoporphyrin Formation Masaaki Tabata Department of Chemistry, Faculty of Science and Engineering, Saga University Honjo-machi, Saga, 840 Japan Abstract The rate of metalloporphyrin formation is accelerated by (1) large metal ions like mercury(II) and cadmium(II), (2) reducing agents like hydroxylamine, and (3) amino acids. The detailed reaction mechanism was studied from kinetic and spectral methods for the incorporation of metal ion into 5,10,15,20-tetralds(4-sulfonatophenyl)porphyrin (H2tpps 4-) or 5,10,15,20-tetrakis(1-methylpyridinium-4-yl)porphyrin (H4tmpyp4+). The main focus is on the intermediates formed in the reaction of metalloporphyrin formation, i.e. heterodinuclear metalloporphyrin, mixed-valence metaUoporphyrin, and molecular complex with amino acid. Cd(tpps) 4- is 7900 times as reactive as H2tpps 4- in the incorporation of manganese(II). The coordination of cadmium(II) deforms the porphyrin ring favorably for the attack of mediumsized metal ions and a heterodinuclear metalloporphyrin was postulated as an intermediat~ ~The heterodinuclear metalloporphyrin was detected kinetically in the reaction of zinc(II) or copper(II) with homodinuclear mercury(II) porphyrin complex of Hg2tpps2-. The reaction showed a biphasic kinetic behavior of the following steps: Hg2(tpps) 2- + M 2+ --, Hg(tpps)M 2+ Hg 2+ - M(tpps) 4" + 2Hg 2+, where M 2+ denotes Cu2+ and Zn 2+. The rate constant for the second-step reaction was characteristic of a unimolecular reaction: the rate constant was independent of copper(II), zinc(II), and mercury(II) concentrations, and also of hydrogen ion concentration at high pH. An extended X-ray absorption fine structure (EXAFS) measurements revealed the deformed structure of Hg2(tpps) 2- for the metal-substitution reaction of Hg2(tpps) 2- with Cu 2+. The rate enhancement by 104 in the presence of reducing agent was attributed to the formation of Cu(1) (r = 96 pro). The Cu(I) behaves similarly to the large metal ions. Amino acids enhanced the formation of Zn(tpps) 4" and formed a molecular complex as an intermediate. The rate constant was linearly correlated to the hydrophobicity scale of the side chain of the amino acid. 18-Crown-6 stabilized the metalloporphyrin towards the ligandsubstitution or acid-dissociation reaction of the metalloporphyrin by the formation of a sandwich-metalloporphyrin [M(tpps)18C6] 4-. The intermediate was confirmed by 1H NMR and spectrophotometry.

I Introduction A number of studies on metalloporphyrin formation have been reported over 20 years, as a result of the important role of metalloporphyrins in biological systems. The general mechanism for the metalation of porphyrins was first ]?l'Oposed by Hambright and Chock, 1 and has been reviewed from time to time by Hambright,Z Lavallee3,4 Schneider,5 and Tanaka. 6 The rate of metalloporphyrin formation is several orders of magnitude slower than that of the 0167-7322/95/$09.50 91995 ElsevierScience B.V. All rights reserved. SSDi 0167-7322 (95) 0090 !-9

222

complex formation of open-chain ligands, 7 and the over all mechanism is not straight forward in some cases. 8 "The great difference in their reaction rate is presumably due to a less flexible porphyrin ring system and a less accessible lone-pair electron on the porphyrin for the incoming metal ions. In order to accelerate the slow metalation, several methods have been proposed:9 (1) use of substitution reaction of cadmium(ll) or mercury(II) porphyrin, (2) use of N-substituted porphyrins at the pyrrole nitrogen, (3) addition of aromatic heterocyclic bases such as pyridine and imidazole, (4) introduction of functional groups to bind metal ions in the vicinity of the porphyrin nucleus (e. g. tetracarboxylic acid "picket-fence" porphyrins) and (5) use of reducing agents such as hydroxylamine and ascorbic acid in copper(lI) incorporation. The present paper describes the mechanism of porphyrin metalation in the presence of catalyst with special emphasis on the reaction intermediates including heterodinuclear metalloporphyrin, mixed-valence metalloporphyrin, and sandwich-metalloporphyrin with 18crown-6. II

Catalytic Effect of Mercury(ll), Cadmium(ll), and Lead(ll) in the Metailoporphyrin Formation I 0-12

The rate of incorporation of manganese(II) into H2tpps 4- is very slow, and a little spectral change was observed even at 60 minutes after the o initiation of the reaction 25 *C. The reaction proceeded only 25 % after two days. However, in the presence of ~e mercury(II) or cadmium(ll) rapid spectral ~' change occured: the absorbance at 413 "nm decreases and the absorbance at 467 nm increases. 11,12 I n the metalloporphyrin formation catalyzed by metal z ion, the ionic radius(r) of the metal ion acting as catalyst is important: large metal I v --J l-t ions such as Cd 2+ (r = 95 pm), Cu+(r = 0~ pH 96 pm), Pb 2+ (r = 118 pm), and Hg 2+ (r =114 pm) give rise to appreciable catalytic effect, while medium-sized metal Figure 2. A typical biphasic kinetic run for the ions like Cu 2+ (r = 73 pro) and Zn 2+ (r = reactionof Hg2(tpps)2- with Zn2+. 75 pm) exert hardly the catalytic effect. In Fig. 1 the observed rate constant is plotted versus pH. 10 The rate of formation of Mn(tpps) 4- in the absence of cadmium(ll) is independent of pH, while in the presence of cadmium(II) the rate depends on pH. Cadmium(lI) accelerates the rate of Mn(tpps) 4formation at pH higher than 6. The following mechanism was proposed for the formation of Mn(tpps) 4- in the presence of cadmium(II). 10 _

,

r

--

_

6

.

(hI

.

-

.a

-

,-

7

8

9

kl Mn 2+ + H2tpps 4-

- 9Mn(tpps)4- + 2H +

(1)

Cd(tpps) 4- + 2H +

(2)

k2 Cd 2+ + H2tpps 4k_2

223 k3 Cd(tpps) 4- + Mn 2+ ---" Mn(tpps) 4- + Cd 2+

(3)

At low pH and/or low concentration of manganese(II), the rate law is rewritten as kCd =

k2k3k-2-1[Mn2+][Cd2+][H+]-2

(4)

On the other hand at higher pH, the rate equation is simplified to kCd = k2[Cd 2+] (5) The rate constants at pH 7.8 to 8.7 are independent of [Mn 2+] over the concentration range from I x 10-4 to 10-3 tool dm -3 as expected from eq.5. An independent experiment revealed that manganese in the product is in the trivalent state and that the rate of oxidation of Mn(II)(tpps) 4- to Mn(III)(tpps) 3- by dissolved oxygen is rapid compared to the formation of Mn(II)(tpps) 4-. The Mn(tpps) 4- formation in the presence of cadmium(II) proceeds through Cd(tpps) 4-Because of large ionic radius of cadmium(II) (r=- 95 pm), the coordination of cadmium will give a highly distorted porphyrin core which favors the attack of porphyrin nucleus by manganese(II) from underneath. Cd(tpps) 4- is 7900 times as reactive as H2tpps 4- in the incorporation of manganese(II). Cadmium(II) liberated after the incorporation of manganese(II) combines again with the free base porphyrin as a catalyst. At pH > 7.8, the formation of Cd(tpps) 4- is rate-determining step (eq.2): the intermediate involves only cadmium(II), and it is of course mononuclear. At low pH and/or lower concentration of manganese(II) eq.3 is the rate-determining step and the rate law given by eq. 4. The formation of Mn(tpps) 4- proceeds through a heterodinuclear intermediate involving cadmium(II) and manganese(II).

III

Heterodinuclear

Metalloporphyrin

as

Intermediatesl

3

Heterodinuclear metallopor~hyrin, postulated in the metalloporphyrin formation catalyzed by mercury(II) or cadmium(II) 1U-12 was detected kinetically in the reaction of zinc(II) or copper(II) with homodinuclear mercury(II) porphyrin complex of Hg2tpps 2-- The following biphasic reaction was observed: Hg2(tpps) 2- + M 2+ --~ Hg(tpps)M2- + Hg 2+ ~ M(tpps)2- + 2Hg2+ (6) where M 2+ = Zn 2+ or Cu 2+Dinuclear mercury(II) porphyrin forms quantitatively in large excess of mercury(II) at pH 6.15 The first-step reaction in eq. 6 completes in a few seconds and it is followed by the second-step reaction with a half-life time of a few minutes (Fig. 2). 13 The rate constant for the first-step reaction increases with increasing c6ncentration of copper(II) or zinc(II) and reaches a plateau. The rate constant also decreases with increasing mercury(II) concentration (Fig. 3a). These observations lead to the following rate law:

0.2

0.1 r~ .< 0.0 0

5

10 tls

15

20

Figure 2. A typical biphasic kinetic run for the reaction of Hg2(tpps)2- with Zn2+

224

(7)

ko f = (k lk2[M2+][OH-])(k, l [Hg(OH)+] + k2[M2+]) -1

The plot of (k0f)" 1 vs. [M2+] - 1 gives a straight line with an intercept. The rate constants for the second step reaction are independent of the concentrations of mercury(II), copper(lI), and "Hg zinc(II) (Fig. 3b). 13 These results indicate; the unimolecular reaction, i.e. the self-dissociation [kz. MV of the intermediate. The kinetic results of the two-step reaction are consistent with the reaction mechanism shown in scheme 1. Hg The reaction paths for k l , k-l, and k2 , , ,,N k3 correspond to the first-step reaction, and the Hg(oa)" ~ ~ / 1 ~ ) ----------reaction paths for k3 and k4 are involved in the ~t...~N :x . / U~/uN second-step reaction. The rate constants are \ H / summarized in Table 1. T he homodinuclear mercury(ll) k, M = znz'. cuz" porphyrin dissociates to a 1:1 mercury(II) Scheme 1. Reaction mechanism for the reaction porphyrin which reacts with z i n c ( l l ) or of Hg2(tpps)2- with Zn 2+ or Cu2+. c o p p e r ( I I ) to f o r m the c o r r e s p o n d i n g heterodinuclear metalloporphyrin. The final step is the dissociation of mercury(II) from the 103[Zn=~ll t o o l d r n " corresponding heterodinuclear metalloo I 2 3 4 porphyrin. Interestingly k l, k3, and k4 values for zinc(ll) are a l m o s t the s a m e as for copper(II), while the rate k-2/k-1 for copper(ll) "7 m z is about 80 times as high as for zinc(lI). These findings are consistent with the p r o p o s e d "~ reaction mechanism. The reaction paths for k 1, t k3, and k4 involve only the dissociation of mercury(II) and thus they are independent of the 0 nature of incoming metal ions. On the other hand the reaction path for k2 depends on b characteristics of incoming metal ions, because "7 :2 "-1 it involves coordination of these metal ions to form heterodinuclear metalloporphyrins. " o The r e a c t i o n m e c h a n i s m was also ,,,-~ / confirmed by a series of absorption spectra o recorded on a rapid-scan spectrophotometer. The c h a n g e in a b s o r b a n c e at 5 6 4 n m 0 (absorption m a x i m u m o f Hg2(tpps) 2-) is o ~ ~. ~ ~ ',o smaller than for the second-step reaction. This Io'(znZ~lmol dm 3 finding points to one mercury(II) ion remaining Figure 3. Dependence of rate constants for the in the intermediate. The increase in absorbance first-step (a)and the second step (b) reactions, a, at 551 nm during the first-step reaction suggests CHg = 1.00 x 10-5; 5.02 x 10"4, b, 5.02 x 10-5; the coordination of zinc(II) to form the 9.58 x l0 -5 tool dm -3. hetrodinuclear metalloporphyrin. 9

,

,

i -

v

,,

- -

~

9

9

~

0

i

225 Table 1. The rate constants for the reaction of Hg2(tpps) 2- with Cu 2+ and Zn 2+ at 25 *C, and I = 0.1 (NAN03).

Metal ion

k21k-1

10-8kl mol- ldm -3 s- 1-

Cu 2+

1.95 • 0.05

Zn 2+

1.56 + 0.06

102k3 s- 1

10-3k4 tool- 1din3 s- 1

1.00 • 0.03

2.70 + 0.06

(9.6 • 0.2) x 10 -2 0.92 • 0.02

1.75 + 0.03

7.1 • 0.3

IV EXAFS Study of Reaction of Hg2(tpps)2- with Copper(ll)lS,16 Kinetic studies have p r o p o s e d evidence for the formation of heterodinuclear intermediate. In order to study the structure of the intermediate in solution as r e l a t e d to the r e a c t i o n mechanism, extended X-ray absorption fine structure (EXAFS) measurements have been u n d e r t a k e n for the metal-substitution reaction of mercury(lI) porphyrin complex with copper(II) in an acetate buffer (pH =

+

?

5.6). Cu 2+ + Hg2(tpps) 2- -~ Cu(tpps) 4- + 2Hg 2+

(8) Mercury(II) is readily replaced by copper(II) ~on at rate faster than direct reaction of copper(II) with the free base porphyrin H2tpps 4-. Nine solutions were prepared and EXAFS was measured at both Hg LIII and Cu K edges. The structure of acetatomercury(II) is tetrahedml and the Hg-O (CH3COO-) bond length of 219 pm is shorter and the Hg-O (H20) bond 262 pm is longer as compared to that (241 pm) of Hg(H20)6 ion.

o

? ,o S

S c h e m e 2. Reaction scheme of the metalsubstitution reaction of Hg2(tpps)2- with

in an acetate buffer. 1, free base porphyrin; 2, mercury(II) acetato complex; 3, homodinuclear mercury(II)porphyrin;4, cotver(II) acetato complex; 5, heterodinuclear intermediate; 6, mereury(II) acetato complex; 7, copper(II)porphyrin.

o 4

o

I o

6

7

226 Mercury(II) ion in Hg2(tpps) 2- is bound to two nitrogen atoms and one acetate ion. The Hg-N and Hg-O bond lengths are 222 and 265 pm, respectively. Copper(II) acetato complexes exhibit a distorted octahedral structure: the axial and equatorial Cu-O bond lengths are 225 and 197 pm respectively. The bond lengths are the same as in the Cu(HO2) 6 ion. Mixing of Hg2(tpps) 2- with copper(ll) ion gives rise to the acetatomercury(II) as well as the copper(II) porphyrin complex of which structure was four-coordinated square planar with the Cu-N bond length of 200 pm. The possible structural change during the reaction of Hg2(tpps) 2- with Cu(ll) is postulated as in Scheme 2. The tetrahedral mercury(II) acetato complex reacts with H2tpps4- to form the deformed homodinuclear mercury(II) porphyrin complex, where two mercury(II) ions bind to pyrrole nitrogens from upper and lower sides and one acetate anion coordinates to each mercury(II). Pyrrole rings are twisted alternatively up and down, like "saddle" porphyrin skeleton, and deviated about 30* from the mean porphyrin plane. The nonbonded Hg Hg distance was estimated to be 310 pm. The deformed structure favors the attack of another metal ion from underneath. Very recently, Ohtaki, et al. 17 have directly determined, by using a stopped-flow EXAFS, structure of the deformed porphyrin. IV

Mixed-Valence

Cu(ll)-Cu(1)

Porphyrin

as

an

Intermediatel8

0 " Reducing agen.ts such as hydroxylamine and ascorbic acid accelerate the formation of copper(lI) porphyrin: in the presence of hydroxyl-1/ amine, formation rate of Cu(lI) porphyrin is about 104 times as high as _ f inits absence (Fig. 4). 18 Some authors ~'1tt o have assumed the effect of these reducing ~,.~-2agents to be attributed to high reactivity _o of the aqua copper(I) ion as compared to g the copper(ll) ion. The copper(ll) ion has o two types of water molecules (axial and -3 / , / / equatorial), and the formation-rate constant of copper(II) porphyrin has been correlated to the dissociation rate of the axial water molecule (k~lO9 s-l),l-4,19 -4 //o which is close to the diffusion-controlled rate. Therefore the rate enhancement by a factor of 104 in the presence of -4 -2 reducing agent cannot be attributable to t og(ccJ3/mot d~ 3) higher reactivity of the copper(1), Figure 4, Dependenceof the formation of Cufl(nnpyp)4+ because the water molecule bound to on the concemratioo of coppe~]:]) in the absence( 9and precopper(I) may dissociate rapidly but only seine(C)) of metallic copper at pH 3.50. by a factor of 10 compared to copper(II) at largest. The ionic radius of Cu+(96 pm) is significantly larger than that of Cu2+(73 pm): sitting on the porphyrin nucleus, Cu + distorts it favorably for the attack by Cu 2+ from underneath. Thereby copper(I) behaves similarly to large metal ions such as mercury(II), cadmium(ll), and lead(lI).10,11,12 We postulate, as intermediate, mixed-valence copper porphyrin, [Cu(II)(tmpyp)Cu(I)], in which copper(I) corresponds to mercury(lI) and copper(II) corresponds to zinc(II) in Zn(tpps)Hg 2-. 13

/

227 From the above experimental results, it is anticipated that copper(I) can also catalyze the incorporation of other medium-sized metal ions, such as manganese(II). As expected copper(I) as low as 10-7 mol dm -3 favored the incorporation of manganese(II) into H2tmpyp ~ . 1 8

V M o l e c u l a r C o m p l e x e s as I n t e r m e d i a t e s 2 0 - 2 2 The incorporation of zinc(II) into H2tpps 4- is accelerated in the presence of some amino acids. 20 The reaction sequence is described as follows: K ZnA + + H2tpps 4" ~ I

ZnA+(H2tpps ~ ) I "~ Zn(tpps) 4" + A- + 2H +

(9)

(10)

ZaA + (HA = amino acid) rapidly associates with the free base porphyrin to form a molecular complex (I) in which ZnA + is weakly bound to the porphyrin plane. Then the water molecule coordinated zinc(II) in I dissociates, and zinc(II) is incorporated into the porphyrin core. Thus the over-all rate constant of formation of zinc(II) porphyrin in the presence of an amino acid is given by k Z n A = Kk

(11) [

9

,

T•r• ,

.

where K is th formation constant of the 2 molecular complex and k is the rate r)p constant of substitution of a water r~ Phe molecule on ZnA + with one of the basic "6 nitrogens in the porphyrin. Figure 5 shows that the rate of incorporation of r~ zinc(II) into H2tpps 4- is linearly related ~,, ! to the hydrophobicity scale of the amino acids which is the free energy of solution "~ of amino acid in kJ mo1-1. Among the 2 studied amino acids L-tryptophan exhibits the largest catalytic effect on the metallo0 porphyrin formation. .gtlkJ mol "110 The formation on the molecular complex of porphyrin or metalloporphyrin with amino acids has been inves- Figure S. A correlationbetweenthe formationrate constant tigated by thermodynamic and 1H NMR of Zn(tpps)4- and the hydrohobicityscale of the amino acid. methods.21 1H NMR experiments on the porphyrin and amino acids system indicate directly the interaction between the side-chain of amino acid and the Po4_rphyrinp l a n ~ / h e up-field s~lft has been observed for L-tryptophan in the presence of H2tpps , H2tmpyp or Zn(tmpyp) at pD 9.0. This is attributable to the hydrophobic interaction between the side-chain of amino acid and the porphyrin plane. Furthermore, in the Zn(II) porphyrin system, the chemical shift of [3-proton of L-Trp separates to two signals due to the axial ligation of the amino group to Zn(II). The ligand-substitution reaction of M(tpps) 4- ( M 2+ = Zn2+, Cd2+, pb2+) with N,N'1,2-ethanediylbis[(N-carboxymethyl)glycine] (H4edta) and the acid-dissociation reaction of the metalloporphyrins are inhibited by the presence of 18-Crown (18C6). 22 The rate suppression by 18C6 was explained by the formation of [M(tpps)(18C6)] as a precursor complex. The

228 intermediate hinders the attack of Hedta3- or H + to the metal in the metalloporphyrins. The formation constants of [M(tpps)(18C6)] are 102-5, 10. 2-7, and 101-8 for zinc(II), cadmium, and lead(II), respectively. The intermediate is formed by the interaction of the metalloporphyrin plane with 18C6 ring, and the interaction was confirmed by 1H NMR and absorption spectra. The 1H NMR signal of 18C6 shifted to a higher field and the change in absorption spectra was larger for Cd(tpps) 4- than for Zn(tpps) 4- and Pb(tpps) 4-.

VI Summary The kinetic studies on metaUoporphyrin formation demonstrate the importance of intermediates such as heterodinuclear metalloporphyrin, mixed-valence metaUoporphyrin, and molecular complex. The important features of catalytic incorporation of metal ions is the deformation of porphyrin ring by coordination of large metal ions and the hydrophobic interaction with amino acid and aromatic bases. While, strong interaction of metaUoporphyrin with 18-crown-6 stabilizes the metalloporphyrin and prevents the attack of Hedta3- or H+ to the metal ion in the metalloporphyrin. Another interesting aspect is high reactivity of copper(I) porphyrin. The deformed structure of Hg2(tpps)4-was revealed by EXAFS-.

Acknowledgments We acknowledge with thanks the supports by the Grant-in aid for Scientific Research (No. 04215218, 05453071) from the Ministry of Education, Science and Culture of Japan.

References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

P. Hambright, P. B. Chock, J. Am. Chem. Soc., 96 3123 (1974). P. Hambright, in Porphyrins andMetalloporphyrins, edited by K. M. Smith, p. 232-278 (Elsevier, Amsterdam, 1975). D.K. Lavallee, Coord. Chem., 6 1, 55 (1985). D.K. Lavallee, Comments Inorg. Chem., 155 (1986). W. Schneider, Struc. Bonding(Berlin), 23, 123 (1975). M. Tanaka, Pure. Appl. Chem., 55, 151(1983). D.W. Margerum, G. R. Cayley, in Coordination Chemistry, edited by A. E. Martell, p 1-194 (American Chemical Society, 1978). S. Funahashi, Y. Yamaguchi, M. Tanaka, Bull. Chem. Soc. Jpn., 5 7, 204 (1984). M. Tabata, M. Tanaka, Trends Anal. Chem., 1 0,126 (1991). M. Tabata, M. Tanaka, J. Chem Socc., Dalton Trans. 1955 (1983). M. Tabata, M. Tanaka, Mikrochim. Acta, 149 (1982). M. Tabata, M. Tanaka, Anal. Lett., 1 3, 427 (1980). M. Tabata, W. Miyata, Chem. Lett., 785 (1991). L. R. Robinson, P. Hambright, Inorg. Chem., 3 1,652 (1992). M. Tabata, K. Ozutumi, BuU. Chem. Soc. Jpn., 65, 1438(1992). M. Tabata, K. Ozutsumi, Bull. Chem. Soc. Jpn., 6 7, 1608 (1994). H. Ohtaki, S. Funahashi, Y. Inada,, M. Tabata, K. Ozutsumi, K. Nakajima, J. Chem. Soc., Chem. Commun., 1023 (1994). M. Tabata, M. Babasaki, Inorg. Chem., 3 1, 5268 (1992). S. E. Hay, P. Hambright, Inorg. Chem., 23, 4777 (1984). M. Tabata, M. Tanaka, Inorg. Chem., 2 7, 203 (1988). M. Tabata, A. Shimada, Bull. Chem. Soc. Jpn., 63, 672 (1990). M. Tabata, K. Suenaga, Inorg. Chem., 3 3, 5503, (1994).

journal of ~IOLF~ULAR

LIQUIDS Journalof MolecularLiquids,65/66 (1995) 229-236

ELSEVIER

Structure and dynamics of solvated ions: new tendencies of research Tamds Radnai Central Research Institute for Chemistry, Hungarian Academy of Sciences, Budapest, Pusztaszeri dt 59-67, H-1025, Hungary Abstract Some recent developments in the research of the structure and dynamics of solvated ions are discussed. The solvate structure of lithium ion in dimethyl formamide and preliminary results on the structure of sodium chloride aqueous solutions under high pressures are presented to demonstrate the capabilities of the traditional X-ray diffraction method at new conditions. Perspectives of solution chemistry studies by combined methods as e.g. diffraction results with reverse Monte Carlo simulations, are also shown. I. Introduction In the last decades the overwhelming majority of the experimental studies of the structure and dynamics of ions targeted the aqueous solutions and the water itself, and less attention has been paid to other solvents and non-aqueous solutions. Theoreticians and "traditional" (e.g. IR, Raman, NMR) showed more interest to non-aqueous systems, but the predominance of aqueous solutions is still well reflected in the reviews [ 1]. A split between scientists involved in structural studies and those dealing with the dynamics can be observed, too. Information obtained about the same solutions was only seldom treated as complementary to each other [2]. Researchers applying a specific method often neglected the results of a related method. The appearance and fast development of computer simulation methods seemed to bridge the gaps between the different fields, but there are only a few studies when a simulation really aimed at a complete study of a system. The last several years brought substantial changes to the field. New systems are studied by traditional methods, and new methods have been also born. More complex studies are reported and often various methods are used to target the same subject. The attention of an increasing number of researchers seems to turn to non-standard (often extreme) physicochemical conditions. Complete series of systems are more often studied in order to find relations rather than to describe simply the properties of the system. Rarely though, new concepts seem to appear as the sign of better understanding of the chemistry of solutions. This paper does not intend to be a review; rather comments and examples are given for some of the recent progress. The related literature is not searched exhaustively and the selection is rather arbitrary. Preliminary results of two new studies by the XD method are presented in order to demonstrate the capabilities of the method at new conditions. The reverse Monte Carlo (RMC) technique is also discussed in more detail to show a new perspective in the structural modelling of solutions. II. New tendencies in structural studies Traditional methods o f investigation - n e w methods o f interpretation

The XD, ND as well as molecular dynamics (MD) and Monte Carlo (MC) computer simulation methods are considered well-established since a great number of investigation has been performed with them. With rare exceptions, experiments on liquids at normal conditions are considered as routine laboratory work by now. Similarly, even commercially available computer software helps the researchers to run simple simulations. However, the interpretation of the results is complicated and therefore a continuous improvement of the interpretation techniques is required. The XD experimental structure functions are often 0167-7322/95/$09.50

91995ElsevierScience B.V. All rights reserved.

SSDI 0167-7322(95) 00902-7

230 interpreted by various geometrical models which extend to the first neighbors of a central atom only, or the second neighbors are also comprised [1,3]. Another method is the separation of some contributions of interest from the total structure- or pair distribution function. For this purpose several XD and ND experiments are carried out with a wellplanned strategy and differences of structure functions are calculated. The isotopic substitution and the subsequent first- or second-order difference method is well established in the ND practice [4]. With its application the local order around the ions can be studied separately. More recently, attempts have also been made to isolate the structure of the bulk solvent from the ion-water and ion-ion distributions, and thus the effect of ions on the solvent structure can be observed. For instance, it was concluded from ND experiments on LiC1 aqueous solutions that the lithium ion does not influence the bulk water structure at 1 molal concentration, but about 70% of H-bonds are broken when the concentration is 10 molal [5]. Instead of isotopic substitution, the isomorphic replacement can be used by the XD method. Here two solutions of equal concentration with the same solvent but with different ions are measured, and the difference of the structure functions is calculated. If the ions are selected carefully, i.e., they have nearly the same ionic radii, ionic charges and similar chemical properties, the isostructural contributions cancel out and the differences in the ionic solvate structure can be analyzed. The method proved to be successful for solutions involving erbium or holmium ions with an isomorphic pair of yttrium. Thus the XD studies showed that the erbium(m) ions form inner complexes with nitrate ions [6], and in high concentration, with chloride, bromide and perchlorate ions [7] in its aqueous solutions. The investigation was later extended to dimethyl sulfoxide solutions in which the difference in complex formation between chloride and nitrate ions proved to be less [8]. The effect could be explained by the fact that the solvating power of the DMSO for chloride and perchlorate ions is lower then that of the water. XD studies with isomorphic replacement in combination with ND studies with isotopic substitution have been reported for nickel(l/) and magnesium(l/) ions [9] as well as sodium(I) and silver(I) ions [10] in aqueous solutions and the cation-water and cation-cation partial pair distribution functions were separated experimentally.

New experimental techniques The appearance of new experimental techniques is connected with, but not exclusively, the establishment of big research centers where high power synchrotron sources and/or neutron generators are available. A fairly large number of liquid structure studies has been performed by now with the help of the EXAFS and XANES spectroscopy [11], especially since laboratory-scale instruments could also been constructed. Their performance is very good in determination of coordination numbers and ion-solvent distances for several suitable ions in the solution, and the applicable concentration is much lower than for the XD or ND method. This is an advantage in non-aqueous solutions, where the solubility is generally more limited. On the other hand, the more quantitative analysis of the ordering in the solutions is not possible without the help of other structural methods. White X-ray sources, energy dispersive techniques, soft x-ray sources offer new and alternative tools for structural studies. Small angle neutron scattering (SANS) is also in development. It offers another tool for experimental separation of contributions, ascribed to the cation's solvate shell, from the total pair distribution function especially for large size ions [12]. Structural properties around hydrophobic solutes in water can also be studied, as it was done for aqueous solutions of tetramethyl urea [13]. Quasi-elastic neutron scattering (QENS) is a promising technique for the determination of some dynamic properties in the solutions at the picosecond timescale, in contrast to the NMR spectroscopy, which works at a scale of milliseconds. Indeed, the self-diffusion coefficient D § could be determined for a series of cations [14], a quantity, which can not be accessed directly from experiments. A few computer simulation studies also succeeded in determination of separate values of selfdiffusion coefficients for cations, anions and bulk water [ 15].

23!

Solutions at non-standard conditions Most of the structural and dynamic studies in solutions have been carded out at ambient temperature and atmospheric pressure or not far from it. An increasing number of papers is devoted to supercooled [16-19] and glassy [ 18,20,21] water and solutions as well as to studies of water [22] and of aqueous solutions [23,24] at high temperature and/or pressure. Computer simulation methods are very flexible and are suitable for various studies at almost any thermodynamic conditions, and therefore a new strategy of the research can be established easily: simulations may predict some properties of the solutions at conditions which can be later verified when the appropriate experimental conditions become available. New range of solutes and solvents Studies on structure and dynamics of liquids have recently been extended to solvate structure of ions in non-aqueous solutions, and to the structure of complexes with relatively complicated ligands. We can also handle special problems like hydrophobic solvation is. Diffraction studies have been performed on new solvents as e.g. trifluoroethanol [25] and tetramethyl urea [26], and on solvent mixtures [27-30]. More recently the preferential solvation of ions has been subjected by an XD investigation in MgC12-water-methanol ternary systems [31 ], and the solvation structure around the cations proved to undergo the change of solvent molecules proportionally to the relative concentration of the two solvents. Extension of the research to new fields of solution chemistry A significant step to the combination of our knowledge about the static structure in liquids and their kinetic behavior has recently been made by application of an in-laboratory stopped flow EXAFS experiment [32]. This is an EXAFS spectrometer operated in the dispersive mode and a stopped-flow unit positioned along the x-ray path. Since results of very short time measurements can be accumulated in this way, with the appropriate selection of the system structural studies of reaction intermediates can be determined, which has not been possible before. Results are reported [33] on a partial structural change around the Cu(II) ion of a reaction intermediate at the formation of a Cu(ID porphyrin complex in the metal substitution reaction of the Hg(II) porhyrin complex with the Cu(II) ion in an aqueous acetate buffer solution. The measurements showed that the Cu-N distance in the reaction intermediate are elongated by about 0.04A in comparison with the final product. Combination of investigative methods and information The separate pieces of information are now often placed into a complex environment by the application of more than one method of investigation. Typical examples are: combination of diffraction experiments of deverse kinds; diffraction experiments with computer simulations and/or with thermodynamic and spectroscopic studies. The further continuation of the above tendencies can hopefully lead us to new and unified concepts of structure and dynamics in solutions. III. Solvation of lithium ion in N,N-dimethyl formamide Lithium(I).is one of the most puzzling ion from structural point of view. Due to its small radius, its surface charge is high and therefore its ability to form stable and well ordered solvate shells is comparable with the transition metal ions. The direct application of both the XD and ND methods to the solvate structure is difficult owing to the special scattering properties of the ion. As a consequence, the structural parameters describing the hydration structure of lithium(I) ion in aqueous solutions, although subjected to intensive studies, show a contradictory picture [1,34]. The average coordination number n varies between 4 and 6, and the average value of Li-O distance shows an unusually large variation from 1.94 to 2.25A. The effect can be explained partly by experimental errors, but a hypothesis has been also formed that the lithium ion tends to have a value of n=6 in its dilute solutions while n decreases at high concentrations [34]. The distance between the ion and the neighboring water molecules changes with the coordination number, the smaller is the latter, the smaller is the

232

distance. It is worth noting that lithium is able to form stable complexes in the solid phase with coordination numbers from 4 to 6 and with different geometries, and the lithium-binding atom distances correlate with n as it was found in aqueous solutions [35]. Only two structural studies have been reported for lithium solvates in non-aqueous solutions. In an XD study of concentrated formamide solution of LiC1 [36] the lithium ion was found to be solvated by 5.4 formamide molecules in average and the Li-O distance was reported to be 2.24./k, in keeping with the values found in diluted aqueous solutions. More recently, a detailed study has been performed by combination of the ND method with a series of theoretical methods on an 0.6 mol dm "3 LiBr solution in acetonitrile [37]. The lithium ion was found to be tetrahedrally coordinated by three solvent molecules and one bromide ion. The Li-N distance resulted in 2.05 ]k. From these data it is suspected that the molecules of the solvate structure of lithium ion might be largely effected by the solvent molecules. Since the solubility of some lithium salts is relatively high in N,N-dimethyl formamide (DMF), concentrated solutions can also be examined. In a previous study the solvate structure of lithium has been described in an 1.5 mol dm "3 LiNCS solution in DMF [38]. A new XD measurement has been carded out for a LiCI solution of the same concentration. Table 1 zhows the structural parameters for the lithium solvates in both solutions. The structural parameters were determined by a leastsquares fitting method (LSQ). After the subtraction of the contributions ascribed to the intramolecular structure of the DMF molecules and to the assumed structure around the anions from the total structure function of the solution, the resulted difference curve was approximated by calculated model curves. The result is shown in Figure 1. From the geometrical model described above, an average coordination number of 6 around a lithium ion was resulted for both solutions. In the LiNCS solution the cation is fully solvated, while in the LiC1 solution 5 DMF molecules and 1 chloride ion are located in the neighborhood of a cation. The Li-O distance values agree within the limits of errors. The contact ion-pair formation seems to be plausible because the solution of LiC1 was already near to saturation and thus the probability of the contact ion-pair formation is more enhanced. Table 1. Structural parameters for solvation shell of lithium ion in DMF as determined by XD measurements and least-squares fitting procedure: average distances rij, root mean square deviations l U, and coordination numbers nij. Solution of LiC1 (left) and of LiNCS (fight).

i,j Li-O O-O C..O Li..C Li..N O..O O..N Li..C Li..C1 CI..O

rii/A 1.97 2.74 a 2.99 2.79 4.00 3.94 a 3.63 "~ 4.56 2.40 3.25 a

Li(dmf)~C1 lii/A 0.07 0.12 0.18 0.14 0.18 0.20 0.20 0.30 0.15 0.20

nil 5 10a 10a 5~ 5~ 3~ 10a 10a 1 2a

.

i,j Li-O O-O C..O Li..C Li..N O..O O..N Li..C

rii/A 1.95 2.76 a 2.95 2.80 4.00 3.96 a 3.50 a 4.60

Li(dmO~§ lii/A 0.07 0.20 0.24 0.20 0.24 0.24 0.24 0.31

nil 6 12a 12a 6a 6a 3a 12a 12a

233 Figure 1. Experimental difference pair-distribution functions g(r) (circles) for solvation shell of lithium ion in a LiCl solution in DMF. The curve corresponding to the octahedral coordination, resulted in the best fit, is drawn by solid lines. Contribution calculated with an assumption of tetrahedral coordination is shown by dots. 0.6

I

I

I

I

I

I

I

I

I

I

I

I

00

0.4

0.2 ~

!

0

2

I

4 r/A

6

8

IV. Structure of an aqueous solution of NaCI at high pressure One of the most exciting questions in solution chemistry is concerned with the effect of the pressure on the solvation shell of ions. From conductance data it was suggested that the pressure breaks up the structure in the bulk water and also in the local water structure near the ions. Opposite opinions also exist according to which the increase in pressure leads to an enhancement of the close hydration. ME) simulation studies on a concentrated aqueous NaC1 solution [23] 3howed almost no changes in the hydrate structures of the ions even at 10 kbar pressure. On the other hand, the H-bonded network of the water molecules is distorted in a similar way as it was found in pure water [40]. Because of extreme technical difficulties, only a few attempts were to determine the structure of pure solvents at elevated pressures and only one ND experiment is reported on aqueous solutions of a LiC1 and a NiC12 aqueous solution [24], leading to contradictory results. No XD diffraction studies were reported. Preliminary results of an XD investigation of 2 molal aqueous NaC1 solution are given here. The pressure changed from 1 to 2000 bars. The measurements were performed with an XD diffractometer equipped with a specially designed high pressure unit. The solution was kept in a cylindrical cell made of beryllium. The details of the experimental technique and the data elaboration are reported elsewhere [22]. Figure 2 shows the total pair-distribution function of the NaC1 solution at different pressures. The radial distributions are broken because of experimental errors and spurious ripples are observable. Nevertheless, the average structural parameters listed in Table 2 seems reasonable. The structural parameters were determined by a LSQ fit to the main peak of the g(r) curve. The starting values of the parameters were taken from a previous study [3] of the same solution at room temperature. The parameters describing the hydration of the chloride ions were kept fixed and the calculated contribution was subtracted from the total curve. The remaining part was analyzed in terms of two contributions, namely, the Na-O and O-O. The results show that the average value of water-water first neighbor distances is contracted, but all other parameters do not change due to compression. The contraction ratio is 0.02 A/kbar, similar to what was found in

234 pure water [22]. However, this tentative results have to be confirmed by more systematic experiments and with improved data elaboration and interpretation technique. Table 2. Estimated structural parameters for sodium and chloride ions and for the first neighbor water molecules in 2 mol dm 3 aqueous solution of sodium chloride at room temperature and 1 to 2000 bar pressure, as derived from X-ray diffraction measurements: average distances rij and coordination numbers nij. pressure/b

rNa~)

ar

nNa-O

rci-o

1a 2.42 4v 3.14 1 2.42 5.5 3.14 c 1000 2.43 5.4 3.14 c 2000 2.42 5.7 3.14 c aRef. [3] bRegular tetrahedral structure of the ionic hydrate was eFixed at values taken from ref. [3].

ncl-O

roo

noo

6c 6e 6e 6e

2.92 2.91 2.88 2.87

4o 4.4 4.7 4.8

assumed.

Figure 2. Experimental pair-distribution functions g(r) for 2 mol dm "3 aqueous solutions of sodium chloride at room temperature and at 1 bar (lower curve) and 1000 bar (upper curve) pressures. 2

/

I

I

I

I

I

i

I

1

/

t--

I

2000 bar

1~1 . . . . . . . . . . .~. . . . . . . . . . . . . "

0L .......

/A

~

.

1000 bar

.

.

-

. .

.

.

.

.

.

-

.

1 bar

-

0 0

2

4

r/A

6

8

i0

V. Reverse M o n t e Carlo simulation of molecular liquids

In spite of the great success of the computer simulation methods in the determination of the microscopic properties of the solutions, the capacity of the traditional MD and MC simulations is always limited by the choice of the suitable potential functions to describe the interatomic interactions. The potentials are most often checked by comparison of the structural properties calculated from the simulation with those determined experimentally. The reverse Monte Carlo (RMC) method, developed by McGreevy and Pusztai [41 ] does not rely upon knowledge of any interaction potential, instead it generates a large set of atomic configurations on the condition that the difference between the experimental and calculated structure functions (or pair-distribution functions) should be minimum. The same structural

235

properties can than be calculated and analyzed as from any traditional simulation. Since no supplementary information on the studied.system is required, the RMC method seems to be a promising substitute for the average geometrical models to describe the static structure in the liquid. The RMC method has been frequently applied to atomic liquids and amorphous materials or two-component melts. There is only one attempt reported when ionic solution has been examined by the RMC method [42]. More recently an RMC simulation of liquid water has been performed [43] and the results were compared to those obtained from an MD simulation. A more distorted geometry of hydrogen bonds was found by the RMC study than in the MD simulation, and a significant fraction of the nearest neighbor molecules were observed to be distributed around a central one randomly rather than forming a tetrahedral network. The first RMC study on a heteroatomic, linear, molecular liquid was performed on liquid acetonitrile [44]. The molecule was described by three sites and deviation from linearity was also allowed. Intramolecular structure, partial pair correlation functions, angular distributions and the orientation of the molecules together with density profiles characteristic to spatial distributions of the neighboring molecules were discussed. One of the most interesting result is that the average coordination number of the first neighbors was found to be about 5-6, but the nearest two or three molecules seem to form a "subshell". This is demonstrated in Figure 3, where the N-CH3 partial pair distribution function is shown, together with the contributions of the f'trst n neighbors. The changes in the peak shapes suggest that the neighbors additional to the first two or three molecules are located at somewhat larger distances. A strong preference for antiparallel orientation of nearest neighbors and slight preferences for other configurations have been found, in qualitative agreement with previous results. However, these preferences decay rapidly after the first two or three neighbors. It can be seen that the RMC method is a more useful modelling tool to analyze the diffraction experiments than the construction of average geometrical models. Since several experimental data sets can be simultaneously input in the RMC procedure, ND and XD studies can be used in combination with it. The further development of the technique will hopefully help us to better understanding of the structures of aqueous and non-aqueous solutions as well. Figure 4. Partial pair-distribution functions gij(r) as computed from an RMC procedure in liquid acetonitrile for N-CH3 pairs (stars) and contributions from the nearest n neighbors of a central molecule (full lines). 3.00

gU 2.50

2.00

-

-

1.50 1.00

1

-

0.50 0.00

2.00

4.00

6.00

8.00

10.00

12.00

236

References 1 H. Ohtaki, and T. Radnai, Chem. Rev., 93, 1157 (1993), and references quoted therein. 2 H.L. Friedman, Chim. Scripta, 25, 42 (1985). 3 G. PAlink,fts, T. Radnai, and F. Hajdu, Z. Naturforsch. 35a, 107 (1980). 4 G.W. Neilson, Z. Naturforsch. 46a, 100 (1990), and references quoted therein. 5 R.H. Tromp, G. W. Neilson, and A. K. Soper, J. Chem. Phys. 96, 8460 (1992). 6 H. Yokoyama and G. Johansson, Acta Chem. Scand. 44, 567 (1990). 7 G. Johansson and H. Yokoyama, lnorg. Chem. 29, 2460 (1990). 8 G. Johansson, H. Yokoyama, and H. Ohtaki, J. Solution Chem. 20, 859 (1991). 9 N.T. Skipper, G. W. Neilson, and S. C. Cummings, J. Phys. Condens. Matter, 1, 3489 (1989). 10 N.T. Skipper and O. W. Neilson, J. Phys. Condens. Matter, 1, 4141 (1989). 11 See e.g. X-Ray Absorption: Principles, Applications, Techniques of EXAFS, SEXAFS and XANES, ed. D. C. Koningsberger and R. Prins, Wiley: New York (1988). 12 W. Kunz and P. Turq, J. Phys. Condens. Matter, 2, SA151 (1990). 13 V. Yu. Bezzabotnov, L. Cser, T. Grass, G. Jancs6, and Yu. M. Ostanevich, J. Phys. Chem. 96, 976 (1992). 14 N.A. Hewish, J. E. Enderby, and W. S. Howells, J. Phys. C: Solid State Phys. 16, 1777 (1983). 15 K. Heinzinger, G. P~linkfis, In: Interactions of Water in Ionic and Nonionic Hydrates, Springer: Berlin (1987). 16 R. Corban and M. D. Zeidler, Ber. Bunsenges. Phys. Chem. 96, (1992). 17 J.C. Dore, J. Mol. Struct. 237, 221 (1990). 18 T. Takamuku, T. Yamaguchi, andH. Wakita, J. Phys. Chem. 95, 10098 (1991). 19 T. Takamuku, K. Yoshikai, T. Yamaguchi, and H. Wakita, 7_, Naturforsch. 47a, 841 (1992). 20 M . C . Bellisent-Funel, L. Bosio, A. Hallbrucker, E. Mayer, and R. Sridi-Dorbez, J. Chem. Phys. 97, 1282 (1992). 21 K. Yamanaka, M. Yamagami, T. Takamuku, T. Yamaguchi, and H. Wakita, J. Phys. Chem. 97, 10835 (1993). 22 T. Radnai, and H. Ohtaki, in preparation. 23 G. Jancs6, K. Heinzinger, and T. Radnai, Chem. Phys. Lett. 110, 196 (1984). 24 G.W. Neilson, Chem. Phys. Lett. 68, 247 (1979). 25 T. Radnai, S. Ishiguro, and H. Ohtaki, J. Solution Chem. 18, 771 (1984). 26 T. Radnai, H. Ohtaki, Z. Naturforsch. 47a, 1003 (1992). 27 T. Radnai, S. Itoh, and H. Ohtaki, Bull Chem. Soc. Jpn. 61, 3845 (1988). 28 T. Radnai, S. Ishiguro, and H. Ohtaki, Chem. Phys. Lett. 159, 532 (1989). 29 G. PAlinkAs, I. Bak6, P. Bopp, and K. Heinzinger, Mol. Phys. 73, 897 (1991). 30 G. PAlinkfis, and I. Bak6, Z Naturforsch. 46a, 95 (1991). 31 T. Radnai, I. Bak6, and G. P~ilink~s, Acta Chim. Hung. in press. 32 Y. Inada, S. Funahashi, and H. Ohtaki, Rev. Sci. Instr. 65, 18 (1994). 33 H. Ohtaki, Pure Appl. Chem. 65, 2589 (1994). 34 Y. Marcus, Chem. Rev. 88, 1475 (1988). 35 U. Olsher, R. M. Izatt, J. S. Bradshaw, and N. K. Dalley, Chem. Rev. 91, 137 (1991). 36 H. Ohtaki and H. Wada, J. Solution Chem. 14, 209 (1985). 37 W. Kunz, J. Barthel, L. Klein, T. Cartailler, P. Turq, and B. Reindl, J. Solution Chem. 20, 875 (1991). 38 T. Radnai, S. Ishiguro, and H. Ohtaki, Bull. Chem. Soc. Jpn. 65, 1445 (1992). 40 G. P~ilinkfis, P. Bopp, G. Jancs6, and K. Heinzinger, Z. Naturforsch. 39a, 179 (1984). 41 R.L. McGreevy and L. Pusztai, Mol. Simul. 1, 359 (1988). 42 M.A. Howe, J. Phys. Condens. Matter, 2, 741 (1990). 43 P. Jedlovszky, I. Bak6, and G. P~ilinkfis, Chem. Phys. Lett. 221, 183 (1994). 44 T. Radnai, and P. Jedlovszky, J. Phys. Chem. 98, 5994 (1994).

"journal of /~OLECULAR

LIQUIDS

ELSEVIER

Journal of Molecular Liquids, 65/66 (1995) 237-244

The Role of Solvent in Inorganic Reaction Mechanisms, as Elucidated by High Pressure Studies Thomas W. Swaddle Department of Chemistry, The University of Calgary Calgary, Alberta, Canada T2N IN4 Abstract

Pressure effects on the rates of simple inorganic reactions in solution act primarily on intermolecular interactions, particularly solvation. They afford the possibility of "tuning" solvent properties without altering the solvent chemically. Outer-sphere self-exchange electron transfer reactions of transition metal complexes provide an opportunity to test this idea quantitatively, through an adaptation of Marcus-Hush theory. The theory is only moderately successful for organic solvents, as the solvent "seen" by the reactant behaves as if it is less compressible than bulk solvent. Furthermore, for multiply-charged ions or for solvents of low relative permittivity, the calculations become unstable even without the likely complication of ion pairing. For aqueous systems, the theory is successful except where one or more of the following complications applies: (a) changes in total spin multiplicity accompany the electron transfer process in complexes with flexible ligand systems; (b) cation-mediated pathways emerge in anion-anion self-exchange reactions; (c) the reactants are so small that the assumption that the solvent is a continuous dielectric fails; or (d) an inner-sphere sphere mechanism is operative. I. Introduction

Rigid solute molecules may generally be expected to be intrinsically one to three orders of magnitude less compressible than the bulk solvent. 1 This may be understood intuitively by comparing the compressibilities ~ of solids such as diamond (which may be regarded as infinitely extended molecules) with those of typical solvents such as methanol, and reflects the availability of free volume in liquids. Some solvent compressibility is lost when ionic solutes are solvated; for example, it has been estimated 2 that the molar volume of solvating water in the outer coordination spheres of cationic cobalt(HI) ammine complexes in aqueous solution is, on the average, some 2.5 cm3 mol"1 less than that of bulk solvent (18.07 cm3 tool"] at 298 K), corresponding to an effective average electrostrictive pressure of about 500 MPa outside the first coordination sphere. Thus, it transpires that the effect of pressure on the kinetics and equilibria of ionic reactions in solution reflects primarily changes in intermolecular interactions rather than intramolecular restructuring of the reacting solute(s). Again with reference to the 0167-7322/95/$09.50 91995 Elsevier Science B.V. All fights reserved. SSD! 0167-7322 (95) 00855-i

238 cobalt(IH) ammine example, the volume of activation A//r (= -RT(O In k/OP)T, where k is the rate constant and P is the pressure) for reaction 1 Co(NH3)sX ~

+ H20 ~

Co(NH3)sOH~ 3§ + X ~"

(1)

varies widely from +1 to -18 cm3 mol"l at the atmospheric-pressure limit as z is increased from 0 (X -- H20) to -2 (X = SO42"), and is markedly pressure dependent for anionic X. These results may be interpreted to mean that bond making~reaking contributes only about +1 cm3 mol"l to AF~ in the series, the balance (and the pressure dependence of A~) being due to solvation of the emerging 3+ and z- ions with concomitant loss of both volume and compressibility of part of the solvent - - an estimated eight water molecules per Co, in the case of the sulfato-complex. 3 A particular advantage in the use of pressure to probe solvational effects is that pressure can "tune" the characteristic bulk properties of the solvent without changing it chemically. The use of mixed solvents to vary the dielectric constant, for example, will likely be confounded by preferential solvation by one of the solvents, while the system will be chemically different if solutions in different neat solvents are considered. Pressure studies, however, have their own limitations. Technical complications 4 limit the pressure range normally used in chemical kinetic studies to about 0.1-200 MPa, and this produces only small changes in such solvent parameters. Furthermore, one needs to have available a realistic theory that relates changes in solvent parameters to their anticipated effects on reaction rates and equilibria, if pressure is to be used as a reliable probe of solvation phenomena. Our recent efforts in Calgary have been directed towards establishing and testing such a theoretical framework for suitable model reactions. The simplest of such reactions are solvent exchange on metal ions (representing substitution processes) and the outer-sphere electron transfer reactions of transition metal complexes (representing redox). For the latter, the theories of Marcus s and Hush 6 have provided a starting point for a theory of pressure effects on reaction rates. ~'7

IL Solvent exchange kinetics Pressure effects on the kinetics of solvent exchange on metal cations have been described at length elsewhere, 4.s and will not be considered in detail here. Suffice it to say that it is possible, using an empirical relation that predicts the molar volumes of aqueous cations, to predict the volume changes that would accompany the gain or loss of one solvent ligand and so to set limits upon AFr for associative (A) and dissociative (D) water exchange (about -13 and +13 cm3 tool"l, respectively). 4's In fact, A ~ values for all water exchange reactions of metal 2+ and 3+ ions studied to date have fallen between these limits (Ti(H20)63§ is close to the associative limitS), implying that the water exchange process is appropriately described as interchange (I,, I~). In particular, the D limit is not approached at all closely, as might be expected in view of the high abundance of water molecules surrounding the metal ion, with the negative ends of their dipoles pointing inwards on a time average. At present, there are insufficient molar volume data for metal ions in nonaqueous solvents to permit construction of empirical relationships like that established for aqueous solutions, and so this approach has so far been limited to solutions in water.

239

IH. Theory of pressure effects on outer-sphere self-exchange reaction rates In the absence of ion pairing and rate limitation by solvent dynamics, the volume of activation AIA for adiabatic outer-sphere electron transfer in couples of the type ML~ez§ can, in principle, be calculated as in equation 2 from an adaptation of MarcusHush theory. ~'7 In equation 2, the subscripts refer respectively to volume contributions from internal (primarily M-L bond length) and solvent reorganization that are prerequisites for electron transfer, medium (Debye-Htickel) effects, the Coulombic work of bringing the reactants together, and the formation of the precursor complex. AV~ = AVIR~:+ AVSR~ + AVDH~+ AVCOUL:~+ AVPRi/C~

(2)

Of these contributions, AVeR* is calculated to be between 0 and 1 cm 3 mol "~ for rigid complexes ~ (a value of +0.6 cm3 mol "] is adopted for the complexes discussed in this paper), AVpREC~ is typically between +1 and +2 cm3 mol'~,7 and, for practical values of the ionic strength I, A VDH~ and A Vco~ ~ will be of opposite sign but similar magnitude unless the relative permittivity D of the solvent is very low" AVDH:l: =

{R~ZIZ2CII/2/(1

-I- Ba/lf2)2}[(O

In D/OP)T(3 + 2 B a I la) - 13)]

AVcouL $ = (NxZ~Z2e214m~oa)(aD'~laP)T

(3)

(4)

If we assume the reactants to be hard spheres of roughly equal radii r and electron transfer to occur with highest probability at an M-M separation a that varies with compression of the solvent (isothermal compressibility 13), we have for solvent reorganization AVsR ~ = (NAe2/1B~F,o)[(r '' -- o"l){0(n "2 - D ' I ) / a P } T

- (n "2 - D ' l ) ~ / 3 o "]

(5)

In equations 3-5, a is the anion-cation close-approach distant, B and C are the DebyeHt~ckel parameters at 0.1 MPa, n is the refractive index of the solvent, and the other symbols have the usual SI meanings. Thus, theory predicts that AV~ can be equated approximately with AVsR~. Since the pressure dependences of both n and D are closely linked to that of the density p of the solvent, i.e., to [3, it follows that AVt is determined in large part by the compressibility of the solvent. Sample calculations for model 3+/2+ couples are given in Table 1. As Table 1 shows, however, the compressibilities of liquids, particularly organic solvents, decrease markedly with increasing pressure, and so the calculated AVsR~ and indeed all the parameters in Table 1 decrease in absolute magnitude over the typical experimental pressure range, especially at low pressures. The result is that A V~ itself can be expected to depend markedly upon pressure, but the effect is less significant for water than for nonaqueous solvents. The implication is that, given the usual experimental uncertainties, one can meaning~lly discuss pressure effects on electron transfer kinetics in aqueous systems over the 0-200 MPa range in terms of either an average value of AV~ over that range (but this raises the question of how the theoretical values of AVt are to be

240 Table 1. Calculated contributions to AF ~for self-exchange of a t~ical couple Ml~3+a+.' Solvent water

P /MPa 0 100 200

[3 AVSR:~ /104o Pa "l /cm3 mol "l 4.5 -7.5 3.6 -6.1 3.0 -5.1

~VDHt /cm 3 mol "1 2.9 2.4 1.9

A VCOUL~: /cm 3 mol "l -3.4 -2.8 -2.2

A V~(calc) /cm 3 mol"l -6.3 -5.1 -4.1

methanol

0 100 200

11.6 5.7 3.9

-18.3 -9.1 -6.2

20.6 10.5 7.0

-20.7 -10.8 -7.3

-14.9 -7.6 -5.2

acetonitrile

0 100 200

11.1 5.8 4.0

-17.8 -9.3 -6.4

16.1 9.3 6.5

-16.3 -9.7 -6.9

-14.7 -7.9 -5.5

0

12.6

-18.4

49.7

-47.6

-12.5

100

6.1

-9.3

19.5

- 18.3

-6.4

acetone

200 4.2 -6.4 12.1 I9= 0.1 mol kg "~, r = 500 pm, o = 1.0 nm, a = 800 pro, T = 25~

-11.3 -4.4 AFrot = 0.6 cm 3 mol"~.

averaged, since their pressure dependence is nonlinear 7) or its value at mid-range (I00 MPa). In practice, experimental values of In k often appear to be linear functions of P within the error limits, although non-linearity does seem to exist in some cases where I AFt I is unusually large 9"ll and direct comparison with theory is then possible. Wherland ]2 has reviewed the experimental results on pressure effects on the kinetics of nonaqueous electron transfer reactions. Table 1 gives theoretical values of ~VDH~ and AYcouL~, and, although few 3+/2+ reactions have been studied in nonaqueous media to date (largely because of solubility and redox stability problems), the point emerges that these opposing contributions can become so very large that the calculation of A Fr becomes numerically unstable. Even for 0/- or +/0 couples, for which the DebyeHfickel and electrostatic work terms should in principle be nonexistent, one suspects that second-order ionic strength and Coulombic effects could contribute significantly and possibly unequally to AF r Furthermore, ion pairing of the reactants (at least one of which has to be ionic) with the counterions that are inevitably present will become increasingly evident as D decreases. If the paired ion(s) are more reactive than the free reactant ions, the contribution AVw ~ of ion pair formation to AVr will be positive, since, as Fuoss theory shows, ~ increasing pressure acts through increasing D to disfavor ion pairing. Conversely, if paired reactant ions are less reactive in electron transfer than the parent species, A Ywt will be negative m Wherland m! has shown that this is more generally the case, although the assumption made for convenience of calculation in some of our publications, ]~ that ion pairs are inactive in electron transfer, is excessive. Of course, the value of AVn,~ will approximate to a constant only if ion pairs constitute a very small or a very large fraction, respectively, of the total reactant in these two cases.

241

Even if ionic strength, Coulombic, and ion pairing effects can be ignored, however, Table 1 shows that AVsR~ (and hence A/~ itself, for 0/- and +/0 couples) in nonaqueous solvents is predicted to be strongly negative at low pressures but to assume values not very different from those for aqueous systems as P increases. In reality, such sharp pressure dependence of AV* (i.e., nonlinearity of the In k vs. P plot) for electron transfer reactions has not been observed to date. For example, for the Ru(hfac)3 ~ couple (hfac- = 1,1,1,5,5,5-hexafluoropentane-2,4-dionate), the In k vs. P plot is linear to within the experimental uncertainty from 0-200 MPa, with AVt = -5.8, -5.5, and -6 cm3 mol"~ in perdeuterated methanol, acetonitrile, and acetone, respectively (cf. -7.3, -7.5, and -7.6 cm 3 mor l, respectively, calculated for 100 MPa as in Table 1 m no measurements are available for water, in which gu(hfac)3 ~ is insoluble), only for methanol is there a hint of nonlinearity, though still less than predicted by equation 5.13 The agreement between theoretical and experimental A ~ values is reasonably close at 100 MPa, and might be better at higher pressures. The implication is that the solvent, as "seen" by the reacting complexes, is more compressed and so less compressible than bulk solvent by virtue of its solvational action (cs the hydration of aqueous ammines as discussed above); as one goes to higher pressures, the errors introduced by equating solvating solvent with bulk solvent

diminish in magnitude.

IV. Electron transfer in aqueous solution

If local loss of solvent compressibility near solute molecules is indeed a major cause of failure of the theory of AVt for electron transfer in organic solvents, then the better record of success of theory in aqueous systems (Table 2) is understandable, as bulk water is less compressible than organic solvents at low pressures, the gap narrowing as P increases (cs Table 1). Aqueous systems listed in Table 2 for which the adiabatic Marcus-Hush-based theory predicts AVt with acceptable accuracy include the hexaaquairon(III/II) couple (which is a benchmark of theoretical analysis), (1,10-phenanthroline)iron(IIIM) and bis(trithiacyclononane)cobalt(IHM) (in which couples both the reduced and oxidized partners are low-spin in their ground states), and cobalt(RIM) complexes in which the metal ions are encapsulated in the rigid cages sepulchrate, diaminosarcophagine, and diprotonated diaminosarcophagine. In contrast, the tris(ethylenediamine)cobalt(UI/R) and tris(1,10-phenanthroline)cobalt(III/II) exchanges give AV~ values that are 10-15 cm3 mol"~ more negative, and are several orders of magnitude slower, than predicted. (The self-exchange reaction of the ethylenedinitrilotetracetatocobalt(III/II) complexes is also of this class, but the numerical analysis of AV~ is complicated by the fact that, in the Co n partner, the EDTA 4" ligand is only quinquedentate, the pendant carboxylate arm being protonated and the sixth coordination site on the Co n being occupied by a water molecule. ~s) This can be understood in one of two ways, both of which relate to the fact that the cobalt(II) is high spin (quartet state) and the cobalt(IL0 is low spin (singlet) in the ground state, so that electron transfer must be accompanied by major multiplicity change and is nominally "spin forbidden". One possibility is that electron transfer is preceded by a cobalt(H) quartetdoublet equilibrium with a volume change of-10 to -15 cm3 mol"~, indeed, a volume

242

Table 2. Volumes of activation at 100 MPa for self-exchange in ML~(z+~)/z+ couples in aqueous media. 9 A/~(expt)/cm 3 mol "l A//C(calc)/cm3 mor t gel. Couple I/mol kg "l T/~ -10.4 11 Fe(H20)63+/'2+ 0.5 2.0 -11.1 • 0.4 b Fe(phen)33+/2+ 0.3 3.0 -2.2 + 0.1 -2.5 c 14 Co([9]aneS3)23+t2§ 0.1 25.0 -4.8 + 0.2 -5.3 15 Co(sep) 3+t2+ 0.2 25.0 -6.4 + 0.2 -6.4 15 Co(diamsar) 3+t2+ 0.1 25.0 -10.5 • 0.6 -7.3 16 Co(diamsarH2) 5+/4+ 0.63 25.0 -9.4 • 0.9 -9.2 16 Co(en)33+/2+ 0.5 65.0 -15.5 • 0.8 b -5.3 10 Co(phen)33+/2+ 0.1 (NOr) 25.0 - 16.0 • 0.7 - 1.7 17 0. I(CI') 25.0 -17.6 • 0.7 -2.2 17 "Co(EDTA) /2'' 0.5 85.0 -3.2 • 0.3 -18 -9 c 9 MnO4"t2. 1.1 45.0 - 17 • 2 b Na+,MnO4"rz" 1.1 45.0 +3 • 1 -6 ~a 9 K+,MnO4"t2" 1.1 45.0 -1 • 1 -6 ~'d 9 (K+)3,Fe(CN)e3"/4" 0.5 25.0 +22 • 2 -5 e'd 19 Fe(I-I20)5OH2+/Felq 2+ 0.5 2.0 +0.8 • 0.9 -11 11 9AVnt: taken as 0.6 cm 3 mol "l except as indicated, b A ~ shows possible pressure dependence, c AVn~:taken as 0. d Includes an estimate of the effect of ion pairing.

change of this magnitude has been reported for the bis(terpyridine)cobalt(II) spin equilibrium, 2~ but there is evidence2~ that dechelation of the high-spin Co(terpyh 2+ is also involved, and furthermore the low-spin cobalt(n) state appears to be energetically inaccessible for Co(phen)3 2+ and especially Co(enh 2§ The other possibility is that electron transfer in the Co(phen)3 3+~+ and Co(enh 3+r2+ couples is nonadiabatic; we have tended to favor this explanation because the contribution of nonadiabaticity to AV~ can be calculated in terms of the distance scaling factor a, and the required values of a (16-19 cm~) fall within the range expected for these couples. This raises the question, however, as to why the Co(sep) 3+r2+, Co(diamsar) 3+~+, and Co(diamsarH2) s+/4+ couples, in which the Co n partners are also high-spin, should conform to expectations based on adiabatic Marcus-Hush theory. The answer seems to be that the encapsulating ligands, while permitting some lengthening of the Co-N bonds when Co m is reduced to Co n, preclude the angular deformations that presumably occur following spinstate change with three independent bidentate ligands. Qualitative arguments to explain the impact on A/~ might include the opening up of spaces between the bidentate ligands to additional solvation on going from high-spin to low-spin Co n, but such explanations are not readily quantified. Significantly, Wherland ]z has identified flexibility of certain ligand systems as a cause of anomalies in AVt for reactions of the Mn(CNR)6 2§ series in nonaqueous solvents. While the role of the counterions in cation-cation electron transfer seems to be confined to Debye-Htickel-type interactions, anion-anion self-exchange can be strongly catalyzed by the cations, so that cation-dependent paths are evident in addition to

243

exchange of the "bare" anions for the aqueous manganate-permanganate couple, 9 while for the ferri/ferrocyanide reaction the only detectable pathway at practical ion concentrations involves three K + ions. ~9 Such cation-dependent pathways are characterized by A/~ values that are much more strongly positive than theory permits, even when the contributions of ion pairing are allowed for using Fuoss theory. 7 The A/~ values for the MnO4r cation-dependent paths need to be judged with reference to the anomalously strongly negative A/~ for the cation-independent path. Part of the negative discrepancy for the latter may be due to the non-adiabaticity invoked by Dolin, Dogonadze and German, 22 but an additional factor is likely to be the unusually small size of the reactant anions, which means that the solvent can no longer be treated as a continuous dielectric. We have attempted to improve the continuous-dielectric model by treating the encounter complex as an eUipsoidal entity rather than as the usual two spherical conductors, 9 but Matyushov23 has tackled the general problem of solvent "graininess" in electron transfer theory directly. Unfortunately, the resulting expressions for AVsg~ are unwieldy and give positive values for model reactions in a range of nonaqueous solvents, contrary to the predictions of equation 5 (to which the Matyushov expressions should reduce when the reactant dimensions are much larger than those of the solvent molecules) and to all experimental results for outer-sphere electron transfer reactions other than some counterion-mediated processes. These positive values of the predicted AVsx~ arise because the pressure dependence of the expression that replaces the Pekar factor ((n "2 - D "~) in equation 5) is overwhelmed by that of solvent density reorganization, contrary to intuitive expectations, and it may be that the promising Matyushov approach simply requires numerical reevaluation. Finally, the apparent failure of Marcus-Hush-based theory of AV~ in electron transfer between Fe(H20)sOH 2§ and Fe(H,O)6 '~+ is quantitatively attributable to the operation of a hydroxo-bridged (inner-sphere) mechanism, 11 and indeed AV* can serve to distinguish between outer- and inner-sphere processes in appropriate cases such as this.

Acknowledgement I thank my coworkers, listed in the references, for their contributions, and the Natural Sciences and Engineering Research Council of Canada for financial support of our work.

References I. 2. 3. 4. 5.

D.g. Stranks, Pure Appl. Chem., 38, 303 (1974). T.W. Swaddle, Adv. Inorg. Bioinorg. Mech. 2, 95 (1983). W.E. Jones, L. g. Carey and T. W. Swaddle, Can. J. Chem. 50, 2739 (1972). T.W. Swaddle, Can. J. Phys., in press. g. A. Marcus, J. Chem. Phys., 24, 966, 979 (1956); Discuss. Faraday Soc., 29, 21 (1960); Faraday Disc. Chem. Soc., 74, 7 (1982). 6. N.S. Hush, Trans. Faraday Soc., 57, 557 (1961). 7. T.W. Swaddle, Inorg. Chem., 29, 5017 (1990).

244 8. A.E. Merbach, Pure Appl. Chem. 59, 161 (1987), and in High Pressure Chemistry and Biochemistry, edited by R. van Eldik and J. Jonas, p. 311 (Reidel, Dordrecht, 1987). 9. L. Spiccia and T. W. Swaddle, Inorg. Chem., 26, 2265 (1987). 10. W. H. Jolley, D. 1L Stranks and T. W. Swaddle, Inorg. Chem., 29, 385 (1990). 11. W. H. Joiley, D. R. Stranks and T. W. Swaddle, Inorg. Chem., 29, 1948 (1990). 12. S. Wherland, Coord. Chem. Rev. 123, 169 (1993). 13. H. Doine and T. W. Swaddle, Inorg. Chem., 27, 665 (1988). 14. H. Doine and T. W. Swaddle, Can. J. Chem. 66, 2763 (1988). 15. H. Doine and T. W. Swaddle, Inorg. Chem., 30, 1858 (1991). 16. R. D. Shalders and T. W. Swaddle, forthcoming publication. 17. M. R. Grace and T. W. Swaddle, Inorg. Chem., 32, 5597 (1993). 18. W. H. Jolley, D. R. Stranks and T. W. Swaddle, Inorg. Chem., 31, 507 (1992). 19. H. Takagi and T. W. Swaddle, Inorg. Chem. 31, 4669 (1992). 20. R. A. Binstead and J. K. Beattie, Inorg. Chem. 25, 1481 (1986). 21. 1L D. Shalders, H. Takagi and T. W. Swaddle, unpublished work. 22. S. P. Dolin, R. 1L Dogonadze and E. D. German, J. Chem. Sor Faraday Trans. I, 73, 648 (1977). 23. D. V. Matyushov, Chem. Phys. 174, 199 (1993); D. V. Matyushov and R. Schmid, J. Phys. Chem. 98, 5152 (1994).

journal of

MOLECULAR

LIQUIDS ELSEVIER

Journal of Molecular Liquids, 65/66 (1995) 245-252

EXAFS of Bromide Ion in Solvents and at Air/Solution Interface Iwao Watanabe Department of Chemistry, Faculty of Science, Osaka University, Toyonaka, Osaka 560, Japan. Abstract Solvation structures of Br- ion dissolved in 23 solvents have been studied at the Br Kedge using extended X-ray absorption fine structure (EXAFS). The results are summarized as follows. 1) Coordination bond lengths r are 0.31-0.32 nm for B r - - - O in protic solvents and 0.35-0.36 ran for B r - - - C in aprotic solvents. 2) The r values for water and formamide are larger than those for other protic solvents, possibly due to the strong solvent-solvent interactions of these two solvents. 3) Coordination numbers N widely differ, ranging between 3-6, from solvent to solvent. The value of N for alcohol linearly correlates with the MayerGutmann's acceptor number A N. 4) In aprotic solvents containing two methyl groups per molecule, Br- is found to contact with the two methyl groups, thus the number of primary solvent molecules must be equal to half the N value. 5) EXAFS amplitude is found to correlate with A N of the solvent. To study the surface structure, a new EXAFS technique, total-reflection total-conversion-electron,yield EXAFS, has been developed and applied. The new technique utilizes polarized X-rays from synchrotron radiation, providing not only information on the solvation structures of ions at the aqueous solution surface but also on the preferential orientation of coordination bond at the solution surface.

I. Introduction Solvation structures of anions in water are difficult to determine due to their weak interactions with the solvent. Various coordination distances r and coordination numbers N have been reported for bromide ion in water. X-my diffraction(XRD) technique predicts an r value ranging between 3.12 and 3.43 ,~, and N values from 6 to 8-9.4.1 Other techniques, such as nmr, neutron diffraction, and ir spectroscopy gave different values, suggesting that the results depend to large degree on the techniques used. The hydration number of Br- obtained by nmr is zero, which is an extreme case. 2 The interactions are even weaker in organic solvents, thus very little is known about the geometry of anion solvation in organic solvents. Computer-simulation calculations describe the solvation structure of Br- as ceaseless motion of solvent molecules distributed around the anion at equilibrium r and N. 3 Diffraction techniques can provide the distribution functions for these values, though they require rather high concentration samples. Concentrated salt solution may have different solvation structures from that of dilute ones, not only because of the smaller number of free solvent molecules but also the higher possibility of ion-pair formation especially in organic solvents. 4 Extended X-ray absorption fine structure (EXAFS) is a useful technique to provide the local structure of solutions. It is able to determine the r and N values at relatively dilute concentrations and in organic solvents as well. The solvation structures of Br- in various solvents as determined by EXAFS 5 is discussed in the present paper. Moreover, the EXAFS technique has been applied to the aqueous solution surface. At the surface the solvation 0167-7322/95/$09.50 91995 Elsevier Science B.V. All rights reserved. SSDI 0167-7322 (95) 00856-X

246 structure of Br- may not be the same as that of the bulk. Some of the molecular dynamics calculations predict that halide anions in water tend to float on the surface of clusters consisting of water molecules rather than within water. 6 This effect may cause a dissimilar solvation structure to that of the bulk. In addition, if the anion is segregated at the surface by surfactants such as large alkylammonium cations, the anion density at the surface should be high and its environment differ from the bulk. This is a preliminary report of the first experimental study of the solution surface by the EXAFS technique. This technique provides us information on the gas/liquid interface, the structure of l.angmuir films, and the effect of the interface on chemical reactions. II. E x p e r i m e n t a l

Br K-edge absorption measurements in transmission mode were performed using a 1 crn or a 5 mm thick cell at BL-6B and -10B of the Photon Factory (National Laboratory for High Energy Physics, Tsukuba). The spectra were taken at the concentrations of 0.1 and 0.05 mol dm -3 at room temperature. The concentration dependence of the spectra was not observed at this concentration range. The surface study was performed at BL-7C of the same facility by the total-reflection XAFS(TR-XAFS) method. The experiments were done at 1 mrad grazing incidence angle, since at the Br K-edge energy, the critical angle for the total-reflection is about 2 mrad at the water surface. In order to reduce the X-ray absorption by air and water vapor, the solution 0 /'~ n H20(1) surface was covered by helium gas. The X-ray absorption was determined by detecting the totalconversion-electron current. When o X./_Wv ,,j-- I the Br- ions at the surface absorb X-rays, they emit Auger electrons of 10 keV energy. The helium is, then, ionized by Auger electron to A Pk fo~amide 17) create many He + and e- couples amplifying the signal. An electrode t-butyl alcohol (12) placed above the solution surface then collects the conversion X./ v V "I electrons. This is a simple and 01~ m A ~ acet~ (14) sensitive technique to measure the

LX'A'A'

LV V ,,,v ,,

' ' I

/\ ,.,,.,, V V

~

%0

X-ray absorption by surface species. By reversing the polarity of the electrode, the He + current can be measured. In both cases (l~sitive and negative polarity) similar results were obtained. The solution was cooled to around I*C in order to reduce the vaporization of solution and the temperature was kept constant during the experiments within 0.1*C.

V

0/~ O~

%/

V

A

v

'

2

,,j

--

--'-I

~-di/~me~ylf~~ ~_~Lide(I

L/

~

v

rN f~ X../ N.J v " '

~ - -

I

I

4

.,~

v

_ I

kl A -~

pyridine 119 -.-,~. , ---I

I

6

I

I

8

Figure 1. The Br K-edge EXAFS k3 Z (k) spectra of Br- ion in several solvents. Taken from ref.5.

247 III. Bromide Ion in A q u e o u s and Organic Solvents

The EXAFS spectra for Br- display weak oscillations, indicating either a small coordination number or a large disorder of the coordination bond lengths due to the weak Br-solvent interactions. Some of the spectra display strong multi-electron excitation structures7 and this structure had to be removed before the EXAFS analysis. The EXAFS osciUations 5 for several typical solutions are given in Fig. 1. In all cases the oscillations for aprotie solutions are weaker compared to aqueous or protic solutions. Most of the spectra could be analyzed by using a one-shell model, but it is clear that the data for acetic acid (4) and tbutyl alcohol (12) can not be adequately analyzed by the one-shell model. The EXAFS oscillation amplitudes are quite different from sample to sample and seem to be correlated with the anion-solvent interaction strength. Here, the EXAFS amplitudes are evaluated with the peak heights h in the Fourier transforms plotted against the anion solvation strengths represented in terms of the Mayer-Gutmann's accepter number AN .8 It is quite interesting to find a linear correlation between them as shown in Fig. 2. In most EXAFS studies it is not considered that the amplitude alone directly reflects a physical or a chemical property of the sample, except for the correlation of the EXAFS amplitudes for transition metal aqua complexes with their ligand exchange reaction rates. 9 Since the Fourier transform calculation gives rather consistent results compared to the curve fitting calculation, it could be suggested that the present h value can be used as another solvent parameter to characterize electron pair acceptors or hydrogen bond donors. The two-shell solvation structure found for acetic acid solution (4) and its difference in behavior in Fig. 2 must indicate that the solvation structure of Br- in acetic acid is quite different from the others. The EXAFS data were analyzed to obtain the r and N values by using a one-shell curve fitting method except for acetic acid and 0.3-' ' ' ' ' ' i , i .. ~ = , t-butyl alcohol solutions. The results are plotted against the A N values in Figs. 3 and 4. The r , values pertain to the distances of m 9 B r - - - O for protic solvents and Br1(1 - - C for aprotie solvents. The == 0 . 2 9 d coordination distances for alcohols are fairly constant irrespective of ~ 08 their wide spread in A N value. Thus, the quite different solvent I properties, e.g., from hexafluoropropanol (1) to butyl alcohol (11), 0.1 ~ ~ 2 1 3 are not reflected in their anionsolvent interatomic distances. This -~.~, . ,., , . , . , finding contradicts the generally 20 40 60 observed fact that stronger interacAN tions lead to shorter distances. There is another interesting finding Figure 2. Correlation of the peak height h of the in Fig. 3. The r value for water (2) Fourier-transform spectrum for Br- ion with the is clearly larger than those for acceptor number A N of the solvent: (O) protic and alcohols. This is also difficult to (O) aprotic solvents. Taken from ref. 5. understand because water solvates i

248 ions far better than alcohols and it is smaller than alcohols in size, thus the geometrical constraints to solvate the anion must be less in water. Another solvent which has an unreasonably larger r value is formamide (7). The suggested mechanism for the large r values for these two solvents is that the second solvation sphere molecules or perhaps more distant solvent molecules pull the primary solvent molecules outward. The position of the primary solvents is determined by two opposing attractions, one from Br- and the other from outer shells. It is well known that water and formamide are the most strongly ordered, thus the interactions between the primary and the secondary solvation shells must also be stronger. Obviously alcohols have weaker solventsolvent interactions and arc able to come closer to Br- than water or formamide. The r values for aprotic solvents arc larger than those for protic solvents and similar to that found for tetraalkylammonium bromide crystal.10 The N values for protic solvents in Fig. 4 are referred to the generally accepted value of six for Br- in water. The values for aprotic solvents are determined by using tetrapropylammonium bromide crystal as a reference material, for which the XRD result is known. 10 The N values are distributed over a wide range and do not seem to correlate with A N value. However, careful inspection gives us the following conclusions. Firstly, the N values for alcohols are linearly correlated with A N values. The solvents, water (2), acedc acid (4) and formamide (7) are exceptions again. Mayer has

I

3.61~ 01; 22

'

I

'

I

'

I

F;~0190 15 L- 0 ~ 6 18 14

,.
;k~. If this explanation is accepted we must conclude that the linear restmnse of the medium does not hold in solvent mixtures. .

Table 3.- Activation free energies estimated for the optical electron transfer within the [Co~H3)4(pzCO2)]2§ *" ion-pair (see the text). T=298.2 K.

D, AGm,~/kJmol -a AG~/l~Jmol -~

78.5 58.8 87.6

76 57.4 86.1

74 51.9 85.0

70 49.2 84.6

66 49.3 84.3

64 47.4 83.8

IV. Acknowledgements The authors wish to thank Professor Sumi, Tsukuba University (Japan) and Professor Balahura, New Guelph University (Canada) for helpful suggestions concerning the interpretation of the results. The authors also wish to ackalowledge the financial support from the Consejeria de Educaci6n y Ciencia de la Junta de Andalucia (D.G.C.Y.T. PB92-0677). V. References and Notes 1 J. Cortes, H. Heitele and J. Jortner, 3. Phys. Chem. 98, 2527 (1994). 2 J.M. Malin, D. A. Ryan and T. V. O'Halloran, J. Am. Chem. Soc. 100, 2097 (1978). 3 F. Sfinchez-Burgos, M. L. Moy~i and M. Galfin, Prog. React. lO'net. 19, 1 (1994) and references therein. 4 N.S. Hush, Electrochim. Acta. 13, 1005 (1968). 5 In fact the reported value corresponds to Co(NH3)4(pzCO2)2+/Ru(CN)6't- ion-pair. But a similar value has been obtained for similar ion-pairs with Fe(CN)64- instead of Ru(CN)64-. See for example A. J. Miralles, A. P. Szecsy and A.Haim, lnorg. Chem. 21, 697 (1982). 6 B.S. Brunschwig, S. Ehrenson and N. Sutin, J. Phys. Chem. 90 (1986) 3657. 7 Standard Potentials in Aqueous Solutions, A. J. Bard, R. Parsons and J. Jordan eds., IUPAC, New York, 1985 chap. 14. 8 M . H . Chou, C. Creutz and N. Sutin, Inorg. Chem. 31, 2318 (1992).

journal of

NIOLECULAR

LIQUIDS ELSEVIER

Journal of Molecular Liquids, 65166 (1995) 265-268

Ion Pair of Tetraalkylammonium Picrates Kiyoshi Sawada and Fumie Chigira Department of Chemistry, Faculty of Science, Niigata University, Niigata 950-21, Japan Abstract The ion-pair formation equilibria of tetraalkylammonium ion with picrate ion (C6H2(NO2)30-) in 1,2-dichloroethane were studied at 25.0 ~ by means of conductivity measurement. The cation studied were tlie symmetric (TAAn+; (CnH2a+I)4N+, n = 1-8) and asymmetric (TOMA§ (CsH17)3(CH3)N§ CTMA; (C16H33)(CH3)3N+, ) tetraalkylammonium ions, Q§ Limiting molar conductivities of salts, A o, and ion-pair formation constants, Kip were obtained by the analysis of the conductometric data with Fuoss-Justice Equation. Stokes radius, r~, of the tetraalkylammonium ions was estimated from the limiting molar conductivity. The closest approach, a, between the cation and anion of the ion pair was estimated from the ion-pair formation constant. The value of r s estimated for asymmetric Q+ is comparable to that of symmetric Q+ having a corresponding number of carbon atoms, whereas the closest approach of the asymmetric Q+ is much smaller than that predicted from the number of carbon atoms. The structures of ions and ion pairs were discussed.

Introduction Tetraalkylammonium salts are the most common electrolytes for the non-aqueous solvent systems and high molecular weight ammoniums have been used for the ion-pair extractant. The thermodynamic properties of the salts such as partition equilibria, solubility, ion-pair formation etc. have been studied in a variety of solvents. The detailed equilibria or structure of ion pair, however, are not fully elucidated. We studied the partition equilibria and structures of the ion pair of cationic complex of polyether compounds with picrate ion and reported that the dissociation of ion pair in the organic phase plays an important role for the partition equilibria. 1-4 In the present paper, the ion-pair formation in 1,2-dichloroethane was studied by using the one of the most simple system of electrolyte, tetraalkylammonium picrate. The effect of the chain length of the alkyl group was studied for the symmetric and asymmetric tetraalkylammonium ions. Experimental The solvent 1,2-dichloroethane was washed twice with deionized water. Tetraalkylammonium bromide Q+Br- was converted to picrate salt Q+pic- by solvent extraction method. A portion of 1,2-dichloroethane saturated with water (40 ml, Cmo = 0.13 mol dm -3) was titrated with 10-3 mol dm -3 tetraalkylammonium picrate by a piston burette in a thermostated vessel (25.0 ~ Conductivity was measured by Toa-denpa Model CG-511C. The cell constant of the electrode was calibrated by KCI aqueous solution and obtained as 0.0920 cm -1. A portion of titrant was dried and dissolved in an alkaline aqueous solution. Then the concentration of picrate ion was determined by spectrophotometry. 0167-7322/95/$09.50 91995 Elsevier Science B.V. All fights reserved. SSDi 0167-7322 (95) 00879-9

266 Results and Discussion The molar conductivity experimentally obtained, Aobsd, is plotted as a function of square root of the concentration of tetraalkylammonium picrate (Q§ V'c. The results of tetrahexylammonium (TAA6+), trioctylmethylammonium (TOMA +) and cetyltrimethylammonium (CTMA § ions are depicted in Fig. 1. Similar results were obtained for other symmetric tetraalkylammonium runs (TAAn*; (CnH2n+I)4N+, n = 1-8). The ion-pair formation of tetraalkylammonium picrate, Q+pic-, is written by

Q* + pic- ~

(1)

Q*'pic-

The ion-pair formation constants, Kip, is given by [Q*-pic-] Kip = [Q+][pic-]

(2)

The conductivity data was analyzed by Fuoss-Justice equation: 5 At,

= A0 - S(cot) u2 + Ecot log(cot) +

JlCot -

(3)

J2(cot) 3/2

where At: is the molar conductivity under the assumption of the complete dissociation of electrolyte. Thus, the degree of dissociation is given by ot = Aobaa/A F and the i o n - p a i r formation constants is Kip = ( l - a ) / ot2cy2. The activity coefficient, y, of 1 19 electrolyte was 50 evaluated by the extended D e b y e - H ~ c k e l -r equation, log y = - A z 2 V'l / (1 + Ba "r A is the limiting molar conductivity of Q*Pic-. The values of parameters of limiting molar conduc,.q tivity, A o, and the ion-pair formation constant, Ki, were evaluated from the data Act,. shown ~ 4t) inr~ig. 1 by the successive approximation with i~ a help of a computer. The value of the closest approach of the ions, a, in the ion pair was = estimated by comparing the value of K l with 8 the prediction of the Bjerrum theory, g' The -~ II r 30 results of A o, K i and a are listed in Table. The value of the m~'lar conductivity calculated by these constants listed in Table are shown in Fig. 1, solid lines. The experimental results show good fitting with the calculated curves. Structure of the ion pair of tetraalkyl20 0 0.5 1. 1.5 ammonium picrate was calculated by molecular mechanics (MM2) with a help of CAShe R ~/c/ 10-2 mollr2 dm-3/2 system. The estimated structure of ion pair of tetraoctylammonium picrate is shown in Fig. 2. Similar structures were obtained for other te- Fig. 1. Plot of molar conductivity as a functraalkylammoniums. The linear chain of alkyl tion of square root of concentration groups spread tetrahedrally from central nitroof tetraalkylammonium picrate. gen atom (left hand moiety of Fig. 2). The A : TAA6+pic phenolate oxygen of picrate ion (right. hand 9 TOMA*pic9 moiety of Fig. 2) is in contact with central part " CTMA+pic of ammonium ion.

",. "-,.

\

267

Table Limiting molar conductivity, ion-pair formation constant and ion size parameters. Cation TAA1 § TAA2 § TAA3 § TAA4 § TAA5 § TAA6 § TAA7 § TAA8 + TOMA § CTMA §

Ao/S cm2mo1-1

log

74.52 69.98 64.08 59.45 54.74 53.19 51.13 49.96 52.77 54.88

Kip

4.29 3.58 3.50 3.43 3.41 3.39 3.37 3.36 3.74 4.11

•A

rsA

rvdwA

4.4 5.8 6.0 6.3 6.3 6.4 6.5 6.6 5.4 4.6

2.43 2.72 3.21 3.73 4.48 4.79 5.35 5.62 4.89 4.45

2.86 3.41 3.82 4.12 4.42 4.69 4.92 5.11 4.74 4.45

:ructure of ion pair of tetraaikylammonium Lcrate calculated by MM2. Left hand moiety: Tetraoctylammonium cation. Right hand moiety: Picrate anion.

Closest approach The closest approach, a, reflecting the distance between the cationic charge of the alkylammonium and anionic charge of the phenolate, are plotted in Fig. 3 as a function of the total number of the carbon atom of the tetraalkylammonium ion. The closest approach, a, of tetramethylammonium (CH.).N § (AT.. = 4) is much smaller than other Q+ and the increment of a of Q§ by the increase m the number N c is very small for other Q§ These results support the structure of the ion pair shown in Fig. 2. That is, the closest approach might scarcely be affected by the increase in the number of the carbon atom except for tetramethylammonium ion. In the case of the CTMA + (N c = 19), only one alkyl group is long chain and others three alkyl groups are methyl groups. Consequently, it is quite reasonable that the value of a of CTMA + is much smaller than that of TAA + having a comparable number of carbon atoms and close to the value of the tetramethylammonium ion. The TOMA + ion which have one methyl group shows also relatively small value of a compared with Q+ having a comparable number of carbon atoms. 9

.

.~

q

.

t.,

.

268

Stokes

radius

The van der Waals radius, r V ..W , . was e s t i m a t e d from the partial molar volume by regarding the Q+ cation as spherical and is plotted in Fig. 3. By the assumption that the Stokes radius of Q+ of low m o l e c u l a r weight is almost the same as r V ..~N , the limiting molar conduc9 . . . tlvlty of t~ose cations m 1,2-dichloroethane were estimated. Thus the limiting molar conductivity of picrate anion was estimated as 35 S cm 2 mo1-1. By using this value, the limiting molar conductivities of other Q+ cations were evaluated. So called Stokes radius, r.., which corresponds to the radius of sphere having the same limiting molar conductivity as that of Q§ was estimated by using the Stokes equation 9Stokes radii, r~, of the tetraalkylammonium ions thus obtained are plotted in Fig. 3 as a9 function of N... The . t., van der Waals radms_ r V GJ.W _is also plotted in Fig. 3. The value of r.. Increases almost l i n e a r l y with the number of carbon atoms of Q+, N c. Although the increment of r V(I.. decr~.ases by the in. crease m the n u d g e r of carbon atoms, the value of r s still increase linearly. These findings support the structure of ion pair shown in Fig. 2. That is, the alkyl group of Q+ is u n f o l d e d and linearly spread outward. In contrast to the results of closest approach, r s, of asymmetric Q§ does not so differ fr6m that of the symmetric Q+ having a corresponding number of carbon atoms. These results indicate that the asymmetric Q§ also has the similar structure as the symmetric Q§

O

o< ~ 6 oo

-

~5

-

o

O

._= O I::1 O 0

4

-

O

~ 3r t/) 4.) o2

-

r..) 1

0 0

-

4

8

12

1

2

24

2

32

Number of carbon atoms Fig. 3. Plot of closest approach and ionic radii of tetraalkylammonium. O "a, Closest approach of ions A : rs, Stokes radius of cation * : r 9, van der Waals radius of cation Filled'~r~arks are asymmetric cations.

References

1 Y. Kikuchi, N. Takahashi, T. Suzuki and K. Sawada, Anal. Chim. Acta, 256, 311(1992). 2 Y. Kikuchi, Y. Nojima, H. Kita, T. Suzuki and K. Sawada, Bull. Chem. Soc. Jpn. 65, 1506(1992). 3 Y. Kikuchi, T. Suzuki and K. Sawada, Anal. Chim. Acta, 264, 65(1992). 4 Y. Kikuchi, M. Kubota, T. Suzuki and K. Sawada, Bull Chem. Soc. Jpn. 67, 2111(1994). 5 E. Renard and J. C. Justice, J. Solution Chem., 3, 633(1974) 6 R.A. Robinson and R. H. Stokes, "Electrolyte Solutions", Butterworths, London (1959)

journal of /91OLECUI~ R

LIQUIDS Journal of MolecularLiquids,65/66 (1995) 269-272

ELSEVIER

Ion-Pairing Effects on the $9Co Electric Field Gradients Relaxations of Tripositive Cobalt(Ill) Complex lons 1

in the NMR

Masayasu lida,* Toshie Nakamori, Yuri Mizuno, and Yuiehi Masuda ? Department of Chemistry, Faculty of Science, Nara Women's University, Nara 630, Japan 1"Department of Chemistry, Faculty of Science, Ochanomizu University, Tokyo 112, Japan Abstract 59Co NMR relaxation rates for the [Co(chxn)3] 3§ ( c h x n - trans-(1RC2R)-l,2diaminocyclohexane) and [Co(en)3] 3§ (en m ethylenediamine) ions were measured in the presence of sulfate or oxalate ions. IH relaxation rates for the chxn ligands in the same systems were also measured. The ratios of the 59Co relaxation rates to the 1H ones indicate that the 59Co electric field gradient of [Co(chxn)3] 3+ is appreciably decreased by the formation of the 1:1 ion pair with the sulfate ion. The difference of the concentration dependence of the 59(]0 NMR relaxations between the sulfate and the oxalate ions can be attributed to the faster change in the configuration of the 1:1 ion pair of the oxalate ion.

I. Introduction NMR relaxation method is a very powerful tool for the study of ionic interactions. 2 Many nuclei studied are with spin quantum number I > 1/2 and their relaxations are governed by quadrupole interaction between the nuclear electric quadrupole moment and the electric field gradient (efg) at the nuclear site. Under extreme narrowing condition, the longitudinal relaxation rate (RI) for the 59Co nuclei(l=7/2) can be expressed as

R1 = 2-~e2qQ !2Tc

(1) 491 h I where xe is the correlation time of the fluctuation of principal axis component of the efg tensor, and eq and eQ are the efg along the principal axis at the nuclear site and the quadrupole moment of the quadrupolar nucleus, respectively. As the 59(]0 NMR relaxation is dominated by the nuclear electric quadrupole relaxation mechanism and as the tripositive cobalt(Ill) complex ions strongly interact with anions, 59Co NMR relaxation is useful to see the effect of the outersphere complex on the relaxation rate. Previous studies for the various [Co(en)3] 3§ salts revealedthat the ion pairing with the sulfate ion significantly reduces the 59(]0 relaxation rate, while those with the succinate and tartrate ions slightly increase the relaxation rate. 3'4 However, the effect of the ion pairing on the 59Co efg did not explicitly appear in the [C~en)3] 3§ system. In the present paper, we report 59Co relaxation studies for the [Co(chxn)3] 3§ and [Co(en)3] 3+ in the presence of excess sulfate or oxalate ions. The chxn complex has 0167-7322/95/$09.50 91995ElsevierScienceB.V. All rights reserved. SSD! 0167-7322 (95) 00818-7

270

hydrophilic amino protons in the direction of the C3 axis and has bulky and hydrophobic cyclohexane-moiety in the direction perpendicular to the C3 axis. We can thus expect larger selectivity in the ion pairing with the anions than the en complex.

II. Experimental Section The complexes of A-[Co(chxn)3]CI3-SH20 and [Co(en)3]CI3.3H20 were prepared by the standard method. 5"6 The sodium sulfate and the potassium oxalate used were guaranteed reagents of Wako Pure Chemical Industries, Ltd. The 59C0 and IH NMR spectra were measured with a JEOL GX-270 FT NMR spectrometer operating at 64.1 and 270.1 MHz, respectively. The temperature of the sample solution was controlled at 27~q3.5 *C. The solvents used were I-t20 or D20(99%, for a comparison with the 1H NMR data) in the 59Co NMR measurement and D20(99%) in the IH one. The concentration of the cobalt(III) complex was adjusted to 5x10 "3 tool dm "3 in all cases. The longitudinal relaxation time(Tl) was determined by using the usual inversion-recovery method and the relaxation rate(R1) was obtained as the reciprocal T 1. For the I H relaxation measurements the solution was bubbled with argon gas for 10 min before each NMR measurement to remove oxygen gas from the solution. The chemical shift was measured from that for a 5x10 "3 mol dm "3 cobalt(Ill) complex solution containing no added salts. III. Results and Discussion The changes in the 59Co relaxation rates for [Co(chxn)3] 3+ with addition of sodium sulfate and potassium oxalate are shown in Fig. l(a). The result i n the presence of the sulfate ion is unusual since the relaxation rates of ions generally increase with increasing the salt concentration as seen for the oxalate ions. 2"4 On the contrary to the relaxation rates, the chemical shift changes in Fig. l(b) show that the sulfate and oxalate ions have similar effect. As the 59Co 400. ,',u,,,u,,,u,,,u,,,

10. ' ' ' u ' ' ' u ' ' ' u ' , , n , , ,

.9

=

35~.

9 9

300:

v~ 2 5 0 nr-"-

200

De

9

9

9

: .10 ~

9

o

D

:~ E -20 Q. ib " ~ -30 ~ 9 ~ o 9

oxalate sulfate o

15(> ~ : oo

o

-4(>

0.2

0.4

-60 0.6

0.8

1

' ." "

~

o

"

9

'''n'''n'''n'''=''' 0

c (Added Salt) / mol dm 3 (a)

oxalate sulfate

-50-

10(2" ' ' ' n ' ' ' n ' ' ' n ' ' ' n ' ' ' 0

o

oOo 9 0 0

0

o

9

0.2

0.4

(I_

,i

-

0.6

0.8

c (Added Salt) / mol dm "3 (b)

Fig. 1. Dependences of the 59Co longitudinal relaxation rates (a) and the chemical shifts (b) on the concentrations of the potassium oxalate or the sodium sulfate.

271

chemical shift generally changes to upfield with increasing the electrostatic interaction, 7 the present result indicates a gradual increase in the ionic interactions. Although the presence of 1:1 ion pairs is usually assumed for the analysis of the experimentally obtained NMR parameters, significant mounts of multiple ion-aggregates are present for the multivalent cations at higher anion ~ ' ' 1 ' ' ' 1 ' ' ' 1 ' ' ' 1 ' ' " concentrations. 1 Reasonable explanations have been 240 performed for the concentration dependences of the relaxation rates and the chemical shifts by assuming the ion-association model. 3"4'8 In order tOtheaSSignthe change in theofrelaxationthe ion "~ 2 0 0 j.~'dc rates to respective steps ~_ aSsociations, we calculated the concentration cC fraction for each species, [Co], [Co * A], and 160"1# oxalate [A * Co * A], by using the association o sulfate constants for the sulfate ion 9 and by considering the change in the ionic strength. It 120"~ was certain that the concentration of the added T ,,, I,.= I , , . I , , , I . . = = anions at the minimum of the relaxation rate 0.2 0.4 0.6 0.8 corresponds to the point where the population 0 of the major ion pairs switch from the 1:1 c (Added Salt) / mol dm 3 species to the 1:2 one. Fig. 2. 59C0 relaxation rates for [Co(en)3]3* The unusual relaxation rate for the [Co(chxn)313+SO42" ion pair is distinct when in the presence of the sulfate or oxalate ions. we compare the relaxation rates with the case of [Co(en)3]3+(Fig. 2) where both the sulfate and oxalate ions have very similar effects. It seems significant to estimate the effect of the ion pairing of [Co(chxn)3] 3+ on the parameters 1-4"1 "' ' I ' ' ' I ' ' ' I ' ' ' I ' ' of eq(efg) or x C in Eq. (1). The rotational correlation time of the complex ion can be .-. 1.2 estimated by the 1H NMR relaxations of the chxn ligands since the proton relaxation is mostly dominated by the magnetic dipolar oxalate interaction with intramolecular protons of the ligands. If the anisotropy of the rotational "" I o sulfate motion of the complex ion induced by the ion-9 O pairing is not appreciable, 10 the proton O relaxation rate(therotationalcorrelationtime of the dipolarinteractingaxis in the complex ion) 0.6 ~ o ~ is approximately proportionalto the correlation time for the main axis component of the efg at 0 . 4 1 , , , I , I , , , I , = I _ 59Co (the rotationalcorrelationtime of the C 3 0 0.2 0.4 0.6 0.8 1 axis of the complex ion). Thus the relative c (Added Salt) / tool drn "3 change in x C in Eq. (I) with the anion concentration can be estimated by the proton Fig. 3. The ratios of the 59Co relaxation rates relaxationtimes. W e then took the ratioof the to the tH ones for [Co(chxn)3]3§ depending 59Co relaxation rate to the IH one which is averaged for the 2 and 3 protons of the on the concentrations of the added salts. chxn ligand; the ratio can be regarded as

o

9

t

1

~~0.8

t

eee I

9

272 relative change in the effective efg caused by the ion pairing. The result is depicted in Fig. 3. The trend still shows similar profiles as shown in the 59Co relaxation rates and is roughly reflected by the change in the 59Co efg. It is clear that the 59Co efg is appreciably decreased by the 1:1 ion pairing with the sulfate ion and that it is increased by the further associations with this anion. The appreciable increase in the effective 59Co efg by the oxalate ion is also characteristic of the [Co(chxn)a] 3+ ions. For the consistency of the distinct features appeared in the [Co(chxn)3] 3+ system, a reasonable explanation is possible on the basis of Eq. (1) with considering the difference in the dynamic behavior of the ion pairs b e t w e e n [Co(chxn)3]3+SO42- and [Co(chxn)313+C2042". The sulfate ion should be located on the C3 axis of the [Co(chxn)3] 3+ ion in the ion pair and its life time is much longer than the rotational correlation time(xc). 3 In this case the C3 axis component of efg can be expressed as: eqMA = eqM+ e ~ (2) where eqMA is the effective efg for the ion pair, eqM the inherent efg for the metal complex ion, and eqA the efg caused by the anion. If the eqA is very effective on the eqM value in the chxn complex, the eqMA value is appreciably smaller than the eqM value. For the ion pair with the oxalate ion, on the other hand, the configuration of the complex ion and the anion is assumed to be quite flexible and the life time of the configuration (the results of the chemical shift measurements indicate that the oxalate ion interacts with the complex ion to a similar extent in average as the sulfate ion does) is much shorter than the rotational correlation time of the unpaired complex ion. In this case there is a slight correlation between the fluctuation of the field gradients of the unpaired complex ion and that of the anionpaired complex ion. Thus the 59Co relaxation rate can be expressed as: R I = Kt(eqM)2XM + (eqA)2XA] (3) where K corresponds to (2x2/49)(eQ/h) 2 in Eq. (1), xi is the correlation time of the fluctuation of the efg of each species. Equation (3) indicates an increase in the R 1 with increasing the field gradient caused by the counter anion irrespective of its sign. The increase in the effective efg by the formation of the triple ions for both the sulfate and the oxalate ions can also be explained from the same model. References 1 A preliminary report on this work has been published in Chem. Lett., 1994, 1433. 2 H.G. Hertz, Water, A Comprehensive Treatise, ed by F. Franks, Plenum Press, New York(1973), Vol. 3, Chap. 7. 3 Y. Masuda and H. Yamatera, J. Phys. Chem., 92, 2067(1988). 4 Y. Masuda and H. Yamatera, J. Phys. Chem., 87, 5339(1983). 5 S.E. Harnung, B. S. Serensen, I. Greaser, H. Maegaard, U. Pfenninger, and C. E. Schaffer, Inorg. Chem., 15, 219_3(1976). 6 J.B. Work, Inorg. Synth., Vol II, ed by W. C. Fernelius, McGraw-Hill, London, 1946, p. 221. 7 M. lida, Y. Miyagawa, and S. Kohri, Bull. Chem. Soc. Jpn., 66, 2398(1993). 8 A. Delville, P. Laszlo, and A. Stockis, J. Am. Chem. Soc. 103, 5991(1981). 9 M. Iida, M. Iwaki, Y. Matsuno, and H. Yokoyama, Bull. Chem. Soc. Jpn., 63, 993(]990). 10 As the conformation of the chxn ligand is rigid in the complex ion, the change in the IH-IH vectors of the ligand by the ion-pair formation would be negligible in the present discussion.

joumaJ of

I~IOLECULAR

LIQUIDS ELSEVIER

Journal of Molecular Liquids, 65/66 (1995) 273-276

Concentration Dependence of s 9Co Relaxation Rates of Tris(acetylacetonato)cobait(III) in Some Organic Solvents Mitsuhiro Kanakubo, Haruko Ikeuehl, and Gen P. Sat5 Department of Chemistry, Faculty of Science and Technology, Sophia University, 7-1 Kioicho, Chiyoda-ku, Tokyo 102 Abstract The 59Co longitudinal relaxation rates of tris(acetylacetonato)cobalt(III) in dichrolomethane and benzene were measured over the concentration range between 20 and 110 mol m-3 at several temperatures. The dependence of the relaxation rate on the temperature and the complex concentration is primarily attributable to the change in the viscosity of solution. The values of eQqlh were calculated from the concentration dependence of the 59Co relaxation rate by usmg the Debye-Stokes-Einstein equation and the Einstein relationship between molar volume and viscosity B coefficient. I. Introduction Tris(acetylacetonato)cobalt(III), [Co(acac)3], is suitable for the study of the complexsolvent interaction because it contains cobalt-59, one of the most sensitive nuclei for the NMR measurement. This diamagnetic complex is soluble in many common organic solvents, and its molecule is bulky and nearly spherical. We have studied the concentration dependence of the 59120 relaxation rate of [Co(acac)3] in acetonitrile, and concluded that the relaxation is attributable to the rotational reorientation of the complex and the macroscopic viscosity of the solution is the dominant factor in this dependence. 1 Busse 2a determined the 59Co relaxation rates of [Co(acac)3] in several solvents by using the dual spin probe technique. Busse and Abbott 2b conclude that the relaxation rate for cobalt in such an ostensibly symmetrical complex can be explained by small dynamic distortion from ideal symmetry that fluctuate owing to rotational reorientation in C6D6, C D s C O C ~ , and diglyme. If the relaxation is through the rotational reorientation, the relaxation rate, lIT1, is given by 1 3 ~ 9- 2 1 + 3 r2 "-TT= 1 0 / 2 ( 2 / - 1) ( 1 + ' ~ - ) (

eOq ~, )2rr

(1)

where I = 7/2, % is the rotational correlation time, and eQq/h is the quadrupole coupling constant The principal axis of efg coincides with the C3 axis of the complex. The asymmetry parameter, ~r will be practically zero because of the highly symmetrical arrangement of ligating oxygen atoms.

II. Experimental Commercial products of [Co(acac)3] were purified through column chromatography as previously described. 1 Reagent-grade CH2C12 obtained from Wako Pure Chemical Industries, Ltd., was purified through fractional distillation from 1:'205. The distillate was dried with Molecular Sieves 4A for more than 12 hours and then distilled again under a reduced pressure. 0167-7322/95/$09.50 91995 Elsevier Science B.V. All fights reserved. SSD10167-7322 (95) 00819-5

274

Spectroscopic-grade C6H6 purchased from Dojindo Laboratories was dried with Molecular Sieves 4A and distilled under a reduced pressure. Dichloromethane-d2 (99.95% up D) obtained from Aldrich Chemical Co., Inc., and benzene-d6 (99.6% up D) from Wako Pure Chemical Industries, Ltd., were used as received. The molalities of the samples are listed in Table 1. The amount concentrations of the complex solutions were calculated at each temperature from the molalities and the partial molar volumes of the components at infinite dilution. For the CH2C12 3 and C6H6 4 solutions, all the relevant partial molar volumes are available. For the C6D6 solutions, 5 the partial molar volume of the solute was assumed to be the same as that in C6H6. For the CD2CI 2 solutions, the partial molar volume of the solvent was replaced by that of CH2C12 and the partial molar volume of the solute by that in CH2CI2. The inversion recovery method was used for measuring the relaxation time. The instruments and the procedure were described previously. 1

Table 1. The molalides of [Co(acac)3] of the sample solutions (mmol kw 1) Sample Solvent number CH2CI2 CD2CI2 C6H6 C6D6 1 15.3 20.5 22.8 29.6 2 30.6 39.1 43.1 55.7 3 46.2 56.7 68.4 86.5 4 62.0 74.9 89.2 118.3 $ 77.6 112.7

280

!

260

"7

279.2 K

289.0 K

240

"7,

298.8 K

220

200

303.7 K

180

,

0

III. R e s u l t s a n d D i s c u s s i o n

The longitudinal relaxation rates are presented in Tables 2 and 3. At each temperature, 1/T1 was a linear function of the amount concentration c of the complex (e.g., Fig. 1),

i

40

, 80

120

c ~ n ~ l rrga

Fig. 1 I / T l as a function of c (solvent, C I-L2C12)

Table 2. The 59Co Lon~tudinal Relaxation Rates of [Co(acac)~] in CHTCI7 andCI~Cl~ a) (sd) Sample CH7C12 CD2C12 number 279.2 289.0 298.8 3(13.7 279.2 289.0 1 254(4) 231(1) 209(2) 196(1) 261(2) 235(2) 2 259(3) 231(1) 210(1) 1970) 265(2) 238(1) 3 262(3) 235(2) 213(1) 200(3) 270(1) 242(2) 4 264(2) 237(2) 214(1) 203(2) 272(1) 243(1) $ 268(2) 239(2) 217(2) 205(3) a) Each figure is the average of more than 4 runs. The 95% confidence limit is given m parentheses.

293.9

223(2) 226(1) 230(1) 230(1)

Table 3. The 59Co Longitudinal Relaxation Rates of [Co(acac)3 ] in C6H6 and C6D6 a) (s-l)

Sample

C6H6

r

number 284.1 289.0 298.8 308.6 284.1 298.8 1 366(2) 337(2) 289(2) 253(1) 388(2) 307(1) 2 373(2) 345(2) 294(1) 256(2) 395(2) 310(1) 3 381(2) 351(2) 298(2) 262(1) 406(3) 318(2) 4 386(2) 355(3) 303(2) 263(2) 420(2) 328(2) 5 392(2) 361(2) 307(1) 267(2) a) Each figure is the average of more than 4 rims. The 95% confidence limit is given in parentheses.

308.6

265(3) 270(2) 275(2) 282(3)

275 Table 4. IITI | and B' for [Co(-~--~-)3]--CH2C12and-CD2Cl2 systems.a) CH2C12 T/ K (1/TI| / sq B' / mol"t dm3 B b) / mol-t dm3 279.2 2510) 0.67(0.15) 0.77 289.0 227(2) 0.51(0.08) 0.72 293.9 298.8 2060) 0.49(0.07) 0.67 303.7 193(2) 0.65(0.13) 0.65 a) The 95% confidence limit is given in parentheses. b) Values of B are obtained from Ref.9 by linear interpolation. Table 5. llTl**and B' for [ C o ( a c a c ) 3 ] ~ md -C-O)6 systems a)

c~

T /K

B,I tool-ldm 3

(IITIco)/ s-I

284.1 360(2) 0.91(0.06) 289.0 332(2) 0.91(0.09) 298.8 2860) 0.78(0.06) 308.6 249(1) 0.75~0.07) a) The 95% confidence limit is given in parentheses.

( I +B' c)

258(1)

232(|) 22o0)

B' 1 moi '-Ia m 3

2980) 259~I)

0.89(0.05) 0.83(0.05)

375(2)

,

CD~I2 B' I mol"1dm3

0~0.0s~ 0.51(0.04)

0.48(0.05)

c~

(I/TI**)I S-l

which is expressed by 1 1 "-~1= T1|

(I/TI,**)/ sq

1.04(0.04)

(2)

with 1//'1'* being the relaxation rate at infinite dilution, and B' a coefficient dependent on the solvent and the temperature. These values are given in Tables 4 and 5. Since the rotation of the complex molecule will be isotropic as in the cases of several tris(didenate)cobalt(III) complexes, 6 and the molecule can be regarded as a sphere, we assume that the rotational correlation time is expressed by the Debye-Stokes-Einstein equationT, 8

~=FY-

Vrn

9

(3)

Here, Vr the volume of the spherical molecule, r I is the viscosity of the solution, k is the Boltzrnarm constant, and T is the thermodynamic temperature. This equation is based on the theory of rotational Brownian motion of rigid spheres in a viscous fluid. Viscosities of the [Co(acac)3]--CH2Cl2 9 and - - C H 3 C N 10 systems at a given temperature increase linearly with the complex concentration for c < ca. 100 tool m-3: r/= r/0 ( 1 + B c )

,

(4)

where r/0 is the viscosity of pure solvent. Substituting Eqs. (3) and (4) into Eq. (1), and identifying the resultant expression with

Eq. (2), we see B'= B

and

3~;2 2 / + 3 e Q q )2 Vr r/o 1,1| = 1--0-/2 ( 2 / - 1) ( . . k T "

(5)

1

(6)

In the case of the acetomtrile solutions, 1 B' agreed well with B. As seen in Table 4, the B' values for the dichloromethane solutions roughly agree with the corresponding B values,

276

but the agreement is not as good as in the case of acetonitrile. Such direct comparison is impossible for the benzene solutions, owing to the lack of the viscosity data. An experimental valueof 111"1"*gives the product(eQqlh )2Vr with Eq. (5). The value of Vr may be estimated by resorting to Einstein's relation as a first approximation Vr = B / 2.5, (7) into which we substitute B' for B, ignoring the difference between them. Thus we have

eQq_4{2.5 h

-

10 P ( 2 1 - 1) 3x z

2 I+

3

k T r/0

1 } B' TI |

(8) "

The values of the right-hand side of Eq. (8) are included in Table 6 as Y along with 11o. In acetonitrile the Y value was 4.8 MHz at 298.8 K (calculated from the data of ref. 1). Busse 2a reported a value of 4.2 MHz for eQq/h by measuring the relaxation times of 59Co and 13C of this complex in C6D6 at 298 IC We see that the Y values for C6H6 and C6D6 are close to Busse's value. The Y value in dichloromethane was appreciably higher than those in the other solvents (eQq/h = 4.5 MHz for CDsCOCD3 and diglyme2a). This discrepancy seems to indicate the failure of Eq. (3) and/or contribution of some relaxation process(es) other than rotational quadrupolar mechanism possibly owing to specific interactions such as observed in chloroform. 12 Table 6. Values of Yfor [Co(acac)3]-CH2CI2, ~ , and -C6D6 systems c.~c12 c~ TIK r/oa) I mPa s YIMHz rlob) I mPa s YIMHz 279.2 0.4902 4.8 284.1 289.0 298.8 303.7 308.6

0.4481 0.4059 0.3849

5.5 5.8 5.0

0.7456 0.6921 0.6006

4.0

0.5259

,

c~ rlob) I mPa s

YIMHz

4.0

0.~

3.7

4.4

0.~

4.1

4.6

0.5586

4.3

a) Values of r/0 are obatainedfrom Ref.9 by linear interpolation. b) Valuesof 1'/0are obatainedfrom Ref.11 Reference

1 M. Kanakubo, H. Ikeuchi, and G. P. Sat6, J. Magn. Reson., Ser. A, in Press. 2 (a) S. C. Busse, Ph.D. Thesis, Montana State University(1986). (b) S. C. Busse and E. H. Abbott, lnorg. Chem., 28, 488(1989). 3 S. Okuno, private commumcation. 4 S. Sato, private communication. 5 J.A. Dixon and W. Schiessler, J. Am. Chem. Soc., 7 6, 2197(1954). 6 Yuichi Masuda and Hideo Yamatera, J. Phys. Chem. 9 2, 2067(1988). 7 A. Einstein, Ann. Phys. Leipzig, 1 9, 371 (1906). 8 P. Debye, "Polar Molecule," traslated by T. Nakamura and K. Sato, Kodansha, Tokyo (1976), p.98. 9 R. Sato, private communication. 10 H. Ikeuchi, M. Takano, Y. Kimata, H. Matsuoka, and G. P. Sat6, Abstracts of the Chemical Society of Japan, 59th National Meeting. Kanagawa, Abstract 11=328(1990). 11 J.A. Dixon and W. Schiessler, J. Phys. Chem., 5 8, 430(1954). 12 J. F. Steinbach and J. H. Burns, J. Am. Chem. Soc., 8 0 , 1839(1958).

journal of

~IOLECULAR

LIQUIDS ELSEVIER

Journal of Molecular Liquids, 65166 (1995) 277-280

Mechanistic Study of Oxidation Reactions of Hydroquinone, Catechoi, and L-Ascorbic Acid by Dicyanobis(l,10-phenanthroline)iron(lll) in Dimethyl Sulfoxide Hideo D. Takagi, Nobuyoshi Kagayama, Mitsuru Matsumoto, Toshiyasu Tarumi, and Shigenobu Funahashi Laboratory of Analytical Chemistry, Faculty of Scienece, Nagoya University, Chikusa, Nagoya 464-01, Japan Abstract Reactions of hydroquinone, catechol, and L-ascorbic acid with dicyanobis(1,10-phenanthroline)iron(M) were studied in dimethyl sulfoxide (DMSO). Application of the Marcus theory to the reactions of catechol and hydroquinone provided the electron exchange rate constant for the Fe(III/II) couple in DMSO. The self-exchange rate constant for the ascorbic acid/radical couple was estimated for the first time in DMSO. The one electron-oxidation process of L-ascorbic acid in an aprotic solvents such as DMSO may be completely different from that in aqueous solutions.

I. Introduction Reactions of ascorbic acid have been intensively studied in relation to the behavior of this familiar compound in biological systems. 1,2 Most of the studies treated ascorbic acid as an simple outersphere reducing reagent, until Creutz published an article concerning the complexity of the reaction pathways of ascorbic acid and related radicals. 3 The authors recently demonstrated that the oxidation reactions of ascorbic acid in acidic aqueous solutions are not adiabatic from the volume analysis of the reactions. 4 As the non-adiabaticity of the ascorbate reactions implies the involvement of the proton dissociation and/or ring-closure processes at the rate-determining step, it is expected that the reactions of ascorbic acid in dipolar aprotic solvents such as dimethyl sulfoxide (DMSO) are adiabatic. 5 The electron exchange rate constant of the iron(IN) complex in DMSO was estimated from the cross reactions with hydroquinone and catechol, which was compared with the rate constant obtained electrochemically. The mechanism of the ascorbic acid oxidation reaction in DMSO is discussed based on the Marcus theory.

II. Experimental DMSO (Wako Pure Chemicals Inc.) was distilled twice from 4A molecular sieves(Wako) under reduced pressure. Dicyanobis(1,10-phenanthroline)iron(II) [Fe(CN)2(phen)2] was synthesized by mixing 0.03 mol of phen and 0.01 mol of ammonium iron(II) sulfate hexahydrate in 400 cm 3 of water, followed by the addition of KCN (0.15 mol). The resulting crude crystals were then dissolved in 30 cm 3 of concentrated sulfuric acid followed by the addition of ldm 3 of water. Dicyanobis(1,10-phenanthroline)iron(III) nitrate was obtained by the oxidation of corresponding iron(II) complex with concentrated nitric acid. The perchlorate salt was obtained by the addition of sodium perchlorate to the nitrate solution. Analytical grade hydroquinone, catechol, and L-ascorbic acid (Wako) were used without further purification. A Shimadzu UV-265FW spectrophotometer was used for the determination of stoichiometry of the reactions. Kinetic measurements were carried out with excess amount of reducing reagents by using a Unisoku RA-401 stopped-flow apparatus. Electrochemical measurements were carried out by a BAS-100B Electrochemical Analyser. 0167-7322/951509.50 91995 Elsevier Science B.V. All rights reserved. SSD! 0167-7322 (95) 00827-6

278

III. R e s u l t s The stoichiometry of the reactions was determined by the spectrophotometric titrations. It was observed that each mole of reductants reduced two equivalent moles of [FeIII(CN)2_ (phen)2] +. The overall reaction was, therefore, expressed by eq. 1 for each reaction: 2[FelII(CN)2(phen)2] + + H2A 2[FeII(CN)2(phen)2] + quinone or dehydroascorbic acid

(1)

where H2A represents hydroquinone, catechol, and ascorbic acid. In dipolar aprotic solvents such as DMSO, proton dissociation from H2A is negligible. The dependences of conditional first-order rate constants on the concentrations of reductants at various temperatures are shown in Fig. 1 A, B, and C for the reactions of hydroquinone, catechol and ascorbic acid, respectively. As the reactivity of the radicals formed as intermediates is expected to be rather high, consecutive one-electron transfer reactions are suggested as follows: 6 k [Felll(CN)2(phen)2] + + H2A

~

[Fell(CN)2(phen)2]

+

H2A .+

(2)

fast [Felll(CN)2(phen)2] + + H2A .+ [Fen(CN)2(phen)2] + quinone or dehydroascorbic acid

(3)

Therefore, kobs was given by eq. 4: /Cobs = 2k[H2A]

(4)

The rate constants, k, and the corresponding activation parameters are summarized in Table 1.

d

40 4 3.

I,,

A

d

"7, 30

B

$0,

40.

c

2.

0

b

i i ~ s o 103[hydroquinonel/moi dm-3

C

d

30.

,,~ o 20

.

~

o

.

.

. s ~o ~s 103[catechol]/moi dm "3

2o.

01}

1 i ~ ~ 103[ascorbic actd}/mol dm-3

F i g u r e 1. Dependence of the conditional first-order rate constants on the concentrations

of reductants (A: hydroquinone; B" catechol; C" L-ascorbic acid) at various temperaures (a: 293K; b: 298K; c: 303K; d: 308K). An attempt was made to obtain the electron self-exchange rate constant for the [Fe(CN)2(phen)2] +/0 couple by an electrochemical method. Real space Laplace analysis6, 7 was used for the chronoamperometric response of 7.05 x 10 -4 M (M = mol dm -3) solutions of the iron(Ill) complex with 0.1 M tetra(n-butyl)ammonium perchlorate as supporting electrolyte. A glassy carbon working electrode with 3 mm diameter was used for the measurements. The ButlerVolmer plot 7 gave an excellent straight line, and the electrochemical self-exchange rate constant was obained to be 1.2 x 10-2 cm s-1 from the In k value at the zero over-potential. From the

279 Table 1. Activation Parameters for the Oxidation Reactions of Various Reductants by Dicyanobis(1,10-phenanthroline)iron(III) in DMSO

Reductants Hydroquinone Catechol Ascorbic acid

k/dm3mol-ls-1 (298K) 1.41 x 102 7.1 3.7 x 103

AH*/kJ mo1-1 46 :t: 1 55:1:1 60 + 3

AS*/J mol-lK -1 -49 + 1 -45 :!: 1 23 + 11

classical Marcus theory, 8 the relationship between electrochemical, kel, and homogeneous, kex, exchange rate constants is derived as follows: kex ] kex0 = ( kel ] kelO)2

(5)

kex0 and kel 0 are the diffusion-controlled rate constants for homogeneous and heterogeneous reactions, respectively, which can be roughly estimated from the following equations. 9 kex0 = 8rdgRNA,

kel0 = 2D/~R

(6)

where D, R, and NA are the average diffusion coefficient of the exchange couple, the distance of the closest approach between the reactants, and the Avogadro number, respectively. Setting the R value to 1200 pm, kex0 and kel 0 are 3.2 x 109 M-ls -1 and 13 cm s -I, respectively, by using 2.1 x 10-6 cm 2 s-1 as D, which was also estimated from the electrochemical measurements. Finally, the homogeneous self-exchange rate constant, kex, was estimated to be 2.6 x 103 M-Is 1 from eq. 5. The redox potential of [Fe(CN)2(phen)zj ~-.~+/0 couple was obtained in DMSO as 0.466 V vs NHE, assuming the redox potential for the ferrocene/ferricinium couple being 0.400 V vs NHE. 10 IV. Discussion Catechol and hydroquinone are well known outersphere reducing reagents for the reactions with inert metal complexes. 11 The self-exchange rate constant of 2 x 106 M - l s -1 for H2Q+./H2Q (H2Q represents catechol and hydroquinone) couple was obtained from the direct measurements using pulse radiolysis. 10 The electron self-exchange rate constant for the [Fe(CN)2(phen)2]+/~ couple was calculated from the cross reactions with catechol and hydroquinone from the Marcus theory. As the effect of electrostriction is minimal for +1/0 redox couples, 10 the redox potentials reported for the aqueous reactions at pH 0 (1.04 V and 1.12 V for hydroquinone and catechol, respectively) were used without corrections for the discussions below. 12 Ignoring the work terms, the self-exchange rate constant for the [Fe(CN)2(phen)2] +/0 couple was calculated to be (2.8 + 2.5) x 107 M-ls -1, which may be compared to the self-exchange rate constants for the tris(1,10-phenanthroline)iron(III/II) and hexacyanoferrate(III/II) couples. 13,14 Electrochemically obtained heterogeneous rate constant, however, was much smaller than that obtained for the homogeneous reactions. The difference may be attributed to the fact that the electron exchange rate of the [Fe(CN)2(phen)2]+/0 couple is fast enough to exceed the application limit of eq. 5. It was suggested that the electrochemical rate constants reach a diffusion-controlled limit significantly below the expected value, i.e. at nearly 1 cm s-1.15 If this applies, the corresponding homogeneous rate constant may be 1 x 106 M-ls-1, which is close to that estimated from the cross relation. The value of 2.8 x 107 M-ls -1 will be used here as the upper limit of the exchange rate constant for the [Fe(CN)2(phen)2] +/0 couple.

28o The complexity in the oxidation reactions of ascorbic acid originates from the uncertainty whether the redox potential reported to date corresponds to the formation of the open-chain radical or not. 3 Considering Scheme 1, the redox potential of the ascorbic acid/radical couple may be expressed by eq. 7 with the use of the equilibrium quotient, K, for the formation of the bicyclic radical from the open-chain ascorbic acid radical: Scheme 1 .~~

O 140

E 0 = E' - (RTIF) In K

o

o

+ H+

14o

(7)

where E' and E0denote the redox potentials between ascorbic acid/open-chain radical and between ascorbic acid/bicyclic radical, respectively. If the oxidation reaction of ascorbic acid involves the ring closure l~rocess within the radical, the redox potential between ascorbic acid/open-chain radical, E , may be higher than the reported value (E 0 = 0.99V in aqueous solution), taking into account the K value larger than unity. The electron exchange rate constant estimated by the Marcus cross relation, therefore, may have been underestimated as pointed out by Sisley and Jordan. 5 In dipolar aprotic solvents such as" DMSO, the dissociation of a proton following the ring closure within the ascorbic acid radical may not be a preferred process. Therefore, the redox potential so far reported (0.99 V) may be taken as a lower limit. Indeed, the cyclic voltammogram of ascorbic acid in DMSO showed an anodic p e a k at 0.64 V vs ferrocene/ferricinium couple, which corresponds to 1.04 V vs N.H.E. 1 0 Using 0.99 V as the redox potential, a value of 1 x 109 M-1 s-1 was calculated as a lower limit of the self-exchange rate constant for the ascorbic acid/open-chain radical couple from the Marcus cross relation. The estimated exchange rate constant here is much larger than the one reported to date for the aqueous reactions. In conclusion, the oxidation reaction of ascorbic acid in DMSO proceeds through a simple adiabatic process, while non-adiabaticity including the ring closure process is suggested in aqueous solutions. 4 References 1 K. Kustin and D. L. Toppen, Inorg. Chem., 12, 1404(1973). 2 E. Pelizzetti, E. Mentasti and E. Pramauro, Inorg. Chem., 15, 2898(1976). 3 C. Creutz, Inorg. Chem., 20, 4452(1981). 4 N. Kagayama, M. Sekiguchi, Y. Inada, H. D. Takagi and S. Funahashi, Inorg. Chem., 33, 1881(1994). 5 M.J. Sisley and R. B. Jordan, Inorg. Chem., 31, 2137(1992). 6 E.D. Moorhead, V. E. Dauyotis and M. M. Stephens, Anal. Chim. Acta, 162, 161(1984). 7 A.J. Bard and L. R. Faulkner, E l e c t r o c h e m i c a l M e t h o d s (John Wiley & Sons, Inc.,1980) 8 R.A. Marcus, Electrochim. Acta, 13, 995(1968). 9 R.A. Marcus, J. Chem. Phys., 43, 679(1965). l0 R. R. Gagne, C. K. Koval and T. J. Smith, J. Amer. Chem. Soc., 101, 4571(1979). 11 J. W. Herbert and D. H. Macartney, J. Chem. Soc., Dalton Trans., 1986, 1931. 12 S. Steenken and P. Neta, J. Phys. Chem., 83, 1134(1979). 13 H. Doine and T. W. Swaddle, Inorg. Chem., 31, 4669(1992). 14 H. Doine and T. W. Swaddle, Can. J. Chem., 66, 2763(1988). 15 T. Saji, T. Yamada and S. Aoyagi, J. Electroanal. Chem., 61, 147(1975).

joumaJof

~OLECULAR

LIQUIDS ELSEVIER

Journal of Molecular Liquids, 65166 (I 995) 281-284

Molecular Orientation in Fluids near Solid-Liquid Interface as Studied by the Density Functional Method Yasuhiro Teramoto

and Koichiro Nakanishi

Division of Molecular Engineering and Department of Industrial Chemistry Kyoto University, Sakyo-ku, Kyoto 606-01, Japan Abstract T h e density functional method as applied by Tarazona to deal with classical fluids has been used to calculate the orientation of triatomic molecular fluids near the solid-liquid interface. T h e results give valuable suggestions about the effect of molecular shape on the orientation of

real molecules such as liquid crystals near the solid-fluid interface. I. I n t r o d u c t i o n

The density functional(DF) method is one of the most promising tools for the calculation of structure and orientation in heterogeneous fluids near phase boundaries.

Among many

proposals for the application of DF method, that by Tarazona 1,2 has been frequently used in the studies of interfaces and phase transitions in hard sphere systems. The purpose of the present study is to apply the Tarazona method to the fluid systems of polyatomic molecules, thereby eliminating some disadvantages inherent to his method. We formulate a weighting function by the intermolecular potential alone 3'4. Another improvement is with the use of the equation of state. A volume-corrected hard-sphere equation of state is used as the equation of state for polyatomic molecular fluids. In the present study, the DF method is used to clarify the molecular orientation in fluids near two-dimensionM solid-liquid interface. Our molecular model is the triatomic molecule shown in Figure 1. We expect that the results of the present study will give valuable information about the effect of molecular shape on the orientation of real molecules such as liquid crystals neaz the solid-fluid interface. II. M e t h o d

of Calculation

The present method is based on that proposed by Tarazona.

Since it is well described

elsewhere 5'6 for two-dimensional system, we will not repeat it here. An ultra-simplified account will be given here for three-dimensional system. We start from the formulation of the grant potential f / o f the system, 0167-7322./95/$09.50 9 1995 Elsevier Science B.V. All righet reserved. SSD!0167-7322 (95) 00916-7

"S

>

Figure 1: The model of a triatomic molecule and the orientation vector: Bond angle(left), atomic diameters(center) and orientation vector(right).

/,

f~[p]

F[p(z, 0)] - J dzdOp(z, 0)[# - r

0)]

(1)

where z is the distance between the center of gravity of the molecule of interest and the interface, 0 is the angle between the molecular orientation vector and the perpendicular vector to the interface as shown in Figure 1, # the chemical potential, and r the potential function between molecule and interface. F is the Helmholtz free energy. Combination of Eq.(1) with 6~

,--: pu

=

(2)

o

leads to

6F~

mp(~, o) = -/3~:(z,O) +/3[# 6s

6/,(z,o) =

:[~(z)]

~/~(z') 6p(~, 0)

- r

O)]- ln[A2A,]

+ J ez'dO'p(z', o'):, ~ ( z ' )

= 2~:l do' W(Iz - z'l, o', o) .1

(3)

(4)

(5)

and the density p(z, O) can be obtained by the self-consistent solution of Eq.(3). III. M o n t e Carlo S i m u l a t i o n Comparison is attempted between the results of density distribution calculated by the DF method and those from Monte Carlo(MC) simulation. The present MC simulations have been

283

performed with usual Metropolis scheme. The basic cell is of two dimension where the cell length is Lz and Ly, the solid surface is in the z direction and the periodic boundaries are considered in the y direction. The basic cell contains N molecules. N is 100 in the present calculation. L, is fixed to be 15a and Lv is adjusted so that Ly = N / L , p where p is the number density. The solid surface is assumed to be a hard sphere. The MC sampling has been performed 3 x l0 s steps for equilibration and further 2x 106 steps for averaging. IV. R e s u l t s a n d D i s c u s s i o n

Results have been obtained for the density distribution, intermolecular excluded volume effect at the interface, the relation between molecular orientation and bulk density, and the relation between molecular orientation and diameter. Only the first one will be discussed here in detail. As a typical example, calculation has been made for density p(z,8) in the condition that bulk density p=0.5, d/a=0.2 and the bond angle a=90 ~ In Figure 2 are shown the results ot the present DF method(left) and Monte Carlo simulation(right).

p(x,o)

0.3

0.25

0.5

o.~

.~

o~

0.30.2

. . . .

O. 05

o.~

o z z

o

o

0

0

Figure 2: Comparison of the DF results with the Monte Carlo simulation: DF(left) ant MC(right). It is seen from the figure that the DF results give a smooth density distribution. Althoug~ the first peak of the density calculated by the DF method is higher than that obtained b] the MC method, the density p vs. tilt angle 0 relation shows qualitative agreement for earl approach as seen in Figure 3(upper). As an application of this kind of calculation, we refer to the case of liquid crystals. Okan( et al. T have discussed the role of excluded volume effect on the molecular orientation in th~ interface involving liquid crystals. They used spherocylinder systems, but considered only limited case of orientation.

,.,

0.4

-9 -

/

'....

. . . . "_ _ s - % ~[: : ,-,,

:

0.2

Ii

/. ]

(b~ ~

p

i

1

',

ts 0.2

0.5

0.5

| .......

0

0.6

=

is ~ . |

100

0

0

30

60

90

(~ (,)

0.)

(')

Figure 3: The molecular density p(solid line) and the length h(dotted line) between the center of the mass of molecule and the surface as a function of the tilt angle from the DF method: Molecule with a = 90~ and molecule with cr = 180~ Molecular density from MC calculation(broken line) is also given for comparison. V. Conclusion

We have successfully used the classical density functional method to investigate the behavior of triatomic molecules near interface. Although perfect agreement with a Monte Carlo simulation cannot be achieved, we have obtained interesting and important information on the surface-molecule excluded volume effect. Acknowledgments

We thank Prof. X. C. Zeng, University of Nebraska, for critical reading of the manuscript and helpful advice. References

[1] Tarazona, P., 1984, Mol. Phys., 52, 81. [2] Tarazona, P., 1985, Phys. Rev. A31, 2672. [3] Poniewierski, A. and Holyst, R., 1990, Phys. Rev. A41, 6871. [4] Sokolowski, S., 1991, J. Chem. Phys., 95, 7513. [5] Curtin, W.A. and Ashcroft, N.W., 1985, Phys. Rev. A32, 2909. [6] Evans, R., 1979, Adv. Phys., 28, 143. [7] Okano, K., 1983, Jpn. J. Appl. Phys., 22, L343.

journal of

MOLECULAR

LIQUIDS ELSEVIER

Journal of MolecularLiquids, 65/66 (1995) 285-288

The Stability and Dynamics of Clathrate Hideki

Hydrates

Tanaka

Division of Polymer Chemistry, Kyoto University, Sakyo, Kyoto

Graduate School 606-01 J a p a n

of

Engineering

Abstract The t h e r m o d y n a m i c

stability of a clathrate hydrate encaging nonspherical ethane molecule has been investigated by examining the free energy of cage occupancy. A generalized van der Waals and Platteeuw theory is extended in order to treat rotational motions of guest molecules in the clathrate hydrate cages.

I.

Introduction

Gas hydrate consists of guest and the host water molecules which form a hydrogen bonded network. The clathrate hydrate is stable only when guest molecules exist in the cages of the hydrate. The thermodynamic stability of the clathrate hydrates has been explained by van der Waals and Platteeuw (vdWP). 1 With some empirical parameters, this theory is applicable over a wide temperature r a n g e . 2,3 However, its application sometimes predicts an incorrect phase behavior for large guest species. We generalized the original vdWP theory for the hydrate encaging a comparable size of a molecule with the larger c a g e ? ,5 It was revealed that this generalization is very important to account for the discrepancy between the prediction from the original vdWP theory and the experimental result. In the present study, we examine the magnitude of the anharmonic contribution from the host water molecules and also the anharmonic free energy arising from the rotational degrees of freedom of guest molecule by Monte Carlo (MC) simulation with the Gaussian statistics. T h e o r y a n d method The water-water intermolecular interaction is described by the TIP4P potential. 6 The ethane molecule consists of two interaction sites, each of which interacts with each other via Lennard-Jones (LJ) potential. 7 The reference of ethane molecule is spherical and is of LJ type interaction with size and energy parameters of 4.18 A and 1.72 kJ/mol, s The LJ parameters for methyl group of ethane are 3.78 A a n d 0.866 kJ/mol. For the water-guest interaction, the Lorentz-Berthelot rule is assumed. The interaction potentials for all pairs of molecules are truncated smoothly at 8.655 A. 9 A generalization of the vdWP theory was made to deal with the coupling of the host m o l e c u l a r motions with those of guests. The original theory and its generalization are detailed elsewhere. 4's We obtain the potential energy minimum structure of clathrate hydrates encaging spherical guest molecules. The potential energy is expanded to a polynomial of the displacement from the equilibrium position. The expansion is truncated at the quadratic order for the small displacement. This truncation is not appropriate for the hydrate of a nonspherical guest molecule because it rotates with a low energy barrier and the anharmonic part of the potential is not negligible. II.

0167-7322/95/509.50 91995 ElsevierScience B.V. All fights reserved. SSDi 0167-7322 (95) 00906-X

286 The anharmonic contribution to the f r e e energy is evaluated by a t h e r m o d y n a m i c integration method with a reference system of harmonic oscillators. This free energy difference between the real and the reference system A - Ao is given by A - Ao = - k T In < exp[-13(O - Oo)] >o,

(1)

where 9and Oo are the real and reference system potential, respectively and the average < >o is taken over the reference harmonic oscillators. Since the potential of the harmonic oscillator system having the potential minimum value Uo is written by

Oo = Uo + ~ o~ q ?/2,

(2)

the probability for the system (ice or empty hydrate) to have a set of normal mode coordinates q =(q~,q2 . . . . q e N . 3 ) is given by P ( q ) = l-li (13to12/2n) l tz exp(-13 ~i2 q ?/2).

(3)

This method provides a much more efficient sampling way for a harmonic system than the usual Metropolis scheme. ~~ This is because the distribution of the amplitudes is the Gaussian and each mode is independent of other modes; the generated configurations have no correlations. In the case of occupation of nonspherical ethane molecules, the reference system is chosen to be the hydrate of spherical guest molecules. The orientations of the guest ethane molecules in the real system are assigned randomly.

discussion I I I . Results a n d The guest molecular motions are examined by performing a molecular dynamics (MD) simulation. The linear and angular velocity correlation functions of guest ethane are depicted in Figure 1 together with their power spectra. The spectra of the translational motions have distinct peaks which shift to lower frequency region with decreasing the temperature. The rotational spectra have peaks at about 0 cm -l. There are small peaks in non-zero frequency region indicating that the rotation of ethane is somewhat hindered. The rotational motions have been studied for mostly polar and some of apolar molecules. 3 Those suggest that guests molecules rotate rather freely, which agrees with our observation. The anharmonic free energy is evaluated for empty hydrate and cubic ice (ice Ic). The calculated free energy due to the anharmonic potential energy surface is given in Table 1. The anharmonic contribution to the free energy of empty hydrate is the same as ice, which is as large as -0.61 kJ per mole of water. The free energy differences between the real and the reference clathrate hydrates are also given in Table 1. The anharmonic free energy change from the spherical guests with harmonic approximation to the nonspherical guests is -0.25 kJ /mol. Thus, we can calculate the total free energy change upon accommodation of nonspherical guest molecules. The dissociation pressure Pd at 273.15 K is obtained from the intersection between the chemical potential curve and the horizontal line corresponding to the difference in chemical potential between ice and empty hydrate ~i-gt~ which is calculated to be - 0.72 kJ/mol, using the previous calculation and the anharmonic free energy obtained in the present study. The chemical potential differences between occupied and empty hydrates are plotted in Figure 2 for the nonspherical (harmonic + anharmonic terms) and the spherical (harmonic term) guest molecules together with that calculated from the original vdWP theory.

287

1

0.5 .5

0 -0.5 0

250

500

0

time/2.5fs

50 100 150 frequency/cm -1

Figure 1, The translational (thin) and rotational (heavy) velocity autocorrelation functions and power spectra at 273.15 K(solid line), 223.15 K(dashed line) and 173.15 K(dash-dot line). Left (time correlations), right (power spectra).

-0.2

I~~I

~-0.4 9

I

I

I

"

~

~-o.6 b \?, -1

I

F_

0

.

.

.

.

'

.

~ '

2

-.............. '

-''--

4

p/O. 1 MPa

1

6

Figure 2. Dissociation pressure of ethane hydrate at 273.15 K. Solid, dashed, and dash-dot lines show the dissociation pressures for the nonspherical guest evaluated by anharmonic and harmonic free energy, for spherical guest molecule evaluated by only harmonic free energy, and for spherical guest according to the original vdWP theory, respectively. The horizontal lines show the chemical potential difference between ice and empty hydrate, dashed; harmonic+anharmonic, dotted; harmonic.

288

Table 1. Free energy due to the anharmonic contributions. Free energy is in kJ/mol. The anharmonic free energy of the guest molecule is denoted by A (kJ per mole of guest). The reference systems for ice, empty hydrate and the hydrate encaging spherical guest molecules are corresponding harmonic oscillators. The reference system for the hydrate encaging nonspherical guest molecules is the hydrate occupied by spherical guest molecules. free energy ice empty occupied A

-0.50 -0.61 -0.25 +2.53

mode energy 6.80 6.80 6.35

The experimental dissociation pressure P a is 0.53 MPa z which is very close to our present result, p d=0.50 MPa, but is different,' from the previous harmonic oscillator a p p r o x i m a t i o n , pd=0.24 MPa, and the original vdWP theory pd=0.16 MPa. The occupation number of the cage per unit lattice is ranging from5.5 to 5.6 in those methods. There is some variation in experimental results, 5.6 to 6.0. tt Although the present method is approximate one and the chemical potential difference between ice and empty hydrate does not agree perfectly with the experimental observation, this provides a way to evaluate the free energy of the cage occupation taking account of nonspherical nature of guest molecules. IV. Concluding Remarks In the present study, a generalized vdWP theory is further extended in order to treat rotational motions in the clathrate hydrate cages. The vibrational free energy of both guest and host molecules is divided into harmonic and anharmonic contributions. The anharmonic free energy associated with the rotational degrees of freedom of the guest molecules is evaluated as a perturbation from the spherical guest. The anharmonic term is found to be essential in determining the free energy of the hindered rotation for the guests. It is revealed that thermodynamic properties according to the present method enable us to evaluate the phase behavior of the clathrate hydrate more accurately. References

1 2

J . H . van der Waals and J. C. Platteeuw, Adv. Chem. Phys., 2, 1 (1959). E. D. Sloan, Clathrate Hydrates of Natural Gases, (Marcel Dekker, New York, 1990). 3 D. W. Davidson, W a t e r - A Comprehensive Treatise, Vol.2, edited by F. Franks, (Plenum, New York, 1973). 4 H. Tanaka and K. Kiyohara, J. Chem. Phys. 98, 4086 (1993). 5 H. Tanaka and K. Kiyohara, J. Chem. Phys. 98, 8110 (1993). 6 W . L . Jorgensen, J. Chandrasekhar, J. D. Madura, R. W. lmpey, and M. L. Klein, J. Chem. Phys. 79, 926 (1983). 7 W . L . Jorgensen, J. D. Madura, C. S. Swenson, J. Am. Chem. Soc. 106, 6638 (1984). 8 J . O . Hirshfelder, C. F. Curtiss, and R, B. Bird, Molecular Theory of Gases and Liquids, (Wiley, New York, 1954). 9 I. Ohmine, H. Tanaka, and P. G. Wolynes, J. Chem. Phys. 89, 5852 (1988) 10 A. Pohorille, L. R. Pratt, R. A. LaViolette, M. A. Wilson, and R. D. MacElroy, J. Chem. Phys. 87, 6070 (1987). 11 Y . P . Handa, J. Chem. Thermodyn, 18, 915 (1986).

journal of MOLECULAR

LIQUIDS ELSEVIER

Journal of Molecular Liquids, 65/66 (1995) 289-292

Deviation of the TST rate constant through the nonlinear couplings Masataka Nagaoka*, Naoto Yoshida a),b), and Tokio Yamabe b) Institute for Fundamental Chemistry, 34-4, Takano-Nishihiraki-cho, Sakyo-ku, Kyoto 606, Japan a)Daicel Chemical Industries, LTD., 1239, Shinzaike, Aboshi-ku, Himeji, Hyogo 671-12, Japan b)Department of Molecular Engineering, Kyoto University, Kyoto 606, Japan Abstract On the assumption of the external bath equilibrium, a set of simultaneous generalized Langevin equations (GLE) for a microscopic Hamiltonian is derived, whose potential function includes cubic (i.e., nonlinear) coupling terms, which are linear in the internal coordinates but quadratic in the external bath coordinates. Furthermore, on the GLE treatment, a closed expression of time-dependent friction coefficient and the rate constant in the Grote~Hynes theory (GHT) axe derived microscopically, reflecting the reactant and solvent structures. Comparing the rate constant of GHT with that of the multi-dimensional transition-state theory (TST) for the whole solution system, we conclude that these rate expressions are different each other and the difference is due to dynamic effects via the nonlinear couplings among the reaction coordinate and the internal and external normal coordinates.

I. Introduction

Recently, the understanding of chemical reaction dynamics has been enriched by extensive experimental and theoretical studies. 1-4 Grote and Hynes (GH)5, 6 generalized Kramers' treatment 7 and formulated the dynamic effect on the rate processes in solution, regarding solvent molecules as a surrounding medium in thermal equilibrium. The generalized Langevin equations (GLE) with respect to the mass-weighted coordinates of the reactive and nonreactive modes are the starting point for GH's treatment. GH solved a set of the simultaneous GLEs in terms of the reactive mode and derived a closed GLE of the reactive mode. Owing to the long time behavior of the solution of the closed GLE, so-called, GroteHynes equation (GHE) was derived. The major result was a simple expression for the escape rate:5,6

korl= K:. kT~ST= ~1... kT~T S~ f21

(I)

where ~ s, is the absolute value of the imaginary normal-mode frequency at a transition state (TS) on the free energy surface and Z.I'is the reactive frequency defined by the GHE and k~rsr is the rate constant on the free energy surface with an abbreviation FE. If the time-dependent friction coefficient ~u(0 > 0 for all t, then Z.T< f~s,, so that the motion in the vicinity of the barrier should slow down. Therefore, GH concluded that the rate constant becomes smaller than k~r. 5,6 According to the molecular dynamics simulations, 8,9 the frictional effect is quite large and solvent molecular motions play an important role in the reaction dynamics. However, since GH started with the GLEs that include phenomenological friction coefficients, microscopic connection between the coefficients and molecular interaction remained unclear. From the chemical point of view, such a theory is more desirable that the influence due to the differences in microscopic interaction of real solute and solvent molecules should be 0167-7322/95/$09.50 91995 Elsevier Science B.V. All rights reserved. SSD! 0167-7322 (95) 00880-2

290

describable. In order to elucidate the influence, van der Zwan and Hynes treated the microscopic model of chemical reactions, where a one-dimensional chemical reaction system couples bilinearly with a one-dimensional bath mode, and Pollak also treated the onedimensional chemical reaction system whose coordinate is coupled bilinearly with each of a large number of harmonic oscillators that constitute the heat bath. They obtained a very interesting and profound result: 10-12 the GH expression for the rate of escape over the barrier is just the continuum limit of the usual gas phase harmonic TST expression. Moreover, we have treated the multi-dimensional chemical reaction system in order to consider the difference of the internal bath mode frequencies at a stable state (SS) and "IS and to evaluate the indirect friction coefficient, which Pollak did not take into account. It was confirmed that the GH rate constant coincides with the multi-dimensional TST for the whole solution system.13,14 It means that the multi-dimensional TST for the whole solution system can contain the dynamic effect treated by GH, assuming the bilinear couplings between the internal and external bath modes. Therefore, in order to deal with more realistic interaction than the bilinear couplings and to treat the dynamic effect that cannot be described by the multi-dimensional TST, we should treat not only bilinear couplings but also nonlinear couplings. In this paper, we will treat the nonlinear couplings, which are linear in the system coordinate but quadratic in the external heat bath coordinates, and show that the GHT is not equivalent to the multi-dimensional TST for the whole solution system if the potential function contains the nonlinear couplings. In See. II, we introduce the microscopic Hamiltonian (IIA), evaluate the GH rate expression (liB), and, in See. IIC, we compare it with the multidimensional TST rate for the whole solution system. Finally, the main points are summarized in See. III. II. Theory A. Microscopic Hamiitonian for reacting system in solution Our starting point is the microscopic Hamiltonian for the chemical reacting system in solution. After the transformation of the coordinates, it can be expressed within the third order approximation in the neighborhood of any equilibrium geometry as follows: 13.14 H= V0+

89

+ 2]..pBTpB + l q S T AS2qs + 89 +

AB2qB

(2)

1 sr~3) .,B)

9 q SBB~'I where V 0 is the potential energy at an equilibrium geometry of the whole solution system. Furthermore, qS and qS express vectorially two sets of normal coordinates of the internal and external bath modes each with the degrees of freedom NS and N B, respectively, and pS and p8 are the corresponding conjugate momenta. As and AB are the diagonal matrices whose elements consist of normal-mode frequencies. The reaction coordiante for the whole solution system corresponds to the component q~. Then, the last term of r.h.s, of Eq.(2) denotes the nonlinear interaction term between the internal and external modes, and can be rewritten as follows: (3) (qa) =~-q s l q sTv SBB

9

=

~ ~ t:SBB,,S,,B,,B r i k l ~li ~lk ~ll

(3)

where Es~B are the cubic coupling coefficients. B. GHE and GH rate expression Cortes et al. obtained the GLE for the one-dimensional system whose coordinate is coupled not only bilinearly but also nonlinearly with each of a number of harmonic oscillators that constitute the external heat bath; i.e., the couplings are linear in the system coordinate but arbitrarily nonlinear in the heat bath coordinates.15,16 We apply the result to the chemical reaction system, which is described by the Hamilonian as Eq.(2). As a result, we obtain

291 perturbatively a set of the simultaneous GLEs on the free energy surface as follows: 13,14 Pl

~js(t) + (As2- Z(0))q s(t) + I^" dxZ(x)ils(t-x) = R(t)

(4)

dU

where R(t) is the random force vector along the internal modes by the external bath and Z(t) denotes the friction coefficient matrix, whose elements are the friction coefficient ~j(0 : NB ~

t:SBB~SBB

"ikl "jkl cos ABt cos 9 Atat

;ij(t) = 1 ~ -~

k l#k

(5)

B2. B2

Ak" A 1

where ~ denotes 1/kBT. By diagonalizing As2 - Z(0) by a unitary matirx U, we obatin the diagonal matrix ta s2 whose diagonal elements are the normal mode frequencies on the free energy surface and a new set of internal normal modes. After averaging the transformed GLEs over the external bath equilibrium distribution, firstly, the GLEs are solved to find the mean internal bath normal coordinate ~u (i = 2 ..... N S) in terms of the mean reactive normal coordinate ~u. 5,6,13,14 Here - mark indicates the average by the external bath equilibrium distribution. By substituting the solutions into the averaged GLE with respect to the reaction coordinate ~v, one obtains finally the following averaged equation of motion: -s#2 _--StJ0 ~'~lu0(t) " t2t ql (t) +

~lU(t-X)~llU0(1;)dx =0

a s..= ~- f~s2

(6)

where ~s,, is the absolute value of the normal-mode frequency of ~tr at the TS on the free energy surface and the superscript 0 indicates that the solution is obtained under the initial .--su condition; ~s~(0) = 0 and q i (0) = 0 (i = 2 ..... N S ), and ~(t) is the time-dependent effective friction coefficient.5,6,13,14 According to Eq.(6), the rate constant expression in solution is obtained as Eq.(1) and the reactive frequency ki' is defined by the GHE as follows: / s~ 2 ~.t =

~:

^U

(7)

:m

where ~(~.t) is the Laplace transform of ~(t).

C. Comparison with TST rate constant for the whole solution system The TST rate constant for the whole solution system is defined as follows: 1,2,17 f ~ ' " "f.**"dpSdqSdpBdqBexp{-I3H(TS) }~5(qS)cls0(cls) kTST = (8(qS)~ISO(~IS)~ =

(8) f-**".... I-**"dpSdqSdpBdqBexp{-lBH(SS)}

where iS(q~)and 0(tis) are the delta and step functions, respectively. Perturbative integration of Eq.(8) with respect to all coordinates with the microscopic Hamiltonian at SS and TS leads to the next formula: kTST _ ASl(TS) i 1 + 1 ~_~ E "+ikl ....._]~. | e-13AV0 --

271:

i A/s(TS) /

4~ i

. B2.AlB2 AS(Ts)2 k l* k Ak

Ais (SS) 2

292 As(TS) 2r:

"ikt (9) I~SBB2 B2 B2 S 2 ' Ak At AI(TS) where AV0 is the difference between the potential energy at the SS and TS and AS(ssfrs) are the internal mode frequencies at the s s f r s on the potential energy surface. The ratio of the microscopic GH rate expression to that of the TST for the whole solution system becomes Na Na t::SBB2 - S~2 B2 B2 kTST

413

As(SS) 1 N~ k Nl~k As(TS) 413

. B2, B2

flA 1 + Where A s..is the absolute value of A~s(TS). Eq.(10) means that G H rate expression deviates from the T S T one by the second term of r.h.s,and k ~ is always smaller than not only k ~ but also kvs-r. The result is contrasted clearly with both Pollak's and the previous ours, where the bilinear couplings were considered. Furthermore, the second term of r.h.s, in Eq.(10), representing the deviation from the T S T one, mainly originates from the Laplace transform of the frictioncoefficient. Therefore, the deviation is due to the dynamic effect via the nonlinear couplings. As is distinct from the treatments of bilincar couplings, the friction cocfficicnt depends on temperature and hence the deviation becomes larger with temperature increasing. Ill. S u m m a r y In this paper, startingwith a microscopic Hamiltonian, whose potential has a cubic form and the internal degrcc of freedom is multi-dimensional, we have obtained the microscopic friction coefficient and the averaged GLE of the reactive mode. Noting the long time behavior of the reactive mode motion, we have derived the GHE. Furthermore, comparing with the TST rate constant for the whole solution system, we have proved that the GH rate expression deviates from that of TST for the whole solution system and ktm is always smaller than both ka~-r and kn-r, because of the dynamic effect via the nonlinear couplings. With temperature increasing, kGn deviates from krsr more largely by the temperature dependence of the friction coefficient. References

1 J.T.Hynes, in Theory of Chemical Reaction Dynamics, edited by M.Baer (CRC, Boca Raton, 1985), Vol. IV. 2 P.H~inggi, P.Talkner and M.Borkovec, Rev.Mod.Phys., 62, 251 (1990). 3 A.Warshel, Computer Modeling of Chemical Reactions in Enzymes and Solutions, (John Wiley & Sons, New York, 1991). 4 W.L.Jorgensen, Adv.Chem.Phys., 70, 469 (1988). 5 R.F.Grote and J.T.Hynes, J.Chem.Phys., 73, 2715 (1980). 6 R.F.Grote and J.T.Hynes, J.Chem.Phys., 74, 4465 (1981). 7 H.A.Kramers, Physica, 7, 284(1940). 8 B.J.Gertner, K.R.Wilson, and J.T.Hynes, J.Chem.Phys., 90, 3537 (1989). 9 S.Hayashi, K.Ando, and S.Kato, J.Phys.Chem., 99, 955 (1995). 10 G.van der Zwan and J.T.Hynes, J.Chem.Chys., 78, 4174 (1983). 11 E.Pollak, J.Chem.Phys., 85, 865 (1986). 12 E.Pollak, Chem.Phys.Lett. 127, 197 (1986). 13 M.Nagaoka, Y.Okuno, N.Yoshida, and T.Yamabe, Int.J.Quantum Chem.,51,519(1994). 14 M.Nagaoka, N.Yoshida, and T.Yamabe, (to be submitted). 15 E.Cortds, B.J.West and K.Lindenberg, J.Chem.Phys., 82, 2708 (1985). 16 K.Lindenberg and B.J.West, The Nonequilibrium Statistical Mechanics of Open and Closed Systems, (VCH, New York, 1990). 17 H.Eyring, J.Chem.Phys., 3, 107 (1934); E.Wigner, ibid, 5, 720 (1937); S.Glasstone, K.J.Laidler and H.Eyring, The Theory of Rate Processes, (McGraw-Hill, New York, 1941).

journal of MOLECULAR

LIQUIDS ELSEVIER

Spatial

Journalof MolecularLiquids,65/66(1995)293-296

Correlations

in Reaction-Diffusion

Systems

in N o n e q u i l i b r i u m Conditions K a z u h i k o Seki I a n d K a z u o K i t a h a r a 2 1 T h e o r e t i c a l C h e m i s t r y Lab., N a t i o n a l I n s t i t u t e of M a t e r i a l s a n d C h e m i c a l R e s e a r c h , T u k u b a s h i H i g a s h i 1-1, I b a r a k i , 305, J a p a n 2 D e p a r t m e n t of A p p l i e d Physics, F a c u l t y of Science, T o k y o I n s t i t u t e of Technology, T o k y o 152, J a p a n

Abstract The steady state spatial correlations in reaction-diffusion systems involving many reversible chemical reactions are examined. It has been already discussed that the spatial correlations are related to the breaking of detailed balance in chemical kinetics for both one species and for two species reversible reactions. Here, we focus our attention on how the spatial correlations of concentration fluctuations in a macroscopically homogeneous systems approach to the instability point. The spatial correlations depend strongly on the stability of systems for two species reactions compared to one species reactions. I.

Introduction

It has been pointed out that the nonequilibrium spatial correlations appear in the system when the reactions are coupled with diffusion of chemical species 1. The appearance of spatial correlations is directly related to the breaking of the detailed balance in chemical kinetics, as it was pointed out for the Schl6gl model by Nicohs and Malek Mansour 2 and later studied in the case of an arbitrary set of reversible reactions by our previous paper 3-4. The microscopic simulations of these correlations were performed with various techniquesS-6; reasonable agreement was found with the analytical expression for the wide range of the length scale. In this note, the spatial correlations in a nonequilibrium steady state involving two variable constituents X and Y are analytically examined in details. Compared to the one-vaxiable reaction diffusion systems, the fluctuations are shown to be significantly enhanced as going to an instability point. The result is in consistent with the divergent form factor found by Lemarchand and Nicolis for a specific model 7. We start from the multivariate master equation for the probability distribution of number of particles in local elements. The local concentration of a species X in a volume element at the position ~' is denoted by x(v-") and its statistical average is denoted by xs, which is assumed to be independent of the position due to the assumption of a homogeneous steady state. Then, the covariance of the fluctuations 0167-7322/95/$09.50 91995ElsevierScienceB.V.All rightsreserved. 0167-7322(95) 00820-9

SSD!

294

~x(~ _---x(r') - x o is obtained in the form Co 1 e-~1r162'1 (,Sx(r-"),Sx(g ')) = x o 6 ( g - ~' ') + 8~rD I F - F -'--~[ '

(1)

where D is the diffusion coefficient. Nicolis and Malek Mansour showed that, in SchlSgl's model, when the detailed balance of the chemical kinetics is broken C, becomes nonvanishing 2. In our previous paper, we generalized the argument of Nicolis and Malek Mansour to an arbitrary set of reversible reactions for one species and show that Co is indeed related to the net flows of reversible chemical reactions 3. The theory is extended to two-species systems 4. In this note, we comment that the spatial correlation amplitude is not just given by 6'8 but is related to the stability of the kinetics for two-species systems. II.

Two-species system

In the previous paper, the derivation of differential equations for spatial correlations is given for the case of two species, X and Y whose concentrations axe denoted by x and y, respectively 4. In this note, we report only the solution. Let us consider the reversible chemical reaction of the scheme,

k~ Aj + n i X + m j Y

(1)

= (nj + Pi)X + (mj + q j ) Y + Bj. k_j

The net rate of the reaction j is defined by

(2)

Jj(x, y) ~ ajx~Jy"~j - bjxnJ+niy'~+q~, where aj and bj axe constants. Introducing quantities f(x,y)

-

g(x,y)

=

(3)

~'~p.igj(x,y), i ~-~qjJj(x,y), J

(4)

the stability condition can be written in terms of Kxx =

,Kxv = $

,Kvx = $

,Kvv = $

,

(5)

$

where the suffix s stands for the homogeneous steady state. The constituents, X and Y, may diffuse with diffusion coefficients, D x and Dr. When the system is stable under the condition, T =_ K x x + K v v < O, A -- K x x K v v - K x y K y x A = (DxKvv - DvKxx) 2 + 4DxDvKxvKvx

> O, < O,

(6) (7)

295

the solution for

pxx(e, ~") = ( , ~ x ( ~ , ( e ' ) ) - x,,5(e- e ')

(8)

is obtained as

pxx(e,~') = 1 Dy Cxx(F + x/~) 2 + 4 D x K x v C x v ( r + v ~ ) + 4D x~ K ~2y C y y e(i.n_~ )~ 8rrv/'A 2Dx (Dy - Dx)r + (Dx + D y ) v ~ +complex conjugate

r

Kxy (Dx + Dy)(KxyCyy -- K y x C x x ) + 2FCxy -r 87rr F 2 + K x y K y x ( D x + Dy) 2

(9)

where

F = DyKxx - DxKyy,

"/1--212(KxxKyy--I'(xyKyxI 2~ .y~ =

( K x x K y y - K x y K y x 1/~ 2 ~, -~x D 7 )

(10)

+

DxKyy + DyKxx , DxDy DxKyy + DyKxx Dx Dy

(11) (12)

(13) and

Cxx

= ~ ( 2 . ~ + pj)p~j~(~o,y.),

(14)

cxy

= ~ ( , . j p j + ,~jq~ + p~qj)Jj(~o, ~~ J = ~(2m~ + qj)q~j~(~o,y.).

(15)

Cxx

(16)

J

CXX~ Cxy aJ:Id Cyy are source terms for the long range correlations, which are related to the chemical reaction flows Jj(x,y). These relations were pointed out previously 4. In this note, we remark on the other point. The first two terms tends to diverge as the system approaches to the instability point, A = 0, because the denominators include vZ'A. The spatial correlations depend strongly on the stability of the systems. Such a strong dependence is not found for the one-species reaction systems. By putting K x y = 0 Eq. (9) reduces to the result of the one-species reaction systems, Eq. (1), where D = Dx and C~ = Cxx. We see that the in the denominator of Eq.(9) cancels out in Eq. (1). In the case of two-species reaction systems with Kxy, ~ in the denominator of Eq. (9) in general remains. For a specific model of two species reaction systems, Lemarchand and Nicolis found that the spatial correlations diverge in the vicinity of the critical state z. Although

296

our result suggests such a divergence, Eq. (9) is derived under the conditions that the system is far from the instability point and is in an uniform steady state on average. The more sophisticated theory is needed to analyze fluctuations around the instability point. The point in this note is that the spatial correlation amplitude is sensitive to the stability of the kinetics for two species in a distinct way from one species. Finally, we comment on the exponents in Eq. (9). The first two terms decrease with oscillations as the distance, r, increases. 3'1 characterizes the wave number of oscillations and selects the typical wave number of spatial pattern at the instability point. 72 and the exponent of the third term are related to the stabihty of kinetics. As long as the system is stable, these two exponents remain finite. References 1. N. G, van Kampen, "Stochastic Processes in Physics and Chemistry", North Holland, Amsterdam. (1981), Chap. XII and references therein. Y. Kuramoto, Prog. Theor. Phys. 52, 711 (1974). 2. G. Nicolis and M. Malek Mansour, Phys. Rev. A 29, 2845 (1984). 3. K. Kitahara, K. Seki and S. Suzuki, J. Phys. Soc. Jpn. 59, 2309 (1990). 4. K. Kitahara, K. Seki and S. Suzuki, in Proceedings of the Emil-Warburg Symposium, "Dynamical processes in condensed molecular systems", eds, A. Blumen, J. Klafter and D. Haarer, World Scientific(1990). 5. F. Baras, J. E. Pearson and M. Malek Mansour, J. Chem. Phys., 93, 5747 (1990). 6. J. Gorecki, K. Kitahara, K. Yoshikawa and I. Hanazaki, Physica A(in press, 1994). 7. H. Lemarchand and G. Nicolis, Physica 82 A, 521 (1976).

joumal of I~'IOLECULA R

LIQUIDS ELSEVIER

Journalof MolecularLiquids,65/66 (1995) 297-300

Nonlinear effects of soivation dynamics Akira Yoshimori

Department of Physics, Faculty of Science, Nagoya University, Nagoya 464-01, Japan Abstract The nonlinear Smoluchowski-Vlasov equation is calculated to investigate nonlinear effects on solvation dynamics. While a linear response has been assumed for free energy in equilibrium solvent, the equation includes dynamical nonlinear terms. The solvent density function is expanded in terms of spherical harmonics for orientation of solvent molecules, and then only terms for s and 1, and m=0 are taken. The calculated results agree qualitatively with that obtained by many molecular dynamics simulations. In the long-term region, solvent relaxation for a change from a neutral solute to a charged one is slower than that obtained by the linearized equation. Further, in the model, the nonlinear terms lessen effects of acceleration by the translational diffusion on solvent relaxation. I. Introduction Many molecular dynamics simulations have shown similar nonlinear effects on solvation dynamics for a change from a neutral solute to a ion or a large-dipole molecule ta. In long-time regions, the simulated relaxation was slower than that of the equilibrium time correlation function (tcf) for a neutral solute. In addition, the tcf relaxed faster for a neutral solute than for a charged solute. On the other hand, in some simulations, ''z solvent relaxed more slowly for a change from a neutral solute to a charged one than for a change from a charged one to a neutral one. All the above relaxation should be exactly the same in the linear response theory. The purpose of the present study is to investigate physical reasons of the nonlinear effects on solvation dynamics in the simulations, using a simple model. Few authors have studied nonlinear effects on solvation dynamics theoretically "=,though such effects were obtained in molecular dynamics simulations. Thus, the physical reasons of the effects have not been established yet. II. Model The basic equation in the present model is

(l) Here, p(r,to, t) is a density function of solvent with the position r and orientation to of the molecules, DR and Dr are the rotational and translational diffusion coefficients and tSF/rp is the functional derivative of free energy F in inhomogeneous-equilibrium solvent. When free energy F is given by the ideal gas expression plnp, eq. (1) reduces to an usual diffusion 0167-7322/95/$09.50 91995 ElsevierScience B.V. All fights reserved. SSD! 0167-7322 (95) 00881-0

298

equation. Equation (1) is called the nonlinear Smoluchowski-Vlasov equation 5 or the molecular hydrodynamics equation in the diffusive and Markovian limit (generalized Smoluchowski equation) 6. If we assume a linear response for the functional derivative of the free energy in the basic equation, then we have4 81:: = r 8p with

f + 4_~--~p(r,o~,t) - [ dr'do~'C(r-r',o~,o~')Sp(r,co,t) po J

8p(r,co,t) = p(r,co,t)

p0 4Jr"

(2)

(3)

Here, P0 is constant number density; C(r-r',co,co') is the two-particle direct correlation function, given by the mean spherical approximation. The first term O(r,co) in eq. (2) denotes the interaction between solute and solvent molecules, assumed to be the following dipole-charge interaction in the present: ~(r,eo) =

-~r.o~),

r> a

(4) 0

r 0. 4~

(6)

The numerical method was the simple Eular discretization. Time step was less than 0.01 (2DR)-'l, the space interval was 0.05 R where R was the diameter of solvent molecules, and the model domain length rmax was 6 R. Note that 13~1 had the dimension of time though the dimension of I3~l is [time][radian] 2, because radians do not have dimensions. Even if the step or interval is small or rmax is large, calculation gives qualitatively similar results.

299

III. Results Numerical calculation of the model gave the interaction between solvent and solute molecules and the normalized function x(t) = f 6p(r, ta, t ) ~ r , to)drdta,

S(t) =

x(t)-x(o0)

.

(7)

x(0)-x(0o) Here the employed parameters were Ix = 2.0Debye, p = 3.3x 1022 cm -3 , Dr = 0.05 (2DRR2), T = 300 K, a = 1.0 R. The calculated results agreed qualitatively with that by molecular dynamics simulations (Fig. 1). In the long-time region, solvent relaxation for a change in a solute charge from 0 to e (z=0--, 1) was slower than that obtained by the linearized equation. In addition, relaxation for z=0--, 1 was slower than that for z= 1---0. On the other hand, in the short-time region, solvent relaxation for z = 0 ~ 1 was similar to that by the linearized equation.

10 ~

z = 0---r 1 z=l-90 linearized eq 10"2

(~

015" ........

Time

1:0

"

(2Dn) - l

'

11.5

. . . . . . .

2.0

Figure 1. Normalized functions S(t) in solvation dynamics calculated by the nonlinear Smoluchowski-Vlasov equation for a change in a solute charge from 0 to e (z=0--- 1) and from e to 0 (z= 1 --,0) (solid lines), and by the linearized equation (dashed line). Calculation with the variation of translational diffusion coefficients showed that the nonlinear effects lessened effects of translational diffusion (Fig. 2). In the linearized equation, solvent relaxed quickly for a large translational diffusion coefficient. That is, a value of S(t) at t=(2DR)l decreased with the increase in the translational diffusion coefficient for the linearized equation. For calculation with the nonlinear Smoluchowski-Vlasov equation (1), however, a value of S(t) at t=(2DR) 1 increased slightly with the translational diffusion coefficient. Thus, the ratio of a nonlinear value to a linear value increased with the translational diffusion coefficient.

300

10 3

J

102

ratio .........----

101 o0~ (L_ 13100 L_

~

z = 0 ---~ 1

0

10 -I

10 -2 9

o

,

10 . I 10 .4

o

o.~s

o.~o

o.~s

0.20

Translational diffusion coefficient D T / 2 D n R 2 Figure 2. Values of S(t) at t=(2DR)"t for some translational diffusion coefficients. Circles show values by the nonlinear equation for z=0--* 1, diamonds show values by the linearized equation, triangles show ratios between them. IV. Discussion The calculated results by the present model agreed qualitatively with that by molecular dynamics simulations. However, it is not clear whether nonlinear results of the simulations can be explained only by the present model. The present model does not include all nonlinear effects in the simulations. In particular, the nonlinear effects in the solvent free energy can be important in the solvation dynamics. Equilibrium values of the number density a00(r,t) can depend on a charge distribution of a solute, though the linear-response free energy does not include the effects. The equilibrium number density for a neutral solute approaches to the homogenous constant density P0. The number density near a charged solute, however, can be larger than that of bulk solvent. The present model does not include such effects. Such cffects of the nonlincar frce energy can change a role of translational diffusion from that in the present model. The present model showed small nonlinear effects for small translational diffusion coefficients. In the model of nonlinear free energy, however, small translation diffusion has slowing effects on relaxation of solvent. This is because nonlinear free energy requires translational relaxation of the number density. The expansion of 8p(r,ta, t) by spherical harmonics has an instability. If the condition (6) is removed, the calculation cannot be stabilized. The reason for this instability is neglect of the higher-order harmonics in eq. (5). The neglect can give negative values of the density function. From time evolution of the free energy F, we can find that the density function in eq. (l) should be positive if a value of F always decreases. The positive density function needs the condition (6).

References 1 M. Maroncelli and G. R. Fleming, J. Chem. Phys., 89, 5044(1988). 2 M. Maroncelli, J. Chem. Phys., 94, 2094(1991). 3 For example, E. A. Carter and J. T. Hynes, J. Chem. Phys., 94, 5961 (1991). 4 A. Yoshimori, Chem., Phys., Letters, 184, 76(1991). 5 D.F. Calef and P. G. Wolynes, J. Chem. Phys., 78, 4145(1983). 6 A. Chandra and B. Bagchi, J. Chem. Phys., 91, 1929(1989).

journal of

MOLECULAR

LIQUIDS ELSEVIER

Journal of Molecular Liquids, 65/66 (1995) 301-304

Solvation Dynamics Studied by Uitrafast Transient Hole Burning Jangseok Ma,* David Vanden Bout + and Mark Berg

Department of Chemistry and Biochemistry, University of South Carolina, Columbia, SC 29208, USA Abstract The time-resolved solvation of s-tetrazine in propylene carbonate is studied by ultrafast transient hole burning. In agreement with mode-coupling theory, the temperature dependence of the average relaxation time follows a power law in which the critical temperature and exponent are the same as in other relaxation experiments. Our recent theory for solvation by mechanical relaxation provides a unified and quantitative explanation of both the subpicosecond phonon-induced relaxation and the slower structural relaxation. 1. Introduction Because of the fundamental importance of solvent-solute interactions in chemical reactions, the dynamics of solvation have been widely studied. However, most studies have focused on systems where charge redistribution within the solute is the dominant effect of changing the electronic state.[1,2] Recently, Fourkas, Benigno and Berg studied the solvation dynamics of a nonpolar solute in a nonpolar solvent, where charge redistribution plays a minor role.[3,4] These studies showed two distinct dynamic components: a subpicosecond, viscosity independent relaxation driven by phonon-like processes, and a slower, viscosity dependent structural relaxation. These results have been explained quantitatively by a theory of solvation based on mechanical relaxation of the solvent in response to changes in the molecular size of the solute on excitation.J6] Here, we present results on the solvation of a nonpolar solute, s-tetrazine, by a polar solvent, propylene carbonate over the temperature range 300-160 K. In this system, comparisons to several theoretical approaches to solvation are possible. 2. Transient Hole Burning Experiments We used transient hole burning to measure the solvation dynamics (Fig. 1).[3-5] These experiments yield both a time-dependent Stokes shift and a time-dependent width, both of which are related to the solvation dynamics. Here we consider the time-dependent Stokes shift. The time-dependent widths will be discussed elsewhere.J9] Detailed measurements of the s-tetrazine gas-phase spectrum were made. With these data, measurement of the absolute Stokes shift S(t) is possible. Because the Stokes shift is zero in the absence of solvent nuclear dynamics, the magnitude of the Stokes shift at the earliest times represents the amount of relaxation within the experimental time resolution. The steady-state absorption and fluorescence spectra were also measured to provide an independent value of the equilibrium Stokes shift S,~ With this data, the absolute solvation response function R(t)=l

S(t)

( 1 )

s(~)

* Current address: Institute for Molecular Science, Myodaiji, Okazaki, 444 Japan + Current address: Department of Chemistry, University of Minnesota, Minneapolis, MN 55455, USA 0167-7322/95/$09.50

91995 Elsevier Science B.V. All rights reserved.

SSD! 0167-7322 (95) 00821-7

302 was calculated without any normalizing factors. Measurements were made at 13 temperatures between 298 and 160 K, spanning a viscosity range of 2.6 cP to 3.2x1011 cP. Comparisons to four different theoretical approaches are made. 3. Results A. Mode-Coupling Theory Mode-coupling theories have recently shown great promise for explaining the microscopic origins of the glass transition.J10,11] These theories predict that the dynamics are dominated by the existence of a critical temperature Tc distincdy above the glass transition temperature. Above Tc, the primary (or) structural relaxation time is predicted to have a power-law temperature dependence, x = ot(T-Tc)-3'. Tc and 3' should be the same for all relaxation processes in the same solvenL In Fig. 1, the average solvation time measured by transient hole burning is compared to Du, et al.'s measurements of relaxation by depolarized light scattering.[12] These experiments measure relaxation on very different length scales; solvation on a molecular length scale, and light scattering on the scale of the wavelength of light. Both sets of data fit with the same exponent of 3'=2.74 and extrapolate to nearly the same value of Tc, in agreement with mode-coupling theory.

.6

9

-

Z ~

O.4

-

~- o.2 0

. 0 ~ 200 250

300

Temperoture (K)

B. Mechanical Relaxation Theory Berg suggested that a change in the solute size on excitation could produce a significant solvent response.[6,8] He treated the solute as a spherical cavity of radius r c and the solvent as a viscoelastic continuum with time-dependent compression and shear moduli K(t) and G(t). For a spherically symmetric change in cavity size, two time scales are relevant,

350

Fig. 1 A fit of solvation times to a power law temperature dependence. Depolarized light scattering (DPLS) times [12] fit to the same power and intercept, in agreement with modecoupling theory. Neutron scattering (NS) times [13] match solvation times, supporting Bagchi's solvation theory.

~

l:ph "-

f

K~ +

G**

'l;s= 8 A -1. The nearest neighbor intermolecular hydrogen-bonded distances, ro... O = 2.7 ,~ and ro... D = 1.7 ,A,, respectively determined from X-ray and neutron intermolecular distribution functions, exhibited both ---0.2 ~ shorter values than those reported for pure liquid water. The isotropic Raman spectra of O-H stretching region for solutions of higher H2SO 4 content (x _-->0.5) indicated an extremely broadened band centered at 3030 cm -1 , which corresponds to ---300 cm -1 lower frequency shift compared with that for pure liquid H20. These results suggest the existence of strong hydrogen-bonded intermolecular interaction in these solutions.

Introduction The information conceming the structural feature of the intermolecular hydrogen-bond in the liquid state is indispensable for understanding of the proton transfer reaction which plays a fundamental role in various chemical and biological processes. 1 The sulfuric acid - water system has been of particular interest due to extremely fast proton transfer property which has been frequently found by Raman 2 and quasielastic neutron scattering 3 studies. Structural investigations on the water-sulfuric acid system have been carded out using X-ray and neutron diffraction techniques. 4-6 Caminiti proposed the eightcoordinated hydration model for SO42- in 3.76 tool% aqueous sulfuric acid solution from X-ray diffraction data. 4 Andreani et al obtained the information concerning the hydrogen-bonded structure in this system from observed X-ray and neutron total distribution functions. 5,6 The combination of X-ray and neutron data has a significant advantage in determining the intermolecular O-H correlation in the system. However, to obtain more definite information on the intermolecular hydrogen-bonded structure, it is necessary to separate the intra- and intermolecular contributions from observed total interference term, which was not applied in the previous works because of the limited Q-range measured (Qsl0 ,~,-1)5,6. In the present paper we describe the results of X-ray and TOF neutron diffraction and Raman scattering measurements for aqueous sulfuric acid solutions with extended composition range in order to obtain the information both on the intermolecular hydrogen-bonded structure and on the intramolecular structural parameters of SO 4 unit in the solutions.

Experimental

X-ray diffraction measurements for sample solutions with natural isotopic composition, (H2SO4)x(H20)1_ x, x=0, 0.25, 0.5, 0.75 and 0.86, were carded out at 25~ in the reflection geometry using a 0-0 X-ray diffractometer manufactured by Rigaku Co. The Mo k(x radiation (k = 0.7107 ,~) was employed. The scattered intensity was counted at an interval of 0.5 ~ over the range of 3 < 20 < 150 ~ corresponding 0.5 < Q < 17.1/~,-1 (Q = 4 :t sin0 / X). The TOF neutron diffraction measurement for the sample solution sealed in a cylindrical quartz cell (8 mm in inner diameter and 0.4 mm in thickness) was 0167-7322/95/$09.50 r 1995 Elsevier Sciencc B.V. All rights rcscrvcd. SSDi 0167-7322 (95) 00882-9

306 performed at 25~

using the HIT spectrometer 7 installed at KENS, Tsukuba, Japan.

Deuterated

samples i> 99% D) were used to avoid large incoherent scattering from the hydrogen atom.

The

scattering data from the forward angle detectors located at 20 = 14, 25, 32 and 44 ~ were used to minimize the inelasticity effect. The data correction and the least squares fitting procedures for X-ray and neutron diffraction data are almost identical to those described previously.8, 9 Raman spectra were observed at 25~

in the frequency region of 1500 - 4500 cm -1 using a JASCO NR-1100 spectrometer

with a 514.5 nm line of NEC GLG-3200 Ar + laser operated at 200 mW. The details of the experimental procedures and data corrections are described elsewhere. 10

Results and Discussion Intramolecular structure of H2SO4 and HSO 4Figure l a shows the observed X-ray total interference term, Qix(Q ).

The least squares fitting analysis was applied to the observed interference term in the range of Q ~ 8 A -1 in order to determine the intramolecular structure of H2SO 4 and HSO 4- in the aqueous solution. The calculated intramolecular interference term was evaluated by the sum of intramolecular contributions from H2SO4, HSO4- , SO42- , H30+ and H20 molecules, icalc(Q) = AiH2so,i(Q ) + BiHSO4_+ Ciso, i2_ + DiH30+ + EiH~(Q),

(1)

where, the coefficients A - E were referred from a paper of Robertson et al. 11 In the fitting procedure, the intramolecular parameters for H30+ and H20 molecules were fixed to the values found in our previous work. 9 The tetrahedral geometry of isolated SO42- (rSo=1.477J,) 12 was assumed. The intramolecular bond lengths, r(S-O) and r(S-O(H)), and the root mean square amplitude, I(S-O), within H2SO 4 and HSO 4- molecules, were treated as the independent parameters. The bond angles, / O - S - O and Z. (H)O-S-O(H) in H2SO 4, and Z_O-S-O(H) in HSO4-, were also refined independently. The molecular structure of H2SO 4 and HSO 4- reported in the gaseous 13 and in the crystalline states,14,15 is characterized by two distinct S-O bond lengths, r(S-O(H)) = 1.54 - 1.57 A and r(S-O) = 1.40 - 1.43 J,. In the present analysis, the fitting procedure was carried out using the model function involving two different intramolecular S - O distances, r(S-O) and r(S-O(H)), however, the optimized solution of the 150 ,,

3

100~' \.

(HiS0i)x(H'O)i-x

-

~~

- i

o ~ .k..It,j./ " - ~ ~ { < ~

o

.,oI~.~L_...." ~

v ' ~

"

A

8 O//~_= 12

16

20

I

.~

-1

'

I

i

I

'

I

x:o.,,

ii . ~

0.75

.-. .....

i ...,.... .. 9 0

'

(HzSO')x(HzO'-x

. . . . .

o

-50 0

''

2

2

.,ob z. r/A

6

L

1 8

A

10

Fig. 1. a) Dots: The observed X-ray total interference term, Qix(Q ), for aqueous sulfuric acid solutions. Solid lines: The calculated intramolecular contribution, b) The observed intermolecular total distribution function, gxinter(r).

3 0 7

o5~

,~ /

s o ~.. -/ ~..-...

04

0[-

)

?,,/ V

o~o

~

o2s

.

o - . . . .o 1 s

o9 0

z.

8

Q/j_,

12

16

20

0

2

~

~ 4

r/A

b 6

8

10

Fig. 2. a) Dots: The observed neutron total interference term, iN(Q), for aqueous sulfuric acid solutions. Solid lines: The calculated intramolecular contribution, b) The observed intermolecular total distribution function, gNinter(r). least squares fit always indicated that the two S-O bonds are identical in the bond length (rso = 1.48 _ 0.01 ,&) with the root mean square amplitude of Iso = 0.05 _+ 0.01 ,& in these solutions. The same analytical procedure was applied to the observed neutron interference term (Fig. 2a). Additional independent parameters, r(O-D), I(O-D) a n d / - S - O - D , were also refined in the fitting procedures for the neutron data. The result again exhibited composition independent single S - O distance of rso = 1.50 _+ 0.01 /~ and r.m.s, amplitude of ISO = 0.04 _ 0.01 A, which are consistent with those obtained from the present X-ray data. These results suggest the regular tetrahedral geometry of SO 4 structural unit in concentrated aqueous sulfuric acid solutions.

Intermolecular hydrogen-bonded structure Figures l b and 2b represent the X-ray and neutron intermolecular distribution functions for aqueous sulfuric acid solutions, respectively. In the gxinter(r) function, the nearest neighbor (hydrogen-bonded) !

!

!

i

I

i

i

i

f

!

(H2SOI.)x(H20)f-x .:. '.-;.. ~; .

-"9

~-

. . . . . .

--"

[:':',;,

1500

"~',-,

"

"

3000 v/cm-i

x=0.86

"

"

"

0"7

......:

i

/.500 1500

3000 u / c m -I

/.,500

Fig. 3. Composition dependence of the isotropic Raman spectrum in the O-H stretching region for aqueous sulfuric acid solutions. -__

308 O..-O interaction can be identified as an incompletely resolved peak at r = 2.7 A. This intermolecular distance is ,--0.2 .~, shorter than that for pure water. A well defined first peak at r = 1.7 ,~, observed in the present gNinter(r) functions can be ascribed to the hydrogen-bonded intermolecular O .--D interaction. This intermolecular O..-D distance is again considerably shorter than that reported for pure liquid water (ro... D = 1.85 ~.).16,17 These short intermolecular hydrogen-bonded distances indicate the existence of strong hydrogen-bonds in these solutions. The composition dependence of the gNinter(r) and gxinter(r) functions seems to be very small for solutions of higher sulfuric acid content above 50 mol%, suggesting the similarity of the hydrogen-bonded liquid structure among these solutions. This similarity can also be found in the isotropic Raman spectra of O-H stretching region shown in Fig. 3. Except for 25 tool% H2SO4 solution, an extremely broad (fwhm = 640_40 cm -1) O-H stretching band at 3030__.20 cm-1 with a small shoulder at 2420_20 cm -1 was observed. According to the vOH - ro... O correlation curve proposed by Wall and Homig, 18 the present value vOH = 3030 cm -1 leads to a very short hydrogenbonded O " - O distance of 2.72 A. The value is in excellent agreement with that determined from the present gxinter(r) function. The peak components at 3300 and 3500 cm -1 observed in 25 mol% solution may be attributed to the O-H stretching modes of remaining H20 molecules in the solution. Acknowledgment

The authors would like to thank Profs. M. Misawa, T. Fukunaga and T. Yamaguchi for their help during the course of the neutron diffraction measurement. All of the calculations were performed using the ACOS $3600 computer at the Computing Center of Yamagata University. References

1. T. Bountis, ed., "Proton Transfer in Hydrogen-Bonded Systems", Plenum Press, New York (1992). 2. 3. 4. 5.

H. Chen and D. E. Irish, J. Phys. Chem., 75, 2672 (1971). D. Cavagnat and J. C. Lass~gues, J. Phys.: Condens. Matter, 2, SA189 (1990). R. Caminiti, Chem. Phys. Lett., 96, 390 (1983). C. Andreani, C. Petrillo and F. Sacchetti, Mol. Phys., 58, 299 (1986).

6. C. Andreani and C. Petrillo, Mol. Phys., 62, 765 (1987). 7. N. Watanabe, T. Fukunaga, T. Shinohe, K. Yamada and T. Mizoguchi, "Proc. 4th International Collaboration on Advanced Neutron Sources (ICANS-IV ), KEK, Tsukuba", eds. by Y. Ishikawa et al, p. 539 (1981). 8. Y. Kameda, R.Takahashi, T. Usuki and O. Uemura, Bull. Chem. Soc. Jpn., 67, 956 (1994). 9. Y. Kameda and O. Uemura, Bull. Chem. Soc. Jpn., 65, 2021 (1992). 10. Y. Kameda, H. Ebata and O. Uemura, Bull. Chem. Soc. Jpn., 67,929 (1994). 11. E. B. Robertson and H. B. Dunford, J. Am. Chem. Soc., 86, 5080 (1964). 12. J.-O. Lundgren, ,~. Kvick, M. Karppinen, R. Liminga and S. C. Abrahams, J. Chem. Phys., 80, 423 (1984). 13. R. L. Kuczkowski, R. D. Suenram and F. J. Lovas, J. Am. Chem. Soc., 103, 2561 (1981). 14. C. Pascard-Billy, Acta CrysL, 18, 829 (1965). 15. I. Taesler and I. Olovsson, Acta CrysL, B24, 299 (1968). 16. A. K. Soper and M. G. Phillips, Chem. Phys., 107, 47 (1986). 17. J. C. Dore, J. Mol. StrucL, 250, 193 (1991). 18. T. T. Wall and D. F. Homig, J. Chem. Phys., 43, 2079 (1965).

journal of MOLECULAR

LIQUIDS ELSEVIER

Journal of Molecular Liquids, 65/66 (1995) 309--312

Raman Spectroscopic Study of Rotational and Vibrational Relaxation of CF3H in the Supercriticai State

Susumu Okazaki, Nobuyuki Terauchi, and Isao Okada

Department of Electronic Chemistry, Tokyo Institute of Technology Nagatsuta, Midori-ku, Yokohama 226, Japan

Abstract Instrumentation of polarized and depolarized Raman scattering measurement for supercritical fluids at high pressures up to 20 MPa along its isotherm of moderate temperatures has been established. Preliminary measurements have been performed for supercritical CF3H to examine density dependence of rotational and vibrational relaxation of the molecule in the fluid. Reorientation of the molecule changed from free-rotor-like motion to liquid-like diffusional one via intermediate specific one with increasing density. Strong density dependence was found for vibrational relaxation time of the supercritical fluid reflecting the collision frequency or inhomogeneity in the fluid.

I. Introduction Supercritical fluid continuously changes its density along isotherms from gas-like one to liquid-like one. This presents a variety of environments to the molecules in the fluid. With respect to the rotational and vibrational relaxation of the component molecule, this characteristic property is very interesting in that collision frequency in a dynamical sense or inhomogcneity in a static sense can be widely controlled as a function of pressure keeping the kinetic cnergy unchanged. 1,2 Thus, polarized and depolarized Raman spectroscopy for this fluid may lead us to a deeper understanding of the fundamental process of the rotational and vibrational relaxation of molecules in condensed phase. In the present study, an instrument has been established for polarized and depolariz~ Raman scattering measurement of supcrcritical fluid along its isotherm to realize the investigations stated above. Preliminary results for supcrcritical CF3H are given to draw a schematic picture of the dynamics.

II. Experimental A sample cell was designed to accomodate supercritical fluids at high pressures up to 20 MPa and at moderate temperatures using stainless steel and fused silica glass, as schematically shown in Fig. 1. The fluid was prepared by compressing the low pressure sample gas from the tube using a piston compressor outside the cell. The cell and the attached part for high pressure lines were immersed in an air thermostat. The pressure and temperature were 0167-7322/95/$09.50 c: 1995 Elsevier Science B.V. All rights reserved. SSDI 0167-7322 (95) 00828-4

310

to spectrometer

~ : ~

i

incident light

/~ ..j~~~~

-"i'~.!:-~;.~.L...-~ --;.::..:.:.-.-- N

windows seals

I

"i

t

Fig. 1 Pressure-resistant sample cell for Raman scattering measurement of supercritical fluids.

monitored during the measurement by a semiconduaor strain gage(Druck PTX 520) and a platinum resistance thermometer, respectively. Arrangement of the spectrometer and data analysis of the observed spectra are the same as those previously employed.3 The measurements were done for the v 1 stretching mode of CF3H molecule in the supercridcal fluid

0.8 0.6 E cnO.4 0

(3.

0.2 ..i--P/MPa Fig. 2 Measured points(closed circle) in the PpT-diagram. isotherm at 313 K.

The solid line represents the

311

.,.., 0 t-"

..Q

--~0 2.0 MPa

3200

1

3000

v/cm-1

2800

Fig. 3 Depolarized(VII) Raman spectra for the v, stretching mode of CF3H in the supercritical fluid.

at 313 K and at 2.0 MPa, 5.0 MPa, and 7.0 MPa. The critical constants of this material are Tc=299.3 K, Pc=4.77 MPa, and pr g cm3. The density region covered in the present study was, thus, the lower one along the isotherm, as shown in Fig. 2.

III. R e s u l t s and D i s c u s s i o n The observed VII spectra are presented in Fig. 3. Although sufficient statistics have not yet been obtained for quantitative evaluation of the rotational autocorrelation function, it is enough to give a qualitative discussion of the relevant dynamics of the molecule. In this sense, one of the most interesting aspects is the shape of the spectra. The spectrum of the fluid at 7.0 MPa is ordinary Gaussian-Lorentzian, representing the almost diffusional reorientation which is generally found in liquids 9On the other hand, for the fluid at 2.0 MPa, the spectrum clearly shows side peaks on both sides. The Fourier transformation of the spectrum gave a rotational autocorrelation function similar to that of the free rotor, although a difference between them is certainly found. It is of a triangular shape for the fluid at 5.0 MPa, showing existence of an intermediate relaxation process between those found in the gaseous and liquid states. Among

312

1"01

9

"~ O.8 0.6 o 0"~:0

015

o oo

110 115 P/g cm -3

2.0

Fig. 4 Vibrational relaxation time x v as a function of densit~ 13 for the v, stretching mode of CF3 H in the supereritical fluid(closed circle) and in the liquid-~(open circle).

the models, the J-extended model4, where rotational libration with large amplitudes is taken into account, may be most suitable for describing this behavior at least qualitatively. The linewidth of VH spectrum for the fluid at 7.0 MPa is as broad as about 54 cm"(FWHH), from which the rotational relaxation time is calculated to be as short as about 0.3 ps. This may be based upon the fact that the density of the fluid is so low that the molecule can reorientate with small perturbation; the collision rate is still low at this density compared with that in the liquid. V~rational relaxation time % evaluated from the linewidth of the isotropic spectrum is plotted in Fig. 4 together with that of the liquid.5 The relaxation time for the supercritical fluid is larger than that in the liquid. The % much depends upon density in the supcrcritical fluid, whereas it does not in the liquid, showing a good contrast between them. The difference in the behavior can be understood in terms of the collision rate of the molecules and inhomogeneity with respect to the environment of the oscillators. Detailed experiments with sufficient statistics to obtain quantitative evaluation of the autocorrelation functions are in progress.

References

1 2 3 4 5

D. Ben-Amotz, F. Laplant, D. Shea, J. Gardecki, and D. List, ACS Symp. Ser., 488, 18(1992). S.M. Howdle and V. N. Bagratashvili, Chem. Phys. Lett. 214,215(1993). S. Okazaki, N. Ohtori, and I. Okada, J. Chem. Phys., 91, 5587(1989). R.G. Gordon, J. Chem. Phys., 44, 1830(1966). J. DeZwaan, D. W. Hess, and C. S. Johnson, Jr., J. Chem. Phys., 63,422(1975).

journal of MOLECULAR

LIQUIDS ELSEVIER

Journal of Molecular Liquids, 65/66 (1995) 313-316

Anomalous Conformational Behavior of Short Poly(oxyethylene) Chains in Water:. An FT-IR Spectroscopic Study Hiroatsu Matsuura and Tatsuya Sagawa Department of Chemistry, Faculty of Science, Hiroshima University, Kagamiyama, Higashi-Hiroshima 739, Japan Abstract Conformational behavior of short poly(oxyethylene) (POE) chains in water has been studied by FT-IR spectroscopy. The spectra of aqueous solutions of CH3(OCH2CH2)mOCH 3 with m = 2--6 were measured for various concentrations by using a horizontal ATR accessory. The observed spectra show that, with increasing water fraction, the population of the gauche conformation about the OC-CO bond increases, but the direction of the conformational preference is reversed for lower concentrations. The observed maximum of the gauche population is interpreted as a consequence of anomalous enhancement of the gauche population in a specific concentration region. This effect is more significant for shorter POE chains. These observations suggest that there exist some specific interactions, which highly favor the gauche conformation of the O-CH2-CH2-O segment, for limited composition regions of the binary systems of short POE chains and water.

I. Introduction Poly(oxyethylene) (POE) (-OCH2CH2-) m is an unusual polyether with practically tmlimited solubility in water, unlike other structurally related polymers. 1 At elevated temperatures, however, the isotropic aqueous solution of POE separates into two phases. 2 The mechanism of the water solubility of POE and the phase behavior has attracted much attention of many investigators. Various mechanistic models have in fact been proposed to account for these phenomena: 3 a water structure model, 4 a hydrogen bond model, 5 and a conformational model. 6 The conformation of POE in aqueous solution has been studied by a number of experimental and theoretical methods. Among those studies, Raman spectroscopy, which provides direct information of relative conformational populations, has shown that the POE chain in water greatly favors the gauche conformation about the OC-CO bond. 7 Raman spectroscopy further indicated that the population of the gauche conformation increases with an increase in water 0167-7322/95/$09.50 ~c) 1995 Elsevier Science B.V. All rights reserved. SSDI 0167-7322 (95) 00883-7

314

fraction of the binary system. In a recent Raman spectroscopic study, we have performed spectral measurements for more diluted aqueous solutions of short POE compounds, s In the present work, we have investigated the conformational behavior of POE chains in water by FT-IR spectroscopy, which is another vibrational spectroscopy that gives important conformational information, to gain a further insight into the structural aspect of the POE-water system. The POE compounds studied are CH3(OCH2CH2)mOCH 3 (C1EmC 1) with m = 2--6.

IL Experimental C1E2C1, C1E3C1, and C1E4C 1 were commercially supplied, while C1E5C 1 and C IE6C 1 were prepared by the Williamson ether synthesis. The infrared spectra of aqueous solutions of these compounds were measured for various concentrations at room temperature by using a horizontal ATR accessory with a ZnSe prism. The lowest concentration studied was a mole fraction of approximately 0.005. The spectra were recorded on a JASCO FT/IR-7300 spectrometer. Each of the spectra was obtained by the coaddition of 200 scans at a resolution of 4 tin--1.

HI. Results and Discussion III.1. Spectral Analysis For studying the conformational behavior of the POE chain in water by infrared spectroscopy, we focused on two distinct marker bands at about 1330 and 1350 cm -1, which are assigned to the CH 2 wagging mode of the O-CH2-CH2-O segment in the trails and gauche conformations, respectively, as established by normal coordinate analysis.9, lo The infrared spectra of aqueous solutions of C1E2C1 in the 1500-1200 cm-1 region are illustrated in Figure 1. It is apparent that the absorbance of the 1330 cm-1 band (the trans band) is greatly diminished relative to that of the 1350 cm -1 band (the gauche band) with an increase in water fraction. In Figure 2, the absorbance ratio of the gauche band to the trans band, Agauche/Atram, is plotted against a mole fraction of C1EmC1. A remarkable observation is that, with increasing water fraction, the population of the gauche conformation about the OC-CO bond increases, but the direction of the conformational preference is reversed for lower concentrations. The mole fractions of C1EmC 1 giving maximum gauche population are 0.0165, 0.027, 0.032, 0.0275, and 0.025 for m = 2, 3, 4, 5, and 6, respectively, with uncertainties of +0.002. These values agree, within the estimated experimental errors, with those obtained from the Raman marker bands, i.e. 0.019, 0.030, and 0.030 for m = 2, 3, and 4, respectively, lo III.2. Stabilization of the Gauche Conformation of POE Chains in Water The increase of the population of the gauche conformation about the OC-CO bond with increasing water fraction can be explained for a considerable part by

315 the dielectric effect, which implies that the conformers with larger dipole moment are more stabilized in the medium with higher dielectric constant. 11 According to the calculation using the atomistic force field, the value of the dipole moment for the O-CH2--CH2--O segment in the gauche conformation is generally larger than that for the same segment in the trans conformation, although the value depends significantly on the conformation about the CO-CC and CC-OC bonds. 12 The second possible factor of the stabilization of the gauche conformation is specific hydrogen bonding between the ether oxygens of the POE chain and water. The importance of the hydrogen bond is suggested by molecular dynamics and Monte Carlo simulations. 13,14 It is shown that the gauche conformation of the O-CH 2CH2-O segment is more favorable than the trans conformation for water molecules to form hydrogen-bonded bridges between the adjacent ether oxygens. 25

(a)

2o

~ ~

15 o

I

i

I

I

10

|

(b)

20

-- 15

o

c.o

~

I

I

l

I

l

o

10

l 0

= 10

0

I

I

o 15 f (d) < ~o 10 o

1

10

1500

1400 1300 Wavenumber / cm-1

1200

Figure 1. FT-IR spectra of aqueous solutions of C 1E2C 1 for mole fractions of (a) 0.202, (b) 0.057, (c) 0.014, and (d) 0.005. The conformational marker bands are indicated by arrows.

~

0.0

o

o

,.

,

011 0:2 0:3 Mole fraction of C 1EmC 1

0.4

Figure 2 Absorbance ratio, Agauehe/ Atrans, "for aqueous solutions of C 1EmC1 as a function of mole fraction; (a) C1E2C1, (b) C1E3C1, (c) C1E4C1, (d) C1E5C 1, and (e) C1E6C 1.

316

Figure 2 indicates that the observed maximum of the gauche population is most likely a consequence of anomalous enhancement of the gauche population in a specific concentration region. It is also shown that this enhancement is more significant for shorter C1EmC 1 compounds. These observations suggest that there exist some specific interactions, which highly favor the gauche conformation of the O-CH2-CH2-O segment, for limited composition regions of the binary system of short POE chains and water. According to our preliminary results, the gauche population for C 1EmC1 (m = 2--4) in methanol increases and that for the same compounds in carbon tetrachloride decreases steadily with increasing solvent fraction without exhibiting ma~mum or minimum. 15 These experimental findings further support the importance of the specific interactions involved in the POE-water system. The mechanism of the anomalous enhancement of the gauche population for short POE chains in water is not clear at present. Possible effects relevant to the specific interactions may be associated with the conformational adaptation of the POE chain to the water structure and/or the amphiphilic behavior of the POE chain in water. A clue to the elucidation of the anomalous conformational behavior probably lies in the observation of the more significant effect for shorter chains and in the particular composition of the binary system at the point of the maximum gauche population. For a more comprehensible understanding of the structural aspect of the POE chain in water, more extensive experimental work and sophisticated theoretical treatment are necessary. References

1 F. E. Bailey, Jr. and J. V. Koleske, Poly(ethylene oxide) (Academic Press, New York, 1976). 2 S. Saeki, N. Kuwahara, M. Nakata, and M. Kaneko, Polymer, 17, 685 (1976). 3 G. KarlstrOm and B. Lindman, in Organized Solutions: Surfactants in Science and Technology, edited by S. E. Friberg and B. IAndman, pp 49--66 (Marcel Dekker, New York, 1992). 4 R. Kjellander and E. Florin, J. Chem. Soc., Faraday Trans. 1, 77, 2053 (1981). 5 R. E. Goldstein, J. Chem. Phys., 80, 5340 (1984). 6 G. Karlstr6m, J. Phys. Chem., 89, 4962 (1985). 7 H. Matsuura and K. Fukuhara, J. Mol. Struct., 126, 251 (1985). 8 H. Matsuura, S. Masatoki, M. Takamura, K. Kamogawa, and T. Kitagawa, to be published. 9 H. Matsuura and K. Fukuhara, J. Polym. Sci., Part B, 24, 1383 (1986). 10 H. Matsuura, K. Fukuhara, and H. Tamaoki, J. Mol. Struct., 156, 293 (1987). 11 R. J. Abraham, L. Cavalli, and K. G. R. Pachler, Mol. Phys., 11,471 (1966). 12 G. D. Smith, R. L. Jaffe, and D. Y. Yoon, J. Am. Chem. Soc., 117, 530 (1995). 13 M. Depner, B. L. Schttrmann, and F. Auriemma, Mol. Phys., 74, 715 (1991). 14 Y. C. Kong, D. Nicholson, N. G. Parsonage, and L. Thompson, J. Chem. Soc., Faraday Trans., 90, 2375 (1994). 15 H. Matsuura, unpublished results.

journal of MOLECULAR

LIQUIDS ELSEVIER

Journal of Molecular Liquids, 65/66 (1995) 317-320

Time-Resolved Resonance Raman Study of the Recombination Dynamics Photodissociated Carbon Monoxide to Sperm Whale Myogiobin and Its Mutants Satoru N a k a s h i m i t , Teizo Kitagawa*, John S. O l s o n * * Department of Chemistry, Faculty of Engineering Science, Osaka University, Toyonaka 560, Japan *Institute for Molecular Science, Okazaki National Research Institute, Okazaki 444, Japan **Department of Biochemistry and Cell Biology, Rice University, Houston, Texas 77251, USA

Abstract Time-resolved resonance Raman (TR 3) spectroscopy was applied to study the recombination process of photodissociated carbon monoxide with recombinant sperm whale myoglobin (Mb) and its several mutants. The measurements were carried out, with various delay times (zxt=-20 ns - 1 ms) following photolysis for several mutants in which dital or E7His (His64) was replaced with a aliphatic or aromatic residue. The Fe-CO stretching bands (vFe-CO) showed that the environments around CO in the steady state as well as the kinetics of the CO rebinding process are very different among mutants and these differences seemed to be correlated with the hydrophobicity of the replaced residues. In spite of these differences for each mutant, a common intermediate species was observed at almost the same time region. In this intermediate CO was not bound to the iron ion yet, but the heme state was different from the initial deoxy form. Since this intermediate is common to all the mutants, the difference of the distal residues did not play an important role. The intermediate may it reflect the global dynamics of the protein, but correspond to so-called "open form" of Mb in which the His-64 swings out and a pathway for the ligand to enter the active site in general.

Introduction Mb is one of the highly characterized proteins and is considered to be a good model molecule for the analysis of the dynamics of the structural changes in general proteins. In attempts to elucidate the role of the protein dynamics toward their function, the recombination of photodissociated CO of carbonmonoxy myoglobin (COMb) has been extensively investigated over times that range from femtoseconds to seconds at various temperatures. 1-3 In x-ray crystallographic analysis of COMb it has been noted that there is no pathway for the migration of CO between the buried binding site and solvent. 4 Therefore, rapid rearrangements of the protein structures should be accompanied by recombination of CO. The transient absorption study on the relaxation process of photolysis product of COMb revealed that the recombination of the photodissociated CO was nonexponential. Fe-CO stretching band that appears in Raman spectra, is a good maker for this distal pocket environment. We pursued the time profile of this band to monitor the dynamics and found an intermediate species common to all the mutants. We will discuss the existence of the intermediate which correspond to "open form". 0167-7322/95/$09.50 'c' 1995 Elsevier Science B.V. All rights reserved. SSDi 0167-7322 (95) 00822-5

318

Experimental Wild type Mb (WT) and several mutants, where distal Histidine was replaced to aliphatic residues (His64Gly, His64Ala, His64Leu) and was replaced aromatic residues (His64Tyr, I-lis64Trp), double mutants (His64TyrLeu29Phe, His64TrpVa168Phe) and Leu29 mutant (Leu29Phe), were examined, s (Their abbreviations are H64G, H64A, H64L, H64Y, H64W, H64YL29F, H64WV68F, and L29F, respectively) Sperm whale Mb was isolated from stored meat and mutant sperm whale Mbs were expressed in E.coli and purified. Mbs solution (50mM Tris-HCl buffer at pH=8.0) were reduced by small amount of dithionite in the CO atmosphere and used in air-tight cell. Nanosecond pump/probe time-resolved resonance Raman experiments were carried out with two Nd:YAG lasers (t~t=7 ns) which provide the pump- (532 nm, 4 mJ) and probe pulses (416 nm, 100 gJ), a triple polychromator equipped with an intensified photodiode array, and a slow spinning cell (25rpm). For every sample, spectra were taken for delay times of At=-20, 0, 20, 100 and 500 ns, 1, 10, 100 and 500 ~ts, and 1ms. 6 To measure all these spectra in the same condition, spectra for each delay time were recorded quasi-simultaneously. The controller of the detector, the pulse generator and mechanical shutter were connected and managed by a personal computer. One spectrum was accumulated for 8 see. in one of the conditions and stored in the memory of the computer. Then the conditions were changed one after the other, and in each case it accumulated the spectra for 8 sec., which were recorded into the corresponding memories. After measuring all these conditions, it went back to the fast condition and repeated this sequence again, where each specman was added onto the corresponding spectrum on the memories. In all it repeated this procedure for 500 times, which was equal to about 12 h for whole accumulation time and to about 70 mills, for each spectrum.

Result and Discussion In the steady state, the VFr band appeared in a frequency range from 490 to 526 cm1. The VFe.COand the vco frequencies for each mutant observed by RR and IR measurements, respectively, are listed in table I. They are classified into three groups, A0, A1 and A3. This classification was originally based on the CO stretching 7 band, but is known that the VFc.CO frequency have a negative linear correlation with the vco frequency. H64G, H64A, H64L, H64W, H64Y and H64WV68F belong to A0, and the wild type to A1 and H64YL29F and L29F to A3 type. These results mean that the replacement of distal residues changes the heme environments and that there are at least three major types in the local field at CO in COMb. Table I. The VFe.CO, bFe-C-Oand VFe-COband of the mutant COMbs. (cm d) 9

VFe.CO

i

Wild Type

H64G

H64A

H64L

H64W

H64Y

H64W V68F

H64Y L29F

L29F

508

496

494

490

494

491

490

519

526

~Fe-C-O

579

-

570

571

550

550

-

579

582

VFe-CO

1945

1965

1966

1965

1969

] 966

-

-

1932

The results of TR 3 measurements are shown in Figure 1-4 for wild type with 12C160, wild type with 13C180, H64A and L29F, respectively. The CO rebinding kineti~ for each

319

mutant is correlated with the frequency of the VFe-COband. The lower the frequency of the VFe. CO band is, the faster the kinetics of CO rebinding becomes. We have reported 6 the linear correlation between the frequencies of the VFe-CO band and the hydropathy indeices of the replaced residues. It is empirically evident that the vre.co frequency becomes lower as the environment around CO becomes more hydrophobic. Therefore the rebinding kinetics is also affected by the hydrophobicity of the replaced distal residues; i.e. when the distal residue favors the presence of solvent water near itself, the rebinding kinetics becomes slow and v.v. In the case of the wild type, which belongs to A1 type, the equih'brium Fe-CO stretching band was identified in the spectrum for t~t=-20 ns (508 cm -1 for 12C]60 and 497 cm -1 for 13C180) and this band was absent in the spectrum for At=0 ns. A new broad band around 497 cm 1 started to appear from t~t=20 ns, which did not show the isotope shift. The VFe.CO band which reappeared from zxt=10 ~ts, was restored by 65% at 1 ms. Although in other two types of mutants the rebinding kinetics were very different from this A1 type, the intermediate band at 497 cm "1 was observed in almost the same time region and didn't show an isotope shift. It provides the evidence for the presence of a transient species, in which CO migrates into the heine pocket but not binds to the heine.

'qldType

m 410

"i

3441 ]'Wild Type

497

9

,.c,.o.o ,

i~

i '-,one__.., 20ns

i

700

-=

600

"L

3~s

J ill

~

V I=~ V ~

'

]

SO0

400

Raman Shift/cm "~

I! 700

,

1 600

I SO0

..

! 400

Raman Shift/cm-1

,

!

Figure 1. TR 3 spectra of wild type 12C]6OMb. Figure 2. TR 3 spectra of wild type 13C18OMb.

320

In spite of the such difference of the heme environments in the resting state for each mutants, there is a common intermediate in the rebinding process of photodissociated COMb. Since this intermediate appears at the initial stage of rebinding, it is considered that this is the precursor of the COMb form. In the time region where this intermediate appears, there is no band to show isotope shift so that CO does not bind to the heme in this stage but affects to the porphyrin to change its state slightly. As this intermediate is common to all the mutants, it is considered that the appearance of the intermediate reflects the (global) dynamics of the whole protein, but not the local dynamics. Therefore we propose that this intermediate can be so caged "open form".

H64A -20ns

I

r,,,

~

[ I L29F 379 t

526 I 497

581

lOOns llOOns

500ns

1lxs 1ixs

1opts

i I 700

I I I 600 500 400 Raman Shift/cm-1

Figure 3. TR 3 spectra of H64A COMb.

,4

700

600 500 400 Raman Shift/cm-1

Figure 4. TR 3 spectra of L29F COMb

References

1 Martin, J. L.; Migus, A.; Poyart, C.; Lecarpentier, Y.; Astier, R.; Antonetti, A. Proc. Natl. Acad. Sci. USA 1983, 80, 173-177. 2 Frauenfelder, H.; Slingar, S. G.; Wolyness, P. G. Science 1991, 254, 1598-1603. 3 Jackson, T. A.; Lim, M.; A.anfinrud, P. Chem. Phys. 1994, 180, 131-140. 4 Kuriyan, J.; Wilz, S.; Karplus, M.; Petsko, G. A.J. Mol. Biol. 1986, 192, 133-154. 5 Springer, B. A.; Sligar, S. G.; Olson, J. S.; Phillips, G. N., Jr.. Chem. Rev. 1994, 94, 699-714. 6 Sakan, Y.; Ogura, T.; Kitagawa, T." Fraunfclter, F. A.; Mattera, R." lkeda-Saito, M. Biochemisty 1993, 32, 5815-5824. 7 Li, T.; Quillin, M. L." Jr., G. N. P." Olson, J. S. Biochemistry 1994, 33, 1433-1446.

journal of

MOLECULAR

LIQUIDS ELSEVIER

Journal of Molecular Liquids, 65/66 (1995) 321-324

Solvent Viscosity Dependence of Bimolecular Reaction Rate Constant of the Excited 9-Cyanoanthracene Quenched by 1,3-Cyciohexadiene Minoru Kitazawa, Tetsuro Yabe, Yoshinori Hirata, and Tadashi Okada Department of Chemistry, Faculty of Engineering Science, Osaka University, Toyonaka, Osaka 560, Japan Abstract The photocyclization reaction rate constant at the encounter in nonpolar solvents has been evaluated for the excited 9-cyanoanthracene-l,3-cyclohexadiene system by analyzing the transient effect in the fluorescence decay curves. The reaction rate decreased with increase of the solvent viscosity, while the increase of the reaction probability in the encounter complex was observed. The reaction dynamics was discussed in relation to the solute orientational motion in the solvent cage.

Introduction The bimolecular reactions in solution are considered to take place in the solvent cage by approaching with mutual diffusion. However, there has rarely been experimental studies to clarify the reaction dynamics between reactants in the solvent cage. The excited 9-cyanoanthracene (CNA) -1,3-cyclohexadiene (CHD) system is considered to be one of the best combinations to study the reaction in the solvent cage. CNA reacts in the excited singlet state with CHD to give the [4+4] cycloadduct with high quantum yield in solution as shown in Scheme 1. The produced [4+4] cycloaddut photodissociates very rapidly to the excited singlet state of CNA and ground state CHD by irradiation of UV lights as indicated in Scheme 21. After the photodissociation of the adduct, the geminate diffusive motion will start from some restricted conformation, probably face-to-face, and reproduce the adduct or escape from the cavity. We can observe this processes by measuring the time dependencies of CNA fluorescence after irradiation of UV laser pulse. Actually, we have observed non-exponential decay curves in some solvents. On the other hand, the fluorescence quenching reaction of CNA with CHD gives us the informations of the dynamics in the encounter pair of the system. In this report, we estimate reaction rate constant in the encounter pair as a function of the solvent viscosity by measuring the fluorescence decay curves with picosecond laser excitation and analyzing the transient effect in the fluorescence quenching process.

9

9 CN

400nm Emission Ex.

I

lMe mbna n

CN

Scheme 1. Bimolecular fluorescence quenching reaction.

~ CN

Scheme 2. Fluorescence quenching by a geminate recombination.

0167-7322/95/$09.50 r 1995 Elsevier Science B.V. All rights reserved. SSD! 0167-7322 (95) 00823-3

322

Experimental Fluorescence decay curves were measured by means of a time correlated single photon counting method using a mode locked Ti:sapphire laser (Spectra Physics, Tsunami) as an exciting light source. The repetition frequency of the excitation pulse was modulated by electro-optical modulator to be 1.6-8 MHz. CNA was excited by the second harmonics of the laser (400nm) under the condition of the polarization at the magic angle. The response time of the apparatus was 35ps fwhm. SAI~ program at the Osaka University Computation Center was used for the nonlinear least-squares analysis of the observed decay curves. All measurements were made at 20"c. Liquid paraffin and decalins were purified by column chromatography on activated silica gel and alumina. Viscosity of liquid paraffin was measured by Ostwald viscometer. Spectrograde n-hexane and cyclohexane were used without further purification. All solutions for the measurements were deoxygenated by flushing with nitrogen gas.

Analysis We use the time dependent "rate constant", k(t), obtained by solving diffusion equation under appropriate boundary conditions 2-4. l _ 1 k(t) (1 + tCS e x p ( x E ) e r f c ( x ) ) N ' (1) with

exp(-A2)dA

erfc(x)-

x .... '

, R

ko

where kR is the reaction rate constants, kD=4~tRDN' the diffusion rate constant, D the sum of the reactants' diffusion coefficients, R the specified encounter distance and N' the Avogadro number in milliliter. When x>> 1, exp(x2)erfc(x) converges to 1 exp(x2)erfc(x) -

and k(t) is given by 1

1+

(2)

The time dependent fluorescence intensity is given by l(t)-

I o e x p ( - a t - bt v2)

where a - zo ~ + 4~rR'DN'[CHD]

b- ~O)"~R'~N'[CnO]

(3) (4)

(5)

R' - k s R / ( k n + k s ) (6) "to is the fluorescence life time of CNA without CHD, and [CHD] the concentration of CHD. By means of eq.(3), we have simulated the observed fluorescence decay curves of CNA in the presence of CHD. In the course of the simulation, the time walk between the response function of the system and the fluorescence decay curve was decided to minimize the chi-square parameter. A small change of the time walk leads to a large difference in the fitting parameter b at the low concentration of CHD. R' and D values were obtained from the linear relation of a and b vs. [CHD] with the aid of eqs.(4) and (5).

Results and discussion Figure 1 shows the non-exponential decay curves of CNA and simulated results in n-hexane and liquid paraffin including 0.100M and 0.508M CHD, respectively. Fitting results seem to be quite well, which indicates that the conventional formula of eq.(3) may be acceptable at the observed time scale. The quencher concentration dependencies of a

323

(a) I

I

I

I

I

(b) a = 6.331x108

a = 1.886x108

b = 1.393x103

b = 9.320x103

--..,.

..

I

I

I

I

I

I

lOOch/div. (20.35ps/ch)

I

lOOch/div. (20.24ps/ch)

Figure 1. The fluorescence decay curve (dotted line) and its simulation with eq.(3) (solid line). (a): [CHD] - 0.100M in n-hexane, x 2 = 1.111, DW (Durbin-Watson parameter)- 1.662 (b): [CHD] - 0.508M in liquid paraffin, x 2 = 1.394, DW = 1.742

3.0xl0g ].[. i I I 2.5 ~o n-Hexane (n a:l

I /o

~ t t

2.0~-&trans'Decali~t 1.5

12x10 3

'o0

1.0

8 4

0.5

o.o k'r'-

J

i

0.0

0.1

0.2

~

~

-H

0.3 0.4

!

0.5

0.6

[CHD]/M

0 0.0

0.1

0.2

0.3

0.4

0.5 0.6

[CHD]/M

Figure 2. The parameter a and b as functions of [CHD] obtained by simulation with eq.(3) for some solvents indicated in the panels. Table 1. R' and D values of CNA-CHD system in different solvents obtained by analysis of fluorescence decay curves. Calculated D values by using empirical equations, D~I., and Stokes-Einstein equation, DSE, are also listed. solvents n-Hexane Cyclohexane trans -Decalin cis-Decalin liquid paraffin

R,/10-Scrn 1.44 2.28 2.65 2.31 5.67

DFl0-Scm-2s-1 4.77 2.04 1.07 0.939 0.0506

DCal./10-Scm-2s-1 6.53" 2.09* 1.24 * 0.778* 0.0935**

DSE,/10-5cm2s-1 4.73 1.53 0.706 0.445 0.00953

* From 9 Wilke-Chang correlation, D~215 10"8(0MB)I/2T/TIBVA0-6 ,where D~ "1 is mutual diffusion coefficient of solute A in solvent B, MB /g-mol "] is molecular weight of solvent B, riB/cp is viscosity of solvent B, VA/cm3"mol "j is molar volume of solute A at its normal boiling temperature, and r is association factor of solvent B. ** 9From Hayduk and Minhas correlation, D~ -0-71 where E-(10.2/VA)-0.791.

324 and b in same solvents are indicated in Figure 2. The lifetime of CNA without CHD in each solution agreed very well with the value obtained from the intercept at [Q]-0 of a vs. [CHD] plot. R' and D values are summarized in Table 1 with calculated D values using empirical equations, Wilke-Chang and Hayduk-Minhas correlations 5. We have also estimated D values by using Stokes-Einstein equation, DSE in Table 1. The mutual diffusion constant obtained from Stokes-Einstein equation shows a large difference with the values obtained from the measurements of fluorescence quenching reaction and also empirical equations especially in viscous solvents. By using the values of R' and D, we estimated the reaction rate constant, kR, and reaction probability in collision complex, rp, when we assumed the van der Waals radii of CNA and CHD estimated from space-fitting molecular model to be 5.0 A and 2.0 ,~,, respectively, that is R=7.0 ,A, in eq.(6).The obtained rp, kD and kR values are listed in Table 2. Table 2. rp, kD and kR values obtained from R' and D assuming R=7.0/~,. solvents n-Hexane Cyclohexane trans-Decalin c/s-Decalin liquid paraffin

rp 0.206 0.326 0.379 0.330 0.810

kD/109s "IM1 25.3 10.8 5.66 4.97 0.268

kR/109s "1M'I 6.56 5.22 3.45 2.45 1.14

It should be noted here that kR decreases with decrease of kD while rp increases. In the fluid solvents such as n-hexane, the kD value is much larger than the value of kR and rp is relatively small, whereas rp is larger and kD is small compared to kR in liquid paraffin. These results may be explained probably as follows. The conformational orientation between the excited CNA and CHD should be restricted very much to produce a photocycloadduct in the collision complex indicated in the scheme 1. In the fluid solvents like hexane, the rotational relaxation times of the solute molecules are rather fast compared to the reaction rate, which increases the escape probability of the reactants from the solvent cavity due to the large value of kD. On the other hand, the transit time in the reactive conformation, probably symmetrical face to face, may be longer in the liquid paraffin. This means that the observed kR may be expressed as a function of the mutual rotational relaxation time of reactants and the real reaction rate in the face-to-face conformation. In this sense, it is very important to make precise time-dependent measurements in the course of geminate recombination reaction indicated in Scheme 2, because the initial conformation after photodecomposition of cycloadduct is considered to be close to the face-to-face conformation. The studies on the geminate processes of the system in solution by the time resolved spectroscopy are now progress in our laboratory.

Acknowledgments This work was partly supported by a Grant-in-Aid (06NP301 and 06453025) to T.O. from the Ministry of Education, Science, and Culture of Japan.

References 1 2 3 4

T. Okada, K. Kida, and N. Mataga, Chem. Phys. Lett., 88, 157 (1982). F . C . Collins and G. E. Kimball, J. Colloid Sci., 4,425 (1949). R. M. Noyes, Progr. React. Kinetics, 1, 129 (1961). S. Nishikawa, T. Asahi, T. Okada, N. Mataga, and T. Kakitani, Chem. Phys. Lett., 185, 237 (1991). 5 R.C. Reid, J. M. Prausnitz and B. E. Poling, The Properties of Gases & Liquids, Fourth Edition p597 (McGraw-Hill Book Company, New York).

journal o f

MOLECULAR

LIQUIDS

Journal of Molecular l.iquids. 65/66 (1995) 325-328

ELSEVIER

Extremely Slow Reorientation Dynamics of Molecular Tracers in Glassy Polymers Qui Tran-Cong, Hirotaka Kanato and Shinya C h i k a k i Department of Polymer Science and Engineering Kyoto Institute of Technology Matsugasaki, Sakyo-ku, Kyoto 606, Japan

Abstract A n e w experimental method based on the polarization-selective photochromic reactions is proposed to monitor extremely slow reorientation dynamics of molecular tracers in glassy polymer matrix. The correlations between the local relaxation processes of polymers and the reorientation dynamics of the tracers with different sizes are found from the experimental results obtained by this method. I. Introduction Reorientation dynamics of molecular tracers in polymers is not only important for the understanding of slow relaxation phenomena in glassy polymers 1, but plays also a critical role in practical problems such as molecular design of nonlinear optical materials with long-term stability based on dyes/polymers complexes 2. We s h o w here the reorientation dynamics of molecular tracers in glassy polymers obtained by the annealing-after-irradiation method described below. These experimental results are compared to the local relaxation processes of glassy polymers obtained by the already established measurement techniques such as dielectric relaxation and solid state NMR. Finally, the molecular interpretation of the relaxation of free-volume distribution in polymers will be discussed. II. Experimental Section A) S a m p l e s . The tracer molecules are 9-hydroxymethyl-10-{(naphthylmethoxy) methyl} anthracene 4 (HNMA, Fig. l-a)and tetraethyl {3.3}(1,4) naphthaleno (9,10) anthracenophane-2,2,15,15-tetracarboxylate5 ( C y c I o p h a n e, F i g. 1 - b ) . T h e intramolecular photodimerization of these molecules is induced by exciting the anthracene moieties with linearly polarized light at 365nm. The polymer matrix is poly(methylmethacrylate)(PMMA, Mw = 1 . 4 4 x 105, Mw /Mn = 1 . 7 ) . T h e microstructures of this polymer are 58.9% syndiotactic, 35.4 % heterotactic and 5.7% isotactic) as observed b~ 1H NMR. The tracers were doped in these PMMA films at the concentration ca.10"~M by using solvent casting method. R : CH=OH

R : COOC2Hs

/ C

0

H

hv

R

hv

~

~

-"

>

~hv',A

h e , A ~

Hg.l(a) Chemical structure of HNMA.

Fig.l(b) Chemical structure of Cyclophane.

B) Data A n a l y s i s . Irradiation was performed with a high pressure mercury lamp (250W, Ushio Electrics Co.). The two dichroic absorbance components of HNMA and Cyclophane at 393.5nm and 402nm were monitored at room temperature after irradiating the sample over different time intervals with linearly polarized light at 365nm. The reorientation dynamics of these molecular tracers were obtained from the analysis of the time-dependent induction efficiency rl0) which is defined as4: r/(t) = 100. { O D • (t) - OD,, (t)}/ O D o (1) 0167-7322/95/$09.50 r 1995 Elsevier Science B.V. All rights reserved. SSDI 0167-7322 (95) 00824-1

326 where OD_t_ (t) and OD II (t) are the absorbance measured in the directions perpendicular and parallel to the polarization of the exciting light, respectively and ODo is the initial absorbance. Experimental data were fitted to an approprmte model function by using a non-linear least square regression program. C) Results

and Discussion.

Upon irradiation with linearly polarized light, the induction efficiency aq(t) increases and reaches a maximum which strongly depends on the experimental temperatures 4. This behavior can be explained as the result of the competitions between the reorientational relaxation and the selective photodimerization of the molecular tracers6. The independent contribution from the reorientational relaxation to rl(t) can be extracted by using the annealing-after-irradiation described hereafter. At first, PMMA films doped with these tracers were irradiated until rl(t) reaches its maximum magnitude rlmax. Subsequently, irradiation was stopped and the sample was annealed at seven temperatures ranging from 40"C to 100"C in the dark. Due to the reorientation of the tracer, rlmax decays with annealing time. This relaxation process can be analyzed by fitting the experimental results to an appropriate decay function. Fig. 2 shows some typical decay curves of the rlmax of H N M A obtained by the annealing-after-irradiation. The change of+lrnax w i t h annealing time can be well expressed by the following function: +7(t) = (+7(0) - +7** ) exp(- kr t ) + +7** (2) where rl(0) is the induction efficiency before annealing, r100 is the equilibrium value of rl(t) obtained at long time of annealing and kr is the reorientational relaxation rate of HNMA. On the other hand, as shown in Fig. 3, the decay curves of the Tlmax obtained for Cyclophane are well fitted to the following equation: +7(t) - A (F1 e -•" + F2 e -k2, ) + +7** where A = (11(0) - rl|

(3)

) is the pre-exponential factor expressing the contribution of the

restricted reorientational process of cyclophane to the decay of +l(t) and kl, k2 are the decay rates of Vl(t) with the corresponding fractions F1 and F2. ~ t

i

i

1~4mA

i

i

Lr

I" "/.Oo - +ct

~

+ + + o

io

wZ /,.

cyclol~hllml i

,

+ 1so Annemiinl T i m e (rain)

i-ig.2 Annealing time dependence of the i.rlducllon efficiency rl0) of H N M A in P M M A at different temperatures.

T-rrz '~ ! o

so

i

!

i slo

Annealing Time (rain)

,]+

l ~,oo

Fig.3 Annealing tame dependence of the indu~ion efficiency rl(t) of Cyclophane m P M M A at dif~rent temperatures.

The solid curves depicted in Figs.2 and 3 are obtained by the fitting using Eqs. (2) and (3), r e s p e c t i v e l y . For both H N M A a n d Cyclophane, the presence of the temperature-dependent base line rloo i m p l i e s that the tracers undergo restricted reorientation in the glassy state of PMMA. A measure of this restriction can be expressed by the quantity +loo/rl(0) whose temperature dependence is shown in Fig.4.

327

The restrictions imposed on Cyclophane are stronger than on HNMA over the whole range of the experimental temperatures, suggesting the size effects on the rotation dynamics of molecular tracers in polymeric glass. The details of this restriction can be clearly seen in Fig.5. Here, the reorientation of Cyclophane and HNMA is assumed to follow the wobbling-in-cone model which has been proposed to analyze the rotational diffusion of fluorescent probes in lipid bilayers 7. Upon approaching the glass transition temperature (Tg = 110"C ) of PMMA, the cone angle 0max which is a measure of the free volumes surrounding the tracers, increases with increasing temperature and is almost 70* at 100*C as seen in Fig.5 . On the other hand, the temperature dependence of the reorientational relaxation rates kr of HNMA and kl, k2 of Cyclophane follows the Arrhenius behavior within the temperature range of this

1.0

|

,!

|

!

l 14NMA

Cyclophane I

]

0.8

0.8

~40d

I

0.4-

0.2-

'o

4;

o.o

0

8 lOO Temperature ('C) Fig.4Temperature dependence of 11,,/riO).

40

6

lo

100

]

'*' 9

HNI~I~ I PMMA

eye.bane

-""

,~

o.1

..................

"ck l o -~

"-

"" "" " A . . , ~ ~ . "-..

l O .2

1.?0

.

i

a.*o

,

I

lo*

.5

4"

o.os

I

SO

Temperature ( ' C ) Fig.5Temperature dependence of Omn.

|

:.oo

,

I

,

i

3.10

.

i

3.20

I / T xlO3 OK'I) Fig.6 Temperature dependence of reorientational rate constants of H N M A in P M M A . (m):lS-relaxation (dielectric relaxation); (----) : y-relaxation ( C P / M A S 1 3 C N M R ) ; For comparison , the relaxation frequencies of these data have been shifted by an appropriate amount along the ordinate.

10-~.70

,

I 2.80

,

I 2.90

A

I

3,00

1 / T x l 0 3 0K'~) Fig 7 Temperature dependence of reorientational rate constants of cyclophane in PMM.A.(--):lS-relaxation (dielectric relaxation); For comparison, the relaxation frequencies of these data have been shifted by an appropriate amount along the ordinate.

328 work. It was found that the activation energy Ea of kr of HNMA is 7.8kcal/mol and is close to the T-relaxation process of PMMA (rotation of the ot-CH3 groups) which has been directly observed by CP/MAS 13C N M R as depicted in Fig. 6 8. F o r Cyclophane, the values Ea of kl and k2 are in the range 16.9kcal/mol - 22.8kcal/mol. These values are close to the activation energy of the 15-process of PMMA (rotation of the -COOCH3 groups) observed previously by dielectric relaxation as illustrated in Fig. 7 9. The above results suggest that the difference in the "best fit" model functions (2) and (3) used in the curve fitting reflects the existence of a free-volume distribution in the sample. As shown in Figs. 6 and 7, the reorientational relaxation of molecular tracers with different sizes is affected by the local relaxation of different segments. In other word, the rearrangements of the free-volume distribution in the glassy state of polymers are driven by the local relaxation of polymer chains. Finally, the equilibrium value rloo probably corresponds to the reorientational relaxation processes of HNMA and Cyclophane in the regions with the free-volumes smaller than their sizes. It is of great interest to compare these results with the temperature dependence of the free-volumes data obtained by positron annihilation techniques. These experiments are currently in progress. In summary, we have demonstrated that extremely slow reorientation dynamics of molecular tracers in glassy polymers can be observed by the annealing-after-irradiation method proposed in this work. The correlations between the rotational motions of the tracers and the local relaxation of polymer matrix can provide an insight into the molecular interpretation of the relaxation of free-volume distribution in glassy polymers. Furthermore, the experimental results obtained here might give some useful guiding principles for the design of nonlinear optical polymers with long-term stability.

Acknowledgements. Q. T.-C. gratefully acknowledges the research fundings from the Ministry of Education, Science and Culture, Japan (Grant-in-Aid No. 06239238), and the Ogasawara Foundation for the Promotion of Science and Engineering. H. K. thanks Nippon Paint Co. for the scholarship.

References 1) See, for example, K.L. Ngai in "Non-Debye Relaxation in Condensed Matter" (World Scientific, Singapore, 1987). 2) M. Eich, B. Reck, D.Y. Yoon, C.G. Wilson and G.C. Bjorklund J. A p p i . P h y s . 66, 3241 (1989). 3) Q. Tran-Cong "Polarization-induced Photochromic Reactions m Polymer Solids " in "The Polymeric Materials Encyclopedia, Synthesis, Properties and Applications", CRC Press, to appear. 4) Q. Tmn-Cong, T. Kumazawa, O. Yano and T. Soen M a c r o m o l e c u l e s 23, 3002 (1990). 5) D. H. Hua, B. Dantoing, P.D. Robinson, Q. Tran-Cong, C.Y. Meyers Acta C r y s t . C 50 , 1090 (1994). 6) Q. Tran-Cong, N. Togoh, A. Miyake and T. Soen M a c r o m o l e c u l e s 25, 6568 (1992). 7) K. Kinosita, Jr., S. Kawato and A. Ikegami B i o p h y s . J. 20, 289 (1977). 8) F. Horii, Y. Chen, M. Nakagawa, B. G a b r v s a n d R. Kitamaru Bull. I n s t . Chem. Res. Kyoto U n i v e r s i t y 66, 317 (1088). 9) J.L.GomezRibelles, R. DiazCalleja J. P o l y m . Sci. P h y s . E d . 23, 1297 (1985).

journal of MOLECULAR

LIQUIDS ELSEVIER

Journal of MolecularLiquids,65166(1995) 329-332

Dynamics near a Liquid Surface: Mechanisms of Evaporation and Condensation K. Y a s u o k a , M . M a t s u m o t o , and Y. K a t a o k a " D e p a r t m e n t of A p p l i e d P h y s i c s , N a g o y a U n i v e r s i t y , F u r o , C h i k u s a - k u , N a g o y a 464-01, Japan *Department of Materials Chemistry, Hosei U n i v e r s i t y , K a j i n o 3-7-2, K o g a n e i 184, J a p a n

Abstract The rates of evaporation and condensation under the vapor-liquid equilibrium condition are investigated with a molecular dynamics computer simulation for argon at 80K, methanol at 300 K, and water at 400 K. The molecular reflection at the surface, which is related to the condensation coefficient a, is divided into two parts, self reflection and molecular exchange. There is no significant difference among the three substances concerning the ratio of self reflection to collision. The total ratio of reflection is estimated as a ~ 0.8 for argon, 0.2 for methanol, and 0.4 for water. The ratio of molecular exchange is much larger for methanol and water than for argon, which suggests that the conventional assumption of condensation as a unimolecular process fails for associating fluids. I. Introduction Evaporation and condensation are fundamental and important in various fields of science and engineering. Although a number of experimental and theoretical studies have been made on evaporation and condensation rates for decades, there still remain many problems. Although the collision rate is easily estimated with the kinetic theory of gas dynamics, all incident molecules are not necessarily caught on the liquid surface, and thus the condensation coefficient a, which is the ratio of the observed condensation rate to the ideal condensation one, becomes important. It is usually assumed that c~ is very close to unity (complete condensation) for many fluids, 1 but there has been controversy over a of associating fluids (e.g., water and alcohols). This arises from the experimental difficulty in estimating the absolute rate of condensation or evaporation under the vapor-liquid equilibrium condition. A transition state theory has been applied to calculate a under the assumption that the condensation process is a unimolecular chemical reaction. 2 It predicts a ~ 1 (complete capture) for simple fluids such as argon. In the case of associating fluids, however, much smaller a is expected due to the potential barrier ca.used by the rotational restriction of liquid molecules. Since the experimental results of c~ widely scatter, 1 we still have to check with great care the validity of assumptions made in the theoretical treatments. Computer simulations with molecllla,r dynanaics (~iD) technique are very suitable to investigate these evaporation-condensation phenomena at a. molecular level. Thus, we have carried out MD simulations for three systems, argon (a typical simple fluid) a,t T = 80 K and two associating fluids, methanol at T - 300 [( and water at T = 400 K. In this paper, we briefly describe the results of our simulations and data. analyses, and discuss the differences among the three from the viewpoint of dynamics a,t the surface. 0167-7322/95/$09.50 (c) 1995ElsevierScience B.V. All rightsreserved. 0 !67-7322 (95) 00892-6

SSDI

330

i_/

Fig. 1 A snapshot of the simulation (Argon at 80 K).

II. Simulation Technique We adopted a microcanonical ensemble MD method. The Lennard-Jones potential was used for the molecular interaction in the argon, OPLS potentials for methanol and water. We make a liquid slab with thickness of about 10 molecules a.t the center of the rectangular unit cell with periodic bo~indary conditions for all three dimentions. Figure 1 is a snapshot of a typical molecular configuration. Both sides of the slab are free liquid surfaces, on which molecules can evaporate and condense. The cell size along the surface normal is typically 100 A. and the surface area is 50 ]k x50 ~. The number of molecules is 1200 for argon, 864 for methanol, and 1024 for water. Other technical details are described elsewhere, a,4 III. Results and Discussion After equilibrating the system, we a ccllmulated the configurations for 997 ps (argon), 300ps (methanol) or 375 ps (water), from which we study dynamic properties concerning evaporation-condensation processes. Self condensation In most of studies so far (experimental as well as theoretical) on the condensation coefficient c~, the condensation process l~as I)een considered as a unimolecular chemical reaction, which means that the evaluation o t ' a is equivalent to estimating how many vapor molecules are reflected after colliding wit.h the liquid surface. In order to avoid confusion, let C~s,if be the condensation coefficient from this point of view, since we show later that the assumption of the unimolecular reaction is llot always correct. In principle, we can evaluate c~sr by direct counting of collision and reflection events from the molecular trajectory data; for both ca.ses, we observed sufficient number (about 200) of collision events. To estimate o'.~lf quantitatively, we have developed an autocorrelation function method. 5 The result is CYself ~ 90 % and there is no qualitative difference among various types of fluids, which suggests that the condensation as a unimolecular chemical reaction is a barrierless ~process. Calculation of the local chemical potential also supports this barrierless pictlire.

Total c o n d e n s a t i o n In visualizing tile nlolecl,lar configllrations, we sometimes observed that vapor molecules colliding with tile liquid s~lrfacc apparently drove other molecules out of the liquid. This kind of correlation bet,weell the conr tltlx and the ex,aporation flux, or ':molecular exchange," lnay llave a significailt effect oil t,lle rate of condensation. Following

331 Table 1 Comparison of condensation behaviors estimated from the simulation data. Argon (T=80K)

Methanol (T=300K)

Water (T=400K)

Self (t asr Exchange Total (1 a)

0.12 0.08 0.20

0.14 0.66 4- 0.10 0.80 4- 0.10

0.05 0.55 4- 0.05 0.60 4- 0.05

Condensation coefficient a

0.80

0.20 4- 0.10

0.40 4- 0.05

Ratio of reflection

1.5

15"-5 Water

E

o

T=400

--" "

1.0

o

K

m o

E

bonding non-bonding

e~

0.5

8

5-6

o.o bonding 9

>,

"" -0.02 r ._o ...., .__ -0.04 v 0

1]

0z

~ o.oo 8

El

L i q u i d I _ Surface region ,

,

10

z

n o n - b o n d i n g I~

9 ,

(h)

_ I

-I-

20

/

Vapor .

]

-I

30

Fig. 2 Surface of liquid water at T = 4 0 0 K. Density profile and number of neighboring molecules (top) and the kinetic energy correlation (bottom). a general framework of chemical reaction theory, we have developed a memory function method to estimate the phenomena. T The total condensation coefficient a is calculated by using the correlation of colliding and evaporating fluxes with a memory function. The estimated value is _~ 0.80 for argon, ~_ 0.20 + 0.1 for methanol, and ~ 0.40 + 0.05 for water. Comparing a with asar, we can also evaluate the ratio of the molecule exchange. The results are summarized in Table I. The ratio of self reflection and molecular exchange is very similar for argon. However, in the case of associating fluids, the ratio of the exchange is several times larger than that of the self reflection. This implies that the condensation cannot be regarded as a unimolecular process, especially in the case of associating fluids. Heat transfer by hydrogen bonds A key point to understand the above difference between simple fluids and associating fluids is the mechanism of molecular heat transfer accompanying tile evaporation and condensation at the surface. If the energy is not transferred (or dissipated) fast enough, the hitting molecule cannot lose the extra energy to condense itself, and will finally re-

332 evaporate, which is the self-reflection. On the other hand, the surface molecules receive the extra energy from the hitting molecule, and if the amount of the received energy is too much, the surface molecule may get evaporated in exchange of the condensation of the hitting molecule, which is the molecular exchange. Since it is difficult to evaluate the precise local heat conductivity from the simulation data, we instead calculate the kinetic energy correlation between neighboring pairs; if a large amount of heat is transfered between a pair of neighboring molecules, there should be a strong correlation between the kinetic energy fluctuations of each molecule. A part of the results is shown in Fig. 2, where the kinetic energy correlations are shown for hydrogen-bonding pairs and non-bonding pairs in the case of water. The correlation is several times stronger for bonding pairs than non-bonding ones; a similar result is obtained for methanol. In the case of argon, the correlation is similar to that between non-bonding pairs of associating fluids. From these evidences, we can easily imagine what happens in the condensation process of associating fluids: The latent heat released in the instance of condensation is rather large, but is transferred efficiently by the strong hydrogen bonds. However, since the number of bonding pairs is only 1 or 2, the neighbor becomes easily evaporated by the transferred heat, and thus the molecular exchange is often observed. Further analyses are now under way. Summary Using a molecular dynamics computer simulation, we have investigated the evaporation-condensation dynamics for argon, methanol, and water. The ratio of condensed molecules to surface-colliding ones, a,~jl, is about 90~7c for all substances, although surface properties of methanol and water are very different from those of argon. However, the total condensation coefficient c~ estimated with flux correlation of evaporation and condensation is much smaller for methanol and water than for argon. The difference between a and a,~ll is caused by molecular exchange at the surface. In the case of methanol and water, the molecular exchange is a dominant factor to determine the condensation-evaporation rate. A rough sketch for the difference among the species is given from the viewpoint of heat transfer near the liquid surface.

Acknowledgments Thanks are also due to the Conlputer Center, Institute for Molecular Science, for the use of their colnputer facilities. This work has been financially supported in part by Grant, s in Aid for Scientific Research (No. 0523901.5) from tile Ministry of Education, Science alid Culture, Japan

References 1 2 3 4 5 6 7

H.K. Cammenga, CurT~ent Topics in ~laterials Science, ed. bv E. Kaldis (NorthHolland, Amsterdam, 1980), \1ol. 5, and references therein. S. Fujikawa and M. Maerefat, JSME II, 33,634 (1990). K. Yasuoka, M. Matsumoto, and Y. I(ataoka, 3. Chem. Phys., 101, 7904 (1994). M. Matsumoto, K. Yasuoka, and Y. I,~a.taol~a, J. C]lem. Pllvs., 101, 7912 (1994). M. Matsumoto and Y. Kataoka., Nlol. Silnlllatiotl. 12, 211 (199,1). K. Yasuoka, M. Matsumoto. ;ttld Y. I(ataoka, l$~lll. (',lleln. Soc..Jpn., 67, 859 (1994). M. l~ia.tsumoto, I,/. Yasuol~a, a llcl Y. I{ataoka, "l'llerln. Sci. Eng., 2, 6,1 (1994).

journal of

MOLECULAR

LIQUIDS ELSEVIER

Journal of Molecular Liquids, 65/66 (1995) 333-336

The Effect of Ionic Atmosphere on the Tracer Diffusion of Miceiles Toshihiro Tominaga and Masayuki Nishinaka Department of Applied Chemistry, Okayama University of Science, 1-1 Ridai-cho, Okayama 700, Japan Abstract By use of the Taylor dispersion method, diffusion coefficients for pyrene solubilized in micelles of octadecyltrimethylammonium chloride (C 18TAC) and tetradecyltrimethylammonium bromide (C14TAB) have been measured in aqueous NaCI and NaBr solutions, respectively, at 35 ~ These values can be regarded as tracer diffusion coefficients for the micelles because essentially all pyrene molecules are solubilized in the micelles. In the range 0.24 < ~r 97 %) was dried in vacuum, was dissolved in hot ethanol under nitrogen atmosphere, and was recrystallized by adding acetone and cooling. C 14TAB (Tokyo Kasei, guaranteed reagent), NaCI, and NaBr (both Nacalai Tesque, guaranteed reagent) were used as received. Pyrene (Wako Pure Chemical Ind.) was purified by sublimation. Water was distilled twice. Diffusion coefficients were measured by the Taylor dispersion method. 7 Other details have been described elsewhere. 1

III. Results and Discussion 0167-7322/95/$09.50 "C)1995 ElsevierScience B.V. All rights reserved. SSD! 0167-7322 (95) 00825-X

334

Figures 1 and 2 show diffusion coefficients of pyrene solubilized in C 18TAC and C 14TAB micelles, respectively, at 35 oC. Because essentially all pyrene molecules are solubilized in the micelles, the diffusion coefficients can be interpreted as tracer diffusion coefficients of the micelles. Diffusion coefficients decrease with increasing concentration of the micelles, and increase with increasing concentration of the salts added. Diffusion coefficients at cme's, Dcmc, were obtained by extrapolation, and are listed in Table 1

0.9

E

in water

a

0.0003MNaCI

zx 0.001MNaCI

r O4

o

v

0.002MNaCI

i

o

0.005MNaCI

~ 0.7

,~ 0.01MNaCI

0

0.8

o

*

0.6 0

0.01

0.02

0.02MNaCI

0.03

018TAC / M Figure 1. Tracer diffusion coefficients of CI8TAC micelles in aqueous NaCl solutions at 35 oC. Cmc's are very close to zero in this abscissa scale. 1.2

r

1.1

i

o

in water

8

0.005M NaBr

O4

E

O

zx 0.01M NaBr

i

o

0.9

-

(

v

0.02M NaBr

o

0.1M NaBr



1

el (..1

'l

_

;66
r o or y > r o or z > ro),

(7)

then the temperature at x=y=z=0 is U(0, 0, 0, t) = {erf( r0/(4K: t) ~n )}3.

(8)

By using the functions (6) and (8) as model functions, we tried to explain the observed time dependence of the solute temperature. The best fits for the both cases are shown in Figure 2. The thermal diffusivity for hexane, 8.24 x 104 m 2 s~, was used in the model functions. When fitting with the model function (6), the time region before 7 ps was excluded from the fitting because of the unrealistically steep change of the function (6) in this time range. The time 0 was also excluded from the fitting for the function (8). The fit with the equation (6) is poor especially at earlier time delays, while the model function (8) gives a good fit when r 0 = 1.6 nm. The other fitting parameters for the function (8) are the value at t=** (offset) and the amplitude of the change. It is interesting to note that the fit with the exponential decay is also quite good, showing that the time constant based on a single exponential decay scheme is a good measure to characterize the kinetics of the vibrational cooling. It is not naturally expected that the vibrational cooling process in a picosecond time range is so well explained by using the function (8) which is based on the thermal properties of the surrounding solvent, and not the character of the solute itself. This fact suggests that the vibrational cooling process of a solute molecule is controlled by the heat conduction in the solvent. In this scheme, the energy flow at the interface between the solute and the nearest solvents, or solvents in the fast layer, is expected to be much faster than the flow at the solvent-solvent interface. The latter serves as the rate determining step. The r0 value of 1.6 nm also implies that the excess energy spreads rapidly to a volume which is larger than the dimension of trans-stilbene, again suggesting that there is an efficient energy transfer between the solute and the fast layer solvent molecules. The observation that the cooling processes for three different vibrational modes of S~ trans-stilbene, 285 cm 1, 1180 cm ~, and 1570 cm 1 are indistinguishable means that the excess energy is well distributed among vibrational degrees of freedom and that this intramolecular redistribution process is much faster than the observed vibrational cooling time scale. Recently we also observed that the vibrational cooling rates in different solutions have a good correlation with the thermal diffusivities of the solvents. These results will be published soon. References 1 T. Elsesser and W. Kaiser, Ann. Rev. Phys. Chem., 42, 83(1991). 2 Y. Hirata and T. Okada, Chem. Phys. Lett., 187, 203(1991). 3 K. Iwata and H. Hamaguchi, Chem. Phys. Lett., 196, 462(1992). 4 K. Iwata, S. Yamaguchi, and H. Hamaguchi, Rev. Sci. Instrum., 64, 2140(1993). 5 K. Iwata and H. Hamaguchi, J. Raman Spectrosc., 25, 615(1994). 6 R.E. Hester, P. Matousek, J. N. Moore, A. W. Parker, W. T. Toner, and M. Towrie, Chem. Phys. Lett., 208, 471 (1993). 7 W.L. Weaver, L. A. Huston, K. Iwata, and T. L. Gustafson, J. Phys. Chem., 96, 8956 (1992). 8 K. Iwata and H. Hamaguchi, to be published. 9 H. Hamaguchi and K. lwata, Chem. Phys. Lett., 208, 465(1993). 10 J. Qian, S. L. Schultz, G. R. Bradburn, and J. M. Jean, J. Phys. Chem., 97, 10638(1993).

journal of MOLECULAR

LIQUIDS ELSEVIER

Journal of Molecular Liquids, 65166 ( i 995) 42 i - 4 2 4

Rotational Relaxation of Rod Like Molecules: Diphenylacetylene in Various Solvents. Yoshinori Hirata, Yasuhiko Kanemoto, Tadashi Okada, and Tateo Nomoto* Department of Chemistry, Faculty of Engineering Science and Research Center for Extreme Materials, Osaka University, Toyonaka 560, Japan and tDepartment of Chemistry, Faculty of Education, Mie University, Tsu, Mie 514, Japan Abstract By using fluorescence anisotropy decay and polarized transient absorption spectrum measurement techniques with a picosecond time resolution, we have studied the rotational relaxation of 4-[[4-(dimethylamino)phenyl]ethynyl]-benzonitrile in various solvents. Our aim is to clarify the solvent-solute interactions revealed as a solvent dependence of the rotational relaxation time of solute molecules. Among the solvents we used, ethanol shows characteristic behavior compared with other polar solvents. The rotational relaxation time in ethanol seem to be close to that calculated on the basis of the slip boundary condition, while in other polar solvents, the stick boundary condition can reproduce the experimental value. The results suggests that the strong hydrogen bonding between the solvent molecules allows the solute to rotate more freely within the solvent cage than in other polar solvents. I. Introduction Rotational diffusion of molecules in liquids should be quite important to establish the microscopic description of chemical reaction dynamics in the solution phase. Sometimes, geminate process was suggested to be governed by rotational diffusion rather than a translational diffusion. It may play an important role in the radical dimer formation process on the geminate encounter of p-aminophenylthiyl radical pair. 1 Reorientation relaxation of a solute molecule is usually measured by monitoring either the time dependent fluorescence depolarization or the transient absorption of a polarized light pulse. Rotational diffusion of dye molecules in various solvents has been investigated extensively. Although many of them aimed for the elucidation of solvent-solute interactions including hydrogen bonding, there are ambiguities which come from the electronic relaxation and geometrical change of solute molecules. In order to simplify the situation and extract the information about the rotational diffusion of solute molecules, it is necessary to reduce the flexibility and complexity of the molecular structure, which cause the change of the direction of the transition dipole moment within the molecular frame. Considering these factors, we have chosen 4-[[4-(dimethylamino)phenyl]ethynyl]-

H3C/

I benzonitrile as a probe molecule. This molecule has a rigid rod-like structure and the transition moment between the ground and fluorescence states (Sx state in nonpolar 0167-7322/95/$09.50 91995 Elsevier Science B.V. All fights reserved. SSDi 0167-7322 (95) 00890-X

422

solvents and charge separated state in polar solvents) are parallel to the long molecular axis. Although the electronic relaxation and twisting of the phenyl rings which occur on the intramolecular charge separation may give some difficulty, such characteristics should allow us a simplified view of the rotational relaxation phenomena. Boundary condition of the rotational motion in the solution phase should reflect the solvent-solute interactions. The solvents used in this work is found to be devided into two rOUpS. One is slip and the other is stick. In ethanol, the rotational relaxation time was und to be shorter than those estimated for aprotic solvents with a similar viscosity. The viscosity dependence of the rotational relaxation time in various solvents will be discussed. II. Experimental The rotational reorientation times of the sample in several solvents at room temperature were measured by picosecond time--resolved fluorescence and absorption depolarization spectroscopy. Details of our experimental setups were described elsewhere? For the time-correlated single photon counting measurement of which the response time is about 40 ps, the sample solution was excited with a second harmonics of a femtosecond Ti:sapphire laser (370 nm) and the fluorescence polarized parallel and perpendicular to the direction of the excitation pulse polarization as well as the magic angle one were monitored. The second harmonics of the rhodamine-640 dye laser (313 nm; 10 ps FWHM) was used to measure the polarized transient absorption spectra. The synthesis of the sample is given elsewhere. 3 All the solvents of spectro-grade were used without further purification.

III. Results and Discussion As shown in Figure 1, fluorescence spectrum of I shows a significant solvent effect. In nonpolar solvents, the fluorescence maximum is observed around 370 nm and the absorption and fluorescence spectra show mirror image symmetry. On the other hand, in polar solvents the mirror image symmetry is broken and the broad fluorescence band of which the maximum appears in the long wavelength region is observed. The band maximum shifts to the red with increasing solvent polarity. Measuring picosecond time resolved absorption spectra of I in polar solvents, we observed the spectral change due to the intramolecular charge separation. In polar solvents such as diethylether ether and acetonitrile, immediately after the excitation, the S, ,--$1 absorption band is observed, while the spectrum ascribed to the charge separated state is dominant in the delay time region longer than 10 ps after the excitation laser pulse. The major part of the observed fluorescence in polar solvents seems to be from the charge separated state of I. Because of the short lifetime of $1 in polar solvents, rotational diffusion of $1 should not be significant. It was suggested that the ground and $1 states of I are almost planar and in the charge separated state, two phenyl rings are perpendicular to each other. The geometrical change on the charge separation may not affect the rotational diffusion of the charge separated state significantly because the molecular volume and the ratio of the long/short molecular axis are essentially the same for the $1 and charge separated states. The time dependence of the fluorescence polarized parallel and perpendicular to the pump polarization direction were fitted simultaneously to

I(t) = (I(O)/3)exp(-t/r!)l + 2r(O)exp(-t/ror )

(1)

I(t) = (I(O)/3)exp(-t/r t)l - v(O)exp(-t/ror).

(2)

423

By using nonlinear least squares fitting, the orientation relaxation time (rot), fluorescence lifetime (rf), and the initial value of anisotropy (r(0)) were obtained. The typical results of the fitting to the time dependence of polarized fluorescence of I in n-hexane is shown in Fig. 1. In order to confirm the validity of the data analysis, the fluorescence lifetime was also measured with the magic angle arrangement. 3_. 8

1 ,..,

7.")("

4 "~""~

' ' '

A4i "i,...\ , -",,"Y,.",. \ -~

,

t

i ", ' ', .'. \1;./

.,

i./

400

',..

"-;x \

~,,,,,,,,,,..

500 600 ~,Vavelength [ nm ]

",,(,,:..,.,,..,,:., 700

F i g u r e 1. Fluorescence spectra of I in cyclohexane (6),trans-decalin(8), diethylether (1), ethanol (7), acetone (3), and acetonitrile (4).

"~ 0

I

i

200 ~00

I

0 200 ~00 600 t [ chonnel ]

F i g u r e 2. Time dependence of the polarized fluorescence of I in n-hexane (1 channel = 2.54 ps). The residuals are also shown in the figure.

Except for ethanol solution, a good fitting was obtained for the fluorescence decay curves. In ethanol, even the fluorescence measured at the magic angle shows a complex decay, which should be due to the dynamic Stokes shift. Although we got a rather poor fitting to the biexponential decay function in the short delay times, the estimated fluorescence decay times obtained from the measurements at the magic angle were about 10 and 220 ps. From the fitting of the polarized fluorescence in the long delay times, the rotational relaxation time was obtained to be 124 ps. Reliable value for r(0) was not obtained for this case. The measured rotational reorientation times, initial value of the fluorescence anisotropy, and fluorescence lifetimes in several solvents are listed in Table I. The initial value of anisotropy is very close to 0.4, which suggests that the directions of the transition dipole of the absorption and the fluorescence are the same and the depolarization not due to the reorientation of the molecule can be ignored. Figure 3 shows the plot of the rotational reorientation time versus the solvent viscosity. The straight lines show the reorientation times calculated as rot = C . f~tick " V r # / k B T ,

(3)

where V is molecular volume of solute, 77 is solvent viscosity, and kB is the Boltzmann constant, fstick depends on the molecular shape and is calculated and tabulated by Hu and Zwanzit~.4 The C value is the ratio of the friction coefficient with slip to the friction coefficient ot stick. The probe molecule has been modeled as a prolate ellipsoid with the molecular volume and the ratio of about 70 A 3. Acetone (3) and N,N-dimethylformamide (5) are on the solid line, which was calculated for stick. On the other hand, several aliphatic hydrocarbon solvents (2, 6, 8) and ethanol (7) seem to be

424

on the broken line. The ratio of the slopes of the broken and solid lines is about 0.78, which is slightly smaller than the calculated value from the molecular shape. It is known that the reorientation relaxation times of uncharged molecules are rather close to those estimated under slip boundary condition. The nonpolar solution of I seems to be the case. On the other hand, the stick boundary condition seems to give a better prediction in polar aprotic solvents. This should be due to the strong solvat]on of the large dipole moment produced by the intramolecular charge separation. The orientation relaxation time of I in ethanol was found to be very close to that predicted for slip boundary condition. Important point of our results is that the rotational diffusion in ethanol is faster than that expected for the stick boundary condition. Our results may suggest that the strong hydrogen bonding between the solvent molecules allows the solute to rotate more freely within the solvent cage than in other polar solvents. Table I. Excited-state rotational reorientation times, fluorescence lifetimes (ps), and initial values of the fluorescence anisotropy of I in several solvents at room temperature.

1 2 3 4 5 6 7 8

to,. 43 38 63 49 130 102 124 226

Solvent (viscosity(cP)) diethylether ether (0.24) n-hexane (0.32) acetone (0.32) acetonitrile (0.38) N,N-dimethylformamide (0.92) cyclohexane (0.94) ethanol (1.19) trans-decalin (2.13)

200

1"/ 1880 600 1230 750 850 670 224 760

-

7"(0) 0.39 0.39 0.37 0.43 0.38 0.39 0.37

t tt

5o

loo

.og

-

~

13

Oo

1

Visc~sity [(:P ] Figure 3. Viscosity dependence of the reorientation relaxation time of I.

Acknowledgement: The present work was partly supported by Monbusho International Scientific Research Program (05044055) to T. O.

References I. Y.Hirata, Y. Niga, and T. Okada, Chem. Phys. Lett. 221,283 (1994) 2.Y. Hirata, T. Okada, and T. Nomoto, J. Phys. Chem., 97, 9677(1993). 3. T. Nomoto, F. Tanaka, and N. Suzuki, Chem. Express 6, 319 (1991) 4. C. M. Hu. and R. Zwanzig, J. Chem. Phys. 60, 4354 (1974)

journal of

MOLECUlaR

LIQUIDS ELSEVIER

Journal of Molecular Liquids, 65/66 (1995) 425--428

Ground State Recovery of Phenol Blue in Fluids near the Gas-Liquid Critical Density Yoshifumi Kimura and Noboru Hirota

Department of Chemistry, Faculty of Science, Kyoto University, Kyoto 606-01, Japan

Abstract We have made a sub-picosecond pump-probe transient absorption study on Phenol Blue at 308 K in trifluoromethane near the gas-liquid critical density and at the high density (about twice of the critical density) where small amount of 2,2,2-trifluoroethanol is added as c ~ solvent. The ground state hole created by the pump pulse is mostly broadened by about 1 ps, and we could not detect any meaningful density effect on this process.

I. Introduction Recently it has been demonstrated by Barbara and co-workers that the ground state recovery of a solvatochromic dye such as betaine-30 gives us a lot of information on the energy dissipation process from the excited state in liquids. They found an important role of a high frequency intramolecular vibration of the ground state on the energy dissipation process from the excited state, and also found a "hot" ground state configuration after the energy transfer from the excited state molecule to the solvent, which is observable as a red-shifted absorption spectrum. 1-5 In the present work, we have tried to measure such an energy dissipation process with a function of solvent density. In considering the problem of the energy transfer, the solvent density plays an important role, since the collision frequency and the thermal diffusivity, which are dominant factors in the energy transfer process, are strongly dependent on the density. 6 By changing the solvent density, we hope to observe such an effect on the energy dissipation rate from the excited state and on the dynamics of the "hot" ground state. We have also another interest in the fluid near the critical density. Near the critical density, there is a developed local structure around the solute molecule, 7 which is also spectroscopically observable. 8 If the relaxation time of the local structure is slow enough, we could see some density effect on the ground state hole broadening process just after the excitation, since this process is related to the relaxation of inhomogeneity. For these purposes we have studied the solvatochromic dye of Phenol Blue (PB, Scheme 1) in trifluoromethane (CF3H) near the critical density. Although betaine-30 is more preferable for the comparison with liquid solvent, it was impossible due to the extremely low solubility of betaine-30 to CF3H. PB is more soluble in CF3H, and has absorption around 560 nm which is accessible by our laser system. Unfortunately the photophysics of PB has not been studied until now even in liquid solution. Therefore we have also studied the ground state recovery in several liquid solvents. According to the theoretical calculation, 9 the charge 0167-7322/95/$09.50 fc3 1995 Elsevier Science B.V. All rights reserved. SSDi 0 i 67-7322 (95) 00836-5

426

O

O-

N~'~N(CH3)2 N~+N(CH~2

Scheme 1. Structure of PB.

a

b

separated state (b) is more stable in the excited state, and non-polar state (a) is more stable in the ground state. The ground state recovery corresponds to the charge recombination process, not to the charge separation process like betaine-30. II. Experimental The ground state recovery was measured by a sub-picosecond pulsed dye laser. A train of frequency doubled pulses from a modelocked Nd:YAG laser (Coherent: Antares 76) synchronously pumped a dye laser (Coherent: Satori) which produced 200 fs pulses centered at 640 nm at 76 MHz. A small fraction of the output of the Nd: YAG laser was used to seed a Nd:YAG regenerative amplifier (Continuum: RGA60). The output from the dye laser was amplified in three flowing dye cells (Continuum: PTA60) by the doubled output of RGA60. The final output (Ca. 300 ~tJ at 50 Hz) was introduced to the standard pump-probe experimental setup. 10 A white continuum generated by focusing the laser pulse on water was used as the probe light, and the transient absorption spectrum was measured by the optical multichannel analyzer. The polarization of the pump light was rotated to the magic angle to that of the probe light to eliminate the effect of molecular rotation. All measurements were performed at 3138 K. A quartz cell with the path length of 1 mm was used for the liquid solution. For the measurement under high pressure conditions, an optical high pressure cell with the path length of 12 mm was used. 11 To obtain enough concentration of PB in the fluid near the critical density, we added a small amount (Ca. 1xl0 -1 mol dm -3) of 2,2,2-trifluoroethanol (TFE) as co-solvent. We have measured at two different pressures of 5.7 MPa (pr4).8) and 18.0 MPa (pr,~l.9), where Pr is the reduced density by the critical density of solvent. The density of CF3H was calculated by the empirical equation of state 12. We neglected the effect of the co-solvent on the PVT relation of solvent. III. Results and Discussions Figure 1 shows the transient absorption spectrum of PB in methanol after the excitation at 640 nm. In the figure we set time zero as the rise of the pump pulse. The ground state hole created by the pump pulse is broadened mostly by 1 ps. Near the absorption maximum of the ground state, more than half of the bleach signal observed at 1 ps is recovered until 2 ps, and the residual bleach is diminished with a decay constant of about 10 ps. The hole broadening

427

0.1

,

,

0

.~

,

o

\ ~ .

-0.2

.

,

0.1

" ~ =..

f/

o

oot

a

~o -

,

0

~

~

~

I

o

I

9 0.2~, 0.4 I ~

9

i

'~

9 o.6.

,

,

a

~

%

&io~

--

o

~, o

I

I

I

I

550

600

650

700

750

9

800

500

1.0 pe

9 ~.o.

o:.o.

-OD

I

,

o

~o

-0.2

I : ._oo. 0~

[: 500

,

_

-OD N

I

I

I

I

I

550

600

650

700

750

Wavelength (nm)

800

Wavelength (nm)

Figure 1. Transient absoprtion spectrum of PB in methanol at 308 K after the excitation at 640 nm. The difference of the absorbance with pump pulse from that without pump pulse is plotted. Solid lines denote the equilibrium absorption spectra, of which the sign is inverted and the peak value is rescaled to that of the latest time data in each figure.

0.05

=

I

=

=

0.05

,

=

=

i

~~176 9 t

o

X

-0.05

o

-0.1

,,

~

,

9

r 0.2 ps 0.4 ps 0.8 ps

o o

"

=,~

o

0

=,,~

,,

-

0.05

",,

-0.1

~o~,~

-

0.8 lOS

450

9 r~

~Y~,

2.0 ps 3.0 pS

~,o o ~176 ~'~'

~ - O D q

-OOeq

-0.15 400

o.

,m,

i

I

I

I

I

500

550

600

650

Wavelength(nrn)

0.15 700

400

I

I

I

I

I

450

500

550

600

650

700

W a v e l e n g t h (nm)

Figure 2. Transient absoprtion spectrum of PB in CF3H with small amout (Ca. l x l 0 -1 mol dm -3) of TEE at 308 K and 5.7 MPa after the excitation at 640 nm. The legend is the same for figure 1. process after 2 ps was not well resolved within our signal to noise ratio. There appears an absorption signal around 750 nm with a decay rate of about 1 ps. The absorption around 750 nm, red-shifted to the ground state, is considered to be due to the non-solvated excited state, not to the "hot" ground state, since absorption due to S0"-'$2 is observed around 340 nm in equilibrium and the sum of the energy of 640 nm and 750 nm corresponds to 340 nm. This fact suggests a possibility that the growth of absorption due to some new "state" from the non-solvated excited state, probably the solvated excited state, contributes partially to the fast component of the bleach recovery near the absorption maximum

428 of the ground state absorption; i.e., in this time range we observe the complex spectrum dynamics related to the solvation and the relaxation of local inhomogeneity. Figure 2 shows the transient absorption spectrum of PB in CF3H at 5.7 MPa. The pattern of the transient spectrum is almost the same as those in methanol. The hole broadening occurs mostly within 0.8 ps, and the bleach is recovered with two different time constants in a similar manner as in the liquid solvents, although the recovery after 2 ps is much slower in the fluid near the critical density (about 40 ps). It is also to be noted that the bleach signal after 2 ps is narrow banded in comparison with the equilibrium absorption. This can be interpreted by the overlapping of the excited state absorption, and/or, the small inhomogeneity remained after 2 ps due to the long time density fluctuation. In the earlier events by 2 ps we could not see any meaningful difference between the medium- and high-density fluids within our time resolution and signal quality. This suggests that the density effect on the solute environment which determines the fast process, the solvation and the relaxation of the inhomogeneity of solvent in this time range, is small under the density region studied. The elucidation of the nature of the long time component of the bleach recovery such as the solvent effects, the density effect and the temperature effect, is now under work.

Acknowledgment This work is supported by the Research Grand-in-Aid from the Ministry of Education, Science and Culture (No. 0674~.A.4). References 1 E. Akesson, G. C. Walker, and P. F. Barbara, J. Chem. Phys., 95, 4188 ( 1991). 2 N. Levinger, A. E. Johnson, G. C. Walker, and P. F. Barabara, Chem. Phys. Lett., 196, 159(1991). 3 E. Akesson, A. E. Johnson, N. E. Levinger, G. C. Walker, T. P. DuBruil, and P. F. Barbara, J. Chem. Phys., 96, 7859 (1992). 4 G.C. Walker, E./~kesson, A. E. Johnson, N. E. Levinger, and P. F. Barbara, J. Phys. Chem., 96, 3728 (1992). 5 A.E. Johnson, N. E. Levinger, W. Jarzeba, R. E. Schlief, D. A. V. Kliner, and P. F. Barbara, Chem. Phys., 176, 555 (1993). See, e.g., A. B. Bhatia, UltrasonicAbsorption (Dover, New York, 1967). Y. Kimura and Y. Yoshimura, Mol. Phys., 72, 279 (1991). See, e.g., O. Kajimoto, M. Futakami, T. Kobayashi, and K. Y amasaki, J. Phys. Chem., 92 1347 (1988). V. Luzhkov and A. Warshel, J. Am. Chem. Soc., 113, 4491 (1991). 9 G. R. Fleming, Chemical Application of Ultrafast Spectroscopy (Oxford University 10 Press, New York, 1986). 11 Y. Kimura, Thesis, Kyoto University 1992. 12 R.G. Rubio, J. A. Zolloweg, and W. B. Streett, Ber. Bunsenges. Phys. Chem., 93, 791 (1989).

journal of

MOLECUlaR

LIQUIDS ELSEVIER

Journal of Molecular Liquids, 65/66 (1995) 429-432

Dynamics of Two-Component Liquids near the Glass Transition Yutaka Kaneko and Jiirgen Bosse Department of Applied Mathematics and Physics, Faculty of Engineering, Kyoto University, Kyoto 606, Japan and Institut fiir Theoretische Physik, Freie Universit~it Berlin, Arnimallee 14, 14195 Berlin, Germany Abstract Dynamics of a supercooled binary hard-sphere liquid is investigated within a modecoupling theory. For a disparate-size mixture, a glass is formed at a critical packing fraction rib by only the big particles, while the small particles diffuse through the voids of the glassy structure. Diffusion of the small particles is blocked in a localization transition at rL4 (> riB). Near the glass transition (r/B), we find a change of the diffusion mechanism for the small particles which we discuss from a dynamical point of view.

I. Introduction The glass transition of simple one-component liquids has been extensively studied within a mode-coupling theory supplying us with many predictions concerning the relaxation dynamics in a supercooled state. 1 Recently, this theory has been extended to multi-component systems with the aim of studying such interesting phenomena as interdiffusion and ionic conductivity. 2'~ The long-time limits of density correlation functions have been determined for disparate-size binary liquids, which allowed to identify the localization-delocalization transition of the small particles within the glassy structure of the big particles. 2'4 In this paper, we study the dynamical properties of a binary hardsphere mixture near the glass transition by solving the full space- and time-dependent mode-coupling equations for this system. The appearance of the delocalized phase of the small particles is confirmed by investigating the diffusion constants of both particle species. We discuss the change in the diffusion mechanism of the small particles from liquid-like diffusion to slow diffusion in a (static) random potential in terms of the incoherent density-relaxation function and the frequency-dependent diffusivity. II. Theory For a system of classical particles, the time evolution of the tagged particle correlation function

r

~)=< exp[-iq. (r0(,) - r0(0))] >

0167-7322/95/$09.50 ( 91995 Elsevier Science B.V. All rights reserved. SSDI 0167-7322 (95) 00837-3

(1)

430

is expressed by the generalized oscillator equation (v~ = kBT/m,) r176

+ q~v~ r

dr' K ~

with the initial conditions r 0) = 1 and r the mode-coupling approximation reads

t') r

= 0

(2)

0) = 0. The relaxation kernel K,(q, t) in

K,(q, t) MCA kBTv~

v, ~ ~ ''c'(')c'''(')r162 k

(3)

U'

where Coo,(q) is the direct correlation function and ~ - [ q - k[. Equation (2) is formally solved by the Fourier-Laplace transformation as

r176

-1

=

2 ~

r176

q v, z--

= 0).

(4)

z + K~

The frequency-dependent diffusion constant D,(w) is determined from the incoherent relaxation kernel as 2

Do(w) = Im

w + K~

v~

= O,w + iO)"

(5)

In order to solve the self-consistent equations (3) and (4), knowledge of the coherent density-correlation functions (I),~ t) is required as an input. We calculated (I)~ t) from the (2 x 2)-matrix equation

r

= - { z I - ( z I + g(q,z)) -t . g~2(q)}- t . (I)(q, t = 0),

(6)

where I denotes a unit matrix, and (I)(q, t = 0) and f~2(q) are determined from the partial structure factors So,,(q). The relaxation-kernel matrix elements g,,,(q, t) reduce to

g,~

t) MCA (kBT)~ 2 )

~

+

V3"rt'~

vo ~ 5-.:~{k2Oo,(k)C,,,,(ic)Ou,(k,t)aoo,(lq _ kl,t) k

U'

k z ( q - k,)Ca(k)Cv~

k[)r162

kl,t)}

(7)

with k~ = k . q/q in the mode-coupling approximation. III. R e s u l t s

The theory described above is applied to the binary hard-sphere system with the size ratio al/a2 = 0.2 and the concentration of small particles cl = 0.5. Figure 1 shows the diffusion constants D, of small (s = 1) and big (s = 2) particles versus the total packing fraction 77. The dotted lines show the power-law fit D = D01o - )7[~ with 7=1.31 and 2.36 for small and big particles, respectively. The diffusion constant of the big particles is found to vanish at T/B=0.52, which is close to the liquid-glass transition point (77=0.516) of a one-component hard-sphere system, s while D1 becomes zero at T/A =0.53 (> r/B). This means that for r/B < T/ < T/A there exists a new phase (delocalized phase) with mobile small particles diffusing through the voids of a glassy structure formed by the immobile big particles.

43 ! -1 ..............

-3

o.

......

o9.

9 .o.~%

_

9 9 ,(~ 9

9 ....

.,~149

9 ,.

ta0 o

-5

9

-

"(~..

9

#

C>

9

Fig.1

_

'

-

(>

-7 -9

.

I

I

0.4

0.44

.,,

1

0.48

1.

. 9

0.52

Diffusion constant D , ( w ) at ~ / ~ 0 = 1 0 - ' ~ i t h ~0 = for s = l (o) and s=2 ().

~/~:sT/(miai)

In Fig.2 we display the incoherent density-relaxation spectra r w) = Imr + i0) as a function of w in a logarithmic scale 9It is interesting to note that there is an additional quasi-elastic peak in r at small w (W/Wo < 10 -s) near the glass transition. This additional low-frequency intensity, which has not been detected for a one-component system, grows further as 77 approaches T/B. Figure 3 shows the frequency-dependent diffusion constants Da(w) for the same values of 77 as in Fig.2. We note that a little bump appears in Dl(w) in the same frequency range as that of the additional quasi-elastic peak in r for corresponding 77. This bump in Dl(w)is also found for c~=O.1 and 0.9. 6 For the big particles, on the other hand, no additional structure at small w is observed in r and D2(w) for all 77 of our calculations. The appearance of the bump is considered to indicate the change in the diffusion mechanism of the small particles. As the glass transition 77 = r/s is approached from the liquid side, the motion of the big particles becomes very slow compared to that of the small particles. Note that D~. is about 10 s times smaller than D~. Near 77=rjB, the big particles are almost frozen, producing an 'almost static' random potential which the small particles will experience when diffusing through the glassy matrix. Therefore, the diffusion mechanism of the small particles is expected to change from liquid-like diffusion to that of a particle moving in a 'static' random potential when passing the transition point ~BVI. S u m m a r y In this paper, we studied the glass transition and the localization-delocalization transition in a disparate-size hard-sphere mixture from a dynamical viewpoint 9 For Cl = 0.5, the existence of the delocalized phase of the small particles is confirmed by investigating the frequency-dependent diffusion constant. Near the glass transition, we and Dl(w) at small w, which sugfound an additional quasi-elastic structure in r gests that the diffusion mechanism of the small particles would change from the liquid-like diffusion to a slow diffusion in a random potential.

432

1

0.518

v

-'=

0

r/--0.395

o

r/:0.395

0-

-,%,

,,--t

-2- (b)

(a)

-2

J

I

-6

1

I

-1.5

2

-8

J

I

J

I

-6

-4

-2

0

logxo(W/Wo)

Incoherent density-relaxation spectra r for s = l (a) and s=2 (b) at q = 7.047a~-1 (the position of the first peak in $22(q)). 7/is chosen as r] = rIB - 1/2" with n = 3, 4 , . . . , 9.

Fig.2

:3

-4

I

-4 -2 loglo(W/Wo)

\

I

I

1

I

[

.... I

I

-

.

I

I

I

I

l

[ J

-2

-1

0

1

T}=0.395

-2 -2.5 -7

-3

-8

-6 Fig.3

-5

-4 -3 -2 -1 loglo(W/Wo)

0

1

-6

-5

-4

-3

loglo(W/Wo)

Frequency-dependent diifusivity D,(w)for s = l (a) and s=2 (b).

This work is supported by the Deutsche Forschungsgemeinschaf~, Sonderforschungsbere-

ich 337. References 1. W. GStze in Liquids, Freezing, and the Glass Transition, eds. D. Levesque, J. P. Hansen, and J. Zinn-Justin p287 ( North Holland, Amsterdam, 1990 ). 2. J. Bosse and J. S. Thakur, Phys. Rev. Lett. 59, 998 (1987). 3. J. Bosse and M. Henel, Ber. Bunsenges. Phys. Chem. 95, 1007 (1991). 4. J. S. Thakur and J. Bosse, Phys. Rev. A 43, 4378, 4388 (1991). 5. U. Bengtzelius, W. GStze, and A. Sj61ander, J. Phys. A 17, 5915 (1984). 6. J. Bosse and Y. Kaneko, in preparation.

journal of MOLECULAR

LIQUIDS ELSEVIER

Journal of Molecular Liquids, 65/66 (1995) 433-436

Relaxation Characteristics of Quantum Filtered (DQf) NMR

Intracellular

Na + as Measured by Double

Yoshiteru Seo and Masataka Murakami Department of Molecular Physiology, Sciences, Okazaki 444, Japan

National

Institute

for Physiological

Abstract We have measured the transverse relaxation rate constants depending on statistic field (Bo) and the diffusion coefficient of 23Na+ in an agar gel as a model of the intracellular Na +. We have estimated a binding site correlation time (x c) and a quadrupole coupling constant (e2qQ/h) on assumption of the discrete-exchange model. Transverse relaxation constants of "free Na+" (Sfree) in the agar gel were estimated from the self-diffusion coefficient of 23Na+ in the agar gel using the observed relationship between the self-diffusion coefficient and the transverse relaxation rate constant of Na+ in glycerol solution. As a result of minimization (r2 = 0.98), the fraction of the 23Na+ under the slow-motion condition (Pb for 1% agar/1 M NaC1/ water gel) was calculated as 9-10 -4. The values of e2qQ/h and the correlation time were 1.0 MHz and 16 ns, respectively, and the calculated value of e2qQ/h (1.0 MHz) lies in the reasonable range (0.2 M H z - 2 MHz). I. Introduction The progress of the multi-quantum nuclear magnetic resonance spectroscopy gave new information about the physical condition of electrolytes in the cells. In the perfused rat salivary gland, we have reported double-quantum filtered resonances due to intracellular 23Na+ signals. The resonance consists of sharp and broad Lorentzian components (the homogeneous biexponential (type c) spectrum). In order to discuss the relaxation mechanism of the intracellular 23Na+, we have measured the transverse (T1) and the longitudinal ('1"2)relaxation rate constants of the intracellular 23Na+ signal from the perfused rat mandibular salivary gland, and have measured their dependencies on Bo, temperature and contentl. The mandibular salivary glands (ca. 0.25 g) were isolated and perfused arterially with a modified Krebs solution. 23Na NMR spectra were collected at 8.4, 4.7 and 2.34 T by using MSL-100, AM-200wb and AMX-360wb, respectively. The T2 double-quantum filter and T1 double-quantum filter were used. Results are summarized in brief: 1) The transverse relaxation rate constants showed a slight Bo dependency, which promises a poor fitting by the single population model. 2) When temperature was decreased (37 - 5~ the ratio of the relaxation rate constants (o~2 = T2s/T2f) and 1/T2f itself increased, and the value of 1/T2s was almost constant. 3) Even when the intracellular Na+ content increased, the relaxation rate constants were almost constant. Results of Bo dependency were applied to the two models: 1) Static model: We assumed a homogeneous population of Na § in the intracellular fluid, 2) Exchange model: We assumed an exchange between Na+ under the slow-motion condition and the Na+ in the extreme narrowing region. Results obtained in this study can be fitted with the two-site exchange 0167-7322/95/$09.50 91995 Elsevier Science B.V. All rights reserved. SSD! 0167-7322 (95) 00891-8

434 model, which postulates the presence of a rapid exchange between 2 populations of Na + ions: a small fraction of Na + ions "trapped" with high-molecular-mass-solutes ("bound Na+"), and a major part moving freely in the cytosol ("free Na+"). One unknown parameter in the exchange model is the relaxation rate constant of the "free Na +'' (Sfree). Measurement of the molecular diffusion coefficient of the intracellular Na+ could give the answer, since this value would mainly reflect the movement of "free Na+". In this paper, we have measured Bo dependencies of the transverse relaxation rate constants and the diffusion coefficient of 23Na+ in an agar gel model. We have estimated a binding site correlation time (Xc) and a quadrupole coupling constant (e2qQ/h) on assumption of the discrete-exchange model.

II. Double-Quantum Filter NMR The relaxation rate constants of 23Na+ in agar gel (1, 2, 3, 4% agar and 1 M NaC1 in water) were measured at 8.45 T and 2.34 T at 25~ 23Na NMR spectra were collected using an AMX-360wb (8.45 T) and an MSL-100 (2.34 T) spectrometer with broad-band probes (10 mm in diameter). The T 2 double-quantum filter (d-90~ - 180~176176 was used. The peak heights of Fourier transformed spectra with various creation time (x) values were used for determining the transverse relaxation rate constants. Figure 1 shows flip angle dependency (0) of the signal passed by the T 2 doublequantum filter (d-90~ - 180~ Since the signal virtually disappeared at the flip angle of 54.7 ~ the observed signal from the agar gel rise from the T32 component and the contribution from the T22 component is negligibly small. When the quadrupolar coupling of 23Na+ is not averaged completely, the T22 component are not suppressed by the doublequantum filter 2. 3. Thus, we can use Na+ in agar gel as a model system for the discreteexchange model.

~>" 3.0

...,, c-

.c: 2.0 e..,

._~ 1.0 o3 0.0

,

0

,

,

,

30

,

,

,

,

,

,

'

60

,

90 e

'

'

,

i

120

'

'

'

i

150

,

,

'

,

,

180

(degree)

Figure 1. Flip angle dependency of double-quantum filtered signal from Na ion in agar gel at 8.45 T and 24~ 0 is the flip angle of the 3rd and 4th pulses.

III. Pulsed Field Gradient NMR The self-diffusion coefficient of 23Na ion in the agar gel was measured at 2.34 T using a micro-imaging unit with a home-built 23Na coil (15 mm in diameter). The conventional pulsed field gradient spin-echo sequence (d-90~ - 180~ was used. Typical values used are a pulsed gradient field strengths of 5.4 mT/cm, 90 ~ pulse of 18 Its, 180 ~ pulse of 36 Its, A (pulse distance = t 1 + 8 + t2) of 40 ms and 5 (width of pulsed gradient) was varied from 0.3 ms to 4 ms 4.

435

IV. Discrete-exchange model We have applied the discrete-exchange model 5 to these data. An exchange between Na ion under a particular slow-motion condition and in the extreme narrowing limit is assumed. Transverse relaxation time and diffusion coefficient are written as follows: 1/T2i = Sfree-(1 - Pb) + si'Pb (1) D = Dfree'(1 - Pb) + Db'Pb (2) Where, 1/T2i and D are the observed values of 1/T2for 1/T2s and diffusion coefficient, respectively, si and D b are the transverse relaxation rate constants (s 1 or s2) and the diffusion coefficient of Na ion under the slow-motion condition, respectively, s 2 and sl correspond to the 11/2> Pb _>0), which is proportional to the fraction of agar. Sfreeand Dfree are the relaxation rate constant and the diffusion coefficient of Z3Na+ under the extreme narrowing condition, respectively. The observed relaxation time is time-averaged value of Sfree and Sl. The fraction of Na ion under the slow-motion condition is expected small, but the transverse relaxation rate constants (s i) are expected larger than Sfree by 10 to 100 times. Therefore, we applied this equation to the observed relaxation rate constants to estimate the 2 compartments. One problem is accurate knowledge of the value of Sfree for Z3Na+ in the agar gel. V. Estimation of Sfree As shown in Eq. 2, the observed diffusion coefficient should be time-averaged value of Dfree and D b. However, the observed value is virtually equal to Dfree since values of D b and Pb are so small compared with values of Dfree and (1 - Pb)- Therefore, observed diffusion coefficient of Na ion in the agar gel mainly represents the motion of Na ion in the extreme narrowing region. Since the relaxation rate constant of 23Na+ depends strongly on the viscosity of the solution, we measured the self-diffusion coefficient of 23Na+ in glycerol/water solution, and found a relationship between the self-diffusion coefficient and the transverse relaxation rate constant on viscosity [Fig. 2-a]. Then, we have estimated the Sfree value of 23Na ion in the agar gel from the self-diffusion coefficient of 23Na ion in the agar gel using the observed relationship [Fig. 2-b].

35

35

a)

30

3O

25

25 -,q,

20 15 0.7

b)

0.8

0.9

1.0

"-....

20 1.1

15 1.2 0.7

0.8

0.9

1.0

1.1

1.2

Diffusion Coefficient (10-5 cm2/s) Figure 2. Relationships of transverse relaxation rate constants (1]T2) and diffusion coefficient of Z3Na ion in glycerol/water solution (a), and estimated 1/T2 value for 23Na ion in the agar gel from the diffusion coefficient of Na ion (b).

436

VI. Results of minimization The result of the minimization is shown in Fig. 3 (Relaxation rate constants (s 1 and s2) of 23Na+ in agar gel at 25~ Solid lines represent result of fitting the data obtained at 2.34 T (x) and at 8.45 T (o). The fraction of the 23Na ion under the slow-motion condition (Pb for 1% agar/1 M NaCI/water gel) was calculated as 9.10 -n. The values of e2qQ/h and the correlation time were 1.0 MHz and 16 n, respectively. The observed data fit this model well (r2 = 0.98), and the calculated value of e2qQ/h (1.0 MHz) lies in the reasonable range (0.2 MHz - 2 MHz). These results support the exchange model. Thus, we will proceed to analyze the relaxation of the intracellular 23Na+ using the discrete-exchange model. v

to

2.4

c...

2.2-

to t-.0 o

2.0-

.-., 9

1.8--

L_ tO

x

n~"

1.60

1.4-

G~ 1.2

o

0

..-0 I

1.0

i

1

i

2.0

i

3.0

I

i

4.0

1 03-Pb

Figure 3. The transverse relaxation rate constants of 23Na ion in agar gel at 2.34 T (x) and at 8.45 T (o) as a function of the fraction of Na ion. Solid lines are results of fitting data to the discrete- exchange model. We have applied 23Na double-quantum filter NMR and Z3Na pulsed field gradient NMR to analyze the relaxation of Na ion in agar gel, which is a model for the intracellular Na+ to test the discrete-exchange model. From diffusion coefficient of Na+ in agar gel, we estimated transverse relaxation rate constant of 23Na+ in extreme narrowing region. The transverse relaxation rate constants obtained by the double-quantum filter NMR (2.34 T and 8.45 T) fit well the exchange model, and we estimated a correlation time (16 ns) and a quadrupole coupling constant (1 MHz) for Z3Na+ under the slow-motion condition.

Acknowledgements

We thank O. Ichikawa, M. Takagi, and H. Ohkawara for their technical assistance, and Professor C. S. Springer Jr., Dr. J.-H. Lee, Dr. S. Wimperis and Dr. H. Shinar for stimulating discussions.

References Y. Seo, M. Murakami and H. Watari, Biochim. Biophys. Acta, 1034, 142 (1990) G. Jaccard, S. Wimperis and G. Bodenhausen, J. Chem. Phys., 85, 6282 (1986) U. Eliav, S. Shinar and G. Navon, J. Magn. Reson., 98, 223 (1992) J. K~irger, H. Pfeifer and W. Heink, Adv. in Magn. Reson., 12, 1 (1988) T. E. Bull, J. Magn. Reson., 8, 334 (1972)

journal of

MOLECULAR

LIQUIDS ELSEVIER

Journal of Molecular Liquids 65/66 (1995) 437-439

Author Index Aicart, E., 195 Amakasu, Y., 377 Asano, Y., 41 Bader, J.S., 31 Barnes, A.C., 99 Barthel, J., 177 Benko, J., 261 Berg, M., 301 Berne, B.J., 31 Blakey, D.M., 85 Bosse, J., 429 Bout, D.V., 301 Buchner, M., 157 Burger, K., 213 Chigira, F., 265 Chikaki, S., 325 Chong, S.-H., 345 Dore, J.C., 85 Dorfmiiller, T., 157 Enderby, J.E., 99 Espenson, J.H., 205 Friedman, H.L., 7, 15 Fujimura, Y., 169 Fujiwara, A., 187 Fukuda, T., 341 Fukuda, Y., 397 Fukushima, K., 369 Funahashi, S., 277 Gardecki, J., 49 Goto, M., 357 Gotoh, T., 341 Gyuresik, B., 213

Hamada, S., 353 Hamaguchi, H., 417 Hashimoto, N., 41 Hattori, S., 357 Hayashi, S., 405 Haymet, A.D.J., 139 Hirata, F., 15,345,381 Hirata, Y., 321, 421 Hirota, N., 401,425 Hiwatari, Y., 123 Horng, M.L., 49 Hosoya, K., 305 Ibuki, K., 385 Iida, M., 269 Ikeuchi, H., 273 Irisa, M., 381 Itoh, S., 373 Iwadate, Y., 369 Iwata, K., 417 Jobe, D.J., 195 Johnson, A.E., 59 Kagayama, N., 277 Kai, Y., 413 Kameda, Y., 305 Kanakubo, M., 273 Kanato, H., 325 Kaneko, Y., 429 Kanemoto, Y., 421 Kataoka, Y., 329 Kato, T., 405 Kawaizumi, F., 377 Keogh, G.P., 389 Kimura, Y., 425 Kinoshita, S., 413 Kitagawa, T., 317

438

Author Index/Journal of Molecular Liquids 65/66 (1995) 437-439

Kitahara, K., 293 Kitazawa, M., 321 Koda, S., 337 Koyama, Y., 369 Kubo, H., 369 Ma, J., 301 Machida, K., 405 Madden, P.A., 373 Maeda, H., 341 Maroncelli, M., 49 Mashita, T., 341 Masuda, A., 397 Masuda, Y., 269, 397 Mataga, N., 393 Matsui, J., 123 Matsumoto, M., 277, 329 Matsuoka, T., 337 Matsuura, H., 313 Miyasaka, H., 393 Miyazaki, F., 357 Mizoguchi, K., 187 Mizuno, Y., 269 Morita, A., 75 Moya, M.L., 261 Munakata, T., 15, 131 Murakami, M., 433 Muranaka, T., 123 Nagaoka, M., 289 Naga~sawa, Y., 59 Nagy, L., 213 Nakagaki, R., 353 Nakahara, M., 149 Nakai, T., 365 Nakamori, T., 269 Nakamura, K., 341 Nakanishi, K., 281 Nakashima, S., 317 Nakazawa, T., 353 Neilson, G.W., 99 Newton, M.D., 7 Nishinaka, M., 333 Nishiyama, K., 41 Nomoto, T., 421 Nomura, H., 337, 377 Oclagaki, T., 123 Ohba, M., 377 Ohtaki, H., 1

Ojima, H., 341 Okada, I., 309 Okada, T., 41, 321,421 Okako, N., 369 Okamoto, K., 401 Okazaki, S., 309 Olson, J.S., 317 Olsson, L.-F., 349 Ozutsumi, K., 361 Papazyan, A., 49 Perez-Tejeda, P., 261 Pemg, B.-C., 7 Radnai, T., 229 Raineri, F., 15 Raineri, F.O., 7 Rick, S.W., 31 Rossky, P.J., 23 Sagawa, T., 313 Sakamoto, S., 305 Sanchez, F., 261 Sasaki, S., 341 Sasaki, Y., 253 Sat6, G.P., 273 Sawada, K., 265 Sawai, N., 353 Sawamura, S., 365 Schr'oer, W., 107 Schwartz, B.J., 23 Seki, K., 293 Seo, Y., 433 Shibata, T., 337 Shinozaki, K., 357 Soper, A.K., 91 Stuart, S.J., 31 Suga, H., 115 Sumi, H., 65 Suzuki, H., 305 Swaddle, T.W., 237 Tabata, M., 221 Takagi, H.D., 277 Takahashi, T., 381 Tanaka, H., 285 Tanida, H., 409 Taniguchi, Y., 365 Tarumi, T., 277 Teramoto, Y., 281

Author Index/Journal of Motecular Liquids 65/66 (1995) 437-439 Terauchi, N., 309 Terazima, M., 401 Tominaga, K., 59, 389 Tominaga, T., 333 Tominaga, Y., 187 Tran-Cong, Q., 325 Tsukahara, K., 353 Uemura, O., 305 Ueno, M., 385 Usuki, T., 305 Verrall, R.E., 195 Wakai, C., 149 Wakita, H., 91 Wang, Y., 187

Watanabe, I., 245,409 Weingfirtner, H., 107 Yabe, T., 321 Yagi, T., 413 Yamabe, T., 289 Yamagami, M., 91 Yamaguchi, M., 413 Yamaguchi, T., 91 Yamanaka, M., 341 Yanagida, T., 381 Yartsev, A., 59 Yasuoka, K., 329 Yokoyama, H., 357 Yoshida, N., 289 Yoshihara, K., 59, 389 Yoshimori, A., 297

439

This Page Intentionally Left Blank

journal of

MOLECULAR

LIQUIDS ELSEVIER

Journal of MolecularLiquids, 65/66 (1995) 441--446

Subject Index absorption curve, 179 acetone solutions, 178 acetonitrile(AN), 13, 18, 177, 180 adiabatic calorimeter, 116 air/solution interface, 250 alkyl radicals, 205 alkylammonium salts, 109 amorphous ice, 85, 87, 89 anharmonic free energy, 286 approximate correlation function, 161 aprotic dipolar liquid, 18, 19 aqueous CsCI solution, 365 aqueous electrolyte solutions, 187 aqueous solution of NaCI at high pressure, 233 aqueous solutions, 9 I, 229 aqueous solvation, 31 aqueous sulfuric acid solutions, 305 argon, 329 argon/a-ice co-deposit, 88 Argand diagram, 181,182 ascorbic acid, 187, 277 association constant, 177, 179, 184 average distances, 232 avian pancreatic polypeptide, 381 azobenzene, 65 benzene, 13, 273 N-benzylideneanilines, 65 biferrocene monocation, 397 bimolecular reaction rate, 321 binary soft-sphere mixtures, 121 bipyridine, 357 bi-exponential decay, 19, 20 Bom-Mayer-Huggins, 373 bromide ion, 230, 245 Brownian motion, 75 butanol, 199 1-butoxyethanol, 199 calcium, 349 Car-Parrinello method, 373 carbonmonoxy myoglobin, 317 catalytic effect, 222 CeCI 3,369 central component, 187 central force (CF) model, 139

CD, 213 CF3H, 313 charged ion pairs, 184 chloride ion, 230 classical (continuum) model of solvent, 261 clathrate, 89, 118, 185 closest approach, 265 cluster form-factor, 87 [Co(NH3)4(pzCO2)] 2+, 261 cobalt (III) ammine complexes, 237 coherent anti-Stokes Raman profiles, 169 Cole-Cole plots, 125 Cole-Cole type relaxation mode, 187 collective jump motions of atoms, 123 collective variables, 15 collectivity, 157 59Co longitudinal relaxation rates, 273 combination reaction, 207 complexes of N-D-gluconylamino acids, 213 computer simulation, 329 condensation coefficent, 329 conducti v ity, 265, 357 configurational enthalpy, 120 conformational behavior, 313 conformational fluctuations, 65 contact ion pair(s), 177, 184 continuous random network, 87 continuum model, 385 coordination distance, 245 coordination numbers, 232, 245 correlated atomic diffusion model, 15 correlated motion coefficient, 127 correlation time, 433 corresponding state, 109 Coulombic phase separations, 108 cresyl violet, 41 critical behavior, 107 critical density, 425 crossover, 107 crystalline solids, 115 crystallization, 115 Cu(II) porphyrin complex, 23 1 9-cyanoanthracene- I, 3-cyclohexadine, 321 Debye type relaxation mode, 187

442 density autocorrelation function, 123 density correlation, 16 density fluctuations, 131 density functional (method), 16, 281 density functional theory, 131 density maximum, 86 density of state, 162 dependence of relaxation rate on the temperature, and the complex concentration, 273 dephasing, 131 dephasing constant, 169 detailed balance, 293 di- and tri-nuclear complexes, 253 diabatic free energy profiles, 8 dichrolomethane, 273 dielectric constant, 114 dielectric depression, 182 difference pair-distribution function, 233 diffusion coefficients, 333 diffusion constant, 17 diffusion controlled reactions, 184 diffusion mechanism, 429 diffusion-controlled rate constant, 207 diffusive Browinan motions, 65 diffusive motions, 65 N, N-dimethylformamide, 180, 229, 361 dimethyle suifoxide solutions, 227, 230, 178 dipolar and non-dipolar (polar) solvents, 7 dipole-dipole interaction, 409 direct correlation, 16 discrete-exchange model, 435 dispersion amplitude, 181 dispersion curve, 179 disproportionation, 205 dissipative structure, 341 dissociation pressure, 286 DLVO approximation, 139 double-quantum filter NMR, 434 dropping effect, 118 dye, 59 dynamic effect, 289 dynamic process in electrolyte solutions, 177 dynamic variables, 15 dynamical nonlinear terms, 297 dynamical structure factor, 15, 16 dynamical structure of water, 187 dynamics, 91

dynamics of solvation, 49 d~ - p~ interactions, 253 effective dipole moments, 184 effective ionic radius, 358 effective volume of dipole rotation, 184 electric field gradients, 269 electrolyte solutions, 107 electron donors, 209 electron exchange rate, 209 electron transfer, 59 electron transfer reaction(s), 7, 205, 237, 345 electrostriction, 359 encounter pair, 321 energetics, 211 energy transfer, 405 enthalpy change of the ion association, 358 enthalpy relaxation, 120 entropy change of the ion association, 358 EPR, 213 erbium (III) ions, 230 evaporation and condensation, 329 EXAFS, 230, 245, 213 EXAFS oscillation amplitudes, 247 excess free energy, 357 excimer, 394 excitation energy migration, 393 excition diffusion, 393 [Fe(CN) 6]4-, 261 femtosecond, 59 femtosecond time-resolved coherent Raman scattering, 169 finger-like structure flow, 341 first excited singlet, 417 first- order difference method, 230 fluctuation dissipation theorem, 18, 414 fluorescence quenching, 321 fractional exponent, 116 free energy profiles, 7, 11 free-volume, 325 friction kemel, 16 frozen-in systems, 115 FT-IR spectroscopy, 177, 313 functional derivative, 16 general susceptibiity, 123 generalized Langevin equation, 15, 289

443 generalized permittivity, 179 glass transition, 115, 126, 429 glassy, 91 glassy crystals, 115 glassy polymers, 325 glassy water and solutions, 231 D-glucose solution, 187 Gouy-Chapman-Stern (GCS) approximation, 139 Grote-Hynes theory, 65, 289 ground state recovery, 425 halogen abstraction, 205 hard-sphere liquid, 429 heat capacity, 118 heat capacity change of the ion association, 358 heat conduction, 417 heat transfer, 331 heavy water, 149 heterodinuclear metalloporphyrin, 221 hexagonal ErCl3, 369 high frequency permittivity, 177, 179 high pressure, 365 homogeneous solvent, 18 homogeneous and inhomogeneous contributions, 389 homogenisation, 158 1H relaxation, 269 iH spin-lattice relaxation, 397 hydrated electron, 23 hydration, 91,357 hydration entropy and enthalpy, 360 hydration free energy, 381 hydrogen abstraction reaction, 401 hydrogen atom abstraction, 205 hydrogen bond, 18, 91,149 hydrogen carbonate, 349 hydrogen-bond connectivity, 89 hydrogen-bond formalisim, 409 hydrogen-bonded intermolecular structure, 305 hydrogen-bonded pair, 86 hydrophobic, 177, 357 hydrophobic complex, 359 hydrophobic interaction(s), 182, 357 hydrophobic structure-makers, 357 hyper-quenced glassy water, 87

inorganic reaction mechanism, 237 Instantaneous normal modes, 157 integral equation method, 15 integral equation theory, 345, 377 Integral motion, 20 interaction site model, 7 lntermolecular, 169 mtermolecular dephasing, 169 mtermolecular interactions, 7, 169 lntramolecular electron transfer, 397 intramolecular photodimerization, 325 ion association, 177, 357 ion solvation, 177 ion-aggregate formation, 177 ion-association theory, 360 ion-pair formation, 265, 358 Ion-pair relaxation, 184 ion-pairing effects, 269 ionic atmosphere, 333 ionic products, 212 lrrotational bonding, 182 lsochoric temperature derivative, 86, 87 Isolobal, 205 isomorphic replacement, 230 isotropic substitution, 99 Jones-Dole B coefficient, 365, 385 kinetic depolarization, 182 kinetic relaxation process, 184 Kohlrausch-Williams-Watts' equation, 116 Kramers theory, 65 Langevin-diffusion equation, 131 laser flash photolysis, 205 Lennard-Jones binary mixture, 377 LiCI solution in DMF, ~ light scattering, 113, 413 limiting molar conductivity, 265 linear response, 19, 261 LiNCS solution in DMF, ~ liquid, 91,169 liquid acetonitrile, 235 liquid benzene, 393 liquid crystal, 281 liquid surface, 330 liquid-liquid phase separation, 107 lithium halides, 91 lithium iodide (LiI), 373 lithium ion, 229

444 local relaxation processes, 325 localization transition, 429 long time limit of the reaction, 75 low-frequency Raman scattering, 187 Marcus equation, 209 Marcus-Hush theory, 237 Markov limit, 16 MD simulation, 17, 229, 286, 329, 405 mean-field-like criticality, 107 mechanical grinding, 120 mechanical relaxation theory, 301 melting behavior, 369 metal radical, 205 metal-to metal charge transfer, 261 metalloporphyrin, 221 metastable phase, 115 methanol, 18, 329 methyl chlorides, 18 MgCIE-water-methanol ternary systems, 231 micelle, 333 microscopic Hamiltonian, 289 microscopic viscosity, 385 mixed micelles, 196 mixed-valence, 253,397 mode coupling theory, 301 mode-coupling theory, 429 molecular liquids, 131 molecular theory of solvation dynamics, 7 molybdenum radical, 209 momentum density, 15 monoclinic ErCl3, 369 monohalogenocadmium (II) complexes, 361 Monte Carlo (MC) computer simulation, 229 Mossbauer structual study, 213 multi-exponential behavior, 17 multi-exponential decay, 17 MW spectra, 177 23Na NMR, 433 N204, 405 naphthalenedisul fonates, 360 neutron diffraction, 85, 99 neutron scattering, 91 neutron scattering, 99 new renormalized linear response development, 7

nickel (II) and magnesium (II) ions, 230 nitrate ions, 230 NMR, 149, 213 NMR relaxations, 20, 269 non-adiabatic relaxation, 23 non-aqueous solutions, 229 non-crystalline solids, 115 non-exponential relaxation, 116 nonlinear coupling terms, 289 nonlinear Smoluchowski-Vlascov equation, 297 normal mode spectra, 158 octadecyltrimethylammonium chloride, 333 open form, 317 optical Kerr effect, 413 organic free radicals. 208 organic halides, 208 organometallic free radical, 205 orientational structure, 158 Ornstein-Zernike equation, 378 oxidation, 277 oxide bridge, 253 pair correlation function(s), 85, 86, 88 partial molar volumes, 358 partial pair-distribution function, 235 partial specific volumes, 341 pentanone, 199 perchlorate (ion), 230, 357 phenanthroline, 357 phenol blue, 425 photoelectron emission spectroscopy, 409 photoexecitation, 15, 18, 23 photohomolysis, 205 photophysical properties, 353 physiological solutions, 349 picosecond laser photolysis, 393 picosecond time-resolved Raman spectroscopy, 417 POE-water system, 313 Poisson-Boltzmann equation, 381 polar and non-dipolar solvents, 7 polar liquid, 15, 18 polarizability, 373 polarizable, 31 polarization charge density, 15 poly (oxyethylene) (POE), 313 polypeptide, 381 porphylin, 221

445 potential height, 81 power spectra, 286 precipitation nuclei, 349 pressure effects on reaction, 237 propanol, 199 propylene carbonate (PC), 180, 301 protein, 381 protein dynamics, 317 proton transfer, 209 pulsed field gradient NMR, 434 PY approximation, 377 quadrupole coupling constant, 433 quantum molecular dynamics, 23 quasi-elastic neutron scattering (QENS), 99, 230 radical, 401 Raman echo experiment, 389 Raman spectra, 305 Raman spectroscopy, 187, 309 rapid transport of a polymer, 341 rate constants, 196 rate of chemical reactions, 81 recombination, 211 recombination process, 317 redox properties, 253 relaxation, 115 relaxation mode, 187 relaxation of inhomogeneity, 425 relaxation process, 180 relaxation time, 116, 180 relaxation time distribution, 180 relaxation times in fluid solution, 41 renormalized solute-solvent interactions, 8 reorganization energy, 7, 409 reorientation dynamics, 325 residuasl entropy, 115 response function, 180 reverse Monte Carlo simulation, 229, 234 rhodium radical, 208 RISM, 10, 15, 16 root mean square deviations, 232 rotational and vibrational relaxation, 309 rotational correlation times, 149 rotational diffusion, 421 rotational friction coefficient, 385 rundom force, 16 S 1-S 1 annihilation, 394

scaled particle theory, 381 scattering, 169 Schlogl model, 293 second order difference method, 230 self-diffusion coefficient, 433 self-exchange reaction rate, 239 short range structure, 369 short-lived intermediates, 221 silver ion, 230 single-particle dynamics, 159 singlet excitation energy transfer, 393 site dependent relaxation time, 48 site-number density, 15, 18 site-site Smoluchowsky-Vlascov (SSSV) equation, 15, 19, 21 small angle neutron scattering (SANS), 230 small model of gilcoproteins, 213 Smoluchowski equation, 75 sodium (I) ion, 230 sodium chloride, 229 solid-fluid interface, 281 solid-state amorphization, 120 solution reactions, 65 solvate structure, 229 solvation, 23, 177 solvation dynamics, 10, 15, 297, 301 solvation free energy, 7, 381 solvation numbers, 177 solvation numbers, 178 solvation of lithium ion in N, N-dimethyl formamide, 231 solvation structure, 245 solvation time, 59 solvation time correlation function (STCF), 18, 19, 20 solvent dynamical effect, 397 solvent exchange, 238 solvent orientational distribution, 48 solvent pressure effect, 149 solvent relaxation, 41 solvent separated ion pair, 177 solvent viscosity, 65 solvent-solute interaction, 421 solvophobic unmixings, 111 spatial correlations, 293 SPC model, 17, 19 stability of ion pairs, 177 stearyltrimethylammonium bromide, 250 sticky ions, 111 trans-stilbene, 417

446 Stokes radius, 265, 358 Stokes-Einstein-Debye law, 149 stopped flow EXAFS experiment, 231 stretched exponential function, 123 structual parameters, 232 structure, 91,361 structure and dynamics of solvated ions, 229 structure of coordination of isomers, 219 structure-breaker, 359 structure-makers, 367 Sumi and Marcus, 65 supercooled, 91, 23 1 supercooled liquids, 131 supercooled fluid phase, 1 ~ supercritical fluid, 309 supersaturated aqueous solutions, 349 surfactant-alcohol, 196 temperature coefficients of the Walden product, 358 temperature pressure effect, 149 temperature dependence of molar conductivities, 357 tetraalkylammonium, 265 n-tetradecyltrimethylammonium bromide, 333,337 tetramethyl urea, 23 1 s-tetrazine, 301 theory of soivation dynamics, 7 thermal dissociation, 405 thermochemistry, 211 thermodynamic derivatives, 377 time correlation function of solvent fluctuation, 46 time evolution of the ground state hole, 41 time resolved absorption spectroscopy, 41 time resolved fluorescence spectroscopy, 41 time resolved hole burning, 41 time resolved resonance Raman, 317 time resolved Stokes shift, 18 time-of-flight (TOF) neutron diffraction, 305 TIPS model, 19 tracer diffusion, 333 transient, 205 transient effect in the fluorescene decay curves, 321 transient grating, 40 1

transient hole burning, 301 transition metal complexes, ~_37 transition-state theory, 289 translational diffusion, 401 translational friction coefficient, 385 transport coefficents, 131 transport of linear polyelectrolytes, 341 transport properties, 385 transverse relaxation rate constants, 433 trajectory, 17 triatomic molecule, 281 trifluoroethanol, 231 trifluoromethane, 425 tris(1, 10-phenanthroline)ion(ll), 357 tri-exponential decay, 19 tungsten, 208 ultrasonic absorption, 195 ultrasonic relaxation method, 337 under-cooled liquids, 87 van der Waals and Platteeuw theory, 285 vapor deposition, 119 variances, 197 velocity correlation function, 157 vertical energy gap, 7, 9 vibrational coiling, 417 vibrational lineshape, 389 viologen-linked N-alkylporphyrins, 353 viscosity, 187, 365 viscosity correlation functions, 286 volume change, 369 volume of activation, 238 XANES, 230 X-ray, 305 X-ray diffraction, 91,229, 361 a-peak, 1~ a - relaxation, 10_3 /3 - relaxation, 123