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(2 x face area) + (6 x edge area) face area x thickness x density
1.881 x 10 6 nrrr' ::;;;:::;;;:(3.723 x 107 nm 3)(2.615 x 103 kg . m 3) 1.93 x 1O5m3nm Ikg 1 = 1.93 x 104m Zkg I
= 19.3mZg 1
where the mass density of kaolinite is taken as 2.615 x 103 kg . m3. The use of l?~?!i.:'h~4I].~~~~.~~~:.~i!X.~!~ in these two examples is pr~9ic'!te,q9:n. .~.~e,.. !!.s.~}!.!!11?!!~~,.t~~~.!~~«~h~..T..~~!..~2~!tio~ o{.1b e smL .par!ifle. is the s~,~~."~~.!h~!.?f ,the,.~~7.Ini~~llXp\};r.e,~ES£!!!l~11,..Q!UYll.icll.!h.e density.me,~sure~e,I!t.~.~e,~e,In!1de,. In soil clays this assumption does not apply if isomorphic substitutions have occured to any extent, as they do, for example, in the 2: 1 phyllosilicates (Table 1.3). For these kinds of minerals, it is possible to use data on the chemical composition directly in the calculation of the specific surface area if Xray crystallographic information is also available. This alternate method of calculation entails computations of the relative molecular mass of a unit cell, based on the structural formula for the mineral, and of the area of a quasicrystal formed by stacking the phyllosilicate layers along the crystallographic caxis (Fig. 1.11).30 The computation can be illustrated with a montmorillonite whose structural formula is NaO.66 Si8 (A I3.o5 Feo.z9Mgo.66)Ozo(OHk The relative molecular mass of the unit cell is calculated by multiplying the relative molecular mass of each clement by its stoichiometric coefficient and summing over ull such products to ontain M, ."" 742.4 for the total. Note
THE REACTIVE SOLID SURFACES IN SOilS
25
that this result depends both on the pattern of isomorphic substitution and on the type of exchangeable cation. The unit cell dimensions for the mineral are" a = 0.517 nm, b = 0.895 nm, and c = 0.95 nm. The surface area per unit cell is then 2ab = 0.9254 nnr' per cell if the edge surfaces are neglected. This neglect of the edge surfaces is justified by the fact that montmorillonite particles typically are plates whose lateral dimensions (about 100 nm) greatly exceed their thickness (1 to 6 nm), so that the edge surface area contributes only a few per cent to the total. The crystallographic specific surface area of an Avogadro number of unit cells of montmorillonite now can be calculated: NA per cell x == So = surface area '0relative mole mass of cell
0.9254 nm 2 x 6.022 x 1023 742.4 g
=
7.51
X
1020 nm 2g 1
= 7.51 x 105 nr'kg" = 751 m2g 1
where N A = 6.022 X 1023 is the Avogadro constant. This wellknown result applies to platy particles whose thickness equals that of the unit cell. If instead there are n layers stacked along the crystallographic caxis to form a quasicrystal, So is calculated by dividing 751 m2g 1 by n, since each pairing of stacked layers places two siloxane surfaces inside the quasicrystal. The procedure illustrated here applies equally well to all the phyllosilicates listed in Table 1.3. Besides the problems of surface alteration that may arise in connection with sample preparation for electron microscopy and Xray diffraction studies, there is also the difficulty of obtaining sufficient data to characterize the broad range of particle shapes and dimensions found in natural soil clay. The magnitude of effort implied by this heterogeneity limits the scope of the physical methods of determining specific surface area to establishing reference values for particular groups of minerals and to calibrating other methods of surface area measurement for selected clay samples. Faced with an array of soil particles like those portrayed in Fig. 1.11 one cannot expect physical methods to enjoy wide application as a routine approach to the measurement of surface area. POSiTIVE, ADSORPIIQN,M,m:tQI>.S. The measurement of specific surface area with a positive adsorption method requires the satisfaction of three basic experimental conditions:
1. There must be a chemical reaction between the surfaces of the clay particles and a molecular unit that results in a pronounced accumulation of the molecular unit on the surfaces, i.e., positive adsorption. The reaction may be between a degassed clay sample and a compound in the gas phase or between a clay in aqueous suspension and a dissolved solute.
26
THE SURFACE CHEMISTRY OF SOILS
2. The mass of adsorbate per unit mass of clay corresponding to one layer of adsorbate on the clay surfaces must be determined. The term adsorbate refers to the accumulating molecular unit mentioned in condition 1. 3. The 1'~,~~!I?:g,,~J:~a2Lt~e.~~~.?rp~!~,~!JE.?~?I.':lyer coveE~~~ ,mus.t_be Qs:t~.nuil,l,ed. The packin? a~eais the aInount?fsurf~ce~rea alloted to each adsorbed mOiecurar··i.init:·~·,,"...... ,,~, . , . " "  ,_... "". s,
When conditions 1 to 3 have been met, the adsorption specific surface area, in the SI units of square meters per kilogram, can be calculated with the equation
sm
= XMm N Am a x 10 15
(1.4)
r
where X m is kilograms of adsorbate per kilogram of sample at monolayer coverage, M, is the relative molecular mass of the absorbate, and am is its packing area in square nanometers. The adsorptive (i.e. adsorbable compound) used to determine specific surface area can be chosen, on the basis of its molecular properties, to react selectively with the particular surface functional groups whose areal distribution is of interest. Often, rather weakly interacting, nonselective adsorptives are used when the objective is to measure as much of the exposed surface area as possible. For example, nitrogen gas is a commonly used adsorptive in surface area measurements because it interacts weakly with a broad array of surface functional groups and therefore permits the determination of exposed surface area in many different kinds of clay. The principal limitation on the use of this adsorptive is stereochemical, since the relatively large van der Waals radius of the N 2 molecule prevents it from interacting with surface functional groups occluded in very small void spaces. The packing area of an adsorbate molecule in the gas phase often has a value close to that predicted by assuming that the molecule forms an ideal monolayer, i.e., one with hexagonal close packing at the density of its bulk liquid phase: (1.5) where p is the mass density of the bulk liquid in kilograms per cubic meter and a~ is expressed in square nanometers. The fact that calculated values of am are close to a~ suggests that the packing area is to some degree the intrinsic property it is supposed to be. However, as shown in Table 1.6, packing areas determined through calibration studies on wellcharacterized solid surfaces vary for the same adsorbate, especially in the case of water vapor. The value of the monolayer parameter, X m , in Eq. 1.4 is determined universally with an adsorption isotherm equation. If it is known from experiment that the adsorption forms no more than a single molecular layer on the surfaces of interest, X m is then the x intercept of the line
27
THE REACTIVE SOLID SURFACES IN SOilS
Table 1.6. Packing areas of gasphase adsorbates used in specific surface area measurements Gasphase adsorbate
T,K
Nitrogen Argon Krypton Ethylene glycol (1,2ethanediol) Ethylene glycol monoethyl ether (2ethoxyethanol) Water
aid m
nrrr' am, nm 2
Range of observed am, nm 2
78 77 78
0.162 0.138 0.152
0.162 0.167 0.202
0.130.20 0.130.18 0.170.22
293
0.224
0.332
0.2300.332
293 293
0.323 0.105
0.523 0.106
0.3960.600 0.0750.195
obtained by fitting adsorption data to a linear form of the Langmuir equationr" (1.6) where q is the mass of adsorbate per unit mass of sample, K is an empirical constant, and K d is the distribution coefficient, the ratio of q to the corresponding adsorptive concentration (aqueous solution) or pressure (gas phase) at equilibrium. The use of Eq. 1.6 to determine X m is illustrated in Fig. 1.12. The derivation of Eq. 1.6 is discussed in Chap. 4. For gasphase adsorptives, it is common practice to equilibrate the sample with the adsorbate at a pressure high enough to make the approximation q = X m valid. This "singlepoint" method of determining X m has the
Figure 1.12. The calculation of the monolayer parameter, X m , for Ncetylpyridinium bromide (CPB) adsorption (Langmuir plot) and water vapor adsorption (BET plot) by soils. 33 •35
BET PLOT H20 Adsorption Otago podzol
xm=1/(23.4+ 1.74) = 0.0398kg H20/kg soil oL.
o
L_ _l.L_ _J
os
1.0
q(mol kcr I)
I.~
oL_l_ _l._ _L_ _J
o
0.10
0.30
0.40
28
THE SURFACE CHEMISTRY OF SOILS
distinct advantage of convenience for routine measurement and is widely used with either ethylene glycol or ethylene glycol monoethyl ether as the adsorbate.F However, the combined uncertainties in the determination of X m by a single measurement and the present lack of extensive calibration of the packing area restrict this approach to use only for a qualitative comparison of specific surface areas in soil clays. If the adsorbate is in the gas phase and tends to form many layers on the surfaces of soil clay particles, as do water vapor and the inert gases listed in Table 1.6, then X m can be calculated as the reciprocal of the sum of slope and y intercept of the line obtained by fitting adsorption data to a linear form of the BrunauerEmmettTeller equationi"
P/ Po q(1  p/Po)
=
1 (C  1) P xmC + xmC Po
(1.7)
where P is the pressure of the adsorbate, Po is its pressure at saturation (i.e., in equilibrium with a bulk liquid phase of the adsorptive), and C is an empirical constant. A graph of the left side of Eq. 1.7 versus the relative pressure, p / Po, is usually a straight line for adsorption data obtained in the domain 0.05 <: p/Po <: 0.30. The use of Eq. 1.7 to calculate X m is also illustrated in Fig. 1.12. The physical model on which the BET equation is based requires that the probabilities for evaporation and condensation of the adsorbate from each molecular layer formed, as well as the energies associated with these two processes, be independent of the amount adsorbed, s" This assumption turns out to be valid approximately in the range of relative pressures indicated above. A combination of nitrogen gas and water vapor is frequently used to measure the adsorption specific surface areas of soil clays containing principally phyllosilicates.P Because of its size and weak interaction characteristics, the N2 molecule is adsorbed only on the external surfaces of phyllosilicate quasicrystals. The water molecule, on the other hand, can penetrate a smectite or vermiculite quasicrystal to enter interlayer regions containing innersphere complexes between metal cations and the siloxane ditrigonal cavities, provided that these complexes are intrinsically less stable than outersphere surface complexes involving the solvated metal cations would be. The intercalation of water molecules to solvate the complexed metal cations is favored when the latter have high ionic potential (the ratio of valence to ionic radius) and can strongly attract and orient dipolar molecules. Therefore, cations such as Li +, Na +, Mg2+, and Ca2+, when complexed by phyllosilicates, are associated with interlayer hydration, whereas K+, Rb ", and Cs" tend not to be. Xray diffraction data show that, when interlayer hydration occurs, X m determined as indicated in Fig. 1.12 actually corresponds to a single layer of intercalated water molecules." Therefore, X m for water vapor adsorption refers to monolayer coverage of the external surfaces plus one half of the accessible internal surfaces of the quasicrystals. This physical interpretation of X m for water vapor, as well as, that of X m measured by nitrogen gas adsorption, permits
THE REACTIVE SOLID SURFACES IN SOilS
29
the calculation of the accessible internal plus external adsorption specific areas of illitic mica, vermiculite, and smectite minerals: If SN represents the specific surface area calculated with Eq. 1.4 from nitrogen adsorption data and Sw is that calculated from water vapor adsorption data, then the total adsorption specific surface area is (1.8)
according to the interpretation of X m values given previously. The adsorption behavior of Ncetylpyridenium bromide (CPB), an organic molecule comprising a cetyl hydrocarbon chain substituted onto a pyridine ring that weakly complexes a bromide ion (C16H33CsHsN+B;), on phyllosilicates is similar to that of water vapor. CPH can be adsorbed from dilute aqueous solution by phyllosilicates and used to determine their specific surface areas." The adsorption follows the Langmuir equation, with X m calculated according to Eq. 1.6 (Fig. 1.12). On external surfaces, monolayers of CPB molecules are adsorbed in headtotail pairs, with one pyridinering head bound to the surface and the cetylchain tail oriented perpendicularly. The packing area is 0.27 nrrr'. This same arrangement is found in the interlayer region, but here both pyridine rings in an adsorbed pair of CPB molecules are in contact with siloxane surfaces. Therefore, X m again corresponds to coverage of the external surfaces plus one half of the accessible internal surfaces and the adsorption specific surface area can be calculated with Eq. 1.8. Typical results of specific surface area determinations on phyllosilicates by nitrogen gas/water vapor or nitrogen gas/CPB adsorption are listed in Table 1.7. For Mgvermiculite and Namontmorillonite, the measured adsorption specific surface area is close to that calculated from the unit cell dimensions and structural formula. For illitic mica, the area is about 14 per cent of the ideal crystallographic value, indicating that this mineral forms particles containing about seven phyllosilicate layers that cannot be penetrated by water vapor or CPB. Although the positive adsorption methods offer the advantage of convenient determination in heterogeneous samples, they suffer from the uncertainty involved in the calibration of the packing area (which usually must be done by comparison with results from a physical method using reference clay materials) and from the fact that the monolayer parameter is modeldependent through Eqs. 1.6 and 1.7. It must also be remembered that the specific surface area determined by positive adsorption is ultimately a function of the reaction between surface functional groups and some probe molecule. If the experimental conditions of the reaction are close to those under which the surface behavior of a sample is of interest, then this estimate of specific surface area has surface chemical relevance. Negative adsorption refers to the phenomenon in which a charged solid surface confronts an ion of like charge in an aqueous suspension and the ion is repelled from the surface by NEGATIVE
ADSORPTION
METHODS.
THE SURFACE CHEMISTRY OF SOilS
30
Table 1.7. Specific surface areas of phyllosilicates determined by nitrogen, water
vapor, or Ncetyl pyridinium bromide adsorption Sm (nitrogen +
water), 104 m 2kg 1 Kaolinite (Naform, Peerless)" Kaolinite (Bath, South Carolina? Illitic mica (Naform, Illinois)" Illitic mica (Naform, Fithian, Illinois)" Vermiculite (Mgform, llano, Texas)" Vermiculite (Kenya)" Montmorillonite (Naform, Wyoming)" Montmorillonite (Naform, Wyoming)' a
+
CPB), 104 m 2kg 1
1.88
1.8
1.5
10.2 9.3
9.6
0.31 <0.1
71.2
3.3
84.7
1.4
72.6
80.0
A. G. Keenan et a!., J. Phys. Colloid Chern. 55: 1462 (1951).
D. C H. d H. e R. b
1.86
Sm (nitrogen
J. Greenland and J. P. Quirk, J. Soil Sci. 15: 178 (1964). D. Orchiston, Soil Sci. 78:463 (1954). van Olphen, Proc. Int. Clay Cant 1969 1:649 (1969). W. Mooney et a!., J. Am. Chern. Soc. 4: 1367 (1952).
D. J. Greenland and C.J.B. Mott, in The Chemistry of Soil Constituents (D. J. Greenland and M.H.B. Hayes, eds.), p.321. Wiley, Chichester, U.K., 1978.
f
coulomb forces. The coulomb repulsion produces a region in the aqueous solution near the surface that is relatively depleted of the ion and a corresponding region, far from the surface, that is relatively enriched in the IOn. This effect can be observed experimentally in the following way. An aqueous solution containing a chosen ion i is poured into two identical chambers separated by a membrane permeable to water and dissolved solutes but not to suspended solids (i.e., a dialysis membrane). The moles of charge contributed by ion i to one of these chambers is IZ i IeOi V, where Z, is the valence of the ion, COi is its concentration, and V is the volume of the chamber. After m; kilograms of a solid are suspended in one of the chambers and equilibrium with respect to the transport of ion i is established across the membrane, the concentration of ion i in the chamber not containing the suspended solid will rise to c, if the surfaces of the solid repel ion i. This increase in concentration is associated quantitatively with a region of depIction of ion i in the chamber containing the suspended solid
THE REACTIVE SOLID SURFACES IN SOILS
31
through the definition
IZ i ICi V ex
IZilcoY
= !ZilciV  ''''''ms
(1.9)
where Vex is called the exclusion volume. The numerator on the right side of Eq. 1.9 is equal to the number of moles of charge of ion i sent into the chamber not containing the suspended solid. The exclusion volume thus represents the volume per unit mass of suspended solid depleted of ion i in the chamber containing the suspension. The development of a negative adsorption method for measuring specific surface area is based on the additional definitiorr" (1.10) where dex(Ci) is the exclusion distance, a function of the concentration, c.. The parameter SE is the combined solid surface area per unit mass from which ion i is repelled in an aqueous suspension. If this surface is also the entirety of that bathed by the aqueous solution, then SE as measured by the combination of Eqs. 1.9 and 1.10 is the full specific surface area of the suspended solid. The parameter d ex represents the mean distance over which the ion i is depleted near the surfaces of the suspended solid. It is evaluated conventionally as a function of c, with the help of the diffuse double layer (DDL) theory of an ion swarm near a charged planar surface in aqueous suspension. 37 The model calculation of dex(c;) is presented here for the important special case of a negatively charged solid suspended in a 1: 1 electrolyte solution. According to the DDL theory,37 the surface charge density neutralized by a swarm of electrolyte ions is
O'a = {2EoDRTc[exp( Fl/Ja/RT) + exp(Fl/Ja/RT)  2]}1/2 (1.11) where O'a is the surface charge density (coulombs per square meter), EO is the permittivity of vacuum, D is the dielectric constant of liquid water, R is the molar gas constant, T is the absolute temperature, C is the same as c, (subscript suppressed), F is the Faraday constant, and l/Ja is the electric potential (volts) at the plane where the diffuse ion swarm comes into contact with the solid. (The derivation of Eq. 1.11 is discussed in Chap. 5). Often the condition  Fl/Ja/RT ~ 1 is met and Eq. 1.11 can be approximated with the expression
O'a = (2EoDRTc)1/2exp( Fl/Ja/2R T)
(1.12)
Equation 1.12 and the standard DDL relationship.F
O'a
= EoD(dl/J/dx)x=a
(1.13)
then lead to the differential equation
dl/J
, = (X
(2RTC/F.f1[)
1/ 2
cxp(Fl/J/2RT)
(X = 8)
(1.14)
32
THE SURFACE CHEMISTRY OF SOILS
where i3 is the distance between two planes: that where l/J = where u" is evaluated. The solution of Eq. 1.14 is
exp(Fl/J,,/2RT)
=
F(2c/ eoDRT)1/2 i3/2
00
and that (1.15)
The definition of dex(c) in DDL theory is38
dex(c) =
L'' [1 
(1.16)
exp(Fl/J(x)/RT)]dx
The right side of Eq. 1.16 is the relative probability that a univalent anion will not be found at a point x near a negatively charged planar surface, integrated over all x values from i3 outward. Thus the mean exclusion distance is equal to the probability that an ion is excluded from the region between x and x + dx, summed over all such regions. The integral in Eq. 1.16 can be calculated with the help of a transformation based on Eqs. 1.11 and 1.13:
dex(c)
= (0 1  exp(Fl/J/RT) )"'3
dl/J/ dx
{O
(1  eY)dy ~ )Y3 [c(e Y + eY  2)]1/2 1
=
dl/J
= 1
jj3C
iO ey/
2
dy
Y.

2
= r;;: [1  exp(y,,/2)]
v f3c
2 =   i3
(1.17)
jj3C
where
f3 == 2F 2/e oDRT = 1.084
X
1016 m . mol 1
(T
=
298.15 K)
and y == Fl/J/RT. The last step in the calculation is made with the help of Eq. 1.15. The introduction of Eq. 1.17 into Eq. 1.10 produces the DDL model equation for the exclusion volume in a 1: 1 electrolyte: (1.18) Equation 1.18 predicts that a graph of measured values of Vex versus the function C 1/2 will be a straight line with a slope proportional to the exclusion specific surface area, SE' This behavior is illustrated in Fig. 1.13 for montmorillonite suspended in NaCI.:w A leastsquares line through the data points in the graph has a slope equal to 0.3046 mol l / 2 dm·l/2kg  I.
33
THE REACTIVE SOLID SURFACES IN SOILS
NoMONTMORILLONITE IN NoCI 10kg CLAY/ m3 SUSPENSION
)(
>0) Vex = 0.5524
+ 0.3046c 1/ 2
r 2 = 0.968
0'4'''
o
30
10
40
Figure 1.13. A plot of the exclusion volume against electrolyte concentration according to Eq. 1.18 for Namontmorillonite suspended in NaC1. 39
Therefore, SE
=~
x (slope/2)
(1.084)1/2 10 3 / 2 m 3 / 2 1/2 1/2 8 = x 10 m molx ;;;",.2 dm 3 / 2 x 0.3046 mo1 1/2 dm 3 / 2kg 1 = 5.01 x
lOS rrr'kg ?
= 501 m 2g 1
The surface area of the montmorillonite sample that repels chloride ions amounts to about 500 m 2g 1 under the conditions of the experiments. Table 1.8 lists specific surface area values for illitic micas as determined by nitrogen gas adsorption and by negative chloride adsorption.t" The specific surface areas calculated from N2 gas adsorption with the help of Eq. 1.7 show no particular trend with type of exchangeable cation. The mean value of SN, 11.2 ± 0.5 x 104 m2kg1, suggests that the mineral forms particles containing seven phyllosilicate layers, as indicated previously. The external surfaces of these particles are expected to repel anions, and therefore the specific surface area determined by negative chloride adsorption should also be around 105 rrr'kg" '. As shown in Table 1.8. however, the values of Sf:. obtained with Eq. 1.18, are always less than SN and decrease sharply with increasing radius of the
34
THE SURFACE CHEMISTRY OF SOilS
Table 1.8. Specific surface areas of illitic micas and montmorillonites determined by Nz gas adsorption (SN) and chloride exclusion (SE)40 Exchangeable cation Li+ Na+ K+ NHt
Rb+ Cs+
Illitic mica, 104 mZkg 1
Montmorillonite, 104 mZkg 1
SN
SE
SN
SE
11.6 10.9 11.3 11.8 10.5 11.2
8.0 7.0 3.5 2.2 1.0 0.0
6.6 4.6 6.4 5.9
65.0 56.0 43.6 25.6
14.6
15.6
exchangeable cation. The cause of this trend is thought to be surface complex formation between, for example, siloxane ditrigonal cavities and the exchangeable cations. 40 Surface complex formation results in the creation of an external surface that is electrically neutral wherever the complexes occur. Therefore, the extent of the surface that can repel chloride anions is reduced below that probed by N2 molecules and the specific surface area estimated with Eq. 1.18 is less than SN' The fact that this difference increases with cation size can be attributed to the higher tendency of larger cations to form innersphere surface complexes because of their stereochemistry and ionic potential. 41 Table 1.8 also compares specific areas for montmorillonite as determined by N z gas adsorption and negative chloride adsorption.t" In this case, the specific surface areas obtained with Eq. 1.18 are less than the crystallographic value of 72.5 x 104 rrr'kg" but are generally larger than SN' The variation in SE with type of cation can be understood in terms of both surface complexation and quasicrystal formation. Smallangle neutron scattering experiments on montmorillonite suspensions suggest that Li and Nasaturated clays are likely to remain as single layers.F If this is true, the reduction in exclusion specific surface area below the crystallographic specific surface area for Li and Namontmorillonite indicated in Table 1.8 must reflect a corresponding reduction, because of surface complexes, in the amount of surface that can repel chloride anions. Surface complexation evidently decreases the charged surface area by 10 and 23 per cent, respectively, for Li and Naclay. On the other hand, Kmontmorillonite can form quasicrystals containing two phyllosilicate layers in suspension and Csmontmorillonite can form quasicrystals containing three layers.F If a fraction f of the total number of phyllosilicate layers in a suspension form quasicrystals containing n layers, then Eq. 1.10 must be replaced by the expressiorr" Vex =
f f( 1
1
~) lSodex(C) + ~ Sod
( 1.19)
THE REACTIVE SOLID SURFACES IN SOilS
35
where So is the crystallographic specific surface area and d is the fixed distance between opposing internal surfaces in a quasicrystal. The derivation of Eq. 1.19 assumes no surface complexation and no chloride anions inside the quasicrystals. It is evident from Eq. 1.19 that the specific surface area determined by negative adsorption is related to the crystallographic value according to the equation (1.20) This expression can reproduce the values of SE for K and Csrnontmorillonite in Table 1.8 if / is given the values 0.80 and 1.2, respectively. The impossibly high value of/for Csmontmorillonite emphasizes that part of the difference between SE and So for Csmontmorillonite and the other clay samples must come from surface complexation of the exchangeable cations. The differences between the nitrogen gas and chloride exclusion specific surface area values for montmorillonite in Table 1.8 bring into relief one of the more important advantages of the negative adsorption method. Since this method requires that an aqueous solution come in contact with the solid surface, the specific surface area measured should reflect the structure of the solid material in natural soil more than, for example, the gas adsorption methods. Evidently the degree of aggregation of montmorillonite (except for Csmontmorillonite) in the degassed state is quite different from what it is in aqueous suspension, with the result that the surface available to repel chloride anions is much larger than that which can adsorb N z moleclues, despite the important effect of surface complexation. With illitic mica minerals, however, it appears that the state of aggregation of the samples does not change a great deal when they are brought into suspension from the dry state, but surface complexes do exert a profound effect on the specific surface area determined by chloride exclusion. 1.5. SURFACE CHARGE DENSITY
It is well established that some of the surface functional groups in soil clays bear electric charge, the sign and magnitude of which depend on the composition of the soil solution and the structure of the solid phase to which the functional groups are bound. The siloxane ditrigonal cavity, for example, often bears a more or less localized negative charge produced by isomorphic cation substitutions, and the s~~~_~x£~2~~Lg~9,Y1?.£'!JlJJ.~i!~ either positive or negative charge depending on thl1.pJ:!":~!~~,9iJh~~2!1 solution. Because the ~e.ac~ive solid surfaces in soils are h.e~er()Ae.!l_C:l:).~~.,.!!!e c:Oiicepf of surface charge density for .th.~.~ is.plu.~.~!i_~~i.c, not,~?n.o..typ~<::; The several kinds of surface charge density in a soil clay are discussed in Chap. 3. In the present section. attention is devoted to introducing surface charge density as an ~"era,~()nal c(!nc:C'I" through a description of some of
THE SURFACE CHEMISTRY OF SOILS
36
the methods used to measure it and are interpretation of these methods from the point of view of surface functional group chemistry. The surface density of intrinsic charge is the number of coulombs per square meter borne by surface functional groups either because of isomorphic substitutions in soil minerals or because of proton association and dissociation reactions. The intrinsic surface charge density, O"in, thus refers to permanent structural charge and to the net charge produced by protonselective functional groups (e.g., aluminol groups) on both inorganic and organic surfaces. This charge density can be measured conveniently by the Schofield method.P which consists of reacting soil clay with an electrolyte solution at a fixed pH value, removing excess electrolyte to retain only adsorbed cations and anions, and determining the moles of cation and anion charge adsorbed by a unit mass of the clay. The intrinsic surface charge density is the product of the Faraday constant and the difference between adsorbed cationic and anionic moles of charge per unit mass of clay, divided by the specific surface area of the clay: INTRINSIC
SURFACE
CHARGE
DENSITY.
 F(q+  q_)
S
(1.21)
where q+ and q_ refer to the moles of adsorbed cation and anion charge, respectively. Note that O"in can be either positive or negative. The chemical interpretation of O"in measured by the Schofield method depends sensitively on the type and concentration of probe electrolyte used. If these properties are chosen so that the cation in the reacting electrolyte neutralizes precisely the exposed functional group charge associated with isomorphic substitutions and dissociated hydroxyls and so that the anion neutralizes only the exposed protonated functional groups, then q + and q _ will have optimal magnitude for the chosen pH value and O"in will be truly an intrinsic surface charge density. On the other hand, if the cation in the probe electrolyte is not able to displace all of the native adsorbed cations in, e.g., innersphere surface complexes, or if the anion cannot displace all of the native anions bound to protonated functional groups, or if either ion does not form only neutral surface complexes in the soil clay, then O"in will differ from its optimal value. Thus the intrinsic surface charge density viewed operationally can exhibit different values for the same soil clay at a given pH. The optimal value of O"in represents the difference between the largest quantities of positive and negative charge achievable intrinsically by exposed surface functional groups. Nonoptimal values of O"in fall into the broad spectrum of possible differences between the varying amounts of positive and negative charge that can be brought to soil clay surfaces by cations and anions of varying adsorption characteristics. If they are positive, these nonoptimal values of q +. and q. usually are termed cation and anion exchange capacities. respectively. The reflect only the reactivities of chosen probe ions with
THE REACTIVE SOLID SURFACES IN SOILS
37
surface functional groups under prescribed conditions. However, if these probe ions and experimental conditions are similar to those in the natural soil clay, the value of Uin they produce can be of practical utility even if it is not optimal. 44 The surface density of permanent structural charge, uo, is the coulombs per square meter borne by surface functional groups that are charged because of isomorphic substitutions in soil minerals. The sign of Uo is nearly always negative in moderately weathered soils and is associated with the charge on siloxane ditrigonal cavities near sites of isomorphic substitution in 2: 1 phyllosilicates. The magnitude of Uo thus can be estimated from chemical composition and Xray crystallographic data, following a procedure similar to that described in Sec. 1.4 for calculating the crystallographic specific surface area of a Namontmorillonite. In that example, chemical composition data indicated 0.66 moles of negative charge, created by the substitution of Mg(II) for Al (III) in the octahedral sheet, per mole of unit cells. Since the basal plane dimensions of the unit cell were a = 0.517 nm and b = 0.895 nm, it follows that, for Uo in coulombs per square meter, STRUCTURAL SURFACE CHARGE DENSITY.
qF) 5 = (2N (10
18
Uo
Aab
)
( 0.66 mol cmol 1)(9.64870 x 104 C'mol;I)(10 18 nmZm Z) 2(6.022 x lO Z3 mol 1)(0.517 nm)(0.895 nm) = 0.114 Cm z (1.22)

where Bq is the charge deficit, F is the Faraday constant, and N A is the Avogadro constant. The same method can be applied to calculate Uo for any 2: 1 phyllosilicate. The magnitude Uo can also be estimated from the properties of the complexes formed between siloxane ditrigonal cavities and Nalkylammonium cations, CnHz n + 1NHj .45 The procedure consists of reacting a Nasaturated soil clay with a series of Nalkylammonium chloride solutions at 65°C, washing the reacted clay with ethanol to remove excess electrolyte, and determining the basal plane [d(001)] spacing in the clay after drying it under vacuum.:" The basal plane spacing is then plotted against n c , the number of carbon atoms in the Nalkylammonium cation used in an adsorption experiment, with the entire series of experiments included in the range 1 < n; < 20. When a monolayer of complexed alkylammonium cations lies in the interlayer region, the basal plane spacing is 1.36 nm and when a bilayer is present, it is 1.77 nm. Besides these conformations of the adsorbed organic cations, one observes pseudotrilayers, in which each alkyl chain in the bilayer kinks toward the basal plane opposite the one it is lying upon, and paraffintype structures, in which each alkyl chain makes a nonzero angle with the basal plane complexing the NH~ cation."
38
THE SURFACE CHEMISTRY OF SOILS
When Nalkylammonium cations form the 1.36nm monolayer structure, they lie flat between opposing basal planes and each cation covers a van der Waals area equal to (0.057n c + 0.14) nm z. Since the cation is univalent, this area is associated with one proton charge. As the value of n; increases, the area required by a cation increases. At some point, the area required becomes larger than the area per electron charge on a basal plane and the monolayer structure is no longer stable. The 1.77nm bilayer structure then becomes the favored one because the area requirement of the adsorbed organic cation can be met independently on each opposing basal plane in the interlayer region (Fig. 1.14). At the monolayerbilayer transition, the area per adsorbed cation just equals the area per electron charge on a basal plane. Therefore, at the transition point, ab 0.057n c + 0.14 = x x =
ab 0.057n c + 0.14
(1.23)
where x is the layer charge of the phyllosilicate, defined in Sec. 1.1. With the values of x indicated in Table 1.3 and a typical value of 0.46 nm z for the product ab, the monolayerbilayer transition can be expected for 4 <: n; :5 14 in smectite and 2 <: n c <: 4 in vermiculite. The layer charge of illitic mica is usually too large for the monolayerbilayer transition to be observed at any n.: Figure 1.14 illustrates the monolayerbilayer transition for a clay fraction deep in the subsoil of a Spanish Vertisol."? As is commonly found, the Figure 1.14. Basal plane spacings of Nalkylammonium complexes with a Vertisol clay fraction and the corresponding layer charge distributiorr." bilayer
monolayer
Layer Charge Distribution
w
o ~
~ 50
~2.0
E .5 o
)
9 1.5 01
~
....' •
• •
l
15
c
a..
SOIL CLAY VERTISOL
1.0 n
u cr w
....L...L.........., 20
0,6
LAYER CHARGE
0.7
THE REACTIVE SOLID SURFACES IN SOILS
39
transition does not take place at a single value of n.; instead it begins at n c = 11 and ends at n c = 14. This gradual transition reflects the fact that the layer charge in the clay does not have a single value, i.e., there is layer charge heterogeneity. In this example, the layer charge distribution can be estimated with the help of Table 1.9, which is based on Eq. 1.23 (with ab = 0.465 nm 2 ) and on the theory of Xray diffraction by randomly interstratified phyllosilicates. 48 The basal plane spacings in Fig. 1.14 are 1.36,1.48,1.60, and 1.77 nm for n c = 11,12,13, and 14, respectively. The data in Table 1.9 show that basal spacings of 1.36 nm at nc = 11 and 1.48 nm at n c = 12 correspond to about 29 per cent of the interlayer regions having layer charges between 0.58 and 0.64. Similarly, 1.6 nm at n c = 13 and 1.48 nm at n c = 12 correspond to 49  29 = 20 per cent of the interlayer regions having layer charges between 0.56 and 0.58, and 1.77 nm at n c = 14 and 1.6 nm at n c = 13 correspond to 51 per cent of the interlayer regions with layer charges between 0.52 and 0.56. This distribution of layer charge is plotted in Fig. 1.14. Similar kinds of charge partitioning involving combinations of Xray diffraction data with theoretical analysis are possible for vermiculitic and mixedphyllosilicate soil clays."? DENSITY. The surface density of net proton is defined by an expression analogous to Eq. 1.21:
PROTON SURFACE CHARGE
charge,
UH,
(1.24) where qH is the moles of complexed proton charge and qOH is the moles of complexed hydroxyl charge on protonselective surface functional groups
Table 1.9. Relations between carbon number (n c ) and layer charge (x), and between basal plane spacing [d(OOl)] and bilayer fraction (p) for Nalkylammoniumsmectite complexes'"
6 7 8 9
10 11
12 13 14 15
x·
d(OOl), nm
p
1.00 0.88 0.80 0.74 0.68 0.64 0.58 0.56 0.52 0.50
1.36 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.73 1.77
0.00 0.13 0.24 0.33 0.40 0.49 0.58 0.70 0.80 1.00
"Bused on Elj, 1,23. with 11/1 ~ 0.46~ nm'. corrected for u purticlc diumctcr of IlKI
11111,
40
THE SURFACE CHEMISTRY OF SOILS
per unit mass of soil clay. The quantity qOH is equal formally to the moles of charge on ionized, protonselective functional groups per unit mass of soil clay. The numerator in Eq. 1.24 applies only to surfaces bearing functional groups whose charge is intrinsically pHdependent, i.e., inorganic hydroxyl groups and most organic functional groups. The maximum values of qH/S and qOH/S for oxide, hydrous oxide, and hydroxide minerals can be estimated from crystallographic data if supporting information concerning the potential reactivity of the surface hydroxyl groups is available. For example, although the plane perpendicular to the crystallographic a axis on the surface of goethite contains four OH groups per unit cell (one type A, two type B, and one type C), only the type A group is believed to react with protons to form OHt groups.P Since the unit cell dimensions of goethite are a = 0.465 nm, b = 1.002 nm, and c = 0.304 nm", there should be one reactive OH group per 0.305 nrrr', corresponding to a maximum qH/S of 5.45 x 10 6 mol.m "? when the plane is fully protonated. Given that 80 per cent of the goethite surface is made up from this plane, the maximum value of qH/S is 4.36 x 10 6 mOlcm Z • The maximum value of qOH/S for goethite can be estimated similarly after making the assumption that all of the type A hydroxyl groups plus the water molecules bound to the Lewis acid sites (Sec. 1.2) can ionize at high pH. Full dissociation of the water molecules, which lie on the plane perpendicular to the crystallographic b axis that makes up the rest of the goethite surface, yields one OH per 0.141 nrrr', or 1.18 x 10 5 mOlcm z. The resulting maximum value for qOH/S is 6.72 x 10 6 mOlcm Z • Crystallographic estimates of maximum qH/S and qOH/S for goethite, gibbsite, and kaolinite are presented in Table 1.10. In each calculation, the assumption was made that only aluminol groups can be protonated, whereas aluminol, silanol, and Lewis acid water molecules can each dissociate one proton. It was assumed also that only the edge surfaces on gibbsite and kaolinite bear reactive hydroxyl groups. This assumption is
Table 1.10. Crystallographic estimates of the maximum values of qHISand qOHIS for selected soil minerals
qOH/S, p,molcm z
Mineral Goethite Gibbsite Kaolinite a
4.4 2.8 0.35
6.7 5.6 1.0
Reactive hydroxyl groups assumed" Type A OH and Lewis acid OHz Edgesurface Lewis acid OH and OHz Edgesurface silanol and aluminol, Lewis acid OH z
Geometric disposition of the OH groups: Goethite one OH per 0.305 nm 2 on the plane perpendicular to a axis (80% of total surface) and one OH 2 per 0.141 nrrr' on the planc pcrpendicular to b axis (20% of total surfacc) Gibbsite one OH and one OH 2 per 0.246 nm 2 on the edge surfaces (41,'1% of totul surface) Kaolinitesone silanol, one alumino/, and one Olll per (U7'1 nm 2 on the edge surfaces (7,'1% of h'lal surfacc)
THE REACTIVE SOLID SURFACES IN SOILS
41
controversial at present but not inconsistent with the results of ion adsorption experiments.Vr'" The most common method for measuring (qH  qOH) under arbitrary conditions is by potentiometric titration. 50 Briefly, the method involves the use of a glass electrode and a doublejunction calomel reference electrode in the titration cell: glass electrode
suspension of solid in background electrolyte
background electrolyte solution
liquid junctions
calomel electrode
The emf of the electrode assembly is measured while known volumes of either acid or base are added to the suspension. These data, in turn, are converted to proton concentrations with the help of a calibration curve prepared from similar titration data obtained without the suspended solid in the cell. The values of (qH  qOH) then can be calculated with the expression (1.25) where CA is the molar concentration of added acid, CB is that of added base, [H+] is the molar proton concentration derived from emf measurements, Cs is the mass of solid in one cubic decimeter of the suspension, and
cK [OH] = [H:]
(1.26)
where C K; is the conditional equilibrium constant for the ionization of water in the background electrolyte solution. As it stands, Eq. 1.25 provides values of qH  qOH referred to an arbitrary zero point. Usually these empirical values are renormalized to the value of qH  qOH at the point of zero salt effect (PZSE), which is the pH value at which plots of qH  qOH versus pH obtained at different ionic strengths in the background electrolyte solution meet. 50 Formally, this point of intersection is defined by the equation
(
iJUH) aI
= 0
(pH = PZSE)
(1.27)
T
where I is the ionic strength of the background electrolyte solution and Tis the absolute temperature. The PZSE and other points of zero charge are discussed in Chap. 3. Equation 1.25 fundamentally is a mass balance expression for protons and hydroxide ions added to a suspension of surfacereactive solids. If V is the volume of the suspension, then (C A  [H+])V and (C B  [OH])V are equal, respectively, to moles of protons and moles of hydroxide ions "bound" in some sense by the suspension constituents. The difference between these two quantities divided by the muss of the solid material in
42
THE SURFACE CHEMISTRY OF SOILS
the suspension is taken to be qH  qOH' In order for this equality to hold, there must be only two final states for a proton or an hydroxide ion added to the suspension: the free ion and the ion complexed by a functional group on a surface whose charge is pHdependent. Therefore, no added proton or hydroxide ion can react with dissolved constituents to form soluble complexes, with solid phases to dissolve them, or with surfaces whose charge is not pHdependent. If these protonconsuming side reactions occur, the values of qH and qOH will be overestimated in the analysis of titration data. In practical terms, the suppression of side reactions for H+ and OH requires a background electrolyte whose component ions do not form significant complexes with protons or hydroxide ions (e.g., NaCI0 4 ) , as well as the elimination of dissolved carbon dioxide, either by purging or by calibration procedures. The unwanted reactions with solid phases are more difficultperhaps even impossibleto suppress if a natural soil clay is being titrated. Should the soil clay contain siloxane surfaces bearing cations that can exchange with' protons, or should it contain hydroxy polymers that consume protons readily and dissolve, there can be little expectation of obtaining values of qH that have surface chemical significance. 50 For this reason, the use.Qf }J()teIltipmetric titration to measur~ ?"flITla~ bel!~~!~~t~ ,,~~~~.J.l~ions ~I!!PE~~.iPg ~~!!.~£~ara~teJi~ed metal()xides,.~)'~~o·usoJ{i~~.~?()rEy~.~?xides
c;>r to s\.lspeps!Qns. of purified QfgapiC::.mate.riilI.
NOTES 1. The geometric relationships among solid particle shape, area, and volume are described in detail in L. D. Baver, W. H. Gardner, and W. R. Gardner, Soil Physics, Chap. 1. Wiley, New York, 1972. 2. A detailed summary of this and other perturbations of the octahedral sheet is given in R. E. Grim, Clay Mineralogy, Chap. 4. McGrawHill, New York, 1968. 3. L. Pauling, The Nature of the Chemical Bond, Chap. 13. Cornell University Press, Ithaca, N.Y., 1960. 4. U. Schwertmann and R. M. Taylor, Iron oxides, in Minerals in Soil Environments (J. B. Dixon and S. B. Weed, eds.) Soil Science Society of America, Madison, Wis., 1977. U. Schwertmann, D. G. Schulze, and E. Murad, Identification offerrihydrite in soils by dissolution kinetics, differential Xray diffraction, and Mossbauer spectroscopy, Soil Sci. Soc. Am. J. 46: 869 (1982). 5. H. D. Megaw, Crystal Structures: A Working Approach, Chap. 13. Saunders, Philadelphia, 1973. 6. R. M. McKenzie, Manganese oxides and hydroxides, in J. B. Dixon and S. B. Weed, op. cit:" 7. G. Brown, A.C.D. Newman, J. H. Rayner, and A. H. Weir, The structures and chemistry of soil clay minerals, in The Chemistry of Soil Constituents (D. J. Greenland and M.H.B. Hayes, eds.). Wiley, Chichester, U.K., 1978. Concerning goethite, see also R. W. Fitzpatrick and U. Schwertmann, AI· substituted goethite: An indicator of pedogenic and other weathering environments in South Africa, Geoderma 27:33; (I \1H2).
THE REACTIVE SOLID SURFACES IN SOILS
43
8. C. E. Weaver and L. D. Pollard, The Chemistry of Clay Minerals. Elsevier, Amsterdam, 1973. The term illitic mica refers to a dioctahedral micaceous mineral weathered in soil. 9. G. Sposito, The chemical forms of trace metals in soils, in Applied Environmental Geochemistry (I. Thornton, ed.). Academic Press, London, 1983. 10. S. Wada and K. Wada, Density and structure of allophane, Clay Minerals 12: 289 (1977). K. Wada, Mineralogical characteristics of andisols, in Soils with Variable Charge (B.K.G. Theng, ed.). New Zealand Society of Soil Science, Lower Hutt, N.Z., 1980. 11. W. Flaig, H.Beutelspacher, and E. Rietz, Chemical composition and physical properties of humic substances, in Soil Components, Vol. 1: Organic Components (J. E. Gieseking, ed.). SpringerVerlag, New York, 1975. 12. A. G. Walton, Polypeptides and Protein Structure. Elsevier, New York, 1981. 13. See Chap. 3 of G. Sposito, The Thermodynamics of Soil Solutions (Clarendon Press, Oxford, 1981) for an introduction to Lewis acids and bases. 14. R. Prost, Interactions between adsorbed water molecules and the structure of clay minerals: Hydration mechanism of smectites, Proc. Int. Clay Conf. 1975, p. 351 (1976). 15. A detailed discussion of the charge distribution and stereochemical aspects of these complexes is given in V. C. Farmer and J. D. Russell, Interlayer complexes in layer silicates, Trans. Far. Soc. 67:2737 (1971). 16. V. C. Farmer and J. D. Russell, Infrared absorption spectrometry in clay studies, Clays and Clay Minerals 15:121 (1967). V. C. Farmer, The characterization of adsorption bonds in clays by infrared spectroscopy, Soil Sci. 112:62 (1971). H. E. Doner and M. M. Mortland, Charge location as a factor in the dehydration of 2:1 clay minerals, Soil Sci. Soc. Am. I, 35:360 (1971). 17. R. J. Atkinson, Crystal morphology and surface reactivity of goethite. PhD dissertation, University of Western Australia, Perth, 1969. J. D. Russell, R. L. Parfitt, A. R. Fraser, and V. C. Farmer, Surface structures of gibbsite, goethite, and phosphated goethite, Nature 248:220 (1974). R. L. Parfitt, R. J. Atkinson, andR. SeC. Smart, The mechanism of phosphate fixation by iron oxides, Soil~c:i.Soc. Am. r. 39:837 (1975). R. L. Parfitt, J. D. Russell, and V. C. Farmer, Confirmation of the surface structures of goethite (aFeOOH) and phosphated goethite by infrared spectroscopy, l.C.S. Faraday I 72:1082 (1976). 18. A review of the molecular structure of innersphere surface complexes between anions and surface OH groups is given in R. L. Parfitt, Anion adsorption by soils and soil materials, Advan. Agron. 30: 1 (1978). 19. R. L. Parfitt. A. R. Fraser, and V. C. Farmer, Adsorption on hydrous oxides. II. Oxalate, benzoate and phosphate on gibbsite, I, Soil Sci. 28: 289 (1977). 20. P. W. Schindler, Surface complexes at oxidewater interfaces, in Adsorption of Inorganics at SolidLiquid Interfaces (M. A. Anderson and A. J. Rubin, eds.). Ann Arbor Science, Ann Arbor, Mich., 1981. J. A. Davis, R. O. James, and J. O. Leckie, Surface ionization and complexation at the oxide/water interface. I. Computation of electrical double layer properties in simple electrolytes, J, Colloid Interface Sci. 63: 480 (1978). 21. F. J. Stevenson, Humus Chemistry, Chap. 9. Wiley, New York, 1982. 22. R. C. Reynolds, Interstratified clay minerals, in Crystal Structures of Clay Minerals and Their Xray Identification (G. W. Brindley and G. Brown, eds.). Mineralogical Society. London. 19HO.
44
THE SURFACE CHEMISTRY OF SOilS
23. K. Norrish, Factors in the weathering of mica to vermiculite, Proc. Int. Clay Conf. 1972, p. 417 (1973). 24. B. L. Sawhney, Interstratification in layer silicates, in J. B. Dixon and S. B. Weed, op. cit.4 25. C. I. Rich, Hydroxy interlayers in expansible layer silicates, Clays and Clay Minerals 16: 15 (1968). P. H. Hsu, Aluminum hydroxides and oxyhydroxides, in J. B. Dixon and S. B. Weed, op. cit.4 26. B. D. Mitchell, Oxides and hydrous oxides of silicon, in Soil Components, Vol. 2: Inorganic Components (1. E. Gieseking, ed.). SpringerVerlag, New York, 1975. 27. B.K.G. Theng, Claypolymer interactions: Summary and perspectives, Clays and Clay Minerals 30: 1 (1982). K. R. Tate and B.K.G. Theng, Organic matter and its interactions with inorganic soil constituents, in B.K.G. Theng, op. cit. 1o 28. E.A.C. Follett, W. J. McHardy, B. D. Mitchell, and B.F.L. Smith, Chemical dissolution techniques in the study of soil clays, Clay Minerals 6: 23 (1965). E.A.C. Follett, The retention of amorphous, colloidal "ferric hydroxide" by kaolinites, J. Soil Sci. 16: 334 (1965). A. W. Fordham and K. Norrish, Electron microprobe and electron microscope studies of soil clay particles, Aust. J. Soil Res. 17:283 (1979). 29. E. A. Jenne, Trace element sorption by sediments and soilsSites and processes, in Molybdenum in the Environment (W. Chappel and K. Petersen, eds.). Dekker, New York, 1976. 30. J. P. Quirk and L.A.G. Aylmore, Domains and quasicrystalline regions in clay systems, Soil Sci. Soc. Am. J. 35: 652 (1971). 31. S. Brunaer, L. E. Copeland, and D. L. Kantro, The Langmuir and BET theories, in The SolidGas Interface (E. A. Flood, ed.), Vol. 1. Dekker, New York, 1967. Equation 1.7 is derived under the assumption that an infinite number of layers build up on the absorbing surface. If the number of layers is finite, a more general expression results, but it cannot be distinguished from Eq. 1.7 when plotted as in Fig. 1.12 unless the number of layers is fewer than three. 32. D. L. Carter, M. D. Heilman, and C. L. Gonzalez, Ethylene glycol monoethyl ether for determining surface area of silicate minerals, Soil Sci. 100: 356 (1965). M. D. Heilman, D. L. Carter and C. L. Gonzalez, The ethylene glycol monoethyl ether (EGME) technique for determining soilsurface area, Soil Sci. 100:409 (1965). L. J. Cihacek and J. M. Bremner, A simplified ethylene glycol monoethyl ether procedure for assessment of soil surface area, Soil Sci. Soc. Am. J. 43: 821 (1979). A "singlepoint" method involving the adsorption of water vapor by a Casaturated soil in equilibrium with a relative humidity of 20 per cent (e.g., a saturated solution of CaBrz) has been suggested by J. P. Quirk, cited in note 33. For critical studies of these singlepoint methods, see I. M. Eltantawy and P. W. Arnold, Reappraisal of the ethylene glycol monoethyl ether (EGME) method for surface area estimations of clays, J. Soil Sci. 24:232 (1973), and Ethylene glycol sorption by homoionic montmorillonites, J. Soil Sci. 25:99 (1974). 33. H. D. Orchiston, Adsorption of water vapor. I: Soils at 25 °C, Soil Sci. 76: 453 (1953). J. P. Quirk, Significance of surface areas calculated from water vapor sorption isotherms by use of the BET equation, Soil Sci. 80: 423 (1955). 34. R. W. Mooney. A. G. Keenan. and L. A. Wood. Adsorption of water vapor by montmorillonite. I: IIcut of desorption lind application of RET theory.
THE REACTIVE SOLID SURFACES IN SOILS
45
J. Am. Chem. Soc. 74: 1367 (1952). II: Effect of exchangeable ions and lattice swelling as measured by Xray diffraction, J. Am. Chem. Soc. 74: 1371 (1952). 35. D. J. Greenland and J. P. Quirk, Surface areas of soil colloids, in Transactions of Comm. IV and V. International Society of Soil Science, Palmerston North, N.Z., 1962. Determination of surface areas by adsorption of cetyl pyridinium bromide from aqueous solution, J. Phys. Chem. 67: 2886 (1963). Determination of the total specific surface areas of soils by adsorption of cetyl pyridinium bromide, J. Soil Sci. 15: 178 (1964). 36. R. K. Schofield, Calculation of surface areas from measurements of negative adsorption, Nature 160: 408 (1947). R. K. Schofield and O. Talibudeen, Measurement of the internal surface by negative adsorption, Disc. Faraday Soc. 3:51 (1948). H. J. van den Hul and J. Lyklema, Determination of specific surface areas of dispersed materials by negative adsorption, J. Colloid Interface Sci. 23: 500 (1967). 37. G. Sposito, The Thermodynamics of Soil Solutions, Chap. 6. Clarendon Press, Oxford, 1981. 38. G. H. Bolt, Soil Chemistry. B: PhysicoChemical Models, Chap. 7. Elsevier, Amsterdam, 1979. 39. G. H. Bolt and B. P. Warkentin, The negative adsorption of anions by clay suspensions, KolloidZ. 156: 41 (1958). 40. D. G. Edwards, A. M. Posner, and J. P. Quirk, Repulsion of chloride ions by negatively charged clay surfaces, I, II, and III, Trans. Faraday Soc. 61: 2808 (1965). 41. P. J. Sullivan, The principle of hard and soft acids and bases as applied to exchangeable cation selectivity in soils, Soil Sci. 124:117 (1977). 42. D. J. Cebula, R. K. Thomas, and J. W. White, Small angle neutron scattering from dilute aqueous dispersions of clay, J.C.S. Faraday I, 76:314 (1980). 43. R. K. Schofield, Effect of pH on electric charges carried by clay particles, J. Soil Sci. 1: 1 (1949). B. van Raij and M. Peech, Electrochemical properties of some Oxisols and Alfisols of the tropics, Soil Sci. Soc. Am. J. 36: 587 (1972). D. J. Greenland, Determination of pH dependent charges of clays using caesium chloride and Xray fluorescence spectrography, Trans. 10th Int. Congr. Soil Sci. (Moscow) 11:278 (1974). D. J. Greenland and C.J.B. Mott, Surfaces of soil particles, in D. J. Greenland and M.H.B. Hayes, op. cit.' 44. This important application of nonoptimal values of ain is discussed in R. L. Parfitt, Chemical properties of variable charge soils, in B.K.G. Theng, op. cit. 1O 45. G. Lagaly and A. Weiss, Determination of the layer charge in micatype layer silicates, Proc. Int. Clay Conf. 1969, p. 61 (1969). G. Lagaly and A. Weiss, The layer charge of smectic layer silicates, Proc. Int. Clay Conf. 1975, p. 157 (1976). G. Lagaly, M. Fernadez Gonzalez, and A. Weiss, Problems in layercharge determination of montmorillonites, Clay Minerals 11: 173 (1976). 46. G. Ruehlicke and E. E. Kohler, A simplified procedure for determining layer charge by the Nalkylammonium method, Clay Minerals 16: 305 (1981). 47. J. L. Perez Rodriguez, A. Weiss, and G. Lagaly, A natural clay organic complex from Andalusian black earth, Clays and Clay Minerals 25: 743 (1977). 48. G. Lagaly, Characterization of clays by organic compounds, Clay Minerals 16:1 (1981). 49. G. Lagaly, The "layer charge" of regular interstratified 2: I clay minerals, Clays and Clay Minerals 27: I (1979). Layer charge heterogeneity in vermiculites, Clays and Clay Minerals 30: 215 (19H2).
46
THE SURFACE CHEMISTRY OF SOilS
50. For good working discussions of potentiometric titration methods, see G. H. Bolt, Determination of the charge density of silica soils, J. Phys. Chern. 61:1166 (1957), and D. E. Yates and T. W. Healy, Titanium dioxideelectrolyte interface. 2. Surface charge (titration) studies, J. C.S. Faraday I 76: 9 (1980). A critical discussion of the uses of potentiometric titration to measure O'H for soil clays is given in J. C. Parker, L. W. Zelazny, S. Sampath, and W. G. Harris, Critical evaluation of the extension of zero point of charge (ZPC) theory to soil systems, Soil Sci. Soc. Am. J. 43: 668 (1979). FOR FURTHER READING
J. B. Dixon and S. B. Weed, Minerals in Soil Environments. Soil Science Society of America, Madison, Wis., 1977. Chapters 4 through 12, 16, and 18 of this comprehensive treatise may be consulted for detailed accounts of the structural chemistry of the solid phase in soils. J. E. Gieseking, Soil Components, Vol. 2: Inorganic Components. SpringerVerlag, New York, 1975. Chapters 1 through 8 of this encyclopedic reference provide perhaps the best advanced discussions available on the structural chemistry of phyllosilicates. D. J. Greenland and M.H.B. Hayes, The Chemistry of Soil Constituents. Wiley, Chichester, U.K., 1978. The first four chapters in this outstanding anthology of soil chemistry may be consulted as background for the topics discussed in the present chapter. Every aspect of soil mineralogy considered in detail in the first two entries of this reading list is described in Greenland and Hayes with equal authority but more briefly. S. J. Gregg and K.S.W. Sing, Adsorption, Surface Area and Porosity. Academic Press, London, 1982. The first two chapters of this well known monograph present a thorough discussion of the concept of the packing area and the measurement of specific surface area by positive adsorption methods. S. J. Gregg and K.S.W. Sing, The adsorption of gases on porous solids, Surface and Colloid Science 9: 231 (1976). A shortened version of Adsorption, Surface Area and Porosity for the reader who wishes a brief review of the concept of packing area and the BET method. \ G. D. Parfitt and K.S.W. Sing, Characterization of Powder Surfaces. Academic Press, London, 1976. Chapter 2 offers an especially good review of the physical and chemical methods for characterizing surface hydroxyl groups. B.K.G. Theng, Soils with Variable Charge. New Zealand Society of Soil Science, Soil Bureau, Department of Scientific and Industrial Research, Lower Hutt, N.Z., 1980. The first 10 chapters of this fine compendium survey the mineralogical and surface chemical properties of soils whose reactive solid surfaces are populated principally by the hydroxyl group.
2 THE STRUCTURE OF WATER NEAR CLAY MINERAL SURFACES
2.1. LIQUID WATER
The most important surface reactions in soils occur when liquid water is the fluid phase in contact with the particles of the clay fraction. An understanding of these reactions requires not only information about the structural chemistry of the solid phases, the subject of Chap. 1, but also an appreciation of what effects the contiguous liquid phase may have on surface functional group behavior. As a first approximation, one can state that these effects should be the same as those observed for functional group reactivity in aqueous solutions containing small molecules. This conjecture can be correct for dilute soil clay suspensions, but it can be quite wrong for soil clays enveloped only by a thin film of water because the solid surfaces could perturb the water molecules enough to alter their configuration from what exists in the bulk liquid phase. The altered water structure, in turn, could exhibit solvent properties different from those of the bulk liquid and therefore affect surface functional group reactivity in a different manner. Any inference concerning the effects of a possibly altered molecular structure of water near the solid surfaces in soil clays must proceed from an acquaintance with the structure of liquid water in bulk and in aqueous electrolyte solutions. In this section, the current picture of the molecular arrangement in bulk water is reviewed. In Sec. 2.2, the same is done for aqueous solutions of inorganic electrolytes. These summaries are followed by discussions of the structure of water near the surfaces of phyllosilicates and the effect of these surfaces on the solvent properties of the water molecule. The characteristic feature that distinguishes liquids from solids, and in particular liquid water from ice, is the influence of time scales on molecular structure. For solids, this influence is minimal. For liquids, it is so important that the very definition of the term structure must incorporate it in an essential way. I Consider a typical water molecule as it moves about
48
THE SURFACE CHEMISTRY OF SOILS
through the bulk liquid phase. On a time scale that is short compared with a period of vibration for a hydrogen bond (about z x 10 13 s), the water molecule "sees" a spatial arrangement of its neighbors that is called the instantaneous structure (I structure). This I structure exhibits water molecules in a highly irregular arrangement because it exists on a time scale so short that the position and orientation of individual molecules can be momentarily far removed from their most probable values. Thus the separation between a typical molecule and its nearest neighbors, as well as the degree of hydrogen bonding among them, deviates considerably in the I structure from the most stable average configuration. If the time scale is lengthened so as to lie somewhere between 2 x 10 13 s and the time required for a water molecule to diffuse in the liquid through a distance equal to its own diameter (about 10 11 s) a typical molecule see a surrounding spatial arrangement called the vibrationally averaged structure (V structure). This structure shows water molecules near their most probable position because it exists on a time scale long enough to include many hydrogen bond bending and stretching vibrations and therefore represents an average over the positions of the molecules during those vibrations. The V structure thus presents more local ordering and less hydrogen bond distortion than the I structure.j Finally, on a time scale that is very long compared with a diffusion time (about 10 6 s), a typical water molecule sees a spatial configuration of its neighbors known as the diffusionally averaged structure (D structure). This structure includes all effects of vibrational, rotational, and translational motion of the water molecules. It is more ordered than the V structure because it represents longtime averages of positions and orientations leading to only the most probable molecular configurations. Since the time scale is long enough for diffusive motions to take place in the liquid, a typical molecule does not see just one set of neighboring molecules in the D structure, of course. Instead, neighboring molecules come and go, leaving the' chosen typical molecule to see the average or most probable sites and orientations they occupy. Even these brief remarks should make it clear that the concept of structure in liquid water is a dynamic one. The molecular arrangements perceived and particularly their degree of ordering very much depend on the time scale involved. It is critically important to bear this feature in mind when discussing the experimental methods used commonly to study the structure of water since each method is itself characterized by a specific time scale during which it probes a molecular environment. Several of these experimental methods are indicated in Fig. 2.1. The molecular structural parameters that can be deduced by applying the methods to liquid water and aqueous solutions are listed in Table 2.1. The infrared (IR) and Raman spectrometers available for studies of liquid water cover a frequency range corresponding to periods of molecular vibration between 10 15 and 10 12 S3. Thus optical spectroscopy can give information concerning the transition from the I structure to the V
THE STRUCTURE OF WATER NEAR CLAY MINERAL SURFACES
49
STRUCTURE TIME SCALE IN SECONDS (log) I R SPECTRA NEUTRON SCATTERING ESR SPECTRA NMR SPECTRA DIELECTRIC RELAXATION NEUTRON AND XRAY DIFFRACTION THERMODYNAMIC PROPERTIES
Figure 2.1. Time scales for methods used to study the molecular structure of liquid water.
Table 2.1. Molecular properties of liquid water and the experimental methods that measure them
Method Infrared and Raman spectroscopy Electron spin resonance
Incoherent neutron scattering
Nuclear magnetic resonance
Dielectric relaxation
Neutron, electron, and Xray diffraction
Molecular parameter and its physical significance OR and hydrogen bond strength, orientation, and length (V structure) Solvation water molecule orientation Tc , correlation time for rotation of a solvation complex Ds , selfdiffusion coefficient TR ~ residence time for jump diffusion TJ, correlation time for rotation of the dipole moment Water molecule orientation (NMR line shape) TZ, correlation time for rotation about the dipolar axis T c , rotational correlation time for solvation complexes D s , selfdiffusion coefficient TJ, correlation time for rotation of the dipole moment a, measure of the spread of correlation times about TI Watermolecule 0 and H positions and bond orientations (0 structure)
50
THE SURFACE CHEMISTRY OF SOILS
structure. The molecular parameters involved pertain to OR bonds in water molecules and hydrogen bonds between water molecules, as indicated in Table 2.1. Electron spin resonance (ESR) spectroscopy probes a molecular environment on the relatively narrow time scale of 10 11 to 10 10 sand therefore gives information related to the transition between the V structure and the D structure. The use of ESR is limited to aqueous solutions containing solute atoms with unpaired electrons, i.e., molecular spin systems that respond to an applied magnetic field." The induced magnetization of these spin systems (e.g., Cu2+ or Mn2+), as well as its subsequent relaxation upon removal of the perturbing magnetic field, are affected strongly by the surrounding molecular environment. Thus one can learn something about the structure of solvation complexes (e.g., CU(R20)~+) by observing the magnetic behavior of an appropriate set of atomic electrons surrounded by liquid water molecules. Incoherent neutron scattering (INS) can be used to study the translational, rotational, and vibrational motion of water protons on a time scale between 10 13 and 10 10 S.5,6 Thus INS provides data pertinent to the V structure and to the transition from the V structure to the D structure in liquid water. The principal use of INS has been to characterize the translational and rotational motion of water molecules through the interpretation of scattering data with model expressions. The three most important model parameters used are the selfdiffusion coefficient, D., which can also be measured in an experiment involving isotopelabeled water molecules; 7 the residence time of a water molecule, 'TR, during which it vibrates about a fixed position before "jumping" to its next position; and the correlation time, 'Tl, which is a time constant for the decay of correlation between the orientation of a water molecule at some initial time and at some later time." Nuclear magnetic resonance (NMR) spectroscopy probes a molecular environment on the broad time scale between 10 10 and 10 3 sand therefore provides data concerning the transition between the V structure and the D structure plus data on the D structure itself. The physical basis for the application of NMR to liquid water and aqueous solutions is parallel to that for ESR, in that one studies the response of a magnetic nucleus (e.g., a water proton) to an applied electromagnetic field." The relaxation of the magnetization induced in a proton by a magnetic field is of particular importance in liquid water studies. An analysis of relaxation data with model expressions describing both intra and intermolecular protonproton interactions leads to a calculation of the correlation time, 'T2, which may be interpreted as a decay time constant for correlation between orientations of the protonproton vector in a water molecule." For solutes in aqueous solutions, it it also possible to determine the time constant, 'Tc ' for the decay of orientation correlation of a solvation complex through an analysis of NMR relaxation data. Dielectric relaxation spectroscopy can probe the very broad time domain between 10 12 lind 10 2 s. In principle. therefore, this method can be used
THE STRUCTURE OF WATER NEAR CLAY MINERAL SURFACES
51
to obtain data on the V structure, the D structure, and the transition between them. The physical basis of the method is connected closely to the fact that the distribution of electic charge in a water molecule is primarily dipolar. Thus, if a water molecule is subjected to an applied electric field, the molecule will attempt to orient itself with its dipole moment pointing along the direction of the field; if the field is timevarying, the molecule also will attempt to follow changes in the field direction by reorienting itself sympathetically. The extent to which this is possible, however, depends on the constraints imposed on the molecule by its environment. Should the molecule be coupled strongly with its neighbors, its ability to follow a fluctuating electric field will be less than if the coupling were weak. Whatever the degree of coupling, it is certain that the water molecule will be less able to reorient in phase as the frequency with which an applied electric field changes direction is increased, and at some frequency it will fail to respond altogether. The mean frequency at which the failure becomes complete is expected to be an indicator of the strength of the bonds that constrain the water molecule. The greater this mean frequency, the weaker the constraining bonds between the molecule and its environment. Thus dielectric relaxation spectroscopy consists of analyzing, with model expressions, measurements of the complex dielectric permittivity as a function of the frequency of an applied electric field. Typically, these model expressions contain the decay time constant, T1, and a parameter a, which equals zero if there is no spread of decay times about the mean value 9 T1 and tends to unity as the spread of decay times becomes larger. Neutron or Xray diffraction is the coherent, elastic scattering of either neutrons or Xrays by atoms arranged ona periodic lattice. 6 ,10 Neutron diffraction is analogous to the better known Xray diffraction but differs from the latter in two important respects. First, neutron diffraction involves scattering by nuclei, whereas Xray diffraction involves scattering by atomic electrons. It follows that the scattering power of a given element is different, in general, for the two processes. For example, deuterium, having but one electron, has a low scattering power for Xrays but a high (coherent) scattering power for neutrons. Second, neutron diffraction probes a larger spatial domain in a target sample than Xray diffraction because of the greater penetration of neutrons into matter. Thus, structural information pertaining to relatively larger molecular units in sample materials can be obtained. Since coherent scattering experiments require the collection of data over long time periods, neutron and Xray diffraction give a picture of the structure of water on an effectively "infinite" time scale. This picture, then, is an account of the D structure in liquid water and aqueous solutions. Thermodynamic data mentioned in Fig. 2.1 refer to the properties of stable states and therefore give information pertaining to a time scale that also is effectively infinite with respect to the dynamics of water molecules. Besides this wellknown fact, there are two important features of thermodynamic methods that set them apart from the other methods indicated in Fig. 2.1. First. since the sole objective of chemical thermodynamics is the
52
THE SURFACE CHEMISTRY OF SOILS
development of exact mathematical relationships among the macroscopic properties of a physical system, thermodynamic data cannot be interpreted directly in terms ofmolecular structure. Thus the thermodynamic properties of liquid water cannot provide unambiguous insights into the structural behavior of water molecules. Second, the thermodynamic properties of mixtures are only formally separable into properties that pertain to the individual components. Any attempt to assign these properties to just the water component in a solution or suspension must be understood as an arbitrary action unless nonthermodynamic evidence exists to support it. The molecular structure of liquid water is not yet a precise quantitative concept despite the many studies carried out using the methods indicated in Fig. 2.1. What has emerged from these studies over the past dozen years is a firm qualitativeor perhaps semiquantitativepicture of the I, V, and D structures that is reasonably selfconsistent and sufficiently detailed to serve as a basis for interpreting data on aqueous solutions and phyllosilicate suspensions. The I structure in liquid water cannot be inferred from the experimental methods listed in Table 2.1 because those methods provide data that are time averages over many I structure configurations. However, the technique of molecular dynamics (MD) computer simulation has led to reliable information about the I structure.lv!' In this technique, a computer is used to solve the classical mechanical equations of motion with a chosen intermolecular potential function for a few hundred water molecules constrained in space to maintaining the equilibrium liquid density, with data on the instantaneous position and velocity of the molecules provided both as numerical output and in the form of stereoscopic pictures. The principal features of the I structure determined in this fashion are 12 1. A clear tendency for neighboring water molecules to orient themselves into a tetrahedral, hydrogenbonded structure 2. The absence of "clusters" that have mass densities very different from the equilibrium liquid average 3. The absence of a monomer population and of structures resembling any of the known ice structures 4. The existence of some nonhydrogenbonded OH groups and of considerable distortion (nonlinearity) in OH··· 0 bonds These characteristics are expected to be refined in the V structure of liquid water in the sense that the positions of the water molecules become more precisely localized and the distortions in the hydrogen bonds are reduced. Both computer simulationvP and IR, Raman, and neutron scattering experiments! confirm this expectation. In particular, there is a significant narrowing in the distributions of nearestneighbor distances and OH· . ·0 bond angles, an increase in hydrogen bonding and in the number of polygon structures with both even and odd numbers of molecules, and a clear indication that the nearest neighbors of II typical molecule in the
THE STRUCTURE OF WATER NEAR CLAY MINERAL SURFACES
53
r
J
b.
~.a. 0 ~ ~~rf.P .P o..~~ 0".
(0)
( b)
Figure 2.2. (a) Ideal local tetrahedral configuration of molecules in liquid water. (b) Monte Carlo computer simulation of the V structure in liquid water. (After Rice 1)
liquid are arranged about it in a tetrahedral configuration, as illustrated in Fig. 2.2. The tetrahedral arrangement that characterizes the local ordering of water molecules in the V structure dissipates after about 10 12 s (at 283 K) because the nearest neighbors of a given molecule are relatively free to change their positions in response to thermal perturbations." This relaxation time is about one order of magnitude smaller than the time scale for diffusive translational and rotational motion of the molecules in liquid water at 283 K, as can be inferred from Table 2.2. The physical meaning of Table 2.2. Correlation time constants for the diffusive translational and rotational motions of a single molecule in liquid water" T,K
273 278 283 288 293 298 303 308
D .. 10 9 ms 21
1.092 1.313
1.543 1.777 2.021 2.302 2.620 2.919
'7"d,
psa
12.7 10.5 9.0 7.8 6.8 6.0 5.3 4.7
'7"1>
psb
17.9 14.9 12.6 10.8 9.3 8.1 7.2 6.4
'7"2,
psc
5.8 4.9 4.3 3.7 3.2 2.9 2.5 2.3
r" = 2a'/JD, (whcrc IJ ~ 0.144 nm is thc van der Waals radius of H,O) is thc time required for a "diffusive step" in thc liquid,
»
Obtnincd from dielectric relaxation datu, • Ohlaincd from proton NMR relaxation data, h
54
THE SURFACE CHEMISTRY OF SOilS
this fact is that the local environment of a water molecule in the liquid undergoes many fluctuations during the course of an elementary "singleparticle" motion through translation or rotation, Therefore, the parameters in Table 2.2, although of molecular significance, describe the transition from V structure to D structure only in the broadest terms and cannot be used to examine either structure in great detail because those details are washed out by many fluctuations. 9 The D structure of liquid water as revealed by Xray, neutron, and electron diffraction experiments'r'" comprises water molecules hydrogenbonded in an extensive network that exhibits local tetrahedral ordering. The persistence of the tetrahedral structure (Fig. 2.2) is exemplified by the fact that the coordination number of a water molecule in the liquid, obtained by integration of the first peak in the radial distribution function determined from Xray diffraction data, is equal to 4.4 throughout the temperature range from the melting point to the boiling point. However, the diffraction data also indicate that water molecules outside the shell of nearest neighbors may deviate considerably from the configurations projected on the basis of, e.g., an icelike ordering. Therefore, a large number of distorted or broken hydrogen bonds exists in the liquid, and it is these bonds that determine the timedependent properties of water. The structure of liquid water as reviewed here is actually a kind of sequence of structures whose degree of ordering and connectivity increases with the time scale of molecular observation. Perhaps the most succinct definition of liquid water structure that encompasses all of the known qualitative characteristics related to time scales is that given recently by F. H. Stillinger;' "Liquid water consists of a macroscopically connected, random network of hydrogen bonds, with frequent strained and broken bonds, that is continually undergoing topological reformation. [The] properties of water arise from the competition between relatively bulky ways of connecting molecules into local patterns characterized by strong bonds and nearly tetrahedral angles and more compact arrangements characterized by more strain and bond breakage." 2.2. ELECTROLYTE SOLUTIONS
The influence of an ion in an aqueous electrolyte solution on the structure of liquid water can be pictured spatially as a localized perturbation of the tetrahedral configuration shown in Fig, 2.2. 15 In the ~()n of t~Lq\lig n~are§j:JM.jQQ.2.Jhe water molecules ar~ dominateci. biaae'5§~..j~le.ctr{) siric,!~~L!J,l!;l§.~.l::~l!~:crt1iepri"!iji.~~l~ation· sheil."tii'the~nexro~'ter region, the water molecules interact weakly WIth the ion and form a structure known as the secondary solvation shell or secondzone structure. Beyond the second zone, the structure of the liquid is indistinguishable from that in the pure bulk phase. The study of aqueous electrolyte solutions with the methods listed in Table 2,1 has as its objective the development of it molecular model of the
THE STRUCTURE OF WATER NEAR CLAY MINERAL SURFACES
55
primary and secondary solvation shells. This model should include the numbers and configurations of the water molecules in the shells, as well as their residence times and the other singleparticle parameters in Table 2.2. All of these properties are expected to vary with the nature of the electrolyte ions (particularly their valence and radius), with the concentration and temperature of the solution, and with the pressure applied to it. The primary solvation shell of a small monovalent cation appears to contain about six water molecules if the solution is dilute and about three if the solution is concentrated. The residence time, Tb' of the water molecules in the primary shell has been estimated on the basis of dielectric and NMR relaxation experiments'? to be about 10 ps. This figure is an order of magnitude larger than the residence time of a water molecule in tetrahedral coordination with a given set of nearest neighbors in the bulk liquid but is equal to the time required for a "diffusive step" (Table 2.2). Thus the primary solvation shell of a small monovalent cation is relatively well defined temporally, although diffusive exchange of solvation water molecules with those in the bulk liquid is expected to be rapid. For larger monovalent cations and for monovalent anions, relaxation experiments indicate Tb < 5 ps, which is comparable with the residence time in the bulk liquid. The uniqueness of the primary solvation shell for these ions is therefore doubtful. The number and orientation of the water molecules in the primary solvation shell of Li+ have been investigated by Xray and neutron diffraction. 15 ,17 In solutions of LiCI, the solvation shell contains about three water molecules in a 10 m solution and about six in a 3.6 m solution. Over the same range of molality, the angle (J between the dipolar axis of a solvating water molecule and a coulomb field line passing through the center of the molecule varies from 52 ± 15° to 40 ± 10°. These angles are near to but less than the 55° angle expected if lonepair electrons in the water oxygen atom interacted with the cation. If the solvating water molecule behaved as a point dipole and aligned itself perfectly with the cationic coulomb field, the angle observed would be 0° instead of 55°. Evidently the tendency toward dipolar orientation increases as solution concentration decreases. The rotational correlation time, T2' for the solvating water molecules around u: in the limit of infinite dilution has been estimated to be about 5 ps on the basis of the NMR relaxation method.l'' This is roughly the same as T2 for bulk water. For the rotational correlation time of the entire solvation complex, T e , a value of 15 ± 3 ps has been determined by the same method. The secondary solvation shell about an ion can be studied by neutron diffraction and incoherent neutron scattering. 15 ,17 ,18 When applied to 5 m LiCI, these methods, indicate that Li+ does not have a secondary solvation shell. The same result would be expected for larger inorganic monovalent cations. The absence of a secondary solvation shell around monovalent ions is not surprising given the relatively small values of Th and T., quoted MONOVALENT IONS.
THE SURFACE CHEMISTRY OF SOILS
56
above. On the other hand, neutron scattering results for dilute solutions are not yet available, and it is possible that INS data will indicate the existence of a weak secondzone structure around widely spaced Li + cations, in agreement with the predictions of Monte Carlo computer simulations of Li+water systems.l" On the basis of NMR relaxation experiments.l" the residence time of a water molecule in the primary solvation shell of a bivalent cation has been estimated to lie in the range 10 9 s < Tb < 10 4 s. This time scale is much longer than that pertaining to selfdiffusion in the bulk liquid, and it implies that the solvation molecules move through a solution of bivalent cations right along with the cations. For these water molecules, both T2 and T c fall in the range 10 to 30 ps. Thus the primary solvation shell is a temporally welldefined structural unit in aqueous solutions containing bivalent cations. The number of water molecules in the primary solvation shell of a bivalent cation as determined by diffraction methods is always between six and eight unless either cation size or ionpair complexes intervene to produce smaller values. 15 ,17 Thus the primary shell can be either an octahedral or cubic complex. Table 2.3 shows how the solvation number and orientation of water molecules in a solvation complex can vary with electrolyte concentration. 17 The variation in (J with the molality of NiH is striking. Evidently lonepair interactions between a water molecule and this cation are favored in concentrated solutions but dipolar interactions are favored in dilute solutions. Diffraction experiments also give evidence for a secondary solvation shell around bivalent cations.Pr" This shell contains about 15 water molecules whose mobility varies with electrolyte concentration. INS data 18 indicate clearly that the selfdiffusion coefficient of the water molecules in the secondzone structure approaches the diffusion coefficient of the solvated cation as the molality of the solution decreases. Thus the secondary solvation shell moves as a solvation complex with the cation in dilute solutions. BIVALENT CATIONS.
Table 2.3. Concentration effects on the number and orientation of solvation water molecules in NiClz solutions'?
Molality , 4.41 3.05 1.46
0.85 0.46 11.1186
Solvation number 5.8 5.8 5.8 6.6 6.8 6.8
± 0.2 ± 0.2 ± 0.3 ± 0.5 ± II.S ± II.S
Orientation angle, (} 42° ± 42° ± 42° ± 27° ± 17° ±
8° 8° 8° 10° 10° on ± 20°
THE STRUCTURE OF WATER NEAR CLAY MINERAL SURFACES
57
This brief review of the structure of water in electrolyte solutions is intended to emphasize three points that will be important in understanding the behavior of water molecules near clay mineral surfaces: 1. The effect of a cation on the structure of bulk water is localized to a suite of no more than 6 to 20 solvation water molecules, even for bivalent cations in a dilute solution. This local character of the cationwater interaction, which has been observed clearly in MD computer simulations.r" indicates that the primary solvation shell screens the coulomb field of the cation very efficiently. 2. The primary solvation shell of a monovalent cation contains between three and six water molecules that exchange relatively rapidly with the surrounding bulk liquid. A secondary solvation shell, if it exists, is very weakly developed. 3. The primary solvation shell of a bivalent cation contains between six and eight water molecules that move with the cation as a unit. A secondary solvation shell containing about 15 water molecules develops as the cation concentration decreases and moves with the cation as a unit.
2.3. WATER NEAR PHYLLOSILICATE SURFACES Phyllosilicates bear siloxane surfaces on their basal planes and hydroxyl groups along with Lewis acid sites on their edge surfaces, as described in Sec. 1.2. The consensus at present is that the basal plane surfaces have the greater potential to alter the configuration of water molecules from what exists in the bulk liquid phase, and it is on siloxane surfaces that most experimental studies of claywater systems have focused. There are two distinguishing properties of siloxane surfaces that are expected to affect the molecular structure of a contiguous liquid water phase: (1) the nature of the charge distribution on the siloxane ditrigonal cavities and (2) the nature of the complexes formed between these surface functional groups and cations. If there is no isomorphic cation substitution in a phyllosilicate layer, its siloxane ditrigonal cavities expose only lonepair electrons on their oxygen atoms and their functional group reactivity has a very soft Lewis base character. Surface complexes with cations are not stable in this case. If there is isomorphic substitution in a phyllosilicate, the charge distribution on its siloxane ditrigonal cavities depends on the location of this substitution (Sec. 1.2). Isomorphic substitution in the tetrahedral sheet localizes charge on the ditrigonal cavities more than does substitution in the octahedral sheet. All of these featuresthe presence or absence of unbalanced negative charge and the degree of charge localizationshould playa role in the organization of water molecules near siloxane surfaces. The same is true of the valence and size of the cations complexed by the siloxanc ditrigonal cavities bearing unbalanced negative charge. The cationic coulomb field is determined by these two properties, as well as by
THE SURFACE CHEMISTRY OF SOilS
58
the inner or outersphere character of the surface complex. Indeed, the existence of an outersphere surface complex implies that a solvation shell has formed around the complexed cation, and this is itself a perturbation of the structure in bulk liquid water. In this section, how surface charge distribution and surface cation complexation in siloxane ditrigonal cavities affect the structure of water is illustrated. The kaolinite group minerals are used to show how an electrically neutral siloxane surface affects the molecular arrangement in bulk liquid water. The vermiculite and smectite group mirierals are then considered to clarify the effect of the isomorphic substitution pattern on the configuration of water molecules whose "unperturbed" structure is that in an aqueous electroyte solution, since these two clay mineral groups form surface complexes with cations. Besides these inferences concerning molecular structure, an estimate of the spatial extent of the influence of the siloxane surface on the properties of water is considered. The spatial domain wherein the water molecules take on a D structure that differs measurably from that in bulk water or in an aqueous electrolyte solution of the appropriate molality defines the region of adsorbed water on a siloxane surface. The solvent properties of adsorbed water are expected to be different from those of bulkphase water and therefore to affect surface functional group reactivity differently. As mentioned in Sec. 1.1, kaolinite group minerals exhibit insignificant layer charge in most cases, the upper limit being x = 0.012 (about 0.02 mole kgI). In many natural kaolinites, 2: 1 phyllosilicates are present in small amounts that nevertheless contribute importantly to the apparent layer charge of the samples (Table 1.3). This kind of contamination makes the unambiguous interpretation of surface chemistry experiments very difficult, if not impossible. Perhaps a good rule of thumb'" is to regard as suspect any sample of a kaolinite group mineral whose cation exchange capacity at pH 7 is larger than 0.02 mole kgI. The D structure of water on the basal plane surfaces of kaolinite group minerals is usually studied using halloysite, which in its dehydrated form (7A halloysite) is a disordered polymorph of kaolinite.F The hydrated form (10A halloysite) has the structural formula [Si4 ] (AI4)OlO(OH)s . 4H zO and exhibits a basal plane spacing of 1.01 nm. The four structural water molecules per unit cell can be removed either by placing the sample in an atmosphere of relative humidity below 30 per cent or by heating it at 60 to 70°C. This removal of the water molecules is quite irreversible kinetically and rehydration does not occur even after exposure to 100 per cent relative humidity for two months. The basal plane spacing of 7A halloysite is precisely 0.72 nm, which means that the interlayer separation in lOA halloysite is 0.29 nmexactly equal to the van der Waals diameter of the water molecule.'} Accordingly, loA halloysite can be envisioned as a disordered kaolinite with a monolayer of adsorbed water in the interlayer space. On the basis of Xray diffraction data. it has KAOLINITE GROUP MINERALS.
THE STRUCTURE OF WATER NEAR CLAY MINERAL SURFACES
59
been suggested that this monolayer comprises water molecules in the hexagonal network configuration shown in Fig. 2.3.12 ,23 The stability of the network derives from hydrogen bonding, both between the molecules and between them and the atoms in the basal planes that enclose the interlayer region. Because of the constraints imposed by the requirement of four water molecules per unit cell and by epitaxy with the basal plane surface atoms, the hydrogen bonds in the monolayer must be about 0.3 nm long and those between the water molecules and the mineral surfaces must deviate considerably from linearity. These structural characteristics are similar to those of bulk liquid water, even to the extent of preserving local tetrahedral ordering. That the hydrogenbond network is more like that in liquid water than that in ice with respect to structural ordering also has been concluded from IR spectroscopic studies.e" Given the structure in Fig. 2.3 as a prototype of the monolayer arrangement of adsorbed water on kaolinite group minerals, there remains only the question of its "singleparticle" properties. Proton and deuteron NMR measurements are instructive in this respect." As indicated in Table 2.1, NMR line shapes show whether a preferred orientation of water molecules exists on the NMR time scale, and NMR relaxation data can yield a value for the rotational correlation time, 72' In the case of lOA halloysite, the NMR signal from water protons or deuterons in the
Figure 2.3. The D structure of water in the interlayers of Hendricks and Jefferson 23 )
1 I I
I
I
,
 M''t)e
~ ~
\ 1\ \
I I
\
I
I
I
lOA
halloysite. (After
60
THE SURFACE CHEMISTRY OF SOilS
adsorbed m<:?nolayer (as opposed to those in "micropore" water or in clay mineral OH groups) consists of a single peak, just as is found for bulk liquid water ,1 indicating no preferred orientation relative to the basal planes on th~ NMR time scale. This result means that the water molecules rotate quick'y enough to sample all possible orientations in the hexagonal network dur~ing the time frame in which NMR probes their structure. An analysis of:rVMR relaxation data for water protons and deuterons on 10A halloysite24teads to the conclusion that TZ = 0.144 exp(2315/T) , where TZ is in picosecc;:mds and T is absolute temperature. At 298 K, TZ = 340 ps, or about two o:::rders of magnitude larger than TZ in liquid water at the same temperature (Table 2.2). The same kind of discrepancy is found for the correlation J:ime, Tl' if the NMR relaxation data are interpreted with a model descr_bing a water molecule rotating rapidly around its dipolar axis while that a~is itself tumbles about an axis parallel to the basal planes. Z4 At 298 K, 1"':1 = 0.2 /LS, according to this estimate, a value four orders of magnitude larger than Tl in bulk water at the same temperature. A confirmatiors of the NMR value for Tl has been established from direct measuremersts of this correlation time for water on kaolinite by dielectric relaxation sI?ectroscopy. Z5 At monolayer coverage and 298 K, Tl = 4 ILs. The static di electric constant of the water is about 2.0, far below the value for liquid w.,.ter but near that of ice Ih(ordinary hexagonal ice). Similarly, Tl = 2 ILS for ice Ih at 250 K, and a value near 3 ILS is found by extrapolating the temperature dependence of Tl for ice Ih to 298 K. However, tlJ.e decaytime spread parameter, a (Table 2.1), is less than 0.03 for either liquid water or ice Ih, whereas for water on kaolinite, 0.5 < a < (1.6, indicating a broad spread of decay times and therefore a broad range' of local molecular environments.F The struvtural concept that emerges for the water monolayer on kaolinite is that of a strained, hydrogenbonded network whose D structure reflects a compromise between the topological disorder of liquid water and the rigid configuration demanded by strict epitaxy with the atoms in the basal pl~nes of the clay mineral. The monolayer is liquidlike in not exhibiting a preferred orientation of its constituent molecules on the NMR time scale and in comprising relatively weak, distorted hydrogen bonds. However, tlJe clay mineral surface is able to slow down the singleparticle motions in the monolayer considerably, as evidenced by the fact that the rotational correlation times, Tl and TZ, have values appropriate to solid water. These structural characteristics are underscored by the temperature dependence of the apparent specific heat capacity of the monolayer water. 24 ,Z6 1his quantity is defined by the equation (2.1) where Cp is the heat capacity at constant pressure of a mixture containing m.; kilograms of water and mk kilograms of kaolinite, c'k is the specific heat capacity of fully dehydrated kaolinite, and ~c is the apparent specific heat capacity of t"'c water. As mentioned in Sec. 2.1, this method of partitioning
THE STRUCTURE OF WATER NEAR CLAY MINERAL SURFACES
61
a thermodynamic property of a mixture into terms pertammg to the components has only a formal significance and caution must be exercised when structural interpretations are made of functions like 4>c in {he absence of supporting nonthermodynamic data. In the case of the wateron lOA halloysite, the fact that 4>c closely follows the temperature dependence of the specific heat capacity of ice Ih for T s 150 K, rises quickly to a sharp maximum at 260 K, and then falls to equal the specific heat capacity of liquid water at 273 K is consistent with a water monolayer containing molecules whose rotational and translational motions are hindered by interactions with the clay mineral surface but whose structural disorder resembles that in liquid water even though it is actually induced partly by the demands of epitaxy. The effect of the kaolinite surface on the structure of water beyond monolayer coverage has not been ascertained conclusively. Multilayers of water are known to form on the clay mineral at relative humidities greater than 20 per cent, and about 10 molecular layers are thought to exist at relative humidities near 98 per cent. 27 Thus an absolute upper limit for the dimension of the region of adsorbed water in a kaolinite suspension should be around 3 nm. Data on the thermodynamic properties (heat of immersion, partial specific entropy, isosteric heat of adsorption) of Lisaturated kaolinitewater systems, which do not show hysteresis, indicate consistently that differences between bulk liquid water and water on the clay are detectable up to about three molecular layers of coverage.r" Perhaps the lower limit for the dimension of the adsorbed water region is then about 1 nm. The D structure of water molecules on the siloxane surfaces of vermiculite group minerals has been investigated only for trioctahedral vermiculites with the general structural formula'? VERMICULITE GROUP MINERALS.
M x[SiaA I8  a](MgbFe(III)c Fe (II)c'TidAI6bcc' d) 020( OH)4
where M represents one mole of cation charge on the basal planes and x = 2
+ b + c'  a  d
(2.2)
is the layer charge, defined conceptually in Sec. 1.1 and given numerically in Table 1.3. The trioctahedral vermiculites offer the distinct advantage of being available in macrocrystalline forms of high purity that permit exhaustive study by Xray diffraction. The interlayer water structures determined for these clay minerals are presumed to be models for those that exist on the surfaces of the more disordered dioctahedral vermiculites found commonly in soils. The configuration of water molecules between the basal planes in vermiculite depends sensitively on the nature of the 'cation complexed on these surfaces to balance the negative charge produced by isomorphic substitution of Al,l for Si4 + in the tetrahedral sheet. Because of this substitution. the siloxanc ditrigonal cavities exhibit a relatively localized j
62
THE SURFACE CHEMISTRY OF SOILS
charge distribution that can interact strongly with both cations and water molecules, as mentioned in Sec. 1.2. The overall effect of the charge localization should be a proximity of the complexed cations to tetrahedral sites containing At3+ and the formation of relatively strong hydrogen bonds between interlayer water molecules and surface oxygen atoms. Aside from these effects of the vermiculite surface, however, it is expected that the organization of water molecules in the interlayer region conforms to the behavior observed in relatively concentrated aqueous solutions, described in Sec. 2.2. In particular, water molecules in a fully hydrated vermiculite should be coordinated in a single solvation shell about monovalent cations and in two shells about bivalent cations unless stereochemical factors intervene to make innersphere surface complexes with the cations more stable than outersphere complexes. Moreover, the solvation water molecules near monovalent cations should be relatively mobile and those in the first solvation shells about bivalent cations should move with the cation as a unit. Reasoning on the basis of the known behavior of water molecules in aqueous electrolyte solutions, one predicts that hydrated vermiculites comprise interlayer ionic solutions, with the cations and solvating water molecules influenced by the coulomb fields emanating from tetrahedral sites containing AI3+. In atmospheres of relative humidity greater than 20 per cent, Mgvermiculite forms a hydrate with a basal plane spacing of 1.436 nm, which is adequate for the accommodation of two monolayers of water molecules in the interlayer region.i" The arrangement of the Mg cations and the water molecules has been studied intensively by Xray diffraction, and the details of the cation and watermolecule oxygen atom positions have been established.l" An illustration of the structure of the interlayer region is given in Fig. 2.4. The magnesium cations are positioned midway between opposing basal planes over sites in the tetrahedral sheet that contain A13+ . This arrangement permits a localized charge balance between the clay
Figure 2.4. The Dstructure of water in the interlayers of the twolayer hydrate of Mgvermiculite. (After Alcover and Gatineau30 )
THE STRUCTURE OF WATER NEAR CLAY MINERAL SURFACES
63
mineral surface and the Mg cations. Each Mg2 + is surrounded by f.wo solvation shells of six water molecules each to give a total solvation number of 12. The molecules in the primary shell are located 0.206 nm from the Mg cation and coordinate to the latter through lonepair electrons. The molecules in the secondary shell are about 0.49 nm away from the cation. All of the solvating water molecules can form hydrogen bonds, both between shells and with the basal plane oxygen atoms. These bonds are about 0.29 nm in length. This configuration of the water molecules is strikingly like that observed around bivalent cations in concentrated aqueous solutions. In particular, NiH (r = 0.069 nm), which has about the same ionic potential as MgH (r = 0.072 nm), also coordinates six water molecules through lonepair electrons (Table 2.3) in a primary solvation shell at 0.207 nm. 31 It appears from this comparison that the twolayer hydrate on Mgvermiculite is indeed similar to what is found in a concentrated aqueous solution. Magnesiumvermiculite also forms monolayer hydrates with basal plane spacings of 1.163 and 1.153 nm. 29 ,30 These hydrates are distinguished by the configuration of the Mg2 + solvation complexes (outersphere surface complexes) in them. The hydrate with the larger basal plane spacing contains MgH in the centers of flattened tetrahedra formed by water molecules; the other hydrate contains MgH at the apex of a pyramid whose base comprises three water molecules. Other bivalent cations tend to form solvation shells on the vermiculite surface in a manner similar to MgH, but structural differences can arise because of differing Lewis acid character (based on ionic potential and polarizability) and stereochemistry. 30 For example, the single monolayer hydrate of Bavermiculite contains BaH partially inside the siloxane ditrigonal cavity, with six water molecules placed in the midplane of the interlayer region in onetoone correspondence with the oxygen atoms of the ditrigonal cavity (i.e., an innersphere surface complex). This arrangement evidently reflects the close fit of BaH (r = 0.136 nm) in the ditrigonal cavity (r = 0.13 nm) and the softer Lewis acid character of the cation, which gives it less affinity for the very hard Lewis base H 20. As another example, the twolayer hydrate of Cavermiculite can contain both octahedral and cubic coordination of the water molecules solvating the Ca 2 + . This possibility, which also exists in aqueous solutions;" evidently is the result of a combination of a relatively high ionic potential and a large radius ratio with 0 (  II). Considerably less information is available concerning the D structure of water molecules hydrating vermiculites that form surface complexes with monovalent cations. It appears that both Li and Navermiculite can form mono and bilayer hydrates, whereas K, Rb, and Csvermiculite cannot. For the latter, innersphere surface complexes are stable against solvation of the cations because of Lewis acid character and stereochemistry. These factors are especially notable when comparing K + with Ba2+, which have almost identical ionic radii. Bariumvermiculite contains a monolayer of
THE SURFACE CHEMISTRY OF SOILS
water molecules even when its Ba2+ ions are in innersphere complexes, evidently because of its higher ionic potential. The twolayer hydrate of Navermiculite contains Na+ with octahedral primary solvation shells.F' Because the cation is monovalent, all possible surface complex sites are filled and no more than six water molecules can solvate a cation uniquely. (By comparison with data on the solvation of Na+ in aqueous solutions, one would conjecture that only a primary solvation shell exists even if all surface complexation sites are not filled.) Thus the interlayer region of the twolayer hydrate consists of a network of solvation octahedra with hydrogen bonding both within the octahedra and with surface oxygen atoms of the clay mineral. 33 These hydrogen bonds are somewhat longer than those in the twolayer hydrate of Mgvermiculite and therefore are expected to be weaker. At relative humidities below 40 per cent, Navermiculite forms a monolayer hydrate wherein Na" coordinates to surface oxygen atoms in one basal plane and rests on three water molecules bonded to the opposing basal plane in a fashion similar to what occurs in the 1. 153nm monolayer hydrate of Mgvermiculite. Model calculations of the arrangement of water molecules in a hypothetical monolayer hydrate of Kvermiculite suggest that the interlayer water structure is like that in the monolayer hydrate of Bavermiculite, described above.i" Thus, to some extent, parallels can be drawn between the structures of the solvating water molecules in monovalent and bivalent cationsaturated vermiculites. The dynamic properties of the interlayer water structures in Ca, Na, and Livermiculite have been investigated by INS. 35 The data for the twolayer hydrate of Cavermiculite were modeled quantitatively under the assumptions (a) that a fraction of the adsorbed water protons are in the octahedral primary solvation shells of the Ca2+ cations and are immobile on the neutron scattering time scale and (b) that some of the remaining adsorbed water protons diffuse by jumps within a region bounded by the opposing siloxane surface and the solvated Ca2+ while others undergo isotropic, translational jump diffusion between adjacent bounded regions. The two jumpdiffusion residence times were found to be about 15 ps and 150 ps. Assumption (a) is in agreement with the residence time of 10 9 to 10 4 s observed for primary solvation shell water molecules in aqueous solutions containing bivalent cations. Moreover, since the diffusion coefficients of bivalent cations on vermiculite." are around 10 12 m2s1, they can move a distance equal to their own diameters (= 0.2 nm) in about 10 8 s, which is also much longer than the neutron scattering time scale (Fig. 2.1). Therefore, water protons in the primary solvation shell should be immobile targets for neutrons. Assumption (b) is consistent geometrically with the D structure in Fig. 2.4. The effective selfdiffusion coefficient for the water protons in the region between solvation shells was determined to be about 10 9 m2s 1 , about one half the value found in bulk liquid water (Table 2.2).
THE STRUCTURE OF WATER NEAR CLAY MINERAL SURFACES
65
Neutron scattering data for Li and Navermiculite, on the other hand, gave no indication of water protons being immobile on the neutron scattering time scale. 35 This result is consistent with the behavior of water molecules in aqueous solution, since the residence time in the primary solvation shell of a monovalent cation is about 10 11 s, well within the time scale probed by neutrons. However, as shown in Table 2.4, the selfdiffusion coefficients of water molecules on Li and Navermiculite were found to be much smaller than the bulk liquid value at 298 K. These data suggest that, even in the twolayer hydrate, the solvating water molecules exhibit only about 5 per cent of the mobility they have in the bulk liquid phase and about 10 per cent of that in the primary solvation shell of a monovalent cation in aqueous solution (D s = 1.3 x 10 9 mZs 1) 16 . This reduction in water molecule mobility is evidently produced by interactions with the charge distribution on the siloxane surface. Magnetic resonance (ESR and NMR) studies''? have provided additional details about the orientational motion of the water molecules adsorbed by vermiculites. ESR spectra of Cuvermiculite and NMR spectra of Mg and Navermiculite indicate clearly that the primary solvation shells of the cations on the twolayer hydrate are octahedral complexes with a preferred orientation relative to the siloxane surface. For Cuvermiculite, the symmetry axis through the solvation complex, Cu(HzO)~+, makes an angle of about 45° with the siloxane surface; on Navermiculite the axis through Na(HzO)t makes an angle of 65°. The value of T e , the correlation time for the rotation of Na(HzO)t around its symmetry axis, is about 10 7 s at 298 K. This value is four orders of magnitude larger than T e for a solvation complex around a monovalent cation in aqueous solution. 16 Not quite as disparate are TZ for Na(HzO)t, equal to 100 ps at 298 K, and TZ for a monovalent solvation complex in dilute aqueous solution, equal to about 5 ps at the same temperature. These data show that the siloxane surface retards the orientational motion of the water molecules. The spatial extent of the adsorbed water layer on vermiculite group minerals has been estimated on the basis of thermodynamic properties and selfdiffusion coefficients for water on Li and Navermiculite.P" The Table 2.4. Selfdiffusion coefficients for water on vermiculite determined by INS 35
Exchangeable cation Li Li Li Na Na Na
Water content, kg H 20/kg clay
d(OOl), nm
0.079 0.114 0.135 0.080 0.111 0:185
1.275 1.33 1.405 1.371 1.392 1.448
«0.1 0.5 1.1
0.6 0.6 1.7
66
THE SURFACE CHEMISTRY OF SOILS
selfdiffusion coefficients have values essentially equal to the bulk water value for basal plane spacings larger than 5 nm, which therefore can be taken as an upper limit for the dimension of the adsorbed water region. The structure of water adsorbed by smectite group minerals has been studied extensively in both its static (D structure) and dynamic aspects.i'? As with water molecules on vermiculite, the behavior of water on smectite surfaces is conditioned sensitively on the type of exchangeable cation and on the location of isomorphic cation substitutions in the layer structure. In many respects, a discussion of the configuration of water molecules hydrating smectites is parallel to that for vermiculite. Almost all of the experimental data pertaining to the structure of the onelayer hydrate of monovalentcationsaturated smectites can be interpreted in terms of the molecular arrangement in montmorillonite illustrated in Fig. 2.5. 40 This is a strained, icelike configuration of water molecules around the exchangeable M+ cations, with bonds formed both intermolecularly and with the ditrigonal cavities in the smectite surface. The nearestneighbor distance between water molecules is 0.32 nm, and five molecules are assigned to each exchangeable cation in the completed monolayer. Since some of the water molecules have a hydroxyl group proton inside a ditrigonal cavity on the siloxane surface, the network of hydrogen bonds in the water molecules is broken in places. These defects permit a variety of reorientational motions that are not possible in ice Ih. The principal lines of experimental evidence that support the water structure portrayed in Fig. 2.5 are as follows. SMECTITE GROUP MINERALS.
1. Studies of Xray diffraction by the water oxygens and of neutron diffraction by the water protons have shown that the molecules in the onelayer hydrate are positioned along the crystallographic c axis 0.55 nm from the aluminum ions in the octahedral sheet of montmorillonite;" in agreement with the structure in Fig. 2.5. Moreover, the lateral position of the water molecules is correlated strongly with the oxygen atom arrangement on the siloxane surface, with some molecules entrained over the ditrigonal cavities. However, the scattering density profile for the hydrate does not exhibit features consistent with a highly ordered D structure. Measurements of the apparent specific heat capacity (Eq. 2.1) support this conclusion, in that they show cPc following the temperature dependence of the specific heat capacity of ice Ih for 100 K < T < 150 K, then rising toward the value for the specific heat capacity of liquid water at 273 K. 42 This behavior suggests that the motion of the water molecules in the onelayer hydrate is not highly restricted near 298 K. 2. Infrared spectroscopic studies'" give evidence for a threemolecule solvation shell around the monovalent cations when the water content is low. The water molecules are coordinated to the cations through
THE STRUCTURE OF WATER NEAR CLAY MINERAL SURFACES
67
(a)
Figure 2.5. The D structure of water in the interlayers of the onelayer hydrate of M+montmorillonite (M = Li, Na, K, etc.). Basal plane oxygens are shown as shaded circles. (a) View along an axis perpendicular to the crystallographic c axis. (b) View along the c axis, with water molecules nearest the upper basal plane (not shown) indicated by dashed lines. (After M amy 4fJ)
lonepair orbitals, and one of the water protons is directed along the crystallographic c axis into a siloxane ditrigonal cavity. If a significant localization of surface charge exists because of isomorphic cation substitution in the tetrahedral sheet, however, hydrogen bonds are formed between the solvating water molecules and surface oxygen atoms, as in the vermiculite group minerals. 3. INS 44 and dielectric relaxatiorr'" studies both indicate that the water molecules solvating the monovalent exchangeable cations on montmorillonite are roughly as mobile, in respect to translational and reorientational motion, as water molecules in the bulk liquid. For example, the INS data show that no water molecule is stationary On the neutron scattering time scale. The data can be described mathematically by a model that includes both jump translational and rotational diffusion. In the onelayer hydrate of Limontmorillonite, D, = 4 X 10 10 m 2sI, with a jump distance of about 0.35 nm, and 'Tl = 15 ps at 293 K. The values of D; and 'Tl suggest a sluggish motion of the water molecules, consistent with what is observed for solvating water molecules around monovalent cations in aqueous solutions. The values of 7"1 for Na and Kmontmorillonites hydrated by a monolayer of watcr are around 5 ps, according to dielectric relaxation
68
THE SURFACE CHEMISTRY OF SOilS
measurements.i" with a broad spread of relaxation times about the mean value (a = 0.7; Table 2.1.). The spectrum of relaxation times is consistent with a defective network of hydrogen bonds like that shown in Fig. 2.5. Proton and electron spin magnetic reasonance studies37 •39 tend to support these data by indicating 72 values around 100 ps and 3 7 c values near 10 ps. The structural characteristics of water on bivalentcationsaturated smectites have not been worked out in enough detail to permit the development of a schematic drawing like that shown in Fig. 2.5. INS data for the twolayer hydrates of Ca and Mgmontmorillonite'v'" can be interpreted with the model used for Cavermiculite: an assembly of octahedral solvation shells with slowly diffusing water molecules (D; = 3.4 x 10 10 m 2s 1) interspersed between them. The residence time and jump distance for the diffusion of water molecules between the intersolvation shell regions are 100 ps and 0.5 nm, respectively. The jump distance agrees well with the value of the mean distance between solvation shells calculated on the basis of specific surface area and surface charge density of the clay mineral.l Dielectric relaxation spectroscopy investigations'f indicate that 71 = 1 /LS, which is about the same as in ice Ih but five orders of magnitude larger than in bulk liquid water. All of these values suggest that the interlayer region is organized more or less as depicted in Fig. 2.4, i.e., like a twodimensional aqueous solution with hydrogen affected by the charge distribution on the siloxane surface. The spatial extent of adsorbed water on smectite surfaces is a matter of some controversy. Infrared spectroscopy, NMR relaxation, and Xray and neutron diffraction experiments all point to a thickness of the adsorbed water film of around 1.0 nm.39 However, certain thermodynamic data, summarized for Namontmorillonite in Table 2.5, suggest a thickness as great as 10 nm or more.t" These data are for partial and apparent specific properties of montmorillonitewater systems whose variation with water
Table 2.5. Dependence of some thermodynamic properties of Namontmorillonitewater mixtures on water content" Property a Partial specific volume (iJcPV/dT)P.8 ( iJcPV/dPh.8 Apparent specific heat capacity == cPc (iJcPc/iJPh.8 (iJcPs/iJPh,8
(acPs / a(Jv h.8
Comparison with value in bulk liquid water
Behavior of value with increasing water content
Larger Larger than (iJvw/ iJ T)p Smaller than (iJvw/iJPh
Decreases Decreases Increases
Larger Larger than (iJew/ iJPh Smaller than (iJsw/dPh Larger than (iJsw/iJvwh
Decreases Decreases Increases Decreases
• "'v  apparen: Npeclflc volume: "'~  uppurenl Npeciflc entropy,
THE STRUCTURE OF WATER NEAR CLAY MINERAL SURFACES
69
content has been interpreted structurally in terms of the water component alone. The dangers inherent in this practice were alluded to in Sec. 2.1, and this point alone may be enough to settle the issue of disagreement between direct structural methods and thermodynamic approaches. Indeed, one alternative for removing the disagreement is to assume that partial and apparent specific quantities reflect changes in the smectite (particularly the exchangeable cations) as well as in the water and that the former changes become dominant as water content increases. This point of view cannot be rejected in the present absence of conclusive experimental evidence against it. On the other hand, if partial and apparent specific properties represent only the adsorbed water, what can be said to bring the results of thermodynamic measurements into agreement with other data? For spectroscopic data, a difference in time scales can be indicated. Thermodynamic data refer to effectively "infinite" scales of time and space, characteristic of the D structure, whereas spectroscopic measurements probe either the V structure or some predecessor of the D structure. The degree of ordering is less for these latter structures because the time scale on which they exist is shorter, and thermodynamic properties may truly reflect a multiplicity of cooperative interactions that can be perceived only after a longtime measurement. This still leaves a question concerning neutron and Xray diffraction data, which refer to the same time scale as the thermodynamic properties but appear to be in conflict with them. It is known that the D structure in bulk liquid water, as deduced from diffraction patterns measured at 273 K, differs only a little from that in ice Ih, whereas the thermodynamic properties of liquid water at 273 K differ greatly from those of ice Ih. If this comparison applies to adsorbed water as well, then perhaps partial specific properties are more sensitive to structural changes than are diffraction patterns. It is also well known! that the mere presence of a spacefilling macromolecule in liquid water causes the structure to be strained while strengthening some of the hydrogen bonds. In effect, some of the topological freedom in the liquid disappears and the fluctuations between bulky and compact networks of water molecules shift to favor the bulky configurations. This picture could be an accurate description, on the level of molecular structure, of how the trends listed in Table 2.5 come about. 2.4. THE SOLVENT PROPERTIES OF ADSORBED WATER
The definition of adsorbed water adopted in Sec. 2.3 requires an arrangement of water molecules that differs significantly from that in an appropriate reference aqueous phase. For water on the surfaces of kaolinite group minerals the reference phase is bulk liquid water, whereas for water on vermiculite and smectite surfaces the reference phase is an aqueous solution because of the presence of exchangeable cations on the 2: 1 layer silicates. On the basis of this definition, the consensus developed in Sec. 2.3 is that the spatial extent of adsorbed water on a phyllosilicate
70
THE SURFACE CHEMISTRY OF SOILS
surface is, conservatively, whatever is included in the region bounded by a plane about 1.0 nm from the basal plane of the clay mineral. This sharp geometric demarcation is, of course, an oversimplification because the influence of the phyllosilicate surface on the configuration of water molecules must decrease in a continuous fashion with distance, but a bounding plane at 1.0 nm is expected to include all but a few per cent of the siloxane surface effects on water structure per se. With the exception of Livermiculite and certain lowlayercharge vermiculites which also swell in water, a 1.0nm thickness for the zone of surface influence and available Xray diffraction data"? imply that the interlayer water in vermiculite group minerals is always adsorbed water. The same is true for smectite group minerals saturated with bivalent exchangeable cations. However, if a smectite carries monovalent exchangeable cations, particularly Li+ and Na +, it will swell in water and the interlayer region will fall within the defined zone of adsorbed water only when free swelling is inhibited by ionic strength or relative humidity control.F In the case of kaolinite group minerals, any interlayer water is also adsorbed water because only a single monolayer is involved. The water on the external surfaces of kaolinite exists within the adsorbed zone for relative humidities below about 80 per cent."? The general conclusion that can be drawn on the basis of the 1.0nm criterion is that, unless free swelling occurs, the interlayer water on phyllosilicates is structurally different from bulk liquid water or water in aqueous solutions, regardless of the overall amount of water in a phyllosilicatewater mixture. Chemical reactions that take place in the interlayer region accordingly can be expected to show some influence from a perturbed water structure. One of the properties of liquid water that relate to its solvent characteristics is the dielectric constant, D, equal to the ratio of the static permittivity to the permittivity of vacuum. At temperatures near 300 K, D = 80 for bulk liquid water. 9 Measurements of the dielectric constant for adsorbed water on phyllosilicates, despite its importance in surface chemical phenomena, are neither abundant nor conclusive because of difficulties involved with separating out ionic surface conductance effects. The data available suggest that D = 20, with values reported from 2 to 50. 25 ,40 ,45 These depressed values of D imply that adsorbed water molecules on phyllosilicates are intrinsically less free to reorient along an applied static electric field than are the molecules in bulk liquid water. This restriction evidently comes about because of preferential orientation in water molecules that are imposed by the strong coulomb field of exchangeable cations and the exigencies of hydrogen bonding. The most significant chemical effect of this loss of orientational polarization and consequent lowered dielectric constant in adsorbed water should be the enhancement of complex formation, both between dissolved species and between exchangeable cations and siloxane ditrigonal cavities. It is well known that, with a reduction in aqueous dielectric permittivity. ion association is favored and the development of a diffuse electrical double layer ncar a colloidal particle is retarded. 414
THE STRUCTURE OF WATER NEAR CLAY MINERAL SURFACES
71
Another important chemical property of adsorbed water on vermiculite and smectite surfaces is its Brensted acidity. This property should refer principally to the acidity of the solvated exchangeable cations, as described by the reaction M(HZo)m+ = MOH(HZo)(m1)+ + H+ n n1
(2.3)
The equilibrium constant of this reaction has been measured for a variety of metal cations in aqueous solutions and is known to correlate positively with both ionic potential and Lewis acid softness.t? As the ionic potential increases, the intensity of the positive coulomb field of the cation increases and repulsion of a solvating water proton becomes more likely. As the Lewis acid softness'" increases, the covalency of the MO bond in a solvation complex increases and electron density is withdrawn from the OH bond, thereby promoting the loss of the proton. The reaction in Eq. 2.3 has been investigated extensively on siloxane surfaces by coupling it with a Brensted base protonation reaction, e.g., M(HZo)m+ + NH3 n
=
MOH(HZo)(m1)+ + NH+4 n1
(2.4)
Table 2.6 shows experimental data pertaining to this reaction on montmorillonite. 51 The last column of the table shows values of the conditional equilibrium constant,
CK = {MOH(HzO)~~11)+}{NHt} = (M(H zO):+)(NH3 )
{NHt}z (HzO)(NH3 )
(2.5)
where the braces refer to concentration in moles per kilogram of clay
Table 2.6. Data relating to the protonation of ammonia on Wyoming montmorillonite'l' Ionic potential," nm""
Misono softness, 50 nm
Li+
13.5
0.053
Na+
9.8
0.111
K+
7.3
0.189
Ca2+
20.0
0.165
Mg2 +
27.8
0.096
Exchangeable cation
{NHt}, mol, kg"
mof
0.20 0.98 0.20 0.98 0.20 0.98 0.20 0.98 0.20 0.98
0.23 0.17 0.16 0.10 0.10 0.11 0.80 0.16 1.01 0.74
1.32b 0.15 0.64 0.05 0.25 0.06 16.0 0.13 25.5 2.79
• Calcuhued u.11I1l dulU from 1'1I"le I. I. hAil vlllue. culeulntcd f"r I kll ",' cllly under the 1I••umpuon Ihlll (NII.l NII.lIII
cK,
Water activity
~ 0.2 III 110,7%
.,,11111011 of
72
THE SURFACE CHEMISTRY OF SOilS
and the parentheses indicate thermodynamic activity. In Eq. 2.5, the stoichiometry of Eq. 2.4 has been noted, and in calculating "K it has been assumed that the activities of adsorbed water and ammonia are equal to their relative vapor pressures. The values of {NHt} and "K at constant water activity in Table 2.6 illustrate two general rulesr'" (1) for cations ofthe same Lewis acid softness (e.g., Na+ and Mg2+), protonation increases with ionic potential, and (2) for cations of the same ionic potential, protonation decreases with Lewis acid softness. The other important feature of the {NHt} and CK values is their increase, for any exchangeable cation, with decreasing water activity. The magnitude of this increase appears to depend on both ionic potential and Lewis acid softness, becoming larger as both parameters increase. The implication of this trend is that a solvated exchangeable cation becomes more acidic as the amount of adsorbed water decreases. Evidently, as the number of water molecules on the siloxane surface is reduced to the point where only primary solvation shells can form, the burden of screening the charge of the exchangeable cations becomes so great that proton dissociation from the solvating water molecules increases significantly. Experimental support for this hypothesis has come from both NMR and IR spectroscopic studies and from conductivity measurernents.P'Y At low water contents on smectite and vermiculite group minerals, the mean lifetime of a hydrated proton, THP+, is about 10 10 sat 300 K and the mean interval between associations of a water molecule with a proton, TH,o, is 10 4 to 10 5 s. The degree of dissociation of the adsorbed water is, by definition.i" equal to the ratio TH)0+/TH 20 = 10 5 to 10 6 , In bulk liquid water, 53 TH ) 0+ = 10 12 sand TH 20 = 5 X 10 4 s, which leads to 2 x 10 8 for the degree of dissociation. Thus it appears that the degree of dissociation in adsorbed water is about two orders of magnitude larger than in bulk liquid water. Model calculations of the distribution of positive charge on water molecules solvating an exchangeable cation on a smectite surface give results comparable with those from quantum mechanical calculations of the positive charge distribution on isolated solvated cations." On the basis of this comparison, one would conclude that the increased acidity in adsorbed water has little to do with the charge distribution on the siloxane surface (e.g., smectite versus vermiculite) but instead is a local effect of the presence of exchangeable cations whose charge is screened by solvating water molecules.
NOTES 1. D. Eisenberg and W. Kauzmann, The Structure and Properties of Water,
Chap. 4. Oxford Univ. Press, New York, 1969. S. A. Rice, Conjectures on the structures of amorphous solid and liquid water, Topics Curro Chem. 60: 109 (1975). F. H. Stillinger, Water revisited, Science 209:451 (1980). 2. These aspects of the V structure of liquid water are discussed in detail in F. Hirata and P. J. Rossky, A realization of the "V structure" in liquid water, J. Chem. Phys, 74:6H67 (IlJHI).
THE STRUCTURE OF WATER NEAR CLAY MINERAL SURFACES
73
3. For a discussion of IR and Raman spectroscopy as applied to liquid water, see W.A.P. Luck, Structure of Water and Aqueous Solutions, Chaps. III and IV. Verlag Chemie GmBH, Weinheim, Germany, 1974. 4. A good introductory discussion of ESR methods is given in P. L. Hall, The application of electron spin resonance spectroscopy to studies of clay minerals, Clay Minerals IS: 321 (1980). 5. S. W. Lovesey and T. Springer, Dynamics of Solids and Liquids by Neutron Scattering. SpringerVerlag, New York, 1977. 6. D. K. Ross and P. L. Hall, Neutron scattering methods of investigating clay systems, in Advanced Chemical Methods for Soil and Clay Minerals Research (J. W. Stucki and W. L. Banwart, eds.). Reidel, Boston, 1980. 7. A careful discussion of the operational meaning of a selfdiffusion coefficient is given in R. Mills, Selfdiffusion in normal and heavy water in the range 1 to 45°, J. Phys. Chem. 77: 685 (1973). 8. J. J. Fripiat, The application of NMR to the study of clay minerals, in J. W. Stucki and W. L. Banwart, op. cit.6 9. G. Sposito, Singleparticle motions in liquid water. II: The hydrodynamic model, J. Chem. Phys. 74: 6943 (1981). 10. For reviews of diffraction methods applied to liquid water, see Chaps. 8 and 9 in Vol. 1 of Water: A Comprehensive Treatise (F. Franks, ed.) Plenum Press, New York, 1972. 11. D. W. Wood, Computer simulation of water and aqueous solutions, in Water: A Comprehensive Treatise, Vol. 6 (F. Franks, ed.). Plenum Press, New York, 1979. 12. A. Rahman and F. H. Stillinger, Molecular dynamics study of liquid water, J. Chem. Phys. 55: 3336 (1971). F. H. Stillinger and A. Rahman, Improved simulation of liquid water by molecular dynamics, J. Chem. Phys. 60: 1545 (1974). 13. W. L. Jorgensen, Monte Carlo results for hydrogen bond distributions in liquid water, Chem. Phys. Lett. 70: 326 (1980). 14. See, e.g., Chaps. 8 and 9 in Vol. 1 of F. Franks, op. cit., 10 and Chap. V of W.A.P. Luck, op. cit.3 15. H. S. Frank and W.Y. Wen, Structural aspects of ionsolvent interactions in aqueous solutions: A suggested picture of water structure, Disc. Faraday Soc. 24: 133 (1957). The earliest studies of ion hydration in relation to the FrankWen model have been summarized in B. E. Conway, Ionic Hydration in Chemistry and Biophysics, Elsevier, Amsterdam, 1981. More recent work is reviewed in J. E. Enderby and G. W. Neilson, The structure of electrolyte solutions, Rep. Prog. Phys. 44: 593 (1981). 16. For a discussion of these experiments and their results, see Chaps. 7 and 8 in Vol. 3 of Water: A Comprehensive Treatise (F. Franks, ed.). Plenum Press, New York, 1973. A brief summary is given by J. E. Enderby and G. W. Neilson, op. cit.,15 pp. 647649. 17. J. E. Enderby and G. W. Neilson, Xray and neutron scattering by aqueous solutions of electrolytes, in Water: A Comprehensive Treatise, Vol. 6 (F. Franks, ed.). Plenum Press, New York, 1979. See also A. H. Narten and R. L. Hahn, Direct determination of ionic solvation from neutron diffraction, Science 217: 1249 (1982). IH. N. A. Hewish, J. E. Enderby, and W. S. Howells. Second zone in ionic solutions. Phys. Rev. Lett. 48: 75fl (19H2).
74
THE SURFACE CHEMISTRY OF SOilS
19. See, e.g., M. Mezei and D. L. Beveridge, Monte Carlo studies ofthe structure of dilute aqueous solutions of Li+ , Na +, K +, F, and Cl" ,J. Chern. Phys. 74: 6902 (1981). 20. M. Rao and B. J. Berne, Molecular dynamic simulation of the structure of water in the vicinity of a solvated ion, J. Phys. Chern. 85: 1498 (1981). J. Chandrasekhar and W. L. Jorgensen, The nature of dilute solutions of sodium ion in water, methanol, and tetrahydrofuran, J. Chern. Phys. 77: 5080 (1982). 21. C. H. Lim, M. L. Jackson, R. D. Koons, and P. A. Helmke, Kaolins: Sources of differences in cationexchange capacities and cesium retention, Clays and Clay Minerals 28: 223 (1980). 22. The structural characteristics of halloysite are discussed in detail in the first three chapters of G. W. Brindley and G. Brown, Crystal Structures of Clay Minerals and Their Xray Identification. Mineralogical Society, London, 1980. 23. S. B. Hendricks, On the crystal structure of the clay minerals: Dickite, halloysite, and hydrated halloysite, Am. Miner. 23:295 (1938). S. B. Hendricks and M. E. Jefferson, Structure of kaolin and talcpyrophyllite hydrates and their bearing on water sorption of the clays, Am. Miner. 23: 863 (1938). 24. S. Yariv and S. Shoval, The nature of the interaction between water molecules and kaolinlike layers in hydrated halloysite, Clays and Clay Minerals 23: 473 (1975). M. I. Cruz, M. Letellier, and J. J. Fripiat, NMR study of adsorbed water. II: Molecular motions in the monolayer hydrate of halloysite, J. Chern. Phys. 69: 2018 (1978). 25. P. G. Hall and M. A. Rose, Dielectric properties of water adsorbed by kaolinite clays, J. C.S. Faraday 174: 1221 (1978). 26. Heat capacity data for halloysite have been reported by M. I. Cruz et aI., op. cit. 24 and by P. M. Costanzo, R. F. Giese Jr., M. Lipsicas, and C. Straley, Nature 296: 549 (1982). 27. J. J. Jurinak, Multilayer adsorption of water by kaolinite, Soil Sci. Soc. Am. J. 27: 270 (1963). 28. J. J. Jurinak and D. H. Volman, Cation hydration effects on the thermodynamics of water adsorption by kaolinite, J. Phys. Chern. 65: 1853 (1961). R. A. Kohl, J. W. Cary, and S. A. Taylor, On the interaction of water with a Likaolinite surface, J. Colloid Sci. 19:699 (1964). See also J. Fripiat, J. Cases, M. Francois, and M. Letellier, Thermodynamic and microdynamic behavior of water in clay suspensions and gels, J. Colloid Interface Sci. 89: 378 (1982). 29. The molecular structure of vermiculite group minerals is discussed comprehensively by G. F. Walker, Vermiculites, in Soil Components, Vol. 2 (J. E. Gieseking, ed.). SpringerVerlag, New York, 1953. 30. J. F. Alcover, L. Gatineau, and J. Mering, Exchangeable cation distribution in nickel and magnesiumvermiculites, Clays and Clay Minerals 21: 131 (1973). M. I. Telleria, P. G. Slade, and E. W. Radoslovich, Xray study of the interlayer region of a bariumvermiculite, Clays and Clay Minerals 25: 119 (1977). J. F. Alcover and L. Gatineau, Structure de l'espace interlamellaire de la vermiculite Mg bicouche, Clay Minerals 15: 25 (1980). J. F. Alcover and L. Gatineau, Facteurs determinant la structure de la couche interlamellaire des vermiculites saturees par des cations divalents, Clay Minerals 15:239 (1980). J. A. RausellColom, M. Fernandez, J. M. Serratosa, J. F. Alcover, and L. Gatincau, Organisation de l'espace lnterlumeilaire dans les vermiculites
THE STRUCTURE OF WATER NEAR CLAY MINERAL SURFACES
X
75
monocouches et anhydres, Clay Minerals 15: 37 (1980). V. Fornes, C. de la Calle, H. Suquet, and H. Pezerat, Etude de la couche interfoliaire des hydrates 11 deux couches des vermiculites calcique et magnesienne, Clay Minerals 15: 399 (1980). 31. J. E. Enderby and G. W. Neilson, op. cit.,15 pp. 626630. 32. C. de la Calle, H. Suquet, and H. Pezerat, Glissement de feuillets accompagnant certains echanges cationiques dans les monocristaux de vermiculites, Bull. Groupe Fr. Argiles 27: 31 (1975). R. F. Giese and J. J. Fripiat, Water molecule positions, orientations, and motions in the dihydrates of Mg and Na vermiculites, J. Colloid Interface Sci. 71: 441 (1979). 33. V. C. Farmer and J. D. Russell, Interlayer complexes in layer silicates, Trans. Faraday Soc. 67: 2737 (1971). 34. H.D.B. Jenkins and P. Hartman, Calculations on a model intercalate containing a single layer of water molecules: A study of potassium vermiculite, Phil. Trans. Royal Soc. (London) A304: 397 (1982). 35. P. L. Hall, Neutron scattering techniques for the study of clay minerals, in Advanced Techniques for Clay Mineral Analysis (1. J. Fripiat, ed.), Elsevier, Amsterdam, 1982. S. Olejnik, G. C. Stirling, and J. W. White, Neutron scattering studies of hydrated layer silicates, Spec. Disc. Faraday Soc. 1:194 (1970). 36. P. H. Nye, Diffusion of ions and uncharged solutes in soils and soil clays, Advan. Argon. 31: 225 (1979). 37. D. M. Clementz, T. J. Pinnavaia, and M. M. Mortland, Stereochemistry of hydrated copper (II) ions on interlamellar surfaces of layer silicates: An electron spin resonance study. J. Phys. Chern. 72:196 (1973). J. Hougardy, W.E.E. Stone, and J. J. Fripiat, NMR study of adsorbed water. I: Molecular orientation and protonic motions in the twolayer hydrate of a Na vermiculite, J. Chern. Phys. 64:3840 (1976). J. P. Hougardy, P. Tougne, D. Bonnin, and A. P. Legrand, Study of adsorbed water: Electric potential calculation and molecular orientation in the twolayer hydrate of a Mg vermiculite, J. Chern. Phys. 67:5252 (1977). J. J. Fripiat, Organisation des molecules d'eau dans les silicates de grande surface specifique, Bull. Mineral. 103:440 (1980). 38. G. D. Boss and E. O. Stejskal, Restricted, anisotropic diffusion and anisotropic nuclear spin relaxation of protons in hydrated vermiculite crystals, J. Colloid Interface Sci. 26: 271 (1968). S. Olejnik and J. W. White, Thin layers of water in vermiculites and montmorillonites: Modification of water diffusion, Nature Phys. Sci. 236: 15 (1972). J. Hougardy, J. M. Serratosa, W. Stone, and H. van Olphen, Interlayer water in vermiculite: Thermodynamic properties, packing density, nuclear pulse resonance, and infrared absorption, Spec. Disc. Faraday Soc. 1: 187 (1970). 39. G. Sposito and R. Prost, Structure of water adsorbed on smectites, Chern. Rev. 82: 553 (1982). See also. J. Fripiat et ai, op. cit.28 40. This structural arrangement was first proposed in J. Mamy, Recherches sur l'hydratation de la montmorillonite: Proprietes dielectriques et structure du film d'eau, Ann. Agron. 19:175 (1968). 41. H. Pezerat and J. Mering, Recherches sur la position des cations echangeables et de l'eau dans les montmorillonites, Compt. Rend. Acad. Sci (Paris) 265: 529 (1967). R. K. Hawkins and P. A. Egelstaff, Interfacial water structure in montmorillonite from neutron diffraction experiments, Clays and Gay Minerals 28: 19 (19XO).
76
THE SURFACE CHEMISTRY OF SOilS
42. I. Eger, M. I. CruzCumplido, and J. J. Fripiat, Quelques donnees sur la capacite calorifique et les proprietes de l'eau dans divers systemes poreux, Clay Minerals 14:161 (1979). 43. R. Prost, Etude de l'hydratation des argiles: Interactions eaumineral et mecanisme de la retention de l'eau. B: Etude d'une smectite (hectorite), Ann. Agron. 26:463 (1975). 44. D. J. Cebula, R. K. Thomas, and J. W. White, Diffusion of water in Limontmorillonite studied by quasielastic neutron scattering, Clays and Clay Minerals 29: 241 (1981). 45. R. Calvet, Dielectric properties of montmorillonites saturated by bivalent cations, Clays and Clay Minerals 23: 257 (1975). 46. P. F. Low, Nature and properties of water in montmorillonitewater systems, Soil Sci. Soc. Am. J. 43: 651 (1979). J. L. Oliphant and P. F. Low, The relative partial specific enthalpy of water in montmorillonitewater systems and its relation to the swelling of these systems, J. Colloid Interface Sci. 89: 366 (1982). 47. See, e.g., D.M.C. MacEwan and M. J. Wilson, Interlayer and intercalation compounds of clay minerals, in G. W. Brindley and G. Brown, op cit. 22 That 1: 1 electrolytes cannot be dissolved completely in adsorbed water on smectites and illitic micas has been shown by A. M. Posner and J. P. Quirk, The adsorption of water from concentrated electrolyte solutions by montmorillonite and illite, Proc. Royal Soc. (London) 278A:35 (1964). 48. See, e.g., Chap. 8 in C. W. Davies, Ion Association (Butterworths, London, 1962) and Chap. 1 in G. H. Bolt, Soil Chemistry. B: PhysicoChemical Models (Elsevier, Amsterdam, 1979). 49. See Chap. 9 in J. Burgess, Metal Ions in Solution (Ellis Horwood, Chichester, U.K., 1978) for a discussion of these trends. 50. For an introduction to Lewis acids and the Misono softness parameter, see, e.g., Chap. 3 in G. Sposito, The Thermodynamics of Soil Solutions. Clarendon Press, Oxford, 1981. 51. M. M. Mortland and K. V. Raman, Surface acidity of smectites in relation to hydration, exchangeable cation, and structure, Clays and Clay Minerals 16: 393 (1968). See also J. D. Russell, Infrared study of the reactions of ammonia with montmorillonite and saponite, Trans. Faraday Soc. 61: 2284 (1965), and M. M. Mortland, Protonation of compounds at clay mineral surfaces, Trans. 9th Int. Congo Soil Sci. (Adelaide) I: 691 (1968). 52. J. J. Fripiat, The NMR study of proton exchange between adsorbed species and oxides and silicate surfaces, in Magnetic Resonance in Colloid and Interface Science (H. A. Resing and C. G. Wade, eds.). American Chemical Society, Washington, D.C., 1976. J. Hougardy et al., op. cit. 3?; R. Touillaux, P. Salvador, C. Vandermeersche, and J. J. Fripiat, Study of water layers adsorbed on Na and Camontmorillonite by the pulsed nuclear magnetic resonance technique, Israel J. Chem. 6: 337 (1968). C. Poinsignon, J. M. Cases, and J. J. Fripiat, Electrical polarization of water molecules adsorbed by smectites: An infrared study, J. Phys. Chem. 82: 1855 (1978). J. J. Fripiat, A. Jelli, G. Poncelet, an J. Andre, Thermodynamic properties of adsorbed water molecules and electrical conduction in montmorillonites and silicas, J. Phys. Chem. 69:2185 (1965). 53. Chapter 4 in D. Eisenberg and W. Kauzmann, op. cit. I "4 C Poi . I op, cit.' . ~2 .J.. omsrgnon et 1\.,
r
~'
THE STRUCTURE OF WATER NEAR CLAY MINERAL SURFACES
77
FOR FURTHER READING
K
:X
G. W. Brindley and G. Brown, Crystal Structures of Clay Minerals and Their Xray Identification. Mineralogical Society, London, 1980. Chapter 3 of this standard reference contains an excellent discussion of Xray diffraction studies of adsorbed water on phyllosilicates. D. Eisenberg and W. Kauzmann, The Structure and Properties of Water. Oxford University Press, New York, 1969. This book remains the best short introduction to the properties of water in all of its phases. Chapter 4 should be read as background for Sec. 2.1 of the present chapter. F. Franks. Water: A Comprehensive Treatise, Plenum Press, New York, 19721981. The seven volumes of this encyclopedic reference work that have appeared thus far contain discussions of all aspects of the chemistry and physics of liquid water and aqueous solutions. Of special interest are the chapters on bulk liquid water (Vol. 1), on water in electrolyte solutions (Vols. 3 and 6), and on claywater systems, (Vol. 5). D. J. Greenland and M.H.B. Hayes, The Chemistry of Soil Constituents. Wiley, Chichester, U.K., 1978. Chapter 6 of this outstanding compendium, written by V. C. Farmer, reviews infrared spectroscopic studies of adsorbed water. J. W. Stucki and W. L. Banwart, Advanced Chemical Methods for Soil and Clay Minerals Research. Reidel, Dordrecht, The Netherlands, 1980. This book provides an excellent introduction to the use of NMR and INS techniques for the investigation of adsorbed water structure. Many experimental results for adsorbed water on phyllosilicates are presented. J. Texter, K. Klier, and A. C. Zettlemoyer, Water at surfaces, Prog. Surface Membrane Sci. 12: 327 (1978). This review gives an account of the available data concerning the properties of water on oxide and organic solid surfaces. The general conclusions drawn are similar to those stated in the present chapter for the structure of adsorbed water on phyllosilicates, except that hydrogen bonding of the water to the surface plays a more prominent role.
3 THE ELECTRIFIED INTERFACE IN SOILS
3.1. THE BALANCE OF SURFACE CHARGE
The creation of an interface between a soil solution and the solid phases of a soil clay induces, by definition, fundamental dissymmetries in the molecular environment of the interfacial region. The forces acting on a cation bound into a siloxane ditrigonal cavity on a dry smectite surface, for example, are entirely different from those acting on the same cation when it is bathed by an aqueous solution phase, and the behavior of a cation immersed in the soil solution near a smectite surface is very different from its behavior near a small anion in the bulk aqueous phase. The net effect of the molecular constituents of one phase on those of an adjacent phase is a structural reorganization at the interface that reflects a compromise among competing interactions originating in the bulk phases. It is, of course, for this reason that the structure of liquid water near a solid phase is different from that in the bulk liquid and the distribution of charge in both the solid and aqueous solution phases near an interface becomes distorted from what exists in bulk matter. Cations bound into innersphere surface complexes may solvate and thereby become farther displaced from the site of the negative charge they balance. Ions in the soil solution can respond differently to an altered water structure or to shifts in the charge distribution in the solid phase at the interface by assuming configurations that are not electrically neutral in a representative volume element in the aqueous phase. These perturbations of the molecular environment lead intrinsically to persistent separation of charge and therefore to an electrified solidliquid interface in soils. The most important physical characteristic of an electrified interface is its surface charge density. The concept of surface charge density was introduced in Sec. 1.5 in the discussion of the surface density of intrinsic, permanent structural, and net proton charge. These three surface charge densities are related by the equation (J.I)
THE ELECTRIFIED INTERFACE IN SOILS
79
where (Tin is the intrinsic surface charge density, (To the permanent structural surface charge density, and (TH the net proton surface charge density. Each term in Eq. 3.1 can be measured either in coulombs per square meter or in moles of charge per square meter, and each can be either positive or negative. Besides the intrinsic surface charge density, two other components of the density of surface charge on a soil particle can be defined. The surface density of innersphere complex charge, (TIS, is equal to the net total surface charge of the ions, other than H+ or OH , that have formed innersphere complexes with the surface functional groups in a soil. Examples of these complexes were given in Figs. 1.8 and 1.9, where surface complexes between vermiculite and K+ and between goethite and HPO~ are illustrated. Other examples include the complex between Pb2+ and the hydroxyl groups on alumina and that between Fe3+ and the carboxyl groups on soil organic matter. 1 The generic term specific adsorption is often used to describe the effects of innersphere surface complexation of ions in the soil solution by surface functional groups on soil clays. The surface density of outersphere complex charge, (Tos, is equal to the net total surface charge of the ions that have formed outersphere complexes with the surface functional groups in a soil. Examples of these complexes are found in Figs. 1.8 and 1.10, where surface complexes between Ca 2+ and montmorillonite and between Na + and kaolinite are shown. Other typical examples are the complex between 0 and protonated aluminol groups and that between Mn2+ and carboxyl groups on soil organic matter. 1 The generic term nonspecific adsorption can be applied to outersphere surface complexation of ions by the functional groups exposed on soil clay particles. With these additional definitions, the surface density of net total particle charge can be expressed mathematically: (Tp => (Tin
= (TO
+
+
(TIS (TH
+
+
(TOS
(TIS
+
(Tos
(3.2)
Each of the terms on the right side of Eq. 3.2 can be either positive or negative, but in general their sum will not equal zero despite the possibility for cancellation. The balance of surface charge, as implied above, cannot be expected to hold, in general, for only part of the interfacial region. What is yet missing is the equivalent surface density of dissociated charge, (To. This quantity is equal to minus the net total particle charge neutralized by ions in the soil solution that have not formed complexes with surface functional groups. These ions, whether positive or negative, are fully dissociated from the surfaces of the solid particles in a soil and are free to move about in the soil solution beyond the interfacial region. The balance of surface charge can now be expressed by a combination of Eq. 3.2 and (Tn:
('0
t
('11
('" + + (T,S
('n = ()
t
(T( IS
+ (TI I
=: ()
(3.3a) (3.3h)
80
THE SURFACE CHEMISTRY OF SOILS
Equation 3.3 is the fundamental conservation law that must be satisfied by the electrified interfaces in any soil. The common methods for measuring 0"0 and O"H are outlined in Sec. 1.5. Conventional methods for determining the remaining densities in Eq. 3.3 have not been established, but there are several techniques that are useful in particular circumstances: 1. If O"in has been measured for an assembly of soil clay particles, then the sum O"IS + O"os + O"D can be calculated with the help of Eq. 3.3. 2. If it is assumed that the cation and anion exchange capacities (CEC and AEC) of a soil clay refer only to those ions in the interfacial region that can be displaced easily by a leaching solution, then the difference CEC  AEC is proportional to the sum O"os + O"D' In mathematical terms, F(CEC  AEC) (3.4) O"os + O"D = S where F is the Faraday constant, S is the specific surface area of the soil clay, and CEC and AEC are expressed in moles of charge per unit mass of soil clay. Equation 3.4 expresses the concept that AEC  CEC is proportional to the surface density of intrinsic charge after correction for any innersphere complex charge. This concept reflects the wellknown low desorbability of specifically adsorbed ions. 3. If O"in is known and O"os + O"D is measured by the method described in item 2, then O"IS can be calculated by rearranging Eq. 3.3: O"IS = O"in +
F(AEC  CEC)
S
(3.5)
The determination of O"in is carried out in the absence of specific adsorption, but otherwise under the same soil conditions as exist for the determination of CEC and AEC in the presence of specific adsorption. 4. If it is assumed that the electrokinetic plane of shear near a soil particle coincides with the outer periphery of its surface complexes, then electrokinetic mobility experiments/ can be interpreted to provide an estimate of O"p and, by Eq. 3.3a, of O"D' The theoretical basis for this method is discussed in Sec. 3.4. It may be noted in passing that no assumptions about the detailed structure of the interfacial region are required in order to measure a zero value for O"D' Given the single assumption about the plane of shear, O"D vanishes at zero electrokinetic mobility. The parameters O"IS' O"os, and O"D reflect the disposition of ions in the soil solution after they have become incorporated into the interfacial region. Therefore, these surface charge densities represent the net charging effects of the surface speciation of the ions. By analogy with the use of speciation models (ionassociation models) to estimate the distribution of ionic charge in aqueous phases like soil solutions;' surface speciation models (surface
THE ELECTRIFIED INTERFACE IN SOILS
81
complexation models) could, in principle, be used to estimate (TIS' (Tos, and (Tn individually. The basic properties of surface complexation models are discussed in Chap. 5. Suffice it to say here that these models have been developed well enough to permit quantitative, verifiable estimates of surface charge densities under reasonable physical assumptions. 3.2 POINTS OF ZERO CHARGE Points of zero charge are Elf values associated with specific qHUliJ\QOs iIllPosed on one or more of the. sqt:fac~ cha.t,gePensiti~s d.es9ri,1?~4jn Sec. 3.1. The definitions ofthe most important points ofzero charge in the mrface chemistry of soils are summarized in Table 3.1. The conventional e~inl~qL;Z!?!2~c:~q,~G!,!R~~2..~~..t~~'4:£,I;ty~lu~. 2L ~~~911.. solution when the.t()t::l1g.~tpartiFle cl:1arg~.YflIli~hc;:s. By Eq. 3.3a, this condition is met when '!n ~O. The PZC. ca~ .be. measured directl.rjn electrokineticexperimentsalld" inconoi~'ar~sfllo~fif"si~~Tes;Ss inceboth invo'lve"phenomeiia sensitive to the"total 'net diarge oo'sU'spended particles. The point of zero net proton charge (PZNPC) is the pH value of the soil solution at which (TH, defined in Eq. 1.24, is equal to zero. As can be inferred from Eq. 1.25, the PZNPC can be measured by potentiometric titration, provided only protonselective surface functional groups on the soil solids are titrated. The point of zero salt effect (PZSE), defined in Eq. 1.27, also can be measured by potentiometric titration. The PZSE is determined by locating the common point of intersection of several graphs of (TH versus pH, each determined at fixed ionic strength of the electrolyte background. Another common method for measuring the PZSE involves the equilibration of a set of soil suspensions, initially adjusted to a range of pH values expected to include the PZSE, with a background electrolyte at two different ionic strengths. After the suspensions have come to equilibrium, the pH values of their aqueous solution phases are determined, and the pH value that shows no change with ionic strength is designated as the PZSE. 6 The point of zero net charge (PZNC) is the pH value of a soil solution at which the difference CEC  AEC equals zero. This difference is proportional to either an optimal or a nonoptimal value of the intrinsic surface Table 3.1. Definitions of some points of zero charge
Name
Symbol PZC a PZNPC PZSE PZNC
Point Point Point Point
of of of of
zero zero zero zero
charge net proton charge salt effect net charge
Defining equation = 0 UH = 0 (auH/alh = 0 UD
Uos
• AINU termed IEI', iNlleleclrk pulnl, when measured by an electroklnetlc experiment.
+
UD
=0
THE SURFACE CHEMISTRY OF SOILS
82
charge density, as pointed out in Sec. 1.5. Therefore, the PZNC can be measured by the Schofield method" applied over a range of pH values. If it is assumed that the reactant salt solution used to saturate the soil with the two index ions can displace only the ions contributing to aos and aD, then a nonoptimal value of ain is measured and the PZNC corresponds to the condition aos + aD = 0 (Table 3.1). Otherwise, if it is known that the reactant salt solution can displace even specifically adsorbed ions, then it is appropriate to write ars + aos + aD =
F(CEC  AEC) S
(3.6)
instead of Eq. 3.4, and the optimal value of ain is measured. In this case, the PZNC corresponds to the condition ain = O. The commonly measured points of zero charge are illustrated in Fig. 3.1. 7 It is evident from Table 3.1 that the surface charge density conditions that define points of zero charge are not the same and therefore that there can be numerical differences among these pH values for the same soil particles. The circumstances that permit equality among the points of zero charge can be ascertained directly, however, through an appeal to the charge conservation law in Eq. 3.3. Consider as a simple case the possibility of equality between the PZC and the PZNPC. According to Table 3.1 and Eq. 3.3b, this possibility is realized when the equation ao
+ ars +
aos = 0
(3.7)
is valid. This charge balance equation can be satisfied in an infinitude of ways, one of which is the independent vanishing of each of the three component surface charge densities. Although this special case is quite unlikely in soils, it can be achieved approximately for reference soil minerals suspended in aqueous solutions of 1 : 1 electrolytes, as exemplified by the data for yA1 203 , birnessite, and corundum in the second and third columns of Table 3.2. On the other hand, Eq. 3.7 does not appear to apply to a comparison of PZC with PZNPC for goethite (unless other factors, such as the method of solid preparation, surface impurities, and crystallinity, are operating). If the PZC and the PZNC are to be equal and if Eq. 3.4 is assumed correct, then Table 3.1 and Eq. 3.3b demand that aos vanish identically. For, if a soil solution is at the PZC, then aD = 0 and the condition for the PZNC (aos + aD = 0) requires that aos = 0 also. Conversely, if a soil is at the PZNC, then aos =  aD by hypothesis and the soil is at the PZC as well only if aos = O. To determine whether aos = 0 at either the PZC or the PZNC, one would need to speciate the adsorbed ions in a soil into outersphere surface complexes versus completely dissociated species. This could be done, for example, by studying the electrokinetic or coagulation behavior of soil particles that have been brought to the PZNC. On the molecular level, equality between the PZC and the PZNC is expected if thc soil particles are suspended in a I : I electrolyte solution wherein both
THE ELECTRIFIED INTERFACE IN SOILS
83
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(\J
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0
E
~
ex>
0 ><
pH
I
::l
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GOETHITE 0.015 M NaCI04 BARYOSEF et al. (1975)
Y AI203 103M NaCI HUANG AND STUMM (1973) 4
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POINTS OF ZERO CHARGE
11.0
Figure 3.1. Experimental examples of the PZC of yAlz0 3 , the PZNPC of goethite, the PZSE of hydroxyapatite, and the PZNC of kaolinite." (u is the electrophoretic mobility.)
the cation and the anion form only outersphere surface complexes. This condition appears to be met approximately for birnessite and kaolinite, according to the data in the second and fifth columns of Table 3.2. Equality between the PZC and the PZSE obtains if the equation (O'IS
+
O'OS)11
=
(O'IS
+
0'0S)12
(3.8)
holds, where 11 and 12 refer to two different ionic strengths of the soil solution. Equation 3.R is derived by applying Eq. 3.3b at each ionic strength. noting the definitions in Table 3.1, and deleting Un because
THE SURFACE CHEMISTRY OF SOILS
84
Table 3.2. Comparison of points of zero charge for several solid phases suspended in solutions of 1 : 1 electrolytes Solid
PZC
PZNPC
PZSE
Alon (yAl z03) Birnessite (8MnOz) Calcite (CaC0 3) Corundum (aAlz03) Goethite (aFeOOH) Hematite (aFeZ03) Hydroxyapatite (Cas(P04hOH) Kaolinite (Si4AI4OlO(OHs)) Quartz (aSiO z)
8.7
8.2 ± 0.5 2.2 ± 0.7
8.5
1.7 10 9.1 6.1
± ± ± ±
0.4 1 0.2 0.6
7.5 ± 0.1 4.7 2.0 ± 0.3
2.3 ± 1.1 9.5
PZNC 1.9 ± 0.5
9.1 7.7 ± 0.2 8.4 ± 0.1
7.3 ± 0.2 8.5 7.6 ± 0.2 4.8 2.9 ± 0.9
Sources of data: Alon, c.P. Huang and W. Stumm, J. Colloid Interface Sci. 43:409 (1973); S. Goldberg, personal communication. Birnessite, L. S. Balistrieri and J. W. Murray, Geochim. Cosmochim. Acta 46: 1041 (1982); R. M. McKenzie, Aust. J. Soil Res. 19:41 (1981). Calcite, G. A. Parks, in Chemical Oceanography, Academic Press, London, 1975, Vol. Y, pp. 241308; R. J. Hunter, Zeta Potential in Colloid Science, Academic Press, New York, 1981, pp. 228ft. Corundum, S. Goldberg, personal communication; R. J. Hunter, op. cit. Goethite, G. A. Parks, op. cit.; S. Goldberg, personal communication; T. L. Theis and R. O. Richter, Advan. Chem. Series 189: 73 (1980); L. S. Balistrieri and J. W. Murray, Am. J. Sci. 281:788 (1981). Hematite, S. Goldberg, personal communication; A. Breeuwsma and J. Lyklema, J. Colloid Interface Sci. 43:437 (1973). Hydroxyapatite, Bell et aI., J. Colloid Interface Sci. 42:250 (1973). Kaolinite, J. Baham, personal communication; A. P. Ferris and W. B. Jepson, J. Colloid Interface Sci. 51:245 (1975). Quartz, R. J. Hunter, op. cit.
permanent structural charge cannot be affected by changes in ionic strength. It follows from this result that the PZC is the same as the PZSE if no surface complexes form. Although this condition is sufficient, it is not likely to occur in soils. A better assumption is the lack of innersphere surface complexes if soil particles are suspended in a 1: 1 electrolyte solution. In that case, Eq. 3.8 reduces to (3.9) which implies that the surface density of outersphere complexes remains invariant under a change in ionic strength. This condition can be met if Uos is at its maximum value at both 11 and 12or if the cation and the anion have about the same affinity for the soil particles and adsorb or desorb equally with changes in ionic strength. Evidently, ions such as Na+ and Cl", which are often used in background electrolytes, meet the criterion of roughly equal affinity for oxide surfaces, as exemplified by birnessite and quartz in Table 3.2. (Goethite appears to be an exception.) If the background electrolyte contains ions that can form innersphere surface complexes (e.g., SO~ or Ca 2+), then Eq. 3.8 must be retained as the general condition for equality between the PZC and the PZSE. The condition applied to Urs separately can be met through a change in ionic strength while the concentration of the specifically adsorbing ion is held constant. For example. the concentration of SO~ could be maintained fixed while: the ionic strength is changed through a shift in the concentra
THE ELECTRIFIED INTERFACE IN SOILS
85
tion of a swamping electrolyte, such as NaCl. In this case multiple plots of (TH versus pH at fixed ionic strength intersect at a common point that determines the PZC as well as the PZSE. However, at any ionic strength, Eq. 3.3b requires the condition (pH =
pzq
(3.10)
to hold at the PZC. If (TIS < 0 (specific anion adsorption), the value of (TH will be larger than when no specific adsorption occurs and, since (TH increases with proton activity, the PZC must shift downward relative to that case. If (TIS> 0 (specific cation adsorption), the value of (TH at the PZC will be smaller than when no specific adsorption occurs and the PZC must shift upward. This kind of shift in the PZC is observed commonly in soils. An example of the case (TIS < 0 (ophosphate adsorption) is shown in Fig. 3.2. 8 Should the swamping electrolyte solution contain an ion that can adsorb specifically, matters change considerably as regards equality between the PZC and the PZSE. In this case, Eq, 3.8 cannot hold unless (TIS has reached a maximum value that remains invariant under a change in the concentration of the specifically adsorbing ion. Otherwise, there must be a different value of the PZC at every ionic strength of the swamping electrolyte, and points of intersection of graphs of (TH versus pH cannot be used to determine the PZC. If (TIS < 0 (specific anion adsorption), Eq. 3.10 implies that (TH increases with increasing ionic strength (which decreases (TIS) and the PZSE shifts upward from the PZC determined when (TIS = O. If (TIS> 0 (specific cation adsorption), the same line of reasoning implies a downward shift of the PZSE. Note that these shifts are opposite in sense of what occurs when the concentration of specifically adsorbing ion is maintained constant while the ionic strength is changed. This fact has led to some confusion about the expected effects of specific adsorption on the PZC when the PZSE has been equated incorrectly to the PZC in a suspension containing a specifically adsorbing, swamping ion. 1 •9 Figure 3.2. The downward shift of the PZSE for an Oxisol soil (Typic Torrox) in response to the specific adsorption of ophosphate." MOLOKAI s.C.1. OM PHOSPHATE
:r
0
cr I
:r cr
MOLOKAI s.c.I, 0.0156 M PHOSPHATE
~ 1M 0 0.1 I!! O.OIM 0 0.001 I!!
• •
THE SURFACE CHEMISTRY OF SOilS
86
It is possible to distill from the present discussion two general rules concerning equality among the points of zero charge summarized in Table 3.1. These rules depend only on the applicability of the balance of surface charge (Eq. 3.3) and not on any detailed model of the interface between the soil solution and soil solid phases. 1. If a soil is suspended in a swamping electrolyte solution of a 1: 1
electrolyte whose cation and anion form only outersphere surface complexes, the PZC, the PZNC, and the PZSE for the soil are likely to be equal. 2. If a soil is suspended in a swamping 1: 1 electrolyte as in rule 1, along with a fixed concentration of an electrolyte containing an ion that adsorbs specifically, the PZC and the PZSE for the soil are likely to be equal. In this case, the PZC changes relative to its value as determined by rule 1 and the sign of the change is the same as the sign of the valence of the specifically adsorbing ion. The relationship between the PZNPC and the PZNC for a soil when the experimental conditions of rule 1 are met can be deduced from Eq. 3.3b and Table 3.1. Consider the PZNPC. Equation 3.3b becomes (To
+
(TOS
+
(TD
= 0
(pH = PZNPC)
(3.11)
Equation 3.11 does not contain (TIS because innersphere surface complexes are assumed to be absent, in accordance with rule 1. At the PZNC, on the other hand, Eq. 3.3b and Table 3.1 lead to the chargebalance expression (pH
= PZNC)
If the PZNPC is larger than the PZNC, then
(3.12)
at the PZNC must be larger than (TH at the PZNPC since (TH increases as the pH decreases. But (TH (PZNPC) = 0 by hypothesis, and therefore (TH (PZNC) must be a positive quantity. It follows immediately from Eq. 3.12 that (To must be a negative quantity. The same kind of reasoning also shows that, if the PZNPC is smaller than the PZNC, then (To must be a positive quantity. These conclusions can be stated as the following general rule: (TH
3. If a soil is suspended in a swamping electrolyte solution of a 1: 1 electrolyte whose cation and anion form only outersphere surface complexes, the sign of the difference PZNPC  PZNC is opposite the sign of the surface density of structural charge, (To. If PZNPC = PZNC, then the structural surface charge density must vanish. l
It should be noted that the relation between the sign of (To and that of PZNPC  PZNC does not depend on equality between the PZC and the PZNC but only on the condition that (Trs = o.
THE ELECTRIFIED INTERFACE IN SOILS
87
Suppose now that Eq. 3.4 applies in addition to Eq. 3.11. The combination of these two equations then produces the expression F(CEC  AEC)
0"0
+=0
(3.13)
S
valid at the PZNPC. Equation 3.13 shows that a measurement of the difference between CEC and AEC at the PZNPC can be used to calculate the structural surface charge density in a soil. Note that the sign of 0"0 is opposite that of the difference CEC AEC. In moderately weathered soils, this difference is expected to be positive and thus 0"0 is negative because of isomorphic substitutions of cations of lower valence for those of higher valence in phyllosilicates. In highly weathered soils, the difference CEC  AEC may be negative at the PZNPC and (To can be positive because of isomorphic substitutions of cations of higher valence for those of lower valence in hydrous oxides. 10 Before leaving this discussion of the conceptual basis of the point of zero charge, two experimental aspects of the measurement of the PZC in a soil should be mentioned. First, note that the condition on O"H stated in Eq. 3.10 is impossible to fulfill experimentally if 0"0 is a negative quantity large enough to make (TH so large at the PZC and the pH value of the soil solution so low that it cannot be achieved experimentally without dissolving the soil particles. This set of circumstances appears to exist for soil clays dominated by 2: 1 phyllosilicates, which exhibit large absolute values of 0"0 because of isomorphic substitutions and for which the PZC has not been measured successfully. 1 A second experimental aspect of the PZC deals with the relationship of the PZC of a soil to those of its individual mineral constituents." As an illustration of this point, consider a simple mechanical mixture of two kinds of mineral particle, A and B. At the PZC, the total particle charge in the mixture is zero: (pH
=
PZC)
(3.14)
where S is the specific surface area and m is the mass of particles of either kind. After dividing Eq. 3.14 by the total mass of the mixture, m = m»: + mB, one can rearrange the expression to have the form O"DASA
:A
+
O"DBSB( 1

:A)
=0
from which it follows that WA
=
O"DBSB
===(TDBnB 
(pH = PZC)
(3.15)
O"DASA
where WA = mAim is the mass fraction of A in the mixture. Equation 3.15 permits the calculation of the PZC of the mixture as a function of W A' If the specific surface areas of the two component solids are known. and if the
88
THE SURFACE CHEMISTRY OF SOILS
surface charge density, lTo (at fixed ionic strength), has been measured for each as a function of pH value, then the value of W A corresponding to each pH value in the measured domain can be calculated with Eq. 3.15. These pH values can be equated to the PZC corresponding to the calculated W A' For example, if at pH 6 the product lTOASA is equal to 0.02 mol.kg"! and lTOBSB is equal to +0.18 mol.kg", then, according to Eq. 3.12, pH 6 is the PZC of a mixture containing a mass fraction of 0.9 for component solid A. As a general rule, Eq. 3.12 does not lead to a linear relationship between the PZC and WAY Thus the PZC of a mixture cannot be predicted by a simple linear interpolation between the PZC of component B and that of component A as W A increases from 0 to 1. For a soil comprising several constituent minerals in the clay fraction, no linear relation between the soil PZC and the PZC of the constituent minerals is expected. 3.3. POTENTIALS NEAR AN ELECTRIFIED INTERFACE
The development of surface charge at the interface between soil particles and the soil solution is a reflection of inhomogeneities in the molecular environment of the interface, as discussed in Sec. 3.1. These molecular inhomogeneities also influence the thermodynamic properties of both the charged species in the soil particles and those in the soil solution. In particular, the distribution of a charged species between the two bulk phases, regardless of their composition, is determined by the electrochemical potential of that species, ji.. The gradient of the electrochemical potential of a species drives its diffusive transfer between phases, and equilibrium with respect to this transfer is described by the equality (3.16) where A and IT denote two different phases that contain the charged chemical species i. The electrochemical potential has the units joules per mole. 12 The measurement of the electrochemical potential can be illustrated by considering the following soil clay suspensionsoil solution system into which two identical electrodes are immersed:
w
L
Ag;AgCl
NaX(s),NaCI(aq)
R NaCI(aq) solution
AgCI;Ag
The single vertical line refers to the interface between a silversilver chloride electrode and either a soil suspension or a soil solution. The double vertical line marked W refers to a membrane that is impermeable to the soil colloidal anion. XI, but permeable to dissolved ions and water. There may be ions other than Na + and CI in the suspension or in the solution, but they are assumed not to interfere with the behavior of the
THE ELECTRIFIED INTERFACE IN SOILS
89
silversilver chloride electrode toward Cl" anions. At the left electrode (L), by convention.P the oxidation reaction Ag(s) + Cl(L,aq) = AgCI(s) + e takes place, where L refers to a point inside the left electrode assembly and e denotes an electron. At the right electrode (R), the reduction reaction AgCI(s) + e = Ag(s) + Cl(R,aq) takes place, where R refers to a point inside the right electrode assembly. The overall electrodepair reaction, obtained by combining the two halfreactions, is (3.17) According to the thermodynamic conventions for the assignment of emf values to electrode assemblies, summarized in Table 3.3, the emf across the silversilver chloride electrode pair is given by the equation (3.18a) where F is the Faraday constant and E is the emf in volts. It is expected that equilibrium exists between Cl(L,aq) and Cl" anions in the suspension as well as between Cl(R,aq) and Cl" anions in the solution. Therefore, by Eq. 3.16, and where so refers to the solution and su to the suspension. The combination of the two parts of Eq. 3.18 leads to an expression for the difference between the electrochemical potential of the chloride ion in the suspension and that in the aqueous solution: (3.19a) Equation 3.19a illustrates the general rule that differences in electrochemical potential for a charged species can be measured by determining the Table 3.3. Conventions in the assignment of emf to galvanic cells13 1. The cell reaction is written as if oxidation occurs spontaneously at the left
electrode and reduction at the right electrode. 2. If the overall cell reaction is aA + bB + ... = xX + yY + ...
the cell emf (in volts) may be defined by the relation XM[X] + YM[Y] + ...  au. [A]  bM[B]  ...
a
FE
where F is the Faraday constant and E is the cell emf. 3. In these conventions. it is assumed that all reduction or oxidation halfreactions are written in terms of the transfer of 1 mole of electrons.
90
THE SURFACE CHEMISTRY OF SOILS
emf developed across a pair of electrodes that behave reversibly toward the charged species. Clearly, the derivation of Eq. 3.18 can be carried through for any charged species in two different aqueous systems by using electrodes that behave reversibly toward the species. The corresponding general result for the electrochemical potential difference is
fl;iLi = iLA[i]  iLCT[i]
=
ZiFE
(3.19b)
where A denotes the phase containing an electrode (reversible to charged species i) at which a reduction occurs and (J" denotes the phase containing the electrode at which an oxidation occurs. The parameter Z, is the valence of species i. If equilibrium exists with respect to the transfer of species i between the phase A and (J", then Eq. 3.16 applies and E = 0 in Eq. 3.19b. Thus the absence of an emf across a pair of electrodes that behave reversibly toward a charged species can be used to indicate equilibrium with respect to the transfer of the species between two phases. The electrochemical potential of a charged species can be envisioned as the potential difference (in the sense of mechanics) involved with the transfer of 1 mole of a charged species from a point at chargefree infinity to a point inside a material phase. 12 It is evident from this conceptualization that iLA[i] depends on the purely chemical nature of the species i as well as on the purely electrostatic interactions that can occur between i and other charged species in the phase A during the transfer process. For example, in the case of the chloride ion discussed above, iLsu[CI] should depend on the chemical properties of chloride in the suspension as well as on the electrostatic interactions between Cl" and either the other ions or the charged solid surfaces in the suspension. Similarly, iLso[CI] should depend on the chemical properties of chloride in the soil solution and on the electrostatic interactions between Cl" and the other dissolved ions. This dual characteristic of the electrochemical potential suggests that it is worthwhile to inquire as to the physical significance of the formal definition:
P[iJ == go + RT In(i) + ZiFcP
(3.20)
where go is a function of temperature and pressure, as well as of the "purely chemical" nature of the species whose activity is (i), R is the molar gas constant, T is the absolute temperature, and cP is the electric potential to which i is subjected. Evidently Eq. 3.20 would separate the electrochemical potential into a purely chemical partthe first two terms on the right sideand a purely electrostatic part containing the potential, cPo Consider now Eq. 3.20 applied to Cl" in the soil clay suspensionsoil solution system diagramed below Eq. 3.16. The left side of Eq. 3.19a can be expressed
flsO su JLCI
= /:
so .so
[Cl]  c. [Cl"] + RT In [(CI)so]  F(.l.. _.l..) so .SII (Cl " )su 'l'so 'l'SIi
p.21)
THE ELECTRIFIED INTERFACE IN SOILS
91
The left side of Eq. 3.21 is well defined and measurable, as indicated in Eq. 3.19a. The right side of Eq. 3.21 contains the difference between go for 0 in the two aqueous systems, the ratio of the activities of 0, and the Donnan potential difference cPso  cPsu. These three quantities have physical meaning if it is possible to measure any two of them unambiguously, i.e., without making unverifiable assumptions about the nature of the two aqueous systems. Unfortunately, no experimental method exists that can determine even ratios of singleion activities without making unverifiable extrathermodynamic assumptions. Moreover, no experimental technique exists for an unambiguous measurement of the difference in go values for two phases of different chemical composition, and no electrode assembly can measure a Donnan potential difference without the data being interpreted through unverifiable extrathermodynamic assumptions. 12 It follows that, in this case, the partitioning of the right side of Eq. 3.21 has no physical significance. Suppose that there is good reason to believe that all of the chloride in the suspension diagramed below Eq, 3.16 is in dissolved form and therefore that the Standard State of Cl" is the same in the suspension and the aqueous solution. In addition, suppose that equilibrium exists with respect to the transfer of chloride between the two aqueous systems. Then Eq. 3.21 can be reduced to the expression cPsu  cPso = RT In ~msu~ l' m so
RT In [Ysu] + l'
Yso
(3.22)
where m is a chloride molality and y is a chloride activity coefficient. 14 The molality of Cl" in the suspension and in the aqueous solution can be determined experimentally. Therefore, the physical significance of the Donnan potential difference hinges on the measurability of the activity coefficient ratio, Ysu/Yso' This ratio might be estimated with the help of model equations based in molecular theory, but no experimental technique exists that can determine the ratio without unverifiable extrathermodynamic assumptions.F Therefore, even in this relatively simple case, the Donnan potential difference remains without empirical meaning. The electric potential on the right side of Eq. 3.20 is known as an inner potential, and the potential difference on the right side of Eq. 3.21 is an example of a Galvani potential difference, (3.23) between two phases denoted A and a. The discussion presented in this section is intended to illustrate the general principle'< that Galvani potential differences between two phases of different chemical composition cannot be measured. The root problem is that the inner potential is the electric potential difference between a point at chargefree infinity and a point inside a material phase. Although this potential is a welldefined entity in classical electrostatics (the theory of a hypothetical charged fluid), it is not well defined in thermodynamics (the macroscopic theory of matter
THE SURFACE CHEMISTRY OF SOilS
92
in stable states) because the interactions that produce the chemical properties of charged species cannot be divided unambiguously into electrostatic and nonelectrostatic categories. However, if a charged species occurs in two phases with identical chemical composition, this difficulty is obviated by the fact that the purely chemical part of the electrochemical potential of a charged species must be the same in the two phases. It follows from Eq. 3.20 that, in this case, (3.24) and therefore that Galvani potential differences between two phases of identical chemical composition are measurable. Examples of the application of Eq. 3.24 include Galvani potential differences between two identical metal wires or between two identical aqueous solutions.F For two aqueous solutions having the same chemical constituents but different concentrations of those constituents, Eq. 3.20 leads to the expression (3.25) where Aand A' denote the two solutions. If the ratio of activities in the two solutions can be determined (e.g., by the use of activity coefficients or with an ionselective electrode), then, within the conventions prescribed for interpreting the activity determination, the Galvani potential difference ~;cP becomes a measurable quantity.F The concepts of electrochemical and inner potential can be used to classify interfaces, as show in Table 3.4. If charged species cannot traverse an interface freely, the interface is called polarizable and the condition for equilibrium across the interface is that zero Galvani potential difference exists across it. If charged species can traverse the interface freely, it is called reversible (or nonpolarizable) and the condition for equilibrium across the interface is that zero electrochemical potential difference exists across it. Thus a polarizable interface is analogous to a capacitor and a Table 3.4. The categories of interfaces
Interface type Polarizable
Ions traverse freely?
Equilibrium condition
Equivalent circuit
No
Rt Reversible
Yes
oo
THE ELECTRIFIED INTERFACE IN SOILS
93
resistor of infinite resistance arranged in parallel, whereas a reversible interface is analogous to a capacitor and a resistor of zero resistance arranged in parallel. Since the behavior of the reversible interface is governed by the electrochemical potentials of the charged species that can cross it freely, these species are called potentialdetermining for the interface. An. example of a polarizable interface is that between a mercury electrode and liquid water, since the concentration of mercury ions in the aqueous phase is quite negligible. In this case, it is common to assume as a practical convention that equilibrium at the interface exists when the emf of the mercury electrodereference electrode pair vanishes, since a Galvani potential difference between mercury and water cannot be measured. An example of a reversible interface is that between a hydrous oxide solid and liquid water. In this case, H+ and OH ions can cross the interface freely and are potentialdetermining. Equilibrium at the interface is established when the net ion transport across the interface vanishes, i.e., when there is no change in the pH value of the aqueous phase. Note that the interface between a soil particle and the soil solution is in general reversible. Any charged species that is adsorbed by the particle and found in the soil solution is potentialdetermining. Although the inner potential has no strict thermodynamic significance, it can always be defined and studied in the context of a model of the interfacial region. The use of the inner potential in this way must be understood clearly to have no physical significance outside the conventions that establish the model. A case in point is the inner potential 0/ defined in diffuse double layer (DDL) theory through the PoissonBoltzmann equation.P This electric potential was used in Sec. 1.4 to derive a relationship between the exclusion volume for soil clay suspended in a 1: 1 electrolyte solution and the electrolyte concentration (Eq. 1.18). The final result did not exhibit 0/ and therefore was verifiable by experiment even though 0/ itself is not measurable. This kind of model definition of the inner potential is not invalid so long as it is selfconsistent. However, in no sense would it be correct to substitute a solution of the PoissonBoltzmann equation into Eq. 3.20 and then claim that c/J had thereby been made legitimate. This step would be incorrect conceptually because c/J in Eq. 3.20 applies to an entire phase whereas 0/ obtained by solving the PoissonBoltzmann equation is an explicit function of position within a phase. Put more generally, 0/ is an inner potential defined solely in a molecular context (DDL theory) whereas c/J in Eq. 3.20 is defined in a macroscopic context (thermodynamics). A point of contact between the two can be determined legitimately by postulating, for example, that the Galvani potential difference across an interface is equal to 0/6  0/0, where 0/6 is the PoissonBoltzmann inner potential evaluated at the interface and % is that evaluated at a point in the aqueous solution phase far from the interface. 14 The concept of modeldependent inner potentials is discussed at length in Chap. 5.
94
THE SURFACE CHEMISTRY OF SOILS
3.4. ELECTROKINETIC PHENOMENA
The ~_of ~!!,,~e.l~E!!:~~~~..~S.2E.~:li9uid in~!faS~_.!2"_~he~r.i!l,g,.1t~~~
..a.1?p.E~~Ug"J)!j!l.~h!~~tl!l...~~.21!!~~Ou~lill¥E!J2h~.i1"ler~,e~t~!1..!!~£!r£. l~,.it!:~~£J!.~!!!;,~;,!'}!'r:.. The fundamental physical assumptions on which the
molecular interpretation of electrokinetic phenomena is based are that an
~!~~~~~~~~~~~~~2*~'m~: i;,jf~~~t~w~~f!A~~f~~~~
p~~ar~t~lc"l"e~su~r'"'1'*'ac"'e"",~t1!h~eriqJrid ph';;e is assumed to be at rest relative to the solid
particle; beyond the plane out into the liquid phase, the liquid moves relative to the solid particle because of the shearing stress it experiences. This relative motion perturbs the interfacial region in a manner that one assumes can be described through the simultaneous application of the Poisson equation in classical electrostatics and the NavierStokes equation in fluid mechanics.l" Alternatively, one can formulate a description of electrokinetic phenomena as an application of methods in the thermodynamics of irreversible processes, with no appeal made to specific models of the interfacial region."? With this approach, of course, detailed information about the molecular properties of an electrified interface cannot be obtained from an analysis of electrokinetic data. For soil clay particles, it is often the case that the radius of curvature of any patch on the particle surface is very much larger than the mean thickness of the interfacial region extending into the soil solution. A perfectly flat clay particle surface meets this condition exactly, for example, because its radius of curvature is infinite by definition. In this case, the general description of electrokinetic phenomena in terms of electrostatics and fluid mechanics is made simpler because there is no perturbation of the interfacial region except along the direction normal to the particle surface and no distortion of the ion swarm in the liquid phase except that produced by the charge on the particle before the plane of shear came into being.J" With
Figure 3.3. Geometric aspects of electrokinetic phenomena. y
SOLID SURFACE
z
THE ELECTRIFIED INTERFACE IN SOILS
95
these two physical conditions in mind, one can define an inner potential in the mobile liquid phase near the solid particle through the Poisson equation: d ( soD dljJ) dx dx =  p(x)
(x
:2:
d)
(3.26)
where ljJ(x) is the inner potential, p(x) is the volumetric charge density (coulombs per square meter), and the other symbols are as defined in connection with Eq. 1.11. As indicated in Fig. 3.3, the coordinate x is measured from the solid particle surface out into the liquid phase. The inner potential, ljJ, is subject to the constraints ljJ(b)
=0
(3.27)
and
where b ~ d is a point in the mobile liquid phase that is far from the plane of shear located at x = d. Equations 3.26 and 3.27 must be regarded as model definitions of the inner potential since ljJ(x) cannot be measured by any modelindependent technique. The other dependent variable of interest is the liquid velocity, V,(x) , defined to be a solution of a linearized form of the NavierStokes equation: dP d ( dVl) f(x)  dz + dx T/ dx
=0
(x
> d)
(3.28)
where P is the pressure applied to the liquid, f(x) is the external force per unit volume applied to it, and T/ is its coefficient of viscosity. Equation 3.28 is a mathematical expression of the balance of forces on a differential element of the liquid under steadystate conditions. The liquid velocity is subject to the constraints (3.29a) and
dV') ( dx x=b =0
(3.29b)
where U is the velocity in the mobile liquid phase, measured relative to the particle surface, at a point x = b far from the plane of shear. The net electric current I, which under steadystate conditions, is produced by the convection of charged species in the mobile region of the liquid phase, can be expressed mathematically with the equation I =
JJ: p(x)vl(x)dxdy .
(3.30)
where frlJl is just the net electric current density through an element of crosssectional area dxdy. The meanvalue theorem of integral calculus and
THE SURFACE CHEMISTRY OF SOILS
96
Eq. 3.29 can be used to simplify Eq. 3.30: 1= vl(d)
=u
If:
Ir
p(x)dxdy
+
VI(b)
JJ:
p(x)dxdy
(3.31)
p(x)dxdy
where x = a lies somewhere between the plane of shear and x = b. Now Eq. 3.30 can also be transformed with the help of Eqs. 3.26 to 3.29 and the assumption that the mobile liquid phase is a homogeneous, viscous dielectric medium:
The first step in Eq. 3.32 is the result of substituting Eq. 3.26 into Eq. 3.30; the second step is an integration by parts; the third step makes use of Eqs. 3.27 and 3.29a and invokes the assumption that the mobile liquid phase is a homogeneous dielectric medium; the fourth step is another integration by parts; the fifth step is the result of Eqs. 3.27 and 3.28 along with the assumption that the mobile liquid phase has a uniform viscosity coefficient; the sixth step involves the identity d(dljl) dx
== dZIjIz dx dx
and the use of Eq. 3.27; and the last step requires Eq. 3.28 again. !he '&lY~.QfJl:teJ!1.I.!.~!..E9telltiaJ . at.1Q~ pl~I!~ gf shear i~ denoted by , ill.Eq, .~, ~~ and is called the zeta. potential of the interface.' . . .To the extent that the liquid phase retains bulk dielectric characteristics outside the region enclosed by the plane of shear. Eqs. 3.31 and 3.32 lead
THE ELECTRIFIED INTERFACE IN SOILS
97
to a general expression for electrokinetic phenomena: U
II:
p(x)dxdy =
_eo~(
II: [1 
o/i)] [f(X) 
~~]dXdY
(3.33)
The mean value theorem can be applied to the right side of this equation in the same manner as in Eq. 3.31 with the quantity [1  (o/(x)/()] taken outside the integral sign. The quantity equals unity when x = b and zero when x = d. Therefore, Eq. 3.33 reduces to U
[b f Ja p(x)dxdy =
e D(
~
ffba' [f(x)
dPJ  dz dxdy
(3.34)
where x = a' lies between x = d and x = b. In applications of Eq. 3.34, it is assumed that the interfacial region is thin enough that VI i U and 0/ ~ 0 so rapidly that the distinction between a, a', and d can be ignored. Under this assumption, the lower limits of both of the explicit integrals in Eq. 3.34 can be set equal to d. The expression then takes a convenient form that can be used to describe the four principal electrokinetic phenomena that are investigated in soil clay suspensions.
where UE is the steadystate velocity of a charged particle moving in response to an electric field of magnitude E. ~l.lnits..Ql!:(,1!r,~....m_2s:~y~:,
;;o~~~t:L1g~;~~iH~elrU;~s~;:~li~;~~~!*~~~~~~i~a~~~:T~)~
positive surface charge density at the plane of shear, and negative if UE is anti parallel with E, indicating a negative surface charge density at the plane of shear. In the case of electrophoresis, the only force on the charged particle is the electric force: dP =0 f(x) = p(x)E dz and Eq. 3.34 reduces to U
f
[b
Jd
p(x)dxdy =
e D(
I[b
~ E Jd p(x)dxdy
or, after cancelling the integral from both sides,
U = 6 oD(E T1
(3.36)
THE SURFACE CHEMISTRY OF SOilS
98
Finally, note that U =  U E because U is the velocity of the liquid phase relative to the particle and that Eqs. 3.35 and 3.36 then lead to the result eoD( u = 
(3.37)
TJ
The sign of u is determined by that of the zeta potential, which in turn depends on that of the surface charge density at the plane of shear. Equation 3.37 depends in an essential way on the stipulation that l/J(x) (and () are solutions of the Poisson equation (Eq. 3.26). It does not require that l/J(x) be a solution of the PoissonBoltzmann equation. If that condition is also imposed, then standard DDL theory may be apj21ied to relate the • surface charge densi~!.~~I::J'l~_~.2~~~ar to (: 19 .. 
_._:;~~ {ZEoDRT+ c,[eXP(~~~/R1) 
!Jr
(3.38)
where sgn«()
+1
= { 1
if if
c> 0 « 0
n
and the other symbols (except have the same meaning as in Eq. 1.11. If it is further assumed that the plane of shear is located at the outer periphery of the outermost surface complexes on the soil particle, then a, = aD and Eq. 3.38 becomes: aD
/ f
= sgn«() {2e oDRT ~cj[exp(ZjFURT)  1]
2
(3.39)
The sum in Eq. 3.39 is over all charged species (with valence ZJ in the mobile liquid phase. Equations 3.37 and 3.39 are the principal electrophoretic expressions applied to soil clay particles. Clearly, Eq. 3.37 is dependent on fewer assumptions concerning the structure of the interfacial region near a soil particle than is Eq. 3.39. However, the present consensus/" is that the use of DDL theory to derive Eq. 3.39 is a valid step for 1(' < 0.1 V and electrolyte concentrations below about 10 molom 3 • A sufficient theoretical basis for die use of electrophoresis to measure the PZC, as discussed in Sec. 3.2, can be developed with Eq. 3.37 and the single assumption that the plane of shear coincides with the periphery of the surface complexes on a soil particle. Under this assumption, the vanishing of aD at the PZC (Table 3.1) implies that the surface charge density on the plane of shear vanishes as well. This condition and its consequence, p(x) = 0, then must also obtain on any plane beyond the plane of shear out into the mobile liquid phase, but Eqs. 1.13 and 3.26 applied to these planes lead to the conclusion that the inner potential, l/J(x), is equal to a constant everywhere in the mobile liquid phase. This constant may be set equal to zero, from which it follows that, = 0 and that u in Eq. 3.37 vanishes at the PZC, as illustrated in Fig. 3.1. Thus it is not
THE ELECTRIFIED INTERFACE IN SOILS
99
necessary to use DDL theory to establish a general relation between the electrophoretic mobility and the PZC. However, an unverifiable assumption about position of the electrokinetic plane of shear must be made. This assumption of congruence between the plane of shear and the periphery of a soil particle has also played a critical role in the quantitative assessment of the degree of surface complexation by montmorillonite.j" Table 3.5 lists representative measured values of the electrophoretic mobility of Namontmorillonite particles suspended in 10 4 M NaCI near pH 6. The compiled data, which show variation over a factor of 2, may be compared with u = 2.5 ± 0.5 x 10 8 m2s 1VI, the value observed in Namontmorillonite suspensions free of background electrolyte.F Evidently, differences in clay mineral preparation and experimental procedure account for this variability. Regardless of which value of u is accepted in the range of available data, the use of Eq. 3.39 to interpret the electrophoretic mobility yields an estimate of 0'0 that lies between 1 and 2 per cent of the absolute value of (Tin for Namontmorillonite.P Therefore, if the plane of shear is indeed at the periphery of the Namontmorillonite particle and DDL theory applies to the electrolyte in the mobile liquid phase, it can be concluded from available electrophoretic mobility measurements that about 98 per cent of the Na + cations on the clay particle are bound into surface complexes. This conclusion is in significant contradiction with the estimate of 23 per cent made in Sec. 1.4 from the results of negative adsorption experiments on 0 anions in Namontmorillonite suspensions. Since Namontmorillonite suspensions in 10 4 M NaCI do not coagulate (Sec. 6.2), the clay particles studied in the electrophoresis experiments should not have been quasicrystals or other kinds of aggregate unit. Therefore, it appears that the high estimate of degree of surface complexation is the result of assuming that the plane of shear and the periphery of the clay particle coincide. If the plane of shear in fact encloses a number of layers of immobile water beyond the periphery of the clay particle, then (TD is underestimated by Eq. 3.39 and the discrepancy can be explained. It is very important to note here that DDL theory can give no information about the location of the clay particle surface because it cannot be applied unambiguously to the region enclosed by the the plane of shear. For example, if it is assumed that any surface complexes on Namontmorillonite occupy only the surface plane in DDL theory (i.e., Table 3.5. Some measured values of u for Namontmorillonite suspended in 10 4 M NaCl at pH values near 621
Source
Measurements
Ravina and Zaslavasky Callaghan and Ottewill
12 30
Low
34
2.2 ± 0.3 3.1 ± 0.2 4.4 ± 0.5
THE SURFACE CHEMISTRY OF SOilS
100
x = 0 in relation to Fig. 3.3), then it is a straightforward matter to show that, at 298 K in a 0.1 mol· m 3 NaCl solution.v'
Iu,1
=
0~04
(3.40)
c
where 5, is the distance, in nanometers, between the particle surface and is in coulombs per square meter. If the plane of shear and 3 = 0.02Uin = 2 X 10 C·m 2 for Namontmorillonite (Eq. 1.22), then it follows from Eq. 3.40 that 5, = 20 nm. Thus DDL theory predicts that the plane of shear is more than sixty molecular diameters away from the plane in which up resides. On the other hand, if it is assumed that = UD, then DDL theory cannot be applied consistently in the region o < x <: d in Fig. 3.3 and Eq. 3.40 is invalidated. Equation 3.37 can be applied to surface complexes on Camontmorillonite without making an assumption about the location of the plane of shear. 24 The data graphed in Fig. 3.4 indicate that the absolute value of the electrophoretic mobility of montmorillonite particles suspended in distilled water decreases as the clay is converted from the sodium form to the calcium form. This decrease does not commence until about 65 per cent of the intrinsic surface charge on the clay is balanced by Ca 2 + cations; thereafter, the decrease is quite rapid. When the charge fraction of Ca 2 + on the clay is near 0.7, it is known that outersphere surface complex formation between Ca 2 + and the siloxane ditrigonal cavity (Fig. 1.8) produces quasicrystals containing several crystallites of unitcell thickness stacked along the direction of the crystallographic c axis. The Na + cations that remain on the clay are relegated to the external surfaces of the quasicrystals, and it is these external surfaces whose charge densities determine the electrophoretic mobility. Figure 3.4 indicates that, as Na + is
u,
u,
u,
Figure 3.4. The electrophoretic mobility of montmorillonite as a function of the charge fraction of exchangeable calcium on the clay. 22
o
WYOMING BENTONITE 0.1% (w/v) SUSPENSION BARON ET AL. (1970)
•
I
> I
1.0
(\J
E
•
CXl
o
2.0
 3.0
•I o
•
•
I..._ _
0.2~
•
•
"_"""~
O.~O
0.7~
1.0
CHARGE FRACTION OF CALCIUM ON CLAY
THE ELECTRIFIED INTERFACE IN SOILS
101
replaced by Ca 2 + on the external surfaces of the quasicrystals, the absolute value of u decreases rapidly. This decrease is consistent with a decrease in induced by enhanced surface complexation of Ca 2 + relative to Na + on the clay. The fact that the value of u for Namontmorillonite is essentially unaffected by an increase in NaCI concentration from zero to 0.1 mol.m"? whereas the value of lui for Camontmorillonite drops by 30 per cent over the same increase in concentration of charge" offers further, indirect experimental support for this interpretation in terms of surface complexation. Additional indirect evidence that the extent of surface complexation on Namontmorillonite is less than on Camontmorillonite is provided by the observations of an increase in the electrophoretic mobility of the Naclay after cation exchange with proteins and of no change in the mobility of the Caclay under the same circumstances.P Evidently, exchangeable proteins can compete effectively with adsorbed Na + to form complexes that screen the siloxane surface charge well and thereby increase a,. These proteins are less able to displace adsorbed Ca2+, and their surface complexes produce values of that are the same as those of the pure Camontmorillonite.
a,
a,
Electroosmosis is the response of an electrolyte solution near an electrified interface to an applied constant electrk..fid<1. 16.t B In electroosmosis, only the liquid phase is free to move (e.g., through a capillary tube or the interstitial space in a plug of soil clay). The force on the electrolyte ions is the electric force, f(x) = p(x)E, and Eq. 3.34 reduces to ELECTROOSMOSIS AND THE STREAMING POTENTIAL.
UE O
fI
b
d
p(x)dxdy
=
eoD(E fIb T/
d
p(x)dxdy
or, with cancellation of the integral factor, UEO
eoD(E
= _.::..::.
(3.41)
T/
where U == UE O is the electroosmotic velocity of the mobile liquid phase. Equation 3.41 predicts that the mobile portion of an electrolyte solution near a stationary electrified interface moves either parallel or antiparallel with the direction of an applied electric field E, depending on the sign of the zeta potential. If the surface charge on the electrokinetic plane of shear is negative, ( < 0 and the electrolyte solution moves in the same direction as E. Mechanistically speaking, UE O is parallel with E in this case because there is a net excess of positive ionic charge in the mobile liquid phase. After the electric field is applied and steadystate motion commences, the excess cations and the liquid they drag along with them must be pushed in the same direction as the applied field. 18 If the surface charge is positive, ( > 0 and UE O is antiparallel with E because a net excess of negative ionic charge exists in the mobile liquid phase. Although in either case UE O refers strictly to a point in the mobile liquid phase far removed from the plane of
a,
102
THE SURFACE CHEMISTRY OF SOilS
shear, the assumption of a rapid approach of Vl(X) to its limiting value, used in the derivation of Eq. 3.34, suggests that almost all of the mobile liquid phase has the velocity UE O under steadystate conditions. For this reason, it is common to equate UE O with the volumetric liquid flux density (volume of liquid transported through unit crosssectional area per unit time) measured in response to an applied electric field. 16 The streaming potential is an electric potential difference induced by the response of an electrolyte solution near an electrified interface to an ~pplied uniform pressure gradient. 16,18 As in electroosmosis, only the liquid phase moves in response to the pressure gradient. The convection current, I, established through this liquid motion can be deduced from Eq. 3.32 in the special case where [(x) = 0, dP/dz = constant: I
AeoD( dP
Tf
(3.42a)
dz
where A is the crosssectional area of the mobile liquid phase perpendicular to the direction of the current. The streaming potential gradient induced by I when it is not shunted is defined by the equation (without the usual minus sign because the liquid phase is moving) I
= AK dVst
(3.42b)
dz
where K is the conductivity of the medium (bulk liquid phase and interfacial region) through which I flows. Equations 3.42 lead to an expression for the streaming potential, .i V st : eoD
(3.43)
.iVst = KTf (.iP
which states that an applied pressure difference .iP induces an electric potential difference .iV st whose sign depends on that of the zeta potential. !? terms of mechanism, this pQtj:mtia) djfference arises because the,..ljg,Wd motion caused by the pressure difference separates the excess charge in the !!!..C?bile liquid phase from the surface charge it balances on the plane of shear. If this surface charge is negative, and a positive potential gradient is induced by a negative pressure gradient. Stated another way, the electric field corresponding to the streaming potential gradient, Est = dVst/dz, is parallel with the pressure gradient if (is negative and antiparallel if ( is positive. There is an essential physical symmetry between electroosmosis and the streaming potential in that, for both phenomena, an applied force causes the mobile portion of a liquid phase near a stationary, electrified interface to flow. In electroosmosis, an applied electric force causes the mobile liquid phase to move with the velocity UE O ' given in Eq. 3.41. The corresponding volume flow is 0  VEoA, where A is as defined in Eq, 3.42a. After multiplying both sides of Eq. 3.41 by A and comparing
«
°
THE ELECTRIFIED INTERFACE IN SOILS
103
the result with Eq. 3.42, one can derive the symmetric relationship
r; Q _.::..:..=dl'[tiz
(3.44)
E
where 1st ==  AKdVstldz is the streaming current. Equation 3.44 is the result of applying the Poisson equation and the NavierStokes equation to an aqueous electrolyte solution near an electrified interface. However, the same expression can be derived without these model equations through an application of the Onsager reciprocal relation in the context of the thermodynamics of irreversible processes.l? Thus, Eq. 3.44 describes a fundamental physical characteristic of electrokinetic phenomena: the reciprocity of the ratio of the response to the driving force . .In soils, precise measurements of electroosmotic flows and streaming potentials are difficult to make, but the available data/" suggest that IVEolEI = 10 8 m2s IV1, which agrees wi ical values of the electrophoretic mobilities of soil clay particles, and t 1.11 Vstll aP is of the 7 order of a few millivolts per bar (= 10 V, Pa 1). Sin e a typical value of K is Eq. 3.43 is around 0.1 C'm 1s 1V 1 r moist soils,26 1 1V 1 7 2N1sKlaVstl/aP = 10 C'mx 10 V'm = 10 8 m2s 1V 1 (lC = Nvm VI). This approximate result shows that Eq. 3.44 is satisfied in the form KiaVstl IVEol aP E (3.45) which can be deduced from Eqs. 3.41 and 3.43. Electroosmosis and the streaming potential play an important role in the response of a soil clay layer saturated with an electrolyte solution to an imposed gradient in the concentration of the electrolyte." Since an electrified clayaqueous solution interface is present, both the concentration and the mobility of the electrolyte cation in the clay material differ from those of the electrolyte anion. When the concentration gradient is imposed, these differences between the two kinds of ion produce different ion fluxes through the clay layer. The different fluxes in turn contribute to an electric potential difference across the clay.28 One effect of the induced electric potential difference is electroosmotic flow. However, if no liquid flow across the clay layer is permitted, there develops a pressure gradient that opposes electroosmosis. This induced pressure gradient contributes to a streaming current through the clay. If no electric current through the clay layer is permitted either, then the applied concentration gradient determines the induced gradients of electric potential and pressure uniquely as the solutions of the simultaneous linear equations/" dP dz
o=
L
o=
LEY 
y
dP dz
+
dC L YD dz
+ LED
+
dC dz

dV LYE dz
+ LE
dV dz

104
THE SURFACE CHEMISTRY OF SOILS
where the L coefficients are constant parameters that characterize the soil clayelectrolyte solution mixture and C is the electrolyte concentration. The first equation describes the flow of water through the clay layer, and the second describes the electric current through the clay. The coefficient LYE is equivalent to the coefficient of E in Eq. 3.41; the coefficient LEY is equivalent to the coefficient of A df/dz in Eq. 3.42a. The equality LYE = LYE is another way of expressing the reciprocity in Eq. 3.45. When a soil particle bearing an electrified interface settles in an aqueous solution under the force of gravity, a plane of shear develops around the particle just as it does in electrophoresis. As the particle settles, the portion of the interfacial region enclosed by the plane of shear moves with it but the remainder is left behind, and this separation of interfacial charge gives rise to an e ctric potential difference called the sedimentation potential. For a suspension 0 soil particles that do dot interact with one another (i.e., that settle independently), the force per unit volume acting on the particles is THE SEDIMENTATION POTENTIAL.
[(x) = cPdpg
(3.46)
where cP is the volume fraction of particles in the suspension, dp is the difference in mass density between a particle and the surrounding liquid phase, and g is the gravitational acceleration. Equation 3.46 may be substituted into Eq. 3.32 (with dP/dz = 0 and neglect of «/I(x)/,) to derive an expression for the convection current produced by sedimentation:
1=
soD
,AcPdpg
(3.47)
T/
A definition exactly analogous to Eq. 3.42b can be given for the gradient of the sedimentation potential, with the result that Eq. 3.47 is transformed to the expression (3.48) (In this case, a minus sign is included in the relation between I and dVsed / dz because it is the liquid phase that does not move. Therefore, no minus sign appears in Eq. 3.48.) Equation 3.48 predicts that the gradient of sedimentation potential has the same sign as , and is proportional to cPo These predictions have been verified experimentally for a variety of colloids.i" but apparently no study has been done on soil clay particles. It may be noted in passing that Eq. 3.48 applies equally to particles undergoing centrifugation if g is replaced by the centrifugal acceleration. Since centrifugal accelerations acheived in laboratory studies of ion adsorption phenomena on soil clays often are tens of thousands of times larger than g, the gradients of Vied generated can be very large. It is possible that these potential gradients and the concomitant shearing away of part of the ion
THE ELECTRIFIED INTERFACE IN SOILS
105
swarm can significantly alter the ion distribution in the interfacial region. If this disruption occurs, centrifugation may introduce an artifact into the measurement of ion adsorption. Several general aspects of electrokinetic phenomena, as summarized in Eqs. 3.36, 3.41, 3.43, and 3.48, should be emphasized at this juncture. First, since ( is an inner potential, it cannot be measured directly. It can only be inferred from electrokinetic data through modeldependent equations. The fact that values of ( calculated from the results of different electrokinetic experiments on the same interface are in agreemenr'" does not demonstrate an objective existence of the zeta potential because all the experiments are described by the same general equation (Eq. 3.34). Second, electrokinetic data can be given molecular significance through the zeta potential simply by assuming the existence of a plane of shear and the applicability of the Poisson and NavierStokes equations. Diffuse double layer theory is not required. Therefore, electrokinetic data offer no direct experimental support for the DDL assumptions. Even the assumption that a definite plane of shear exists can be modified. Consider, for example, electroosmosis. This phenomenon is the result of an applied electric force balanced by the viscous force under steadystate conditions (Eq. 3.28): p(x)E
d (T/ dVl) + dx dx = 0
(3.49a)
With the help of Eq. 3.26 this expression takes the form
E~(eoD:) = ~ (T/~l)
(3.49b)
A single integration of both sides of this equation and the evaluation of the constant of integration with the help of Eqs. 3.27 and 3.29b give the differential equation
dl/J EeoD/ dx This expression can be divided by
=
de, T/dx
T/ on both sides and then
UEo =  eoE
(3.49c) integrated:
{D
I T/ o
 dl/J
(3.49d)
where the boundary conditions in Eqs. 3.27 and 3.29 (with U = UE O ) have been noted again. Equation 3.49d is a generalization of Eq. 3.41 to permit D and T/ to be functions of the potential l/J (or of the coordinate x). The observed electroosmotic velocity, UE O , thus depends on the variability of both the dielectric and the viscosity properties of the liquid phase. The possibility that UE O results only from continuously variable D and 71, without the existence of a plane of shear, is consistent with Eq, 3.49d':~o
~

106
THE SURFACE CHEMISTRY OF SOilS
This conclusion, which can be extended to the other electrokinetic phenomena considered in this section, illustrates the tenuous nature of any assumption concerning the exact location of the plane of shear. Any position of the plane at x = d in Fig. 3.3 is, in principle, consistent with the results of an electrokinetic experiment. Finally, it should be evident that the principal utility of electrokinetic data is qualitative and comparative. The demonstration that an electrokinetic phenomenon exists is a demonstration that an electrified interface ~ exists. This broad implication is conclusive. In a quantitative sense, however, measurements of electrokinetic phenomena on the same kind of interface under different conditions have only a comparative value. Changes in the zeta potential as the composition of the interfacial region is varied through adsorption can be a useful guide to molecular interpretation even though' itself has little objective significance. 3.5. NEGATIVE ADSORPTION
The general mechanism of negative ion adsorption is described in Sec. 1.4, where the relevance of this phenomenon to the measurement of specific surface area is discussed. The prototypical experiment for observing negative adsorption involves the effect of a suspended soil clay on the concentration of an ion whose valence has the same sign as that of the charge on the soil clay particles, O"p (Eq. 3.2). If O"p is not zero, the concentration of the coion is larger in a supernatant solution in contact with an equal volume of suspension of the solid than it was before the solid was suspended. This strictly macroscopic phenomenon can be characterized quantitatively through the definition of the relative surface excess of an ion i in a suspension: (3.50)
where n, is total moles of ion i in the suspension per unit mass of solid, Mw is total kilograms of water in the suspension per unit mass of solid, m, is the molality of ion i in the supernatant solution, and S is the specific surface area of the suspended solid. Thus rf w ) is the excess moles of the ion (per unit area of suspended solid) relative to an aqueous solution containing M w kilograms of water and the ion at molality m.. The chemical foundation of the definition of the relative surface excess is examined in Sec. 4.1. For the present discussion, it is sufficient to note that r}w) can be positive, zero, or negative, in principle, and that the condition (3.51)
is a formal, macroscopic definition of negative adsorption for any ion i. As a numerical example, suppose that a soil clay with a specific surface area of 2 x 104 m2kg 1 is suspended in a solution of NaCi following the prototypical twochamber experiment described in Sec. 1.4. The chamber
THE ELECTRIFIED INTERFACE IN SOILS
107
containing the soil clay suspension is found to hold 0.6 kilogram of water and 2.8 millimoles of CI per kilogram of clay. The supernatant solution in contact with the suspension through a membrane permeable to water and ions is 0.007 molal in chloride. Therefore, according to Eq. 3.50, (w) _ 
r Cl
0.0028  (0.6 x 0.007) 2
X
104
2
molrn
=  7 X 10 8 molm F
and the chloride ion is said to be negatively adsorbed by the soil clay. It must be emphasized that the definition of negative adsorption epitomized by Eqs. 3.50 and 3.51 is strictly macroscopic and does not depend in any way on the concepts of DDL theory applied in Sec. 1.4. If a DDL theory interpretation of Eq. 3.50 is desired, it can be developed through the definitions" n, == ( ci(x)d 3x/m s
Jsu
u; ==
Pw (
Jsu
d 3x / m s
(3.52a) (3.53b)
where Ci(X) is the concentration (moles per unit volume) of ion i in the aqueous solution portion of a suspension containing m; kilograms of soil clay, Pw is the mass density of water in the suspension, and the integrals extend over the entire suspension volume. Under the assumption that Pwmi = Ci'" (the concentration of ion i in the supernatant solution), Eqs. 3.50 and 3.52 can be combined to produce
r~w) =
Sl ( [c;(x)  ci",]d 3x m; Jsu
(3.53)
Equation 3.53 provides a molecularlevel interpretation of Eq. 3.50. The exclusion volume, introduced in Eq. 1.9, is related to Eq. 3.53 through the macroscopic definition = Vex

sr(w)/c i ioo
(3.54)
Equation 3.54 can be interpreted on the molecular level with the help of Eq.3.53: (3.55) In conventional DDL theory applied to an electrolyte solution bathing solid particles with planar surfaces, Eq. 3.55 simplifies to VC K = SE
L'" [1  c~~:)] dx
(3.56)
THE SURFACE CHEMISTRY OF SOilS
108
where x = 8 defines the plane where the ion swarm is in contact with solid particle and SE is the surface area of this plane divided by m.. Equation 3.56 can be developed further in DDL theory as indicated following Eq. 1.10. None of this development is necessary to the experimental description of negative adsorption, of course. That description depends only on Eqs. 3.50 and 3.51. As with electrokinetic phenomena, the existence of negative adsorption implies the existence of an electrified interface. The behavior of this interface toward charged particles can always be investigated with the help of a particular molecular model, such as DDL theory, but it is useful to see how much information can be obtained without a detailed model, in keeping wih the spirit of the previous sections in this chapter. Consider, for example, the application of thermodynamics to the prototypical twochamber.experiment on negative adsorption. If the very small osmotic pressure created by the suspended soil clay is neglected, the activity of any electrolyte in the two chambers is the same in both the suspension and the supernatant solution: 14 (MaLb)su = (MaLb)so
(3.57)
where MaLb(aq) is the electrolyte (M = metal; L = ligand) and the su and so have the same meanings as in Eq. 3.18b. Both of the electrolyte activities in Eq. 3.57 can be measured electrochemically without making unverifiable extrathermodynamic assumptions.I' Thus both activities are welldefined macroscopic quantities. They can be partitioned further with the use of mean ionic activity coefficients: 14 (3.58) where y± is a mean ionic activity coefficient and m«
==
(mM mt)1/(a+b)
(3.59)
and mi. being the total molalities of the metal M and ligand L. Equation 3.58 is an exact result in thermodynamics, but it cannot be used to characterize negative adsorption without making some kind of assumption as to the nature of m";:. Suppose that M = Na, a = 1, L = CI, and b = 1 in Eq. 3.57. Suppose further that both Na + and Cl" are dissociated fully from the soil clay particles in the suspension and that the only important contribution to up is a negative uo, the surface density of structural charge. These conditions apply reasonably well to a suspension of montmorillonite clay particles in a dilute solution of NaCl at pH 7.0.32 In this case, it is possible to write the following relationship between m~a and mel: mM
su mNa
=
su mCi 
uoSm s FM
(
36Oa)
w
where uoS/ F represents the cation exchange capacity of the soil clay particles. In the suspension, it is possible that the contributions of Na of and
THE ELECTRIFIED INTERFACE IN SOILS
Cl" to
'Y~u
109
are compensating in such a way that (3.60b)
Equation 3.60b is a model assumption that can be verified experimentally given Eqs. 3.58, 3.59, and 3.60a. For the present discussion, Eq. 3.60 will be taken to constitute what may be termed the Babcock model of the suspension. 33 The equilibrium condition Eq. 3.58 applied to the Babcock model yields the expression mSu mSu Cl ( Cl

uosms) = m 2 FMw
(3.61)
where m = m~ is the mean ionic molality of NaCl in the supernatant solution. The negative adsorption of Cl" by the soil clay is given by Eq.3.50:
r CI(w)
_ 
Mw(m~
 m)
'''':':'''_'
Sm;
(3.62)
For convenience, the definitions (w ) 11m == S msr Cl
Q==
Mw
uoSm s FMw
(3.63)
can be introduced into Eq. 3.61 to give an equation for 11m:
(11m + m)(l1m + m + Q) = m 2 The solution of this quadratic equation is
.::1m
=
em + tQ) + ctQ 2 + m 2)1 / 2
(3.64)
where the positive square root is chosen because 11m must vanish with both m and Q. Eq. 3.64 shows that, as m increases, 11m decreases from 0 to the asymptotic value tQ = uoSmsl2FMw . The asymptotic result can be derived by writing (tQ2 + m 2)1 /2 = m[1 + (Q/2mf]1 / 2 in Eq. 3.64 and noting that this term approaches m as m becomes arbitrarily large. Therefore, lim mtoo
rCl(w) =
Mw lim 11m = Smsmt oo
(3.65)
according to the Babcock model. The chemical significance of Eq. 3.65 can be understood after Eq. 350 is applied to Na" to derive the expression r(w)
Na
= Mw
(m~a  m) Sm
•
(3.66)
THE SURFACE CHEMISTRY OF SOilS
110
It follows from Eqs. 3.60a, 3.62, and 3.66 that r(w) _ Na
r(w) CI
(T = __ 0
F
(3.67)
in the Babcock model. The (positive) adsorption of Na + minus the (negative) adsorption of CI must always equal minus the surface charge density of the soil clay expressed in moles per square meter. Equation 3.65 shows that, according to the model, the lowest possible value of r~'r) is half the surface charge density of the soil clay. Therefore, by Eq. 3.67, the corresponding smallest possible value of r~l is minus half the surface charge density of the clay. Under these conditions, half the cation exchange of the clay is satisfied by the positive adsorption of Na + and half is satisfied by the negative adsorption of CI. As the electrolyte concentration decreases, less and less of the surface charge is neutralized by a deficit of chloride anions.
NOTES 1. G. Sposito, The operational definition of the zero point of charge in soils, Soil Sci. Soc. Am. J. 45: 292 (1981). 2. These kinds of experiments are described in A. M. James, Electrophoresis of particles in suspension, Surface and Colloid Science 11:121 (1979). 3. Speciation models for aqueous solutions are discussed in Chap. 3 of G. Sposito, The Thermodynamics of Soil Solutions. Clarendon Press, Oxford, 1981. 4. See, e.g., D. H. Everett, Manual of Symbols and Terminology for Physicochemical Quantities and Units. Appendix II: Definitions, Terminology and Symbols in Colloid and Surface Chemistry. Butterworths, London, 1972. When the PZC is measured by an electrokinetic experiment (Sec. 3.4), it is often termed an isoelectric point (IEP). However, other definitions of the IEP are used in the soil chemistry literature. 1 5. See, e.g., Chap. 6 in R. J. Hunter, Zeta Potential in Colloid Science. Academic Press, London, 1981. 6. Methods for measuring the PZSE and the PZNC in soils are discussed in Chap. 6 of G. Uehara and G. Gillman, The Mineralogy, Chemistry, and Physics of Tropical Soils with Variable Charge Clays. Westview Press, Boulder, Colo., 1981. 7. Sources of data: c.P. Huang and W. Stumm, Specific adsorption of cations on hydrous yAl z0 3 , J. Colloid Interface Sci. 43:409 (1973). B. BarYosef, A. M. Posner, and J. P. Quirk, Zinc adsorption and diffusion in goethite pastes, J. Soil Sci. 26: 1 (1975). L. C Bell, A. M. Posner, and J. P. Quirk, The point of zero charge of hydroxyapatite and fluorapatite in aqueous solutions, J. Colloid Interface Sci. 42: 250 (1973). A. P. Ferris and W. B. Jepson, The exchange capacities of kaolinite and the preparation of homoionic clays, J. Colloid Interface Sci. 51:245 (1975). 8. S. S. Wann and G. Uehara, Surface charge manipulation of constant surface potential soil colloids. I: Relation to sorbed phosphorus, Soil Sci. Soc. Am. J. 42:~6~ (1978).
THE ELECTRIFIED INTERFACE IN SOILS
111
9. This point is discussed in the context of doublelayer theory in M.A.F. Pyman, J. W. Bowden, and A. M. Posner, The movement of titration curves in the presence of specific adsorption, Aust. J. Soil Res. 17: 191 (1979). 10. E. Tessens and S. Zauyah, Positive permanent charge in Oxisols, Soil Sci. Soc. Am. J. 46: 1103 (1982). Equation 3.13 was derived in the context of DDL theory in G. Uehara and G. P. Gillman, Charge characteristics of soils with variable and permanent charge minerals. I: Theory. II: Experimental, Soil Sci. Soc. Am. J. 44: 250 (1980). 11. M.A.F. Pyman, J. W. Bowden, and A. M. Posner, The point of zero charge of amorphous coprecipitates of silica with hydrous aluminum or ferric hydroxide, Clay Minerals 14:87 (1979). 12. The clearest introduction to the electrochemical potential is given by its creator in Chap. 8 of E. A. Guggenheim, Thermodynamics (NorthHolland, Amsterdam, 1967). Applications to soil solutions are reviewed in Chap. 4 of G. Sposito, op. cit? The issue of electric potentials near interfaces is discussed in detail in R. Parsons, Equilibrium properties of electrified interphases, Modern Aspects of Electrochemistry 1: 103 (1954). 13. R. Parsons, Manual of symbols and terminology for physicochemical quantities and units. Appendix III: Electrochemical nomenclature, Pure Appl. Chem. 37: 500 (1974). 14. For a discussion of these thermodynamic parameters, see Chaps. 1 and 2 in G. Sposito, op. cit.3 15. The DDL theory is discussed critically in J.T.G. Overbeek, Electrochemistry of the double layer, in Colloid Science (H. R. Kruyt, ed.), Vol. I. Elsevier, Amsterdam, 1952. 16. The most thorough modern introduction to the physical basis of electrokinetic phenomena is given in Chap. 3 of R. J. Hunter, op. cit? See also J.T.G.Overbeek. 18 17. P. H. Groenevelt and G. H. Bolt, Nonequilibrium thermodynamics of the soilwater system, J. Hydrol. 7: 358 (1969). 18. These conditions are discussed carefully in J.T.G. Overbeek, Electrokinetic phenomena, in Colloid Science (H. R. Kruyt, ed.), Vol. I. Elsevier, Amsterdam, 1952. 19. See, e.g., D. C. Grahame, Diffuse double layer theory for electrolytes of unsymmetrical valence types, J. Chem. Phys. 21: 1054 (1953). 20. G. R. Wiese, R. O. James, D. E. Yates, and T. W. Healy, Electrochemistry of the colloidwater interface, in Electrochemistry (J. O'M. Bockris, ed.), Butterworths, London, 1976. 21. I. Ravina and D. Zaslavsky, Nonlinear electrokinetic phenomena. Part II: Experiments with electrophoresis of clay particles. Soil Sci. 106:94 (1968). I. C. Callaghan and R. H. Ottewill, Interparticle forces in montmorillonite gels, Faraday Disc. Chem. Soc. 57: 110 (1974). P. F. Low, The swelling of clay. III: Dissociation of exchangeable cations, Soil Sci. Soc. Am. J. 45: 1074 (1981). 22. P. BarOn, I. Shainberg, and I. Michaeli, Electrophoretic mobility of montmorillonite particles saturated with Na/Ca ions, J. Colloid Interface Sci. 33:471 (1970). R. D. Harter and G. Stotzky, Xray diffraction, electron microscopy, electrophoretic mobility, and pH of some stable smectiteprotein complexes, Soil Sci. Soc. Am. J. 37: 116 (1973). S. L. SwartzenAllen and E. Matijevi~. Colloid and surface properties of clay suspensions. II: Electrophoresisand cation adsorption of montmorillonite. J. Colloid Interface Sci. so: 143 (llJ75).
112
THE SURFACE CHEMISTRY OF SOilS
23. See, e.g., Chap. 1 in G. H. Bolt, Soil Chemistry. B: PhysicoChemical Models. Elsevier, Amsterdam, 1979. 24. See P. BarOn et al., op. cit.,22 and 1. Ravina and D. Zaslavski, op. cit.21 25. R. D. Harter and G. Stotzky, op. cit.22 26. 1. Ravina and D. Zaslavsky, Nonlinear electrokinetic phenomena. I: Review ofliterature, Soil Sci. 106: 60 (1968). See also Chap. 11 in G. H. Bolt, op. cit.23 27. D. E. Elrick, D. E. Smiles, N. Baumgartner, and P. H. Groenevelt, Coupling phenomena in saturated homoionic montmorillonite. I: Experimental, Soil Sci. Soc. Am. J. 40: 490 (1976). P. H. Groenevelt and D. E. Elrick, Coupling phenomena in saturated homoionic montmorillonite. II: Theoretical, Soil Sci. Soc. Am. J. 40: 820 (1976). P. H. Groenevelt D. E. Elrick, and T.J.M. Blom, Coupling phenomena in saturated homoionic montmorillonite. III: Analysis, Soil Sci. Soc. Am. J. 42: 671 (1978). See also W. D. Kemper, 1. Shainberg, and J. P. Quirk, Swelling pressures, electric potentials, and ion concentrations: Their role in hydraulic and osmotic flow through clays, Soil Sci. Soc. Am. J. 26: 229 (1972). 28. Contributions to the observed electric potential difference are also made from inherent differences in the measuring electrodes and, more important, from the Nernstian response of the electrodes to the imposed concentration difference. 29. See, e.g., Chap. 3 in J. T. Davies and E. K. Rideal, Interfacial Phenomena. Academic Press, New York, 1961. 30. The general question of the interpretation of ( is discussed at length in S. S. Dukhin and B. V. Derjaguin, Electrokinetic phenomena, Surface Colloid Sci. 7: 1 (1974). See especially pp. 2932 and 5355. 31. I. Shainberg and A. Caiserman, Electrochemical potential of NaCl in Namontmorillonite suspensions, Soil Sci. 104:410 (1967). See also Chap. 4 in ·3 · , op. cit. G . Sposito 32. For other clay minerals, UH contributes importantly to up and the positive adsorption of anions cannot be neglected. See, e.g., J. P. Quirk, Negative and positive adsorption of chloride by kaolinite, Nature 188: 253 (1960). 33. The model is described in detail by K. L. Babcock, Some characteristics of a model Donnan system, Soil Sci. 90: 245 (1960). FOR FURTHER READING
K. L. Babcock, Theory of the chemical properties of soil colloidal systems at equilibrium, Hilgardia 34: 417 (1963). Section II of this classic review describes the Babcock model of negative adsorption in great detail. G. H. Bolt, Soil Chemistry. B: PhysicoChemical Models. Elsevier, Amsterdam, 1979. Chapter 7 of this comprehensive textbook reviews negative anion adsorption experiments and their interpretation in DDL theory. R. J. Hunter, Zeta Potential in Colloid Science. Academic Press, London, 1981. This excellent monograph gives a thorough, modern introduction to all aspects of electrokinetic phenomena, both experimental and theoretical. H. R. Kruyt, Colloid Science. Elsevier, Amsterdam, 1952. Chapters IV and V in Vol. I, of this classic treatise, written by J.T.G. Overbeek, provide a thorough, highlevel introduction to the properties of the electrified interface discussed in the present chapter.
,:'
'\
,\
4 INORGANIC AND ORGANIC SOLUTE ADSORPTION IN SOILS
4.1. THE ADSORPTION ISOTHERM
Adsorption is the process through which a net accumulation of a substance occurs at the common boundary of two contiguous phases. I The study of adsorption in soils is characterized by three laboratory operations that define the net accumulation of a substance at the interface between solid soil particles and a contiguous fluid: (1) reaction of the soil with a fluid of prescribed composition for a prescribed period of time, (2) isolation of the soil from the reactant fluid phase, and (3) chemical analysis of the soil and/ or the reactant fluid phase. Step_1 ca!1 take place either with the fluig phase at rest relative to the soil particles ("batch process") or with the fluist phase in uI.!.iform motion relative to the soil particles ('1!2':.':..tl!!:.ou&.1l, erocess"). The reaction tIme should be long enough to permIt a close, approach to thermodynamic e uilibrium but short enough to prevent IOns. tep 2 is usually carried out in batch processes unwanted side ihrougll the applicatIon of centrifugal or gravitational force. It is understood that some of the reactant fluid phase is always entrained with the soil in this kind of separation.f The quantitative description of adsoption as a purely macrosc,?pic heno . . hrou h the conce t of relative su ace excess.I T,his quantity, denoted by the symbol r iI, is the number of excess moles of '!. su6stance i per unit area of adsorbing soil solids, determined re!~tiye !o a datum fluid phase that contains the same number of moles Of a reference substance j as are in the soil. The concentration of i in the datum fluid phase is the same aSfhat in the reactant fluid phase separated from the soil at the end of the adsorption experiment. In mathematical terms, rp) is defined by the equation •.
~._
. 0 .
.
•
reac
(4.1)
THE SURFACE CHEMISTRY OF SOilS
114
where n, and nj are the moles of i and j per unit mass of soil solids, Xi and Xj are the mole fractions of i and j in the reactant fluid phase after it has been separated from the soil, and S is the specific surface area of the soil solids. (The mole fraction of a substance in a solution is the ratio of moles of the substance in the solution to the total number of moles of all substances in the solution.) This definition of relative surface excess assumes that neither i nor j enters into the structure of the adsorbing soil solid phase. 1 Note that r~j) can be either positive or negative because it describes a net accumulation. Also note that there is no adsorption of i when the condition
n, Xi =nj Xj
(4.2)
is fulfilled. The role of reference substance j is evident on the basis of the fact that (4.3) By definition, there is no surface excess ofj. Thus r}j) is a surface excess of i referred to an interface at which no net accumulation of j occurs."
The natural choice for j in Eq. 4.1 is the substance having the largest concentration in the fluid phase from which a soil adsorbs the constituent i, provided there is no significant competition between i and j for adsorbing surface. If the reactant fluid phase is soil air, the reference substance should be nitrogen gas; if it is the soil solution, the reference substance should be liquid water. In the case of a soil adsorbing a vapor from air, it is expected that the number of moles of nitrogen gas in the interstitial space of the soil will be. negligible because of the low density of soil air. For example, a cubic centimeter of soil with a porosity of 0.5 contains only about 1.5 micromoles of (nonadsorbing) nitrogen gas but could contain 104 times as many moles of adsorbed water vapor. Thus nj in Eq. 4.1 can be neglected with no loss of accuracy, and the relative surface excess can be expressed by the equation I', "'" ni I
S
(4.4)
for any substance i adsorbed strongly by the soil particles. If nitrogen gas itself, or some other weakly adsorbing vapor, is to be adsorbed by the soil (e.g., to determine its specific surface area), then only that gas should be present in the soil interstitial space and Eq. 4.4 is still the expression to use to calculate the amount adsorbed since the number of moles of nonadsorbed gas in the soil will again be negligibly small. 1 In the case of a soil adsorbing a dissolved solute from an aqueous solution, Eq. 4.1 can be reduced to (4.5)
INORGANIC AND ORGANIC SOLUTE ADSORPTION IN SOILS
115
where M w is the mass of water in the soil per unit mass of soil solids (the gravimetric water content) and m; is the molality of the adsorbing substance i in the aqueous solution isolated from the soil after reaction. The product Mwmj can be represented accurately by (JcJ Pb, where (Jis the volumetric water content of the soil, Pb is its bulk density, and c, is the molarity of i in the isolated aqueous solution phase. If the adsorption reaction is initiated by immersing 1 kilogram of a soil into M T w kilograms of water containing i at molality m?, then the law of conservation of mass requires that
n, = m? M Tw

mj(M T w

Mw )
This condition can be introduced into Eq. 4.5 to derive the useful expression (4.6) where Sm, == m?  m, is the change in molality caused by adsorption. Equation 4.6 provides the theoretical basis for the common method of measuring the amount adsorbed through chemical analysis of the aqueous solution phase only. 2 Equation 4.5 represents the surface excess of substance i relative to an aqueous solution that contains M w kilograms of water plus substance i at molality m.. This surface excess is assigned to a surface at which there is no net accumulation ofwater. If water in the interstitial space is not adsorbed (in the sense defined in Chap. 2), then this surface can be taken as congruent with the geometric boundaries of the adsorbing soil particles. If some of the interstitial water is adsorbed, say, within the region bounded by a surface 1.0 nm from the boundary of a soil particle, then the surface of zero net accumulation of water could differ slightly from the soil particle surface. As a numerical example of the application of Eq. 4.5, consider a montmorillonitic soil with a gravimetric water content of 0.6 kg· kg 1 and from which 110 mmol of calcium per kilogram of soil has been extracted after a brief reaction with an aqueous solution whose final calcium molality was 5 x 10 3 m. The specific surface area of the soil is 180 m2g 1 . The relative surface excess of calcium in the soil is then w r () Ca
(0.11 mol· kgI)  (0.6 x 0.005) mol· kg ? (180 m gkg"")
= '   =',:='   ', =:.2g 1)(1000
= +0.594 JLmol·m 2
Frequently the value of qj == r}W) S is reported instead of the relative surface excess. In the present example, qCa = +0.107 mol· kg 1 is the positive excess moles of calcium per unit mass of soil. An example of the application of Eq. 4.5 to calculate the negative surface excess of chloride in a soil clay is given in Sec. 3.5.
116
THE SURFACE CHEMISTRY OF SOilS
It is ~IEp...2E.".pr~cti~~~~~ig!!~J..'Y~~.~ soil aQd an aqueous solution at a controlled temperature and applied pressure. T~ resulting adsorption data are either (r~w>,mi) or (qi,Ci) eairs that can be e!£!!~d against one another with eith~r r~w) or q i l!L1hsU!~J2~!"~~nt variabi'e:"This kind of graph is called an adsorption isotherm. Adsorption isotherms for many substances in soils have been determined over the past century since the pioneering work of the soil chemist J. M. van Bemmelen." Enough data for the case of positive adsorption are available to permit a broad classification of isotherms according to initial slope. 5 Illustrative examples of this classification system are shown in Fig. 4.1. The Scurve isotherm is characterized by an initial slope that increases with the concentration of a substance in the soil solution. This property suggests that the relative affinity of the soil solid phases for the substance at low concentration is less than the affinity of the soil solution. In the example of copper adsorption by the Altamont soil given in Fig. 4.1, it is believed that natural organic compounds in the soil solution form strong, non adsorbing complexes with the metal. After the complexing capacity of these compounds is exceeded through an increase in the amount of copper added to the soil solution, the solid particles in the soil gain in the competition and begin to adsorb copper ions. Thereafter the isotherm takes on its characteristic S shape. In some. instances, especially when organic compounds are being adsorbed, the Scurve isotherm is the result of cooperative interactions among the adsorbed molecules. These interactions (e.g., surface polymerization or stereochemical interactions) cause the adsorbate to become stabilized on a solid surface, and they produce an enhanced affinity of the surface for the adsorbate as its surface excess increases. The Lcurve isotherm is characterized by an initial slope that does not increase with the concentration of a substance in the soil solution. This property is the result of a high relative affinity of the soil solid phases for the substance at low concentrations coupled with a decreasing amount of adsorbing surface as the surface excess of the adsorbate incteases. The example of ophosphate adsorption in Fig. 4.1 illustrates a universal Lcurve feature: an isotherm that is concave to the concentration axis because of the combination of affinity and steric factors. The Hcurve isotherm is an extreme version ofthe Lcurve isotherm. Its characteristic large initial slope (in comparison with the Lcurve isotherm) suggests a very high relative affinity of the soil solid phases for an adsorbing substance. This condition is usually produced either by highly specific interactions between the solid phase and the adsorbing substance or by significant van der Waals interactions contributing to the adsorption process. The example of cadmium adsorption at very low concentrations by a kaolinitic soil shown in Fig. 4.1 illustrates an Hcurve isotherm caused by very specific interactions. Large organic molecules and inorganic polymers provide Hcurve isotherms resulting from van der Waals interactions.
INORGANIC AND ORGANIC SOLUTE ADSORPTION IN SOilS 5
117
L curve
Scurve
I
01
'"
I
"0 E E
01
'"
"0 E E
Anderson sandy cloy loom pH 6.2 25°C r = 0.02M.
Q.
0"
Altamont cloy loom pH 5.1 25°C r = O.OIM
::>
u
0"
00
CUT (rnrnol Hcurve 0.60
150
I
Ccurve
01
'"
"0 0.40
I
E E
"0
u
0"
01
Boomer loom pH 7.0 25°C
0
E
Il':l0.005M.
0.20
100
'"
::l..
~
0"
50
HarBarqan cloy parathion adsorption from hexane 50% RH hydration
0
0
0.05
0.10
0.15
0.20
0.25
Cdr (mmol m 3)
Figure 4.1. General classes of adsorption isotherms. S curve, data courtesy of C. S. LeVesque; L curve, data from I.C.R. Holford et a/.8 ; H curve, data from J. GarciaMirayagaya and A. L. Page, Sorption of trace quantities of cadmium by soils with different chemical and mineralogical composition Water, Air, and Soil Pollution 9: 289 (1978); C curve, data from B. Yaron and S. Saltzman, Influence of water and temperature on adsorption of parathion by soils Soil Sci. Soc. Am. J. 36:583 (1972).
The Ccurve isotherm is characterized by an initial slope that remains independent of the concentration of a substance in the soil solution until the maximum possible adsorption. This kind of isotherm can be produced either by a constant partitioning of a substance between the interfacial region and an external solution or by a proportional increase in the amount of adsorbing surface as the surface excess of an absorbate increases. The example of parathion (diethyl p nitrophenyl monothiophosphate) adsorption in Fig. 4.1 shows constant partitioning of this compound between hexane and the layers of water on a soil at 50 per cent relative humidity. The adsorption of amino acids by Camontmorillonite also exhibits a
40
THE SURFACE CHEMISTRY OF SOilS
118
Ccurve isotherm, this time because the adsorbate can penetrate the interlayer regions of quasicrystals, thereby creating new adsorbing surface for itself. 5 T~ Lcurve isotherm is by far the ~~~.ommonlyencountered in the literature of soil chemistry. The mathematical description of this isotherm almost invariably involves either the Langmuir equation or the '0n BemmelenFreundlich equation." The Langmuir efl,:"atio~.has the form q
=
bKc 1 + Kc
(4.7)
where band K are adjustable parameters. The parameter b represents the value of q that is approached asymptotically as c becomes arbitrarily large. The parameter K determines the magnitude of the initial slope of the isotherm. The most precise way to determine these two parameters with experimental data is to plot the ratio (4.8) known as the distribution coefficient, against the surface excess, q.' After multiplying both sides of Eq. 4.7 by 1/c + K and solving for K d , one finds that the Langmuir equation is equivalent to the linear expression Kd
=
bK  Kq
(4.9)
~ to s~ould be
+ "''' Thus a graph of K d ~ainst q a straight line with slope  K and an xintercept equal to b if the LanewJ,!ir ~QyatiQn is appli"able. An example of this kind of graph was presented in Fig. 1.12. Not uncommonly, it is observed that a graph of K d against q is a curve convex to the qaxis instead of a straight line. An example of this kind of graph is shown in Fig. 4.2 for phosphate adsorption by a clay loam soil. 8 If the value of K d tends to a finite constant as q tends to zero and if K d extrapolates to zero at some finite value of q , then the adsorption isotherm can always be fit to a twoterm series of Langmuir equations:" II
q
blKlc b + 2K2c 1 + Klc 1 + K 2c
(4.10)
where b l , b2 , Kl> and K 2 are adjustable parameters. This fact can be illustrated by setting c = q I K d in Eq. 4.10 and clearing the fractions on the right side to obtain the seconddegree equation K~
+ (K, + K 2)Kd q + K lK2q 2  (blK l + b 2K2)Kd

bKlK2 q
=0 (4.11)
where b = b l + b 2 • The derivative of K d with respect to q follows from Eq. 4.11:
ss,
=
dq
(K. + K 2)Kd + 2K.K 2 q  bK tK 2 2K.. + (K. + K 2)q  (b.K. + b 2K 2 )
(4.12)
119
INORGANIC AND ORGANIC SOLUTE ADSORPTION IN SOILS 1.0 (
~
P SORPTION WATTS SOIL t = 25 ± I·C
0.8
o
II>
C'
.><
<,
c:
0.6
o ..:;,
o II>
0.4
'"E "0
INTERCEPT = a~1 I a II
~ 0.2
D
D
SLOPE =fJO 1"'1
2
4
6
INTERCEPT=l3o
10
8
q (mmol PI kg soil)
Figure 4.2. A graph of the distribution coefficient against the amount adsorbed for ophosphate adsorption by a clay loam soil. 8 The parameters labeling the lines through the data points are defined in Eqs, 4.13 and 4.14.
As q tends to zero, Eqs. 4.11 and 4.12 show that K d = ao
+ (adao)q
(q ~ 0)
·"(4. 13a)
where ao = blK I + b 2K2
al =
(4.13b) (4. 13c)
(bIKi + b 2KD
Thus the distribution coefficient is linear in q near the origin, with a slope equal to al/aO' According to Eq. 4.13a, the x intercept of the linear expression is a5llall, as indicated in Fig. 4.2. On the other hand, when K d extrapolates to zero, q = b according to Eq. 4.11. Equation 4.12 can then be used to demonstrate that (q
t
b)
(4. 14a)
where
f30
= b = bl
+ b2
b l b2 {31 =  K1 K2
(4.14b) (4. 14c)
Thus the distribution coefficient again becomes linear in q as q tends to b, its maximum value according to Eq. 4.10. The slope of the line is {Jo/{3t, and its x intercept is, of course, b. If adsorption data are plotted as in
THE SURFACE CHEMISTRY OF SOILS
120
Fig. 4.2, then the limiting slopes and the two x intercepts can be determined graphically. The values found can be substituted into Eqs. 4.13b, 4.13c, 4.14b and 4.14c to solve uniquely for the Langmuir parameters b 1 , K 1 , b z, and K Z • 9 The van BemmelenFreundlich isothe!!!! equation ha.s the form q = Ac f3
(4.15)
where A and f3 are positive, adjustable parameters, with f3 constrained to lie between 0 and 1. This expression can be derived by generalizing Eq. 4.10 to an integral over a continuum of Langmuir equations.!" q =
f
OO
()
m y
00
exp(y)c dy 1 + exp(y)c
(4.16)
where y = In K and m(y) is the weighting factor for the Langmuir term in the integrand whose K parameter equals exp(y). This weighting factor is subject to the constraint b =
f~oo m(y)dy
(4.17)
where b is the maximum possible value of q, as before. As it is written, Eq. 4.16 is completely general and can be used to derive any isotherm equation by insertion of an appropriate choice for the weighting factor .10,11 For example, if m(y) is set equal to a sum of two delta "functions,"
m(y) = b 1 5(y  In Kd + b z5(y  In K z) where b 1 , K 1 , b z , and K z are constant parameters, then Eqs. 4.16 and 4.17 become the same as Eqs. 4.10 and 4.14b, respectively. (The defining relationship for the delta function,
f~oo f(x)5(x 
a)dx == f(a)
where a is a constant parameter, is used in the calculation.V) In order to derive the van BemmelenFreundlich equation, m(y) must take the form:
m(y)
=
2 Cos(7Tf3)exp[f3(Ym  y)] + 2 exp[f3(Ym  y)] mmax 1 + 2 Cos(7Tf3)exp[f3(Ym  y)] + exp[2f3(Ym  y)] (4.18)
where b mmax = 27T tan( 7Tf3/2) = m(Ym)
Ym =
In (A/b) f3
(4.19) (4.20)
INORGANIC AND ORGANIC SOLUTE ADSORPTION IN SOilS
121
Then it can be shown thatlO,ll q
=
Ac 13 1 + (A/b)c13
(0 < (3 < 1)
(4.21)
In the limit of (A/b)cl3~ 1, Eq. 4.21 reduces to Eq. 4.15. The weighting factor m (y ) is very similar to a gaussian function centered on Ym, as illustrated in Fig. 4.3. Thus the van BemmelenFreundlich isotherm can be thought of as the result of a lognormal distribution of Langmuir parameters K (i.e., a normal distribution of In K) in a soil. The parameter (3 determines the narrowness of this distribution, in thatlO,ll liml3t1 m(y) = b 8(y  Ym)
(4.22)
follows from letting {3 approach unity in Eq. 4.18. As shown in Fig. 4.3, the closer {3 is to zero, the broader is the distribution m (y ); the closer (3 is to unity, the more m(y) approaches the delta function centered on Ym' given in Eq. 4.22. In this limit, the introduction of the right side of Eq. 4.22 into Eq. 4.16 reduces Eq. 4.16 to Eq. 4.7, the Langmuir equation, since the distribution is now just an extremely sharppeaked spike at Ym = In(A/b) == In K. The weighting factor, m (y) in Eq. 4.18 can be calculated explicitly for any soil if A, b, and (3 have been determined experimentally from adsorption data. This estimation of parameters can be done by plotting log Figure 4.3. A graph of the distribution of In K values, m(y) (y = In K), that leads to the van BemmelenFreundlich isotherm: Each curve corresponds to the same value of Ym but to different values of ~ in Eq. 4.18. m(y)/b
{3 =0.9
I
/
" ,
x t
................ ". 'I
/
\
I
......................._....:.;;.;1 ....
{3 = 0.8
\
\
\
{305
....,.,.:.:::.:...:.......
_

'1 m
. +'1
122
THE SURFACE CHEMISTRY OF SOILS
q against log c for the range of concentrations over which Eq. 4.15 applies, in order c ulate log A and· {3 from the y intercept and slope of the resultin straigh ine. Then the variable q / c(3 is plotted against q to defermine the value f A / b according to the expression q/c(3 = A  (A/b)q
which is derived from Eq. 4.21 after both sides are multiplied by c (3 + (A / b) and the ratio q / c(3 is solved for. The x intercept for the linear plot equals the parameter b. These operations emphasize the point that the van BemmelenFreundlich equation applies strictly to adsorption data obtained for low values of c. 4.2. ADSORPTION VERSUS PRECIPITATION
Fundamental to the interpretation of a loss of some substance from a soil solution as an adsorption process is the hypothesis that the phenomenon involved actually occurs on a surface. Adsorption is defined in Sec. 4.1 as a net accumulation at an interface; precipitation can be defined as an accumulation of a substance to form a new bulk solid phase. Both of these concepts imply a loss of material from an aqueous solution phase, but one of them is inherently twodimensional and the other is inherently threedimensional. 13 However, the distinction between the two begins to blur after one realizes that the chemical bonds formed in both can be very similar, and that mixed precipitates can be inhomogeneous solids with one component restricted to a thin outer layer because of poor diffusion. In .. soils, the problem of differentiating adsorption from precipitation is made especially severe by the facts that new solid phases can precipitate homogeneously onto the surfaces of existing solid phases and that weathering solids may provide host surfaces for the more stable phases into which they transform chemically. These conditions serve as a caveat against the hasty application of Eq. 4.6 when only the loss of a substance from an aqueous solution phase has been measured. When no independent data on which to base a decision are available, this loss of material to the solid phases in a soil can be termed simply sorption in order to avoid the implication that either adsorption or precipitation is occurring. The natural question to pose at this juncture is, what experimental evidence is sufficient to determine whether a substance lost from the soil solution has, in fact, been adsorbed? An answer to this difficult and complex question can perhaps best be introduced by a discussion of experimental criteria that cannot be used to distinguish adsorption from precipitation in soils. This kind of discussion should be of help in any critical reading of the abundant literature on sorption studies, as well as in the design of experiments on surface phenomena in soils. The adherence of experimental sorption data to an adsorption Isotherm equation provides no evidence as to the actuaJ mechanism of a sorption process In a soli.
,
'I \, :1
j
!
, ,j, I
,I
INORGANIC AND ORGANIC SOLUTE ADSORPTION IN SOilS
123
~ent can be validated both through model experiments and with
rigorous mathematical analyses of the properties of adsorption isotherm equations.l" However, the point that these equations are not unique mathematical descriptions of surface reactions in soils can be made effectively by a simple counterexample. Consider a typical batch sorption experiment in which ophosphate is reacted with soil material and suppose that in this reaction an amorphous aluminum phosphate phase is formed.P It will be assumed that the conditional solubility product )
applies to the amorphous solid phase, where AIT and P0 4T are the total molar concentrations of aluminum and ophosphate in the soil solution. If n AI is the total number of moles of aluminum in the soil available to react with added ophosphate, then it is reasonable to expect that the following inequality holds: (4.23) where V w is the volume of soil solution in cubic decimeters. Further, if the concentration of added ophosphate is large enough to convert most of the available "reactive" aluminum in the soil to aluminum phosphate, then (4.24) where n AlPO. is the number of moles of phosphate precipitated. With the definitions
where M; is the mass of solid soil material reacted with phosphate, Eq. 4.24 can be written in the form T
qpo. = b po . ( 1  AI V nAI
The use of definition
cKso
w)
(4.25a)
to eliminate AIT from Eq. 4.25a and the additional
(4.26) lead to the expression
(4.25b) Finally, since
THE SURFACE CHEMISTRY OF SOILS
124
acco the expression for cKso and the inequality 4.23, Eq. 4.25b can De approxim ted closely with the inverse binomial expansion of the factor in parentheses n the right side: \. b po 4P0 b po KP0 4T QP04 = 1 + (1/ K ) = 1 / KP0 4T 4T
(4.25c)
Under the conditions described in Eqs. 4.23 and 4.24, the quantity of aphosphate precipitated is described by a Langmuir equation (Eq. 4.7) even though surface reactions are not involved. Note that a graph of nAJPO/P04T against nAJP04, based on the sorption data collected, leads to a determination of nAl as the x intercept, in keeping with Eq. 4.9, and that the "affinity parameter" K, calculated from the slope of a line cutting the x axis, has no possible interpretation as a surface complexation equilibrium constant. Instead, K is determined by the amount of reactive aluminum in the soil, the soil water content, and cKso, as shown by Eq. 4.26. These results have a direct bearing on batch sorption experiments designed with relatively high concentrations of added aphosphate as a means of estimating the maximum surface capacity of a soil for phosphate. If the added phosphate is precipitated instead of adsorbed, Eq. 4.25 may apply and the estimated capacity parameter has no particular relation with the phosphateadsorbing surfaces in the soil. The experimental observation that an ion activity product in a soil solution is smaller than a corresponding solubility product constant provides no evidence as to the actual mechanism of a sorption process in the soil.
This statement refers to a comparison between the ion activity product (lAP),
lAP
= (Mm+)a(LI)b
(4.27)
and the solubility product constant, K so
=
(Mm+)a (Llt (MaLb(s))
(4.28)
that pertain to the dissolution reaction MaLb(s) = aMm+(aq) + b Ll(aq)
(4.29)
In Eq. 4.28, M is a metal and L is a ligand that precipitate to form the solid MaLb(s), ( ) is a thermodynamic activity, and a and b are stoichiometric coefficients subject to the constraint of electroneutrality.P am = bl
(4.30)
It is evident from Eqs. 4.27 and 4.28 that
lAP
K
."
= (MaLh(s»
(4.31)
and therefore that the relation between lAP and K." (at fixed temperature
1NC)R(:1At"rrc7\ND ORGANIC SOLUTE ADSORPTION IN SOILS
125
and pressure) is termined by the activity of the precipitated solid phase, MaLb(s). An expe 'mental finding that lAP is less than Ksooften interpreted as evidence for an adsorption reactionmay mean only that the activity of the solid phase in the precipitate formed is less than unity. The principal mechanism for a reduction in the activity of a solid phase below its standardstate value of unity in soils is copreeipitation, which is interpreted in chemical composition data as isomorphic substitution of one ion for another of comparable radius in a soil mineral. It is illustrated in Table 1.4 that isomorphic substitutions of cations cover a broad range of both metals and minerals in soils. The same is true for inorganic anions, and this fact is especially pertinent to investigations of the sorption behavior of trace constituents of soil solutions, whose content in the solid phases is expected to be small enough to preclude direct detection of their presence in a precipitate. For example, if M is a trace metal that has coprecipitated with a macroconstituent metal in a soil solution, then the activity of the component containing M is likely to be quite low, decreasing with the mole fraction of M in the mixture. 16 This reduction of the activity of the solid component is accompanied by a corresponding reduction in the activity of Mm+(aq), as can be seen by solving Eq. 4.28 for (M m+):
( M m+) '= [Kso(MaLb(S))]l/a (L1 )b = (M m+)O(MaLb(s))l /a
(4.32)
where (4.33) is the activity the metal cation would have in the soil solution if MaLb(s) were in the standard state with unit activity. Equation 4.32 shows that (M'?") is reduced below (Mm+)o when (MaLb(s)) is less than unity. As a numerical illustration of this idea, consider a calcareous soil to which a wastewater containing cadmium has been applied, with the result that a coprecipitate of CdC0 3(s) and CaC0 3(s) forms. Measurements on the aqueous phase of the soil indicate that (Cd2+) = 10 6 . 5 and (HCO)) = 10 3 at pH 7.6. Because K so = 10 1 1.2 for the reaction CdC03(s) = Cd2+(aq)
+
CO~(aq)
and (HC()t)7(C()~\) = 102 .67 at pH 7.6,17 the measured bicarbonate activity and ECq.·~;·31 produce the result /'~
(Cd2+)O = 10 1 1.2
X
,i
._____n" ...
105 .67 ~·(1O5.53
It follows that the observed activity of Cd 2+(aq) can be interpreted with Eq. 4.32 as an effect of the precipitation of a mixed Cd/Ca carbonate. with
THE SURFACE CHEMISTRY OF SOILS
126
the CdC0 3 component having an activity of about 0.1: (Cd2+)
(CdC03(s))
= (Cd2+)o
_ = 10
1
The single fact that lAP = (Cd2+)(CO~) = 1012 . 2 is much smaller than K so = 1011.2 in this example cannot be used unambiguously to infer that cadmium has been adsorbed by the soil. Both ~4so,rptiona9d precipitation are consistent with an lAP diminished below the solubility product constant for a possible solid phase. The experimental observation that an ion activity product in a soil solution is larger than a corresponding solubility product constant is not prima facie evidence of precipitation.
If a solid phase has precipitated according to the reverse of the reaction
in Eq. 4.29, the lAP can be larger than the corresponding solubility product constant for the solid if the activity of the solid is greater than unity (Eq. 4.31). This circumstance occurs commonly when the precipitate comprises particles whose radii are smaller than about 1 JLm. 16 The surface energy of these very small particles is large enough to contribute importantly to the Gibbs energy of the precipitate and therefore to increase its activity relative to that in the standard state, where the interfacial energy component of the Gibbs energy is negligible by definition. On the other hand, the simple condition of supersaturation, lAP/ K so > 1, is not sufficient. for the actual formation of a solid phase at a measurable rate. The rate of homogeneous precipitation depends, for example, sensitively on the degree of supersaturation such that, under circumstances typical of soil solutions, solid formation requires geological time intervals if lAP/ K so is smaller than about 20. 16 If nucleating agents are present in a soil, the rate of heterogeneous precipitation from a supersaturated soil solution should be large and the mechanism of sorption should be solid formation, not adsorption. This mechanism is especially probable when solid phases that are similar to the one expected are already present in a soil, as when carbonateforming trace metals are introduced at supersaturation levels into the aqueous phase of a calcareous soil. It should be clear at this point that classical thermodynamic methods involving adsorption isotherm equations and the solubility product principle cannot distinguish adsorption from precipitation unambiguously. This fact is just another illustration of the impossibility of inferring underlying mechanisms from thermodynamic data on soils. Of course, a relatively complete determination of the chemical composition of a soil solution after sorption has occurred can provide useful circumstantial evidence. For example, a measurement of the concentration of silicon in a soil solution is essential if the sorption of an oxyanion by a soil is under investigation, since the precipitation of an oxyanion through the incongruent dissolution of aluminosilicates is accompanied by the release of silicon. As a general
~.. INORGANIC AND ORGANIC SOLUTE ADSORPTION IN SOILS
127
rule, the chemical analysis done after a sorption experiment with soil should include all possible relevant elements in the soil solution, not just the one that is the chief object of investigation. J Perhaps the best methods for demonstrating the existence of adsorption in a soil are optical, magnetic resonance, and Xray photoelectron spectroscopy, which give direct evidence for the presence of adsorbed species. These methods currently are under development for application to soils extensive calibration with wellcharacterized, reference soil minerals. is Until this calibration is completed, it is possible to use kinetics data to make an operational distinction between adsorption and precipitation. This strictly empirical method of analyzing sorption data can be illustrated with the important case of ophosphate reactions. It has been recognized for about 40 years that the reaction between ophosphate and soil exhibits rapid and slow stages.l" The rapid stage almost invariably persists for less than 50 hours, and the slow stage continues well beyond 50 days in many instances. No particular mechanism of phosphate sorption can be inferred uniquely from the kinetics data that show these two stages, but it is not unreasonable to suppose that, if the initial concentration of phosphate in the soil solution is below supersaturation for any possible phosphate solid, the rapid stage corresponds principally to adsorption. Besides the expectation that a surface reaction should proceed quickly in the absence of diffusional barriers, supporting evidence for this hypothesis comes from the fact that rapidly sorbed phosphate is also readily desorbable.l? On the other hand, a classification of a sorption process on the basis of kinetics data must be conditioned by other chemical properties of thFphosphatesoil mixture. For example, if the soil solution is supersaturated initially with respect to some phosphate solid, precipitation is likely to influence the sorption reaction from the beginning.F" If the soil minerals have a low degree of crystallinity and/or a high degree of hydration, precipitation may be the dominant sorption mechanism even in the rapid stage." In general, low phosphate concentrations and wellcrystallized, relatively unhydrated soil minerals tend to favor adsorption as the phosphate reaction mechanism. Other chemical properties, such as the pH value of the soil solution and the kinds of metals in soil clay minerals, exert a quantitative influence on the rapid stage of phosphate sorption, as do such physical properties as temperature. 22 A large number of mathematical expressions have been applied to describe the rate of phosphate sorption in soils, but no clear consensus on which equations are most suitable has yet emerged. 22 ,23 There is at present a growing use of the Elovich equation'" to represent the rapid stage: dq
dt = k, exp( k2q )
(4.34)
where q is the amount of phosphate sorbed per unit mass of dry soil and k, and k2 are constant parameters. Although Eq. 4.34 can be derived from
THE SURFACE CHEMISTRY OF SOILS
128
more general ratelaw expressions under the assumption of an exponential decrease in number of available sorption sites with q and/or a linear increase in activation energy of sorption with q,25 the Elovich equation is perhaps best regarded as an empirical one for the characterization of rate data. The solution of Eq. 4.34 is: 25
t)
q(t) = k1 In(k 1k2to) + k1 In ( 1 + to
(4.35)
2
2
where
to =
exp(k 2 qc) k

1k2
tc
(tc
>
0)
and qc is the value of q at time tc, the time at which the rate of sorption begins to be described by Eq. 4.34. In most applications, tc is set equal to zero and qc is the initial value of q in the soil. Equation 4.35 appears to describe phosphate sorption by soils quite well for t < 200 hours.r" Some evidence exists to suggest that, over this period, phosphate sorption involves principally a multilayer adsorption mechanism, i.e., the formation of metal phosphate coatings on the surfaces of soil particles.P This hypothesis has the attractive feature that it is consistent with the ultimate formation of a precipitate in the slow stage of phosphate sorption. The latter appears to be described well by the linear rate law26 dP0 4T dt =  K P0 4T
(
4.36
)
where P0 4T is the total molar concentration of phosphate in the aqueous solution phase and K is a constant parameter. Equation 4.36 has been shown to apply for times of reaction longer than about 140 hours and to be associated with the appearance of discrete crystallites of phosphate solids.r" Evidently the transition from monolayer adsorption to multilayer adsorption to precipitation is marked by a change in the rate law from Eq. 4.34 to Eq. 4.36. As a rule of thumb, the adsorptiondominated stage of phosphate sorption can be assumed to exist for reaction times less than about 50 hours. 4.3. METAL CAliON ADSORPTION
The positive adsorption of metal cations by the solid phases in soil can involve the formation of either innersphere or outersphere surface complexes, or the simple accumulation of an ion swarm near the solid surface without complex formation. These adsorption mechanisms are implied in the development of the concept of surface charge balance (Eq. 3.3) and were illustrated, for the case of surface complex formation, in Figs. 1.8 and 1.10. The quantitative relationship between these mechanisms and measured surface excesses of metals on soil minerals is taken up in Chap. S. In the present section, emphasis is placed on the qualitative
INORGANIC AND ORGANIC SOLUTE ADSORPTION IN SOILS
129
aspects of metal cation adsorption in soils oisaois surface complexation phenomena. An important leitmotiv throughout the long !!!story of metal cilJ:i2!!..~sOrI?ti<2!!E.!:Is!i~.L~l~1liU'.ttt~.!:!1q.~. 27 This preoccupation with the relative affinity of soil particle surfaces for metal cations is reflected in the abundant literature on cation exchange selectivity coefficients and the frequent published attempts to deduce "replaceability series" from experimental adsorption data. 28 It is an unfortunate fact that, in most studies, no effort has been made either to define affinity and selectivity precisely or to exclude from the experiments the confounding effects of multiple cation adsorption and soluble complex formation between the metal cations under investigation and the ligands in the soil solution. The result of these common oversights has been the emergence of a variety of selectivity sequences, with no particular uniformity even among those deduced for a single, wellcharacterized soil mineral. 28,29 These difficulties are least troublesome for monovalent metal cations, however, because the different definitions of selectivity based either on chemical thermodynamics or on a direct comparison of adsorption isotherms coincide when only monovalent cations are involved and because the extent to which these cations form soluble complexes in a soil solution is usually very small.i" Accordingly selectivity sequences for the adsorption of monovalent cations by soil particles are the most easily interpreted mechanistically. The smectite minerals offer perhaps the clearest opportunity to examine how surface complexation by the siloxane ditrigonal cavity affects monovalent cation adsorption. Since it is quite reasonable to assume that there will be no differences in monovalent cation selectivity on smectite surfaces if the only mechanism of adsorption is the accumulation of a cation swarm in the soil solution near the solidliquid interface." the existence of a selectivity sequence for smectites must imply the formation of surface complexes, such as those illustrated in Fig. 1.8. If the observed differences in monovalent cation selectivity are principally the result of innersphere complex formation (i.e., a monovalent cation settled into a siloxane ditrigonal cavity), then the expected selectivity sequence should be Cs+ > Rb+ > K+ > Na+ > Li+ for the Group IA metal cations.P The molecular basis for this sequence can be understood as follows. Innersphere complex formation with a siloxane ditrigonal cavity requires the exchange of some of the water molecules solvating the adsorptive cation for the oxygen ions that constitute the surface functional group. As discussed in Sec. 1.2, these oxygen ions are relatively soft Lewis bases when compared with the oxygen atoms in water. It follows from the principle of hard and soft acids and bases (HSAB) that the most stable innersphere complexes involving the siloxane ditrigonal cavity form with the Group fA cations that are the softer Lewis acids because these cations more readily exchange their solvation water molecules for a softer Lewis ADSORPTION SELECTIVITY.
lin SUIUAU CHfMISTRY Of SOILS
130
base.:" The relative Lewis acid softness of a Group IA cation can be estimated numerically with the Misono softness parameter, y:34 lOIzr
y = =::...;= I Z +1
(4.37)
JZ
where I z is the ionization energy for a cation of valence Z and radius r. For the Group IA cations, Z = 1 and the sequence of decreasing Y values is Cs+(O.287) > Rb+(O.228) > K+(O.189) > Na+(O.lll) > Li+(O.053) (4.38) where Y is in units of nanometers. This sequence is identical with that of decreasing stability of innersphere complexes formed with the siloxane ditrigonal cavity through the elimination of solvation water molecules. Figure 4.4 shows values of the standard Gibbs energy, ~G~x, at 298 K for the reaction LiX(s) + M+(aq)
= MX(s) + Li Taq)
(4.39)
Figure 4.4. The relation between the standard Gibbs energy for Li +  M+ exchange on montmorillonite and the Misono softness parameter ofM+ (M = Na, K, Rb, CS).35 12 Cs+
Li+  M+ EXCHANGE ON MONTMORILLONITE
10
• 0
Camp Berteau Wyoming
Rb+
•
10 0
E
•
8
J

'I;
~
+
~
'i,i,"
'I
6
~'I
t
':,/j
+
'" ...J
•
4
OQl
.~
0
K+
I ' ,~
i
II
<.!l
'I
<J
',I
0
I
'I I
I
2
',I
0
0
•
)
Na+
',I
0
0
0.05
0.10 YM+
0.15
 YL1+(nm)
0.20
0.25
INOKGANIC AND ()K(;ANIC SOllJ II ADSOKI'1I0N IN SOli S
III
plotted against the difference in Misono parameters, Y M'  Y Li " for M+ = Na+, K+, Rb+, and Cs+ on montrnorillonite.P (In Eq. 4.39, X refers to one mole of negative montmorillonite charge.) The standard Gibbs energy for the exchange reaction in Eq. 4.39 is a quantitative measure of cation selectivity. It is evident in Fig. 4.4 that aG~x decreases as the Misono parameter of M+ increases relative to the value for Li+. This trend is in agreement with what is observed typically for smectites32.33.36 and with the sequence in Eq. 4.38. For a given value of (YM+  YLi+). Fig. 4.4 also shows that aG~x is smaller (i.e., the clay is more selective for M+) for Camp Berteau montmorillonite than for Wyoming montmorillonite. These two smectites differ in that all of the negative charge on the siloxane surface of the Camp Berteau montmorillonite originates from isomorphic cation substitutions in the octahedral sheet, whereas only about two thirds of the negative charge on the siloxane surface of Wyoming montmorillonite originates in the octahedral sheet, with the remainder produced by isomorphic cation substitutions in the tetrahedral sheet. According to the discussion in Sec. 1.2, this difference in isomorphic substitution makes the siloxane ditrigonal cavity on Camp Berteau montmorillonite a softer Lewis base than that on Wyoming montmorillonite. It follows from this conclusion and the HSAB principle that, as the Lewis acid softness of the complexed cation increases, Camp Berteau montmorillonite should form more stable innersphere complexes than Wyoming montmorillonite. The hypothesis of innersphere complexation as the basis for differences in monovalent cation selectivity on siloxane surfaces is consistent with the observed decrease in SE, the specific surface area measured by chloride exclusion, with an increase in Lewis acid softness of the exchangeable cation, shown in Table 1.8. It is pointed out in Sec. 1.4 that surface complexation between siloxane ditrigonal cavities and monovalent cations reduces the negative charge that repels chloride ions from a siloxane surface. Additional, indirect evidence supporting this view comes from the results of Na" + Cs" exchange experiments with reducedcharge montmorillonites.P As the negative charge on the siloxane surface of Camp Berteau montmorillonite is reduced permanently through lithium migration into the octahedral sheet at high temperature (the HoffmannKlemen method), the value of aG~x for the exchange of Na+ by Cs" increases monotonically toward zero. This trend can be interpreted as the effect of an overall increase in the Lewis base softness of the siloxane surface induced by the decrease in surface charge density and a concomitant further delocalization of the negative charge produced through isomorphic substitution. Since both Na + and Cs" actually are hard Lewis acids (with Cs" the softer of the twO),33 an increase in the Lewis base softness of the siloxane surface tends to decrease innersphere coinplex formation for both cations, according to the HSAB principle. This decrease should be accompanied by enhanced dissociation of both cations from the siloxane surface and therefore an increase in aG~x for Na +  Cs+ exchange toward the zero value. indicative of no
132
THE SURFACE CHEMISTRY OF SOILS
thermodynamic preference for either cation by the clay mineral, as occurs when the only adsorption mechanism is accumulation of an ion swarm in the aqueous solution phase near the adsorbing surface. Comparable statements concerning the basis for selectivity differences among bivalent metal cations adsorbed by siloxane surfaces cannot be made with certainty for two primary reasons. First, because of quasicrystal formation, the extent to which outersphere complexes form between bivalent metal cations and siloxane ditrigonal cavities is quite pronounced and the degree of dissociation of these cations from a siloxane surface is correspondingly very small. It follows that selectivity differences among metals in oxidation state II are likely to be small, even if innersphere complex formation is the causative factor. This expectation appears to be in agreement with bivalent cation exchange data on smectites and vermiculites.Pr" A second complicating difficulty is the fact that there are almost no reports of experiments on bivalent cation exchange in which soluble, complexforming ligands were excluded from the aqueous solution phase. Without this precaution, the measured surface excess and selectivity coefficient must reflect the adsorption of both free bivalent cations and their complexes and no unambiguous inference concerning the role of surface complexes can be made.?? Despite these problems, it can be stated that innersphere surface complexes do form between bivalent metal cations and siloxane ditrigonal cavities, as discussed in Sec. 2.3, and that the possibility of their having a role in determining differences in adsorption affinity remains open. Similar difficulties beset the interpretation of data on metal cation adsorption by surfaces bearing inorganic hydroxyl groups. Besides the paucity of data on adsorption from aqueous solutions free of metalcomplexing ligands, the fact that the hydroxide ion is a much harder Lewis base than the oxygen ion in a siloxane ditrigonal cavity must be considered. Since both OH and H 2 0 are very hard Lewis bases, a pronounced tendency for the hard Lewis acids in Groups IA and IIA of the Periodic Table to desolvate and form complexes with surface hydroxyl groups as the Lewis acid softness of the metals increases are not likely. In this case, more subtle effects relating to the distribution of surface charge (e.g., the Brensted acidity of the surface hydroxyl group) may determine the extent of innersphere complex formation. The selectivity sequences reported for monovalent and bivalent cation adsorption by hydrous oxides support this hypothesis, in that strongly (Brensted) acidic surfaces tend to show increasing selectivity with increasing Lewis acid softness, whereas weakly acidic surfaces show the opposite trend. 29 The effects of metalcomplexing ligands in a soil solution on the adsorption of metal cations by soil constituents can be classified into four general categories;" LIGAND EFFECTS.
1. The ligand has a high affinity for the metal and forms a soluble complex with it, and this complex has a high affinity for the adsorbent.
INORGANIC AND ORGANIC SOLUTE ADSORPTION IN SOILS
133
Figure 4.5. A schematic diagram of interactions in an aqueous metalligandsurface system. The parameters K refer to equilibrium constants for reactions in the direction of the arrows.
2. The ligand has a high affinity for the absorbent and is adsorbed, and the adsorbed ligand has a high affinity for the metal. 3. The ligand has a high affinity for the metal and forms a soluble complex with it, and this complex has a low affinity for the absorbent. 4. The ligand has a high affinity for the adsorbent and is adsorbed, and the adsorbed ligand has a low affinity for the metal. A fifth category could be the ligand that has a low affinity for both the metal and the adsorbent and therefore little or no effect on trace metal adsorntlOn (e.g., clu 4 at pH > PZC for the adsorbing solid). The four main categories can be deduced from the overall scheme of metalligandsurface interactions depicted in Fig. 4.5, as shown in Table 4.1. The scheme of interactions emphasizes the competition between the metal and the adsorbent for the ligand. Categories 1 and 2 in Table 4.1 should result in enhanced adsorption of the metal. If the ligand and metal do not interact with the same surface functional groups, category 4 produces little effect on metal adsorption; if there is competition, metal adsorption is reduced. The model systems listed in Table 4.1 represent wellcharacterized metalligandadsorbent combinations whose observed behavior is consistent with at least one category of ligand effecta" On kaolinite, a sharp Table 4.1. Categories of ligand effects on metal cation adsorption Category 1 2
Equilibrium constant relations
3
K ML• K ML X large; K OM• K L X• K M/ LX large; K OM• K ML large; KMl. X small
4
K L X• K Il M
large;
KM/LX
K OL small KOL small
small
Model system example.'? Cuhydroxidekaolinite CuglutamateFe (OHM am) Cuglycinernontmorillonite Cuphosphateillite
134
THE SURFACE CHEMISTRY OF SOILS
increase in the adsorption of copper is produced by a change in pH from 5.5 to 6.0, suggesting the adsorption of Cuhydroxy complexes by the clay mineral. On amorphous iron oxyhydroxide, glutamic acid is expected to be complexed through one of its carboxyl groups to a surface hydroxyl group, leaving a zwitterion exposed to the aqueous solution phase. The carboxylate in the zwitterion can then complex a Cu2+ ion. On montmorillonite, the adsorption of copper is reduced through the formation of monovalent and neutral Cuglycine complexes that do not react well with the negatively charged clay surface. On illite, the adsorption of phosphate is thought to involve principally aluminol groups, which are not significant in copper adsorption by the clay mineral. The adsorbed phosphate evidently is not effective in forming complexes with Cu2+ ions in the aqueous solution phase, since no enhancement of copper adsorption is observed. However, the situation can be different when the adsorbent is a hydrous oxide instead of a phyllosilicate. In this case, oxyanions such as ophosphate can react strongly with the surface hydroxyl groups to accumulate in multilayers that in turn act as a new adsorbent for metal cations.t" Perhaps the most important soil solution ligand that affects metal cation adsorption is the hydroxide ion. Figure 4.6 shows four representative examples of the effect of increasing OH activity on metal adsorption by inorganic and organic surfaces of soil constituents. 41 Data pertaining to this effect are almost always summarized in a graph that pairs some quantitative measure of the extent of adsorption with the pH value of the aqueous solution phase. In each of the graphs in Fig. 4.6, the adsorptions of metals from solutions containing a given total metal concentration are compared at different pH values. The curves show that increasing the OH activity always increases the extent of metal adsorption. Therefore, OH is a ligand whose effects on adsorption fall into categories 1 and 2. At present, there are different opinions about which category is the more appropriate. For example, it is possible that hydrolytic species of metals exhibit a very high affinity for protonselective surface functional groups, such as those on oxide minerals. Alternatively, it can be proposed that OH is adsorbed by protonselective surface functional groups with great affinity and then serves as a bridge between the adsorbent surface and an adsorptive metal cation. It is often observed that metal cation adsorption data obtained over a range of pH values can be described mathematically with the equation'?
= a + bpH
(4.40)
_/sorb D  K d C 
(4.41)
In D where
s
Isoln
K d is the distribution coefficient, c, is the (fixed) mass of adsorbent per unit volume of aqueous solution phase, I."rh is the ratio of moles of metal adsorbed to (fixed) moles added initially, and 1."ln = 1  I..,rh is the
135
INORGANIC AND ORGANIC SOLUTE ADSORPTION IN SOILS
aFeOOH !AT =104M O.IM KN03
8 120r,,..,,, Cu
Pb
Co
... <,
'0 E· 80
::l..
~ u
d
c 0=3::::::
8 pH
pH
Figure 4.6. The effect of increasing OH activity on the adsorption of metal cations by solid soil constituents."
fraction of initially added metal that is not adsorbed. The parameter D is called the distribution ratio and a graph of In D against pH according to Eq. 4.40 is termed a Kurbatov plotY A chemical interpretation ofthe constant parameters a and b in Eq. 4.40 can be made as follows. The pH value at which half of the added metal is adsorbed is designated pH so . Since D = 1 at this pH value, according to Eq. 4.41, it follows from Eq. 4.40 that pH so
a
=
b
Moreover, after substituting fsorb/(l  fsorb) for D in Eq, 4.40, one can derive the result dflOrb) = b ( dpH pHpH", 4
(4.42)
136
THE SURFACE CHEMISTRY OF SOILS
Therefore, Eq. 4.40 can be rewritten in the form In D = b(pH  pHso)
(4.43a)
Isorb = {l + exp[  b(pH  pHSO)]}l
(4.43b)
or
with b as expressed in Eq. 4.42. The values of pHso for a series of bivalent metal cations at the same initial molar concentration, reacted with the same hydrous oxide adsorbent suspended at the same solids concentration in the same background electrolyte solution offer a relative measure of the selectivity of the adsorbent for the metal cations. 29 The smaller the pHso , the more selective the adsorbent for the metal cation. With a given metal, pHso is usually well below the negative common logarithm of the stability constant for the formation of the complex MOH+(aq) and often decreases as the initial molar concentration of the metal decreases, unless the quantity of metal adsorbed is far below the maximum possible, in which case pHso often remains independent of the initial metal concentration.r" The slope parameter b in Eq. 4.43 provides a measure of the steepness of the "adsorption edge" at pHso (Fig. 4.6). This characteristic of a plot of Isorb against pH cannot be attributed to anyone feature of the metal adsorption mechanism, but the sign of b can be used to classify the plot as either "metallike" (b > 0) or "ligandlike" (b < 0) when metalcomplexing anions besides OH are present. 38,44 (These terms are compared further in Sec. 4.4.) Further insight as to the effect of hydroxide ion on the mechanism of metal cation adsorption by surfaces bearing hydroxyl groups can be obtained from the results of electrophoretic mobility measurements. It has been known for about 40 years that the electrophoretic mobility of an oxide or phyllosilicate particle can be made to change sign as the pH value is increased in the presence of a sufficiently high concentration of bivalent, trivalent, or tetravalent metal cations.P An example of this behavior is shown in Fig. 4.7 for particles of Ti0 2 (rutile) suspended in solutions of Ca(N03 h .46 The minima in the plots of u against pH that appear as the concentration of calcium is increased are typical. For metal cations that form more stable hydroxy complexes than Ca2+ (e.g., C0 2+), u exhibits a maximum in the highpH region and declines thereafter back toward negative values.f? Thus the protoypical mobilitypH curve at sufficiently high adsorptive metal concentrations simply tracks the mobilitypH curve determined at very low (or vanishing) metal concentrations at low pH values, then shows a minimum and reversal of the sign of the mobility at intermediate pH values, and finally exhibits a maximum followed by decline as pH is increased further. The declining portion of the curve at high pH values lies close to the electrophoretic mobilitypH curve of the hydroxide solid formed by the metal cation. 47
137
INORGANIC AND ORGANIC SOLUTE ADSORPTION IN SOILS
Rutile in Co (N03)2 Fuerstenou et 01. (198()
4
Car 1.67 x 10 3 M

2
I
>
I
0
l/)
C\J
° E
00
1.67x1O:5M
0
x
:J
I
4
6
7
8
9
10
II
pH Figure 4.7. The dependence of the electrophoretic mobility of rutile particles on the pH value in solutions of Ca(N03h .46
These characteristics of the electrophoretic mobilitypH relationship suggest that metal cation adsorption by oxide surfaces (including the edge surfaces of phyllosilicates) is accompanied by the formation of a metal hydroxypolymer coating on the adsorbent. The extent of this coating depends on the pH, on the initial concentration of metal cations, and on the ionic potential of these cations, along with other factors that determine their hydrolysis. Ionic potential (the ratio of valence to ionic radius) is an especially important property, in that metal cations with ionic potentials between 30 and 100 nm 1 (e.g., Al (III) ) can be expected to form extensive coatings readily, even on siloxane surfaces (Fig. 1.11), whereas metal cations with ionic potentials less then 30 nm ? (metals of Group II in the Periodic Table) do so only at relatively high pH values. However, it does not seem possible to ascribe the formation of hydroxide coatings to an ordinary precipitation reaction involving the metal cation. The observed values of pH~lI for metal adsorption on hydrous oxides are well below the
138
THE SURFACE CHEMISTRY OF SOilS
pH range of homogeneous precipitation, as is the pH value at which the minimum occurs in electrophoretic mobilitypH curves. 29 ,4S In addition, the frequently observed shift of pHso toward lower values as the initial concentration of metal is decreased is just the opposite of what one would expect if a precipitation reaction were taking place.r" Metal cation adsorption by the solid phases in soils should be governed by some combination of the surface complexation mechanisms deduced from experiments on wellcharacterized minerals and organic solids. In soils whose clay fraction is dominated by 2: 1 phyllosilicates, metal cation adsorption should involve principally both inner and outersphere complexes with siloxane ditrigonal cavities, although highly selective adsorption of bivalent trace metals may occur through complexes with edgesurface hydroxyl groups. In soils whose clay fraction is dominated by 1: 1 phyllosilicates and hydrous oxides, metal cation adsorption should involve the formation of hydroxypolymer coatings whose extent of surface coverage depends sensitively on the Lewis acid strength (ionic potential) of the metal cation as well as on the pH value of the soil solution. In soils wherein organic surfaces are important to metal adsorption, it is likely that both surface complexation by organic functional groups (see Table 1.5) and hydroxypolymer formation (Fig. 4.6) are involved. Superimposed on these basic mechanisms are the effects of metalcomplexing ligands summarized in Fig. 4.5 and Table 4.1. These effects and the multiplicity of inorganic and organic ligands expected typically in soil solutions combine to make the detailed, quantitative description of metal cation adsorption in soils a formidable task.
4.4. INORGANIC OXYANION ADSORPTION The ionic potentials of the nonmetal elements in Groups IlIA to VIA exceed 100 nm ? for their common oxidation states, and therefore these elements form oxyanions instead of hydrolytic species in soil solutions. 49 The same tendency is observed for the Group VIB metals chromium and molybdenum. Examples of inorganic oxyanions commonly found in the aqueous phases of soil are B(OH)i, CO~, N03", H 3SiOi, PO~, SO~, AsO~, SeO~, MoO~, and, when the oxyanion is multivalent, some of the protonated forms. The qualitative and mechanistic features of the adsorption of these oxyanionsa topic on which there is an abundant literaturesO s2are the principal concerns of the present section. Quantitative models of inorganic oxyanion adsorption are described in Chap. 5. A consensus exists that inorganic oxyanion adsorption by soil minerals involves almost universally the twostep ligand exchange reaction SOH(s)
+ H''{aq)
= SOH:t(s)
SOH:t(s) + L/(aq) = SL1/(S) + HzO(l)
(4.44a) (4.44b)
where S is a metal cation, SOH(S) is one mole of inorganic surface
INORGANIC AND ORGANIC SOLUTE ADSORPTION IN SOILS
139
hydroxyl groups, and L l  is an inorganic oxyanion of valence l. The protonation step (Eq. 4.44a) is thought to render the surface hydroxyl group more exchangeable; if the concentration of the oxyanion in the soil solution is sufficiently high, this step may not be necessary.P On the other hand, the exchange reaction (Eq. 4.44b) does not occur readily until very high concentrations of nitrate are reached in soil solutions. 51 The situation with carbonate and sulfate anions may be intermediate in that these oxyanions may sometimes adsorb by forming an outersphere surface complex, like nitrate usually does, with the protonated hydroxyl groupr'" (4.44c) and sometimes engage in ligand exchange instead. 51 The reactions of oxyanions with phyllosilicates appear to follow Eq. 4.44 as much as do those with metal oxides in soils. In the case of the phyllosilicates, the reactive surfaces are both the edge surfaces of broken crystallites and the exposed surfaces of adsorbed hydroxy polymers. 51,55 Much experimental evidence has been adduced in support of the ligand exchange mechanism for oxyanion adsorption. 5052 The principal lines of reasoning that lead to this mechanism can be summarized as follows. 1. The maximal oxyanion adsorption by a soil mineral under a prescribed set of conditions depends on the pH of the soil solution. If only one species of oxyanion exists, a graph of the maximal adsorption versus pH value (the "adsorption envelope") exhibits a broad peak at a pH value near the pKa for the conjugate Brensted acid, as illustrated in Fig. 4.8. 56 If several protonated species of an oxyanion exist, the adsorption envelope usually shows a monotonic decline with increasing pH value, the decline becoming sharper as the valence of the principal oxyanion species decreases (Fig. 4.8). These trends are consistent with Eqs. 4.44 in that they suggest decreasing adsorption as the protonation of the surface decreases but increasing adsorption as the valence of the oxyanion decreases. With B(OH)4' the decrease in positive surface charge and the increase in concentration of the single oxyanion species with increasing pH value are not comparable above pH 7 and a peak in the adsorption envelope is observed. For oxyanions with multiple species, the small differences in adsorption affinity among species leads to an adsorption envelope more conditioned by surface protonation than by oxyanion valence. In agreement with this point of view is the fact that arsenate and phosphate adsorption data on oxyhydroxides can be renormalized and correlated successfully with the PZC of these adsorbents." The characteristic adsorption envelopes in Fig. 4.8. are to be contrasted with the "adsorption edge" curves in Fig, 4.6. It is evident that the ligandlike behavior in Fig, 4.8, which is indicative of decreasing anion valence and surface charge, is the complement of the metallike behavior in Fig, 4,6, which is indicative of decreasing cation valence and surface charge.
140
THE SURFACE CHEMISTRY OF SOILS
2000~
10' oX
0
COO PhOSPhat~ aFeOOH
0 00
0
150
E E
0
0 00
0 0
"0 Q)
.a 100
(ArSenate AI(OH)3(am)
L
0
(/)
"0 0
c: 0
MA
A At:A
A
50
A
c:
Borate~
Fe(OH)3(am) 
0
4
6
8
~
10

12
pH Figure 4.8. Adsorption evelopes for phosphate on goethite, arsenate on amorphous aluminium hydroxide, and borate on amorphous iron hydroxide. 56 The . ordinate values should be multiplied by ten for the arsenate data.
2. The rate of 3Zp exchange between dissolved ophosphate and phosphate adsorbed on goethite or gibbsite follows the Elovich equation (Eq. 4.34).58 The parameter k z in Eq. 4.34 is observed to be a function only of temperature, whereas k 1 depends on the temperature and a fractional power of the proton concentration in the aqueous solution phase. The latter parameter also includes a firstorder rate dependence on the concentration of phosphate surface complexes. The dependence of k 1 on a fractional power of the proton concentration reflects the effect of the protonation reaction in Eq. 4.44a, and the firstorder dependence on the adsorbed phosphate concentration is expected if the ratedetermining step in 3Zp exchange is the breaking of either the metalphosphate bond in an innersphere surface complex or the metaloxygen bond in the adsorbent. 58,59 Thus the kinetics data for 3Zp exchange, like the pH effect on the maximal adsorption of phosphate, are consistent with the ligand exchange mechanism. 3. The rate of hydroxyl exchange on «CrO, is known to be orders of magnitude lower than that on goethite (aFeOOH).6o The rate and extent of nitrate adsorption by these two reference minerals in suspension are essentially the same, with equilibrium attained in minutes. This fact suggests that nitrate adsorbs according to outersphere complex formation (Eq. 4.44c), not ligand exchange (Eq. 4.44b). Sulfate adsorption by the two minerals is also similar in rate and extent;
INORGANIC AND ORGANIC SOLUTE ADSORPTION IN SOILS
141
however, the PZSE of the minerals is shifted upward in a sulfate background solution. These results illustrate the "intermediate" surface complexation behavior of sulfate, already mentioned above. The adsorption data are consistent with outersphere complex formation, but the PZSE shift upward could reflect innersphere complex formation, as discussed in Sec. 3.2. By contrast, the rate and extent of phosphate adsorption by the two minerals are markedly different, the rate being much lower and the extent of adsorption much larger on goethite. This difference is consistent with a ligand exchange mechanism for phosphate adsorption by goethite and outersphere complex formation on a Cr2 0 3 ' 60 4. The infrared spectra of evacuated or moist metal oxyhydroxide films . bearing adsorbed phosphate and other oxyanions have been interpreted in support of a ligand exchange mechanisrn.W'' Perhaps the best evidence comes from studies on goethite, in which the. decrease in absorbance of the reactive Atype surface hydroxyl (Fig. 1.9) can be monitored readily as a function of extent of oxyanion adsorption. Band assignments in the infrared spectrum of phosphated goethite have been used to propose the innersphere surface complex structure illustrated in Fig. 1.9. 61 However, the spectroscopic approach is not conclusive in this respect since not all of the bands expected for the surface complex can be observed and those that are occur where absorptions are found for aphosphate in a variety of coordination environments (Table 4.2).61,62 Added to this ambiguity is the possibility that oxyanion complexation mechanisms can depend sensitively on the concentration of the adsorptive anion in the aqueous solution phase, such that data pertaining to evacuated films or even moist ones can be misleading in relation to what happens in aqueous suspensions or wet soils. As the example of nitrate adsorption at high concentrations shows.i" drying an adsorbent in the presence of an oxyanion can promote ligand exchange well out of proportion to its importance as an adsorption mechanism under the conditions expected in natural soils. Although no one of the above pieces of experimental evidence is conclusive in itself, the group taken together constitute a powerful argument for the applicability of Eq. 4.44b to oxyanion adsorption by soil minerals. Other indirect evidence, such as the low rate and extent of desorbability of phosphate versus nitrate,50 only tends to support this conclusion. In a natural soil, the reactive inorganic surface hydroxyls exist in a variety of adsorbents exhibiting a broad range of chemical composition and crystallinity, This fact suggests that the activation energy for oxyanion adsorption is likely to take on a continuum of values instead of being monolithic. That the Elovich equation (Eq. 4.34) is so successful in describing the kinetics of oxyanion adsorption 20,24,52 may derive from its having, its basis in a continuous distribution of activation energies."
Table 4.2. Infrared absorption band centers for goethite, phosphated goethites, phosphate minerals, and aqueous phosphate anions 61 ,6Z
Species Goethite Phosphated (H 3P04) goethite (dry) Phosphated (H 3P04) goethite (wet) Phosphated (Ca(HZP04)z) goethite (dry) Phosphated (Ca(HZP04)z) goethite (wet) (
Band centers, em"!
Species
Band centers, cm"
805, 900, 1000, 1110, 1190 734, 891, 996, 1030, 1191 1000, 1115
Strengite (FeP0 4 • 2HzO) Metastrengite (FeP04 • 2HzO) HZP04(aq)
1000, 1030, 1100, 1191 1050, 1090
HPO~(aq)
750, 994, 1012, 1040 752, 992, 1007, 1044, 1104 878, 947, 1072, 1150, 1230 862, 988, 1076, 1230 1004
PO~(aq)
INORGANIC AND ORGANIC SOLUTE ADSORPTION IN SOILS
143
4.5.· ORGANIC MATTER ADSORPTION
The complexes formed between the solid phases in soil and native organic compounds in the soil solution are not yet well understood because the ~
(4.45)
Table 4.3. Mechanisms of adsorption for organic compounds in soil solutions63 Mechanism Cation exchange ......Protonation .....Anion exchange ..... Water bridging v Cation bridging ..... Ligand exchange .... Hydrogen bonding  Van der Waals interactions
Principal organic functional groups involved Amines, ring NH, heterocyclic N Amines, heterocyclic N, carbonyl, carboxylate Carboxylate Amino, carboxylate, carbonyl, alcoholic OH Carboxylate, amines, carbonyl, alcoholic OH Carboxylate Amines, carbonyl, carboxyl, phenylhydroxyl Uncharged, nonpolar organic functional groups
144
THE SURFACE CHEMISTRY OF SOilS
where B is typically a molecular unit comprising a quaternized nitrogen atom in an aliphatic or a heterocylic aromatic structure and M+ is a monovalent metal cation in a surface complex depicted by ==. The most important specific example of Bin Eq. 4.45 is a proteinaceous fragment or a carbohydrate unit containing the protonated amino group, NHt. The metal cation M+ may be complexed by anyone of the surface functional groups described in Sec. 1.2 under those conditions that permit either inner or outersphere complexes to form with positive ions. An important feature of the exchange reaction in Eq. 4.45 is the subsequent "demixing" of the two adsorbates, M+== and B+==, which is commonly observed when the adsorbent is a 2: 1 phyllosilicate.P" Perhaps because of significant alterations induced in the structure of adsorbed water and differences in the stereochemistry of the inorganic cation and organocation surface complexes, the coexistence of the two kinds of complex on the same patch of siloxane surface is not favored. Instead, a random interstratification of unit layers, in each of which one kind of complex predominates, develops as the exchange of M+ for B + takes place. This segregation of the two absorbates helps to limit the extent of conformational changes the organocation must undergo upon adsorption. If M+ in Eq. 4.45 is replaced by a bivalent metal cation, demixing is usually reduced sharply, evidently because organocation adsorption is now restricted to the external surfaces of quasicrystals. The protonation mechanism in Table 4.3 refers to the reaction whereby an organic functional group forms a complex with a surface proton that either is itself in an inner or outersphere surface complex or is in an acidic water molecule solvating a metal cation in an outersphere surface complex (Sec. 2.4). The solid surfaces in soils can develop Breasted acidity in a variety of ways (cation exchange, dissociation of hydroxyls and carboxyls, hydrolysis of solvated metal cations, and so on), and this acidity offers the possibility that protonselective organic functional groups on dissolved solutes can be adsorbed through a protonation reaction. This mechanism is expected to be most important at low pH values and/or low water contents in soils, i.e., when the Brensted acidity of the solid surfaces is greatest. Organic solutes containing amino or carbonyl groupsnotably proteinaceous materialss should be most susceptible to surface protonation. 63 ,64 The anion exchange mechanism in Table 4.3 is the analog of the reaction in Eq. 4.45, wherein the signs of the valences are reversed: B symbolizes a carboxylate group (COO) and M is replaced by a univalent, inorganic anion that forms outersphere complexes with protonated surface hydroxyl or amine groups. This mechanism is not observed often, possibly because of the weakness of the surface complexes involved, but it should be prominent in acidic soils whose clay fraction comprises primarily metal oxides. Another weak adsorption mechanism for either anionic or polar organic functional groups is water bridging; which involves complexation with the
INORGANIC AND ORGANIC SOLUTE ADSORPTION IN SOILS
145
proton in a water molecule solvating an exchangeable cation: Bb(aq) + (HzO)pM m +==
=
Bb(HzO)pMm +==
(4.46)
where B is a molecular unit containing the anionic or polar moiety and M m + is the exchangeable cation. In Eq. 4.46, b = 0 or 1, p = 3, 4, or 6 usually, and m = 1 or 2. Water briding is expected to occur particularly when M is a relatively hard Lewis acid since, in that case, B is less likely to displace a solvating water molecule during surface complex formation. If displacement of the water molecule does occur, an innersphere complex is formed between B b  and M m + and the adsorption mechanism is termed cation bridging. Clearly, whether water bridging or cation bridging takes place during the adsorption of an anionic or polar functional group by a surface bearing solvated exchangeable cations depends on the relative Lewis base character of the functional group and the relative Lewis acid character of the exchangeable cation. For example, the carboxylate groups in humic substances may adsorb on montmorillonite through cation bridging when monovalent exchangeable cations are present and through water bridging when bivalent exchangeable cations are present. 65 Ligand exchange refers specifically to innersphere complex formation between a carboxylate group and either Al(III) or Fe(III) ,in a soil miI)~.r~1 bearing inorganic.hydroxyl groups. This mechanism is exactly analogous to that discussed in Sec. 4.4 for inorganic oxyanion adsorption. The chemical bonds involved are much stronger. 01. course, ~!L.that in aniq~ .S:2'change or in the two bridging mechanisms. Evidence for the ligand exchange mechanism in carboxylate adsorption from soil solutions is abundant but indirect.P" The inorganic surfaces involved are 'on metal oxides and the edges of phyllosilicates in soils. Hydrogen bonding between organic functional groups and either siloxane oxygen atoms or surface hydroxyl groups does not appear to be a significant factor in the adsorption of organic matter, except possibly where it is stabilized by charge localization on the adsorbing surface (Sec. 1.2).63 On the other hand, there is evidence that this mechanism is important in the adsorption of organic compounds by organic surfaces.P? Of much more significance is the role of van der Waals' dispersion interactions, which are multipole (principally dipoledipole) iateractions produced by correlations between fluctuating induced multipole (principally dipole) moments in two nearby uncharged, nonpolar molecules. Although the timeaveraged induced multipole moment in each molecule is zero (otherwise it would not be nonpolar), the correlations between the two induced moments do not average to zero, with the result that a net attractive interaction between the two is produced at very small intermolecular distances. The van der Waals dispersion interaction between two molecules is necessarily very weak, but when many molecules in a polymeric structure interact simultaneously. the van der Waals component is additive. These characteristic features of the van der Waals interaction are discussed further in Sec. 6.2.
146
THE SURFACE CHEMISTRY OF SOILS
For polymeric organic solutes in soil solutions, the van der Waals interaction with the atoms in a solid surface can be quite strong and relatively longrange. The influence of this interaction in biopolymers, such as proteins and carbohydrates, is believed to be the fundamental reason for the very frequent appearance of Hstype adsorption isotherms when these large molecules react with soil minerals.P" The effects of van der Waals interactions are especially apparent when the ionic strength of the soil solution is high enough to suppress the ionization of acidic functional groups on large organic solute molecules or when the pH has been adjusted to make the net charge on them vanish. (See Sec. 6.3.) The adsorption mechanisms listed in Table 4.3 are expected to operate when dissolved soil organic matter reacts with solid soil particles. Although the structural chemistry of soluble organic matter in soils is not well understood, certain generalizations concerning adsorption can be made on the basis of studies in which the pH and surface characteristics of model adsorbents have been varied systematically. One of the most important of t!tese generalizations is that the quantity of dissolved organic matter adsorbed tends to decrease as the pH increases above 4.0. 69 This fact suggests that dissolved soil organic matter forms ligandlike surface complexes, as described in Sec. 4.4 f~r inorganic ox~anions, and therefore tJiat the Eredominant adsoq~tion mechanisms are those appropriate to anions.  The surfaces bearing charged siloxane ditrigonal cavities in soils reacts with dissolved organic matter in two principal ways. First, the permanent, negative surface charge produces a negative adsorption of the organic matter that should become more pronounced as the pH value of the soil solution increases and the organic matter becomes more anionic. Second, carboxylate and phenolic hydroxyl groups in the organic matter particularly should form complexes with the siloxane ditrigonal cavities through exchangeable cations in surface complexes with these cavities. These two kinds of interaction oppose one another on the external surfaces of quasicrystals or other aggregate units; no interlayer adsorption, negative or positive, is involved. !!. the exchangeable cation is monovalent. the amoullt of organic matter adsorbed increases as the Lewis acidsc;>ftness of tlJe cation increases, indicating that the organic ligands involved are softer Lewis bases than solvation wilter molecules and that cation bridging is the main adsorption mechanism.F If the exchangeable cation is bivalent, the amount of organic matter adsorbed increases as the ionic potential of the cation increases, suggesting that weak protonation of the organic ligands through water bridging is the principal adsorption mechanism, since purely electrostatic interactions across a solvation shell should be favored with cations of high ionic potential. 65 Cation bridging does not seem likely in this case because there is no correlation between the amount adsorbed and the Lewis acid softness of the exchangeable action. The edge surfaces of soil phyllosilicates and the surfaces of metal oxyhydroxides react with dissolved organic matter through the ligand
INORGANIC AND ORGANIC SOLUTE ADSORPTION IN SOilS
147
exchange mechanism.?" which operates in much the same way as described for inorganic oxyanions in Sec. 4.4. Because of the polymeric, polyfunctional nature of dissolved soil organic matter, however, it is expected that protonation and van der Waals interactions play a role in adsorption, as does negative adsorption when the net oxidic surface charge is negative. Increasing soil pH both enhances negative adsorption and diminishes the number of protons available to create the surface OH; groups that mediate the ligand exchange reaction. Thus the acid dissociation constants of both the organic matter and the soil adsorbents are pertinent. Ligand exchange reactions between inorganic surface hydroxyl groups and carboxyl groups in dissolved soil organic matter produce innersphere complexes between the metal cations AI(III) and Fe(III) and the carboxyls. These reactions are relatively fast, and their effect on the metal cation is to weaken its bonds to the oxygen ions surrounding,lt .io!he adsorbent throu~h an accompanying redistribution of cbargr:.~§ This effect is the first step in the subsequent d,etachment of the metalorganic hgana complex into the soil solution, the ratedetermining step in the ultimate dissolution of the solid adsorbent. In this way, the adsorption of organic matter plays a critical role in the weathering of kaolinite, amorphous aluminosilicates, and aluminum or iron oxyhydroxides in soils. 71 NOTES 1. The concepts and terminology of adsorption phenomena are discussed in detail in D. H. Everett, Manual of Symbols and Terminology for Physicochemical Quantities and Units. Appendix II: Definitions, Terminology and Symbols in Colloid and Surface Chemistry. Butterworths, London, 1972. 2. For a brief review of experimental methods, see the first four sections in S. Burchill, M.H.B. Hayes, and D. J. Greenland, Adsorption, in The Chemistry of Soil Processes (D. J. Greenland and M.H.B. Hayes, eds.), Wiley, Chichester, U.K., 1978. 3. A complete discussion of the relative surface excess is given in Chap. II of R. Defay and I. Prigogine, Surface Tension and Adsorption. Wiley, New York. 1966. 4. S. D. Forrester and C. H. Giles, From manure heaps to monolayers: One hundred years of solutesolvent adsorption isotherm studies, Chemistry and Industry, April 15, 1972, p. 318. 5. C. H. Giles, T. H. MacEwan, S. N. Nakhwa, and D. Smith, Studies in adsorption. Part XI: A system of classification of solution adsorption isotherms and its use in diagnosis of adsorption mechanisms and in measurement of specific surface areas of solids, J. Chem. Soc., London, 3973 (1960). C. H. Giles, D. Smith, and A. Huitson, A general treatment and classification of the solute adsorption isotherm. I: Theoretical, J. Colloid Interface Sci. 47: 755 (1974). C. H. Giles, A. P. D'Silva, and I. A. Easton, A general treatment and classification of the solute adsorption isotherm. Part II: Experimental interpretation. J. Colloid Interface Sci. 47: 766 (1974). 6. The development of these two equations to describe adsorption from a~ueous solution» hall been reviewed in S. D. Forrester and C. H. Giles, op. cit. For a
148
THE SURFACE CHEMISTRY OF SOILS
comprehensive review of adsorption isotherm equations in soil chemical studies, see C. C. Travis and E. L. Etnier, A survey of sorption relationships for reactive solutes in soil, J. Environ. Qual. 10:8 (1981). 7. The advantages of Eq, 4.9 over other linear forms of the Langmuir equation are discussed in J. A. Veith and G. Sposito, On the use of the Langmuir equation in the interpretation of "adsorption" phenomena. Soil Sci. Soc. Am. J. 41:697 (1977). 8. I.C.R Holford, RW.M. Wedderburn, and G.E.G. Mattingly, A Langmuir twosurface equation as a model for phosphate adsorption by soils. J. Soil Sci. 25:242 (1974). 9. G. Sposito, On the use of the Langmuir equation in the interpretation of "adsorption" phenomena. II: The "twosurface" Langmuir equation, Soil Sci. Soc. Am. J. 46:1147 (1982). See also I. M. Klotz, Numbers of receptor sites from Scatchard graphs: Facts and fantasies. Science 217: 1247 (1982). (In the literature of macromolecular chemistry, Fig. 4.2 is known as a Seatchard plot.) 10. G. Sposito, Derivation of the Freundlich equation for ion exhange reactions in soils. Soil Sci. Soc. Am. J. 44:652 (1980). 11. R Sips, On the structure of a catalyst surface. J. Chem. Phys. 16:490 (1948). 12. See, e.g., Chap. 6 in E. Butkov, Mathematical Physics. AddisonWesley, Reading, Mass., 1968. 13. A thoughtful review of the problems discussed in this section is given in R B. Corey, Adsorption vs precipitation, in Adsorption of Inorganics at SolidLiquid Interfaces (M. A. Anderson and A. J. Rubin, eds.). Ann Arbor Science, Ann Arbor, Mich., 1981. 14. Demonstrations have been given in J. A. Veith and G. Sposito, op. cit.,? G. Sposito, op. cit. ,9 and A. M. Elprince and G. Sposito, Thermodynamic derivation of equations of the Langmuir type for ion equilibria in soils, Soil Sci. Soc. Am. J. 45:277 (1981). 15. For a discussion of lAP, see Chap. 3 in G. Sposito, The Thermodynamics of Soil Solutions. Clarendon Press, Oxford, 1981. 16. See, e.g., Chap. 5 in W. Stumm and J. J. Morgan, Aquatic Chemistry. Wiley, r:">. New York, 1981. 17. See, e.g., pp. 67ft in G. ~, op. cit.1s 18. J. W. Stucki and W. L. Banwart, Advanced Chemical Methods for Soil and Clay Minerals Research. Reidel, Dordrecht, Holland, 1980. J. J. Fripiat, Advanced Techniques for Clay Mineral Analysis. Elsevier, Amsterdam, 1982. 19. A review of the early sorption rate literature for phosphate is given in J. C. Ryden and P. F. Pratt, Phosphorus removal from wastewater applied to land, Hilgardia 48:1 (1980). See also J. A. Veith and G. Sposito.P 20. W. H. van Riemsdijk and F.A.M. de Haan, Reaction of orthophosphate with a sandy soil at constant supersaturation, Soil Sci. Soc. Am. J. 45:261 (1981). 21. J. A. Veith and G. Sposito, Reactions of aluminosilicates, aluminum hydrous oxides, and aluminum oxide with ophosphate: The formation of Xray and amorphous analogs of variscite and montebrasite, Soil Sci. Soc. Am. J 41:870 (1977). 22. V. E. Berkheiser, J. J. Street, P.S.C. Rao, and T. L. Yuan, Partitioning of inorganic orthophosphate in soilwater systems, CRe Critical Reviews in Environmental Control 10:179 (1980). 23. C. C. Travis and E. L. Etnier, op. cit. 6
INORGANIC AND ORGANIC SOLUTE ADSORPTION IN SOILS
149
24. J. de Kanel and J. W. Morse, The chemistry of orthophosphate uptake from seawater onto calcite and aragonite, Geochim. Cosmochim. Acta 42:1335 (1978). S. H. Chien and W. R. Clayton, Application of the Elovich equation to the kinetics of phosphate release and sorption in soils, Soil Sci. Soc. Am. J. 44:265 (1980). W. H. van Riemsdijk and F.A.M. deHaan, op. cit.2o 25. C. Aharoni and M. Ungarish, Kinetics of activated chemisorption. 2: Theoretical models, J.C.S. Faraday 173:456 (1977). 26. Y.S.R. Chen, J. N. Butler, and W. Stumm, Kinetic study of phosphate reaction with aluminum oxide and kaolinite, Env. Sci. Technol. 7: 327 (1973). D. N. Munns and R. L. Fox, The slow reaction which continues after phosphate adsorption: Kinetics and equilibrium in some tropical soils, Soil Sci. Soc. Am. J. 40:46 (1976). 27. See, e.g., Chap. 4 in W. P. Kelley, Cation Exchange in Soils. Reinhold, New York, 1948. 28. M.G.M. Bruggenwert and A. Kamphorst, Survey of experimental information on cation exchange in soil systems, in Soil Chemistry. B. PhysicoChemical Models (G. H. Bolt, ed.). Elsevier, Amsterdam, 1979. M. M. Reddy, Ionexchange materials in natural water systems, Ion Exchange and Solvent Extraction 7: 165 (1977). 29. D. G. Kinniburgh and M. L. Jackson, Cation adsorption by hydrous metal oxides and clay, in M. A. Anderson and A. J. Rubin, op. cit. 13 30. See, e.g., Chap. 3 and 5 in G. Sposito, op. citY 31. See Sec. 6.4 in G. Sposito, op. cit. 15 32. The concept of innersphere surface complexation as the basis for relative metal adsorption selectivity in soils was introduced in W. R. Heald, M. H. Frere, and C. T. deWit, Ion adsorption on charged surfaces, Soil Sci. Soc. Am. J. 28: 622 (1964). Further quantitative development of tlris concept was given in I. Shainberg and W. D. Kemper, Ion exchange equilibria on montmorillonite, Soil Sci. 103:4 (1967). See also the discussion of this paper in Soil Sci. 104:444 (1967). 33. The HSAB principle is discussed in an introductory fashion in P. J. Sullivan, The principle of hard and soft acids and bases as applied to exchangeable cation selectivity in soils, Soil Sci. 124:117 (1977). See also Sec. 3.3 in G. Sposito, op. cit.15 34. M. Misono, E. Ochai, Y. Saito, and Y. Yoneda, A new dual parameter scale for the strength of Lewis acids and bases with the evaluation of their softness, J. Inorg. Nucl. Chem. 29: 2685 (1967). 35. A. Maes and A. Cremers, Charge density effects in ion exchange. Part 2. Homovalent exchange equilibria, J.C.S. Faraday I 74: 1234 (1978). 36. M.G.M. Bruggenwert and A. Kamphorst, op. cit.28 37. The difficulties of this kind that arise when chloride ions are present in the aqueous solution phase are investigated in G. Sposito, K. M. Holtzclaw, C. Jouany, L. Charlet, and A. L. Page, Sodiumcalcium and sodiummagnesium exchange on Wyoming bentonite in perchlorate and chloride background ionic media, Soil Sci. Soc. Am. J. 47: 51 (1983). 38. A similar organization of ligand effects is presented in M. M. Benjamin and J. O. Leckie, Conceptual model for metalligandsurface interactions during adsorption, Environ. Sci. Technol. 15:1050 (1981). 39. H. Farrah and W. Pickering, The sorption of copper species by clays. I: Kaolinite, AWl. J. Chern. 29: 1167 (1976). II: Illite and montmorillonite, AWl.
150
THE SURFACE CHEMISTRY OF SOILS
J. Chem. 29:1177 (1976). J. A. Davis and J. 0. Leckie, Effect of adsorbed
complexing ligands on trace metal uptake by hydrous oxides, Environ. Sci. Technol. 12: 1309 (1978). See also the discussion of the third paper in Environ. Sci. Techol. 13:1289 (1979). 40. M.D.A. Bolland, A. M. Posner, and J. P. Quirk, Zinc adsorption by goethite in the absence and presence of phosphate, Aust. J. Soil Res. 15: 279 (1977). M. M. Benjamin and N. S. Bloom, Effects of strong binding of anionic adsorbates on adsorption of trace metals on amorphous iron oxyhydroxide, in Adsorption from Aqueous Solutions (P. H. Tewari, ed.). Plenum, New York, 1981. 41. R. M. McKenzie, The adsorption of lead and other heavy metals on oxides of manganese and iron, Aust. J. Soil Res. 18:61 (1980). H. Kerndorf and M. Schnitzer, Sorption of metals on humic acid, Geochim. Cosmochim. Acta 44:1701 (1980). D. G. Kinniburgh, M. L. Jackson, and J. K. Syers, Adsorption of alkaline earth, transition, and heavy metal cations by hydrous oxide gels of iron and aluminium, Soil Sci. Soc. Am. J. 40:796 (1976). H. Farrah and W. F. Pickering, Influence of claysolute interactions on aqueous heavy metal ion levels, Water, Air and Soil Pollution 8: 189 (1977). 42. D. G. Kinniburgh and M. L. Jackson, op. cit.29 H. Farrah and W. F. Pickering, op. cit.39 D. G. Kinniburgh and M. L. Jackson, Concentration and pH dependence of calcium and zinc adsorption by iron hydrous oxide gel, Soil Sci. Soc. Am. J. 46: 56 (1982). 43. M. H. Kurbatov, G. B. Wood, and J. D. Kurbatov. Isothermal adsorption of cobalt from dilute solutions, J. Phys. Chem. 55:1170 (1951). The term was coined in D. G. Kinniburgh and M. L. Jackson, op. cit. ,29 p. lOI. 44. M. M. Benjamin and J. 0. Leckie, Effects of complexation by CI, S04, and S203 on adsorption behavior of Cd on oxide surfaces, Environ. Sci. Technol. 16: 162 (1982). 45. J.T.G. Overbeek, Electrokinetic phenomena, in Colloid Science, Vol. I (H. R. Kruyt, ed.). Elsevier, Amsterdam, 1952. R.O. James and T. W. Healy, Adsorption of hydrolyzable metal ions at the oxidewater interface. II: Charge reversal of Si02 and Ti0 2 colloids by adsorbed Co(I1), La(I1I) , and Th(IV) as model systems, J. Colloid Interface Science 40: 53 (1972). c.P. Huang and W. Stumm, Specific adsorption of cations on hydrous aAh03, J. Colloid Interface Science 43: 409 (1973). S. L. SwartzenAllen and E. Matijevic, Colloid and surface properties of clay suspensions. II: Electrophoresis 'and cation adsorption of montmorillonite, J. Colloid Interface Sci. 50:143(1975). G. R. Wiese, R. 0. James, D. E. Yates, and T. W. Healy, Electrochemistry of the colloidwater interface, in Electrochemistry (J. O'M. Bockris, ed.). Butterworths, London, 1976. D. W. Fuerstenau, D. Manmohan, and S. Raghavan, The adsorption of alkalineearth metal ions at the rutile/aqueous solution interface, in P. H. Tewari, op. cit.40 46. D. W. Fuerstenau et al., op. cit.45 47. R. 0. James and T. W. Healy, op. cit. 45 48. See, e.g., M. M. Benjamin and J. 0. Leckie, Adsorption of metals at oxide interfaces: Effects of the concentrations of adsorbate and competing metals, in Contaminants and Sediments, Vol. 2 (R. A. Baker, ed.), Ann Arbor Science, Ann Arbor, Mich., 1980. 49. See, e.g., p. 51 in F. C. Loughnan, Chemical Weathering of the Silicate Mtnerals. American Elsevier. New York. 1969.
INORGANIC AND ORGANIC SOLUTE ADSORPTION IN SOILS
151
50. C.J.B. Mott, Anion and ligand exchange, in D. J. Greenland and M.H.B.
Hayes, op, cit.2 51. R. L. Parfitt, Anion adsorption by soils and soil materials, Advan. Agron. 30: 1 (1978). 52. F. J. Hingston, A review of anion adsorption, in M. A. Anderson and A. J.
Rubin, op. cit. 13 53. R. E. White, Retention and release of phosphate by soil and soil constituents, in Soils and Agriculture (P. B. Tinker, ed.). Wiley, New York, 1981. 54. J. A. Davis and J. O. Leckie, Surface ionization and complexation at the oxide/water interface. 3: Adsorption of anions, J. Colloid Interface Sci. 74: 32 (1980). 55. See, e.g., J. R. Sims and F. T. Bingham, Retention of boron by layer silicates, sesquioxides, and soil materials: I: Layer silicates, Soil Sci. Soc. Am. J. 31: 728 (1967). III: Iron and aluminumcoated layer silicates and soil materials, Soil Sci. Soc. Am. J. 32: 369 (1968). 56. J. R. Sims and F. T. Bingham, Retention of boron by layer silicates, sesquioxides, and soil materials, Soil Sci. Soc. Am. J. 32: 364 (1968). M. A. Anderson,
57.
58.
59.
60. 61.
62.
J. F. Ferguson, and J. Gravis, Arsenate adsorption on amorphous aluminum hydroxide, J. Colloid Interface Sci. 54: 391 (1976). F. J. Hingston, A. M. Posner, and J. P. Quirk, Competitive adsorption of negatively charged ligands on oxide surfaces, Disc. Faraday Soc. 52: 334 (1971). D. T. Malotky and M. A. Anderson, The adsorption of the potential determining arsenate anion on oxide surfaces, Colloid Interface Sci. 4: 281 (1976). M. A. Anderson and D. T. Malotky, The adsorption of protolyzable anions on hydrous oxides at the isoelectric pH, J. Colloid Interface Sci. 72: 413 (1979). R. J. Atkinson, A. M. Posner, and J. P. Quirk, Kinetics of isotopic exchange of phosphate at the aFeOOHaqueous solution interface, J. Inorg. Nucl. Chem. 34: 2201 (1972). J. H. Kyle, A. M. Posner, and J. P. Quirk, Kinetics of isotopic exchange of phosphate adsorbed on gibbsite, J. Soil Sci. 26: 32 (1975). Note that the parameters A and B in these two papers correspond to k l and k 2 in Eq. 4.34. A comprehensive discussion of this and other aspects of the ligand exchange reaction in dissolutionprecipitation reactions is given in W. Stumm, G. Furrer, and B. Kunz, The role of surface coordination in precipitation and dissolution of mineral phases, Croatica Chem. Acta 58:593 (1983). D. E. Yates and T. W. Healy, Mechanism of anion adsorption at the ferric and chromic oxide/water interfaces, J. Colloid Interface Sci. 52: 222 (1975). R. L. Parfitt, J. D. Russell, and V. C. Farmer, Confirmation of the surface structures of goethite (aFeOOH) and phosphated goethite by infrared spectroscopy, i.c.s. Faraday I 72: 1082 (1976). R. L. Parfitt, Phosphate adsorption on an oxisol, Soil Sci. Soc. Am. J. 41: 1065 (1977). R. L. Parfitt, R. J. Atkinson, and R. St. C. Smart, The mechanism of phosphate fixation on iron oxides, Soil Sci. Soc. Am. J. 39: 837 (1975). R. L. Parfitt, The nature of the phosphategoethite (aFeOOH) complex formed with Ca(H2P04h at different surface coverage, Soil Sci. Soc. Am. J. 43:623 (1979). J. B. Harrison and V. E. Berkheiser, Anion interactions with freshly prepared hydrous iron oxides, Clays and Clay Minerals 30: 97 (1982). The data in Table 4.2 are extracted in part from a compilation in S. R. Goldberg, A Chemical Model of Phosphate Adsorption on Oxide Minerals and Soils. Ph.D. dissertation. University of Califcrnia, Riverside. 1983.
152
THE SURFACE CHEMISTRY OF SOilS
63. A summary of the earlier studies with model compounds is in the classic review by M. M. Mortland, Clayorganic complexes and interactions, Advan. Agron. 22: 75 (1970). See also D. J. Greenland, Interactions between humic and fulvic acids and clays, Soil Sci. 111:34 (1971). 64. See, e.g., Chap. 7 in B.K.G. Theng, Formation and Properties of ClayPolymer Complexes. Elsevier, Amsterdam, 1979. 65. See Chap. 12 of B.K.G. Theng, op. cit. ,64 and Claypolymer interactions: Summary and perspectives, Clays and Clay Minerals 30: 1 (1982). 66. R. L. Parfitt, A. R. Fraser, J. D. Russell, and V. C. Farmer, Adsorption on hydrous oxides. II: Oxalate, benzoate and phosphate on gibbsite, J. Soil Sci. 28:40 (1977). R. L. Parfitt, A. R. Fraser, and V. C. Farmer, Adsorption on hydrous oxides. III. Fulvic acid and humic acid on goethite, gibbsite, and imogolite, J. Soil Sci. 28: 289 (1977). R. Kummert and W. Stumm, The surface complexation of organic acids on hydrous aAI2 0 3 , J. Colloid. Interface Sci. 75: 373 (1980). S. N. Yap, R. K. Mishra, S. Raghavan, and D. W. Fuerstenau, The adsorpton of oleate from aqueous solution onto hematite, in P. H. Tewari, op. cit/" J. A. Davis, Adsorption of natural dissolved organic matter at the oxide/water interface, Geochim. Cosmochim. Acta 46: 2381 (1982). 67. See, e.g., S. Burchill et al., op. cit.2 pp. 325ff. 68. See, e.g., Chaps. 7 and 10 of B.K.G. Theng, op. cit.64 69. Chapter 12 in B.K.G. Theng, op. cit.64 J. A. Davis, op. cit.66 J. A. Davis, in Vol. 2 of R. A. Baker, op. cit.48 70. P. Chassin, N. Nakaya, and B. Le Berre, Influence des substances hurniques sur les proprietes des argiles. II. Adsorption des acides humiques et fulviques par la montmorillonite, Clay Minerals 12: 261 (1977). R. L. Parfitt et aI., op. cit.66 K. R. Tate and B.K.G. Theng, Organic matter and its interactions with inorganic soil constituents, in Soils with Variable Charge (B.K.G. Theng, ed.) New Zealand Society of Soil Science, Lower Hutt, N.Z., 1980. 71. K. H. Tan, The catalytic decomposition of clay minerals by complex reaction with humic and fulvic acid, Soil Sci. 120: 188 (1975). K. R. Tate and B.K.G. . 70 Th eng, op. CIt.
FOR FURTHER READING
M. G. Browman and G. Chesters, The solidwater interface: Transfer of organic pollutants across the solidwater interface. Advan. Environ. Sci. Techno!. 8(1): 49 (1977). The adsorption mechanisms for pesticides in soils are discussed in the first three sections of this review article. C. H. Giles and S. D. Forrester, Studies in the early history of surface chemistry, Chemistry and Industry, Nov. 8, 1969; Jan. 17, 1970; Jan. 9, 1971; July 24, 1971; Nov. 13,1971; April 15,1972. This history of surface phenomena is a must for any serious student of the subject. Parts V and VI, on solute adsorption by solid surfaces, give and wellillustrated, lively account of the role of soil chemists in the development of the adsorption isotherm concept. D. J. Greenland and M.H.B. Hayes, The Chemistry of Soil Processes. Wiley, Chicester, U.K., 1981. Chapters 5 and 6 in this comprehensive treatise provide detailed surveys of experimental methods and molecular mechanisms for adsorption phenomena in soils.
INORGANIC AND ORGANIC SOLUTE ADSORPTION IN SOilS
153
M. M. Mortland, Clayorganic complexes and interactions, Advan. Agron. 22: 75 (1970). This classic review article remains the best comprehensive introduction to adsorption mechanisms for organic compounds. B.K.G. Theng, Formation and Properties of ClayPolymer Complexes. Elsevier, Amsterdam, 1979. Chapters 7, 10, and 12 of this encyclopedic treatise present detailed discussions of the adsorption of compounds in soil organic matter by clay minerals.
5 CHEMICAL MODELS OF SURFACE COMPLEXATION
5.1. THE DIFFUSE DOUBLE LAYER MODEL
Diffuse double layer (DDL) theory as applied to the surface chemistry of soils refers to the description of ion charge and inner potential contained in the PoissonBoltzmann equation.' (5.1) where «/I(x) is the inner potential at a distance x from the surface of a soil particle along a normal extending into the soil solution. The sum includes all charged species in the soil solution, with species i having the valence Z, and the bulk concentration c, in moles per cubic meter. The other parameters are as described following Eq. 1.11. Besides the hypothesis that the Poisson equation (Eq. 3.26), from which Eq. 5.1 is derived, is physically meaningful when x is measured over molecular dimensions, there are four basic assumptions embodied in the PoissonBoltzmann equation as written above: 1. The surface from which x is measured is a uniform, infinite plane of charge characterized by a density a expressed in coulombs per square meter. 2. The charged species in the soil solution are point ions dissociated completely from the planar surface lying at x = O. These ions interact among themselves and with the surface through the coulomb force. 3. The water in the soil solution is a uniform continuum liquid characterized by the dielectric constant, D. 4. The inner potential, «/I(x), is proportional to W/(x), the average energy required to bring an ion i from a point at infinity to a point at x in the soil solution. Since W,(x) should include the effects of both noncoulombic interactions (e.g., shortrange repulsive forces that deter
CHEMICAL MODELS OF SURFACE COMPLEXATION
155
mine ion size) and fluctuations of the true inner potential about its mean value, l/J(x), it follows that these effects are neglected when the DDL assumption (5.2)
is invoked. The limitations imposed on DDL theory as a molecular model by these four basic assumptions have been discussed frequently and remain the subject of current research.v? In Sees, 1.4 and 3.4 it is shown that DDL theory provides a useful framework in which to interpret negative adsorption and electrokinetic experiments on soil clay particles. This fact suggests that the several differences between DDL theory and an exact statistical mechanical description of the behavior of ion swarms near soil particle surfaces must compensate one another in some way, at least in certain applications. Evidence supporting this conclusion is considered at the end of the present section, whose principal objective is to trace out the broad implications of Eq. 5.1 as a theory of the interfacial region. The approach taken serves to develop an appreciation of the limitations of DDL theory that emerge from the mathematical structure of the PoissonBoltzmann equation and from the requirement that its solutions be selfconsistent in their physical interpretation. The limitations of DDL theory presented in this way lead naturally to the concept of surface complexation. The surface charge density that accumulates in a plane lying at a distance x from a soil particle surface along a normal extending into the soil solution can be calculated with the equation! u(x)
= (00 ~ CiZiF exp(  ZiFl/J(X')jRT)dx'
Jx
(5.3)
I
In Eq. 5.3, it is assumed that the concentration of each ion in the soil solution achieves its "bulk value", c., well before another soil particle surface is encountered along the x direction moving out from the origin of spatial coordinates at x = O. Thus the distance separating soil particle surfaces is assumed to be much larger than the domain over which l/J(x) differs significantly from zero. 3 With this assumption, the upper limit of the integral defining u(x) can be set at infinity and the boundary condition, that the DDL potential and electric field intensity vanish at this upper limit, can be applied. The mathematical identity 2l/J
d(dl/J) == d 2 dx dx dx
(5.4a)
and Eq, 5.3 can be used to convert Eq. 5,1 to the differential equation dl/J
u(x)
dx
enD
=
(5,5)
156
THE SURFACE CHEMISTRY OF SOILS
where the vanishing of the electric field intensity, dl/J/dx, at a point at infinity has been invoked. This formal result can be developed into an explicit equation for O"(x) by integrating both sides of the PoissonBoltzmann equation with the help of another mathematical identity: d2l/J dl/J) 2 d ( dx == 2 dx2 dl/J
(5.4b)
The integration of Eq. 5.1 with respect to l/J from l/J((0) = 0 to l/J(x) yields the differential equation 2
dl/J) = 2RT L dexp( ZiFl/J(X)/RT)  1] ( d x eoD i
(5.6)
The square root of both sides of Eq. 5.6 can be taken under the convention that the sign of the root is opposite to that of l/J(x). Then Eqs. 5.5 and 5.6 produce the expression 1/ 2
O"(x) = sgn(l/J) { 2eoDRT ~ dexp( ZiFl/J(X)/RT)  1]}
(5.7)
where sgn( l/J)
+1
= { 1
l/J>O l/J
Equation 5.7 is a generalization of Eq. 3.39, which was used in the interpretation of electrokinetic phenomena. It establishes the DDL model relationship between the electric potential at a point and the accumulated density of surface charge at the point, subject to the condition that 0" vanish with l/J. Equation 5.5, a general expression that relates the electric field to the density of surface charge in a system exhibiting rectangular symmetry, 1 is equivalent to the differential equation 2 dl/J {2RT (5.8) dx = sgn(l/J) eoD~ ci[exp(ZiFl/J(X)/RT) 1]
}1/
according to Eq. 5.7. The solution of this equation to obtain l/J(x) permits the calculation of O"(x) and the volumetric charge density, p(x) =
L
CiZiF exp( ZiFl/J(X)/RT)
(5.9)
i
These two charge densities and the inner potential provide a complete description of the interfacial region according to DDL theory. Equation 5.8 can be solved analytically in three special cases wherein the aqueous solution phase contains a single strong electrolyte." These are the symmetric electrolyte (e.g., NaCI0 4), the 2: 1 electrolyte, (e.g., Ca(CI04h ), and the 1: 2 electrolyte (e.g., Na2S04)' The mathematical manipulations involved are simplified after the transformations
y • Fl/J/RT
f3 • 2F 2/ F. oDRT
157
CHEMICAL MODELS OF SURFACE COMPLEXATION
introduced in connection with Eq. 1.17, are applied to Eq. 5.8:
dy
dx = sgn(y)J{i{c+[exp(Z+y)  1] + c[exp(Z_y)  I]P/2
(5.10)
where c., and Z+ refer to the cation and c: and Z_ refer to the anion in the electrolyte. Equation 5.10 is the working DDL equation to be solved in the three special cases. The particular forms of this equation are •
Symmetric electrolyte: Z+ == Z = Z_, C+
dy dx
=
= Co = c:
sgn(y)K[exp( Zy) + exp(Zy)  2r/2
=  K exp( Zy/2) [exp (Zy)  1] •
2: 1 electrolyte: Z+ = 2, Z_ = 1, C+
= Co, c:
(5.lIa)
== 2co
dy
dx = sgn(y)K[exp( 2y) + 2 exp(y)  3]1/2
+ 2 exp(y)]l/2 (5. Llb) • 1:2 electrolyte: Z+ = 1, Z_ = 2, c., == 2co, c: == Co = K exp( y)[exp(y)  1][1
dy
dx = sgn(Y)K'[2 exp( y) + exp(2y)  3]1/2
= K' exp(y) [exp( y)  1][1 + 2 exp( _y)]1/2
(5.lIc)
where K = J f3co and K' = J f3co. The solutions of these equations are listed in Table 5.1. As an illustration of the method by which they are obtained, consider Eq. 5.lIa. A separation of variables and the subsequent integration of both sides of this equation yields the result Y(X) eZy/2 dy eZY  1 =
1 iY(X)
2:
i Yo
csch(Zy/2)dy Yo
=
.!.In[tanh(ZY(X)/4)] Z tanh (ZYo/4)
=
K
J: dx' = KX
where cschu=
2 U
e  e
U
e"  e u tanh u = U u e +e
and Yo ;& yeO). Upon rearranging this result to be an equation for ",(x), one obtains ",(x) = 4 RT tanh 1(ae Z.'<X) ZF
(5.12)
158
THE SURFACE CHEMISTRY OF SOILS
Table 5.1. Analytical solutions of the PoissonBoltzmann equation for single
.
electrolytes'' Electrolyte
DDL electric potential"
Symmetric
l/J(X) = (4RTjZF)tanh 1(aeZKX ) with a = tanh(ZFl/J(O)j4RT)
2:1
l/J(x) =
(RTjF)ln[~ tanh
2
(V;
KX +
b) ~]
with b = tanh 1{[1 + 2 exp(Fl/J(O)jRT)F/ 2j J3} 2: 1
6b' exp(J3Kx) } l/J(x) = (RTjF) In { 1 + [b' exp(J3Kx)  IF
. (1 + 2eYO)1/2 + J3 With b' = (1 + 2eYO)1/2 _ J3' Yo = Fl/J(O)jRT
1:2
6c exp(J3K'X) } l/J(x) = (RTjF) In { 1 + [c exp(J3K'X) _ 1)2 . (1 + 2e YO)1/2 + J3 with c = (1 + 2e YO)1/2 _ J3' Yo = Fl/J(O)jRT
1:2
l/J(x)
=
(RTjF)
In[~ tanh
2
(1
K'X +
C') ~]
with c' = tanh I{[1 + 2 exp(Fl/J(O)jRT)]1/2jJ3} = J f3c+ and 1<' = J f3c. When two entries appear for ",(x), the first applies to negative potentials, the second to positive potentials.
• I<
where a == tanh(ZFr/1(O)/4RT). The corresponding surface charge density follows from Eq. 5.5: 8FKa exp(ZKX) O'(X) = ,8[1  a2 exp( 2ZKX)] (5.13) where the formula
has been used. The inverse hyperbolic tangent has the MacLaurin expansion u3 tanh1u = u +  + ... 3 which, for large values of the distance x (i.e., ZKX to be replaced by the approximation RT r/1(x) == 4 ZF a exp(  ZKX)
~
1), permits Eq. 5.12
(5.14)
Equation 5.14 shows that the DOL inner potential decreases exponentially
CHEMICAL MODELS OF SURFACE COMPLEXATION
159
in absolute magnitude at very large distances. Note that this decrease is more rapid as the valence Z increases. The solutions of Eqs. 5.11b and 5.11c are found in a similar manner." (Note that Eq. 5.11c can be derived from Eq. 5.11b by replacingy withy everywhere.) For these cases, the mathematical form of the solution depends on whether the DDL potential is negative or positive. However, in each case it can be demonstrated that the absolute magnitude of the potential approaches its asymptotic value exponentially, as in Eq. 5.14. The applicability of the analytical results in Table 5.1, or of any solution to Eq. 5.8 obtained by numerical integration, to the chemical modeling of the interfacial region can be examined in the context of the balance of surface charge, discussed in Sec. 3.1. The obvious relevance of DDL theory to surface charge balance is as a method for estimating 0'0, the equivalent surface density of dissociated charge. If it is reasonable to locate this surface density in a single plane lying at a distance x from a soil particle surface, then 0'0 = O'(x) and 0'0
= sgn("') {2e oDRT
~ e;[exp(  ZiF",(X)/ RT) 
1]f/2 (5.15)
according to Eq. 5.7. The special case of Eq. 5.15 that occurs when x is the was presented position of the electrokinetic plane of shear (and ",(x) = in Eq. 3.39. Equation 1.11, which figures in the DDL model of negative anion adsorption, can be derived from Eq. 5.15 under the assumptions that the soil solution contains only a 1: 1 electrolyte and that the diffuse ion swarm comes into contact with a soil particle in the plane x = 8. The explicit x dependence of 0'0 is then
n
8FK
O'o(x)
= f3
a exp( KX) 1 _ a2 exp( 2KX)
(x
= 8)
(5.16)
according to Eq. 5.13. A detailed model of the interfacial region requires the specification of the position of the plane where the diffuse ion swarm begins. A popular choice in the literature of soil chemistry' has been x = 0, which means that outersphere surface complexes are neglected entirely and innersphere surface complexes are ignored if they would protrude beyond the plane to which O'in' the intrinsic surface charge density, refers. (See Sees. 1.5 and 3.1 for a discussion of O'in') That this choice is not reasonable physically, however, can be seen from a simple calculation involving Eq. 5.16. Consider a 1: 1 electrolyte at the concentration Co = 100 mol· m 3 and suppose that ",(0) = 8RT/F, a value that is not unrealistic for a smectite siloxane surface. Then K = J f3co = 1.04 X 109 m 1 at 298 K, a = tanh (2) = 0.96403, and . 0.96403 8(9.6487)(1.04) 10 3 x O'D(O) = 1.084 x 1  (0.96403)2  1.01 C·m
2
THE SURFACE CHEMISTRY OF SOilS
160
according to Eq.5.16, with F = 9.6487 X 104 Cvmol ? and f3 = 16 1.084 X 10 m mol"! at 298 K. This result is about 10 times greater than a typical value of 10"01 for a smectite, according to the calculation presented in Eq. 1.22. It is therefore impossibly large. The root cause of the difficulty encountered when the DDL model is applied at the surface to which O"in refers is the neglect of ion size effects. If IO"in I were as large as what DDL theory predicts, the soil particle would be very likely to form inner and outersphere surface complexes that would decrease lO"pl in Eq. 3.2 and lead to a choice of x > O. For example, if the formation of outersphere complexes on a smectite siloxane surface required that the diffuse ion swarm in a 0.1 M 1: 1 electrolyte begin at x = 0.7 nm, then a calculation of 0"0(0.7 nm) would result in 0"0 = 0.032 C om 2 , a reasonable estimate of lO"pl. Looking at the computation in reverse, one could set 0"0 = 2/310"91, according to the estimate of the effect of outersphere surface complexation on Namontmorillonite in NaC! given in connection with the discussion of Table 1.8. The corresponding value of x in Eq. 5.16 would then be x = 0.5 nm, which is again quite reasonable. These examples should make it clear that Eq. 5.15 must be understood to refer to a point somewhere around 0.5 nm from the surface bearing the intrinsic charge on a soil particle in order that the DDL model be realistically applicable to the interfacial region. 6 A more elegant way to illustrate the constraint that 0"0 in Eq. 5.15 be evaluated at a point at least 0.5 nm from the "bare" soil particle surface comes from the results of Monte Carlo computer simulations of ionic solutions near charged planes." This technique, which was mentioned in Sec. 2.1 in connection with the simulation of the I structure in liquid water (Fig. 2.2), permits the calculation of the molecular configuration in any physical system of known density, given its intermolecular potential function. In the case of the DDL model, an appropriate physical system is a set of hardsphere cations and anions immersed in a dielectric continuum and interacting with a charged plane and among themselves as a result of the coulomb force." Because of the finite size of the ions, their centers cannot be found closer to the charged plane than a distance equal to their hardsphere radius, and the results of a computer simulation of their molecular behavior must be compared with the solution of Eq. 5.8 restricted to x values larger than this radius. The same condition applies to Eqs. 5.9 and 5.15. Figure 5.1 shows the x dependence of the components of p(x) in Eq. 5.9 as deduced from Monte Carlo computer simulations of 1 : 1 and 2: 1 electrolytes near a negatively charged plane. 7 The simulations were made for cations and anions with a radius of 0.213 nm immersed in a continuum with a dielectric constant equal to 78.5 (that of liquid water at 298 K). The concentration of the 1: 1 electrolyte was 100 mol m 3, and the ions confronted a plane whose surface charge density equaled 0.266 Com 2. The concentration of the 2: 1 electrolyte was 50 mol m 3, and it confronted a plane of charge density 0.177 C om 2 • For the 1: 1 electrolyte. there is excellent agreement between the data points provided 0
3~
I: I ELECTROLYTE Co =100 mol m 3 CT =0.266C m 2
\
0
u
3 0
o C\J
<,
<,
I
I
Q.. 2 ~
0
~
0 0
0
o
u
+
0 0
Q... 2
CATIONS
0
<,
CATIONS
2:1 ELECTROLYTE c 0 =50molm 3 CT =0.177C m 2
\
0
I
0 0
<,
I
~
Q..
5
10
15
x/d {d=0.425nm}
20
·1 0'
o
ANIONS. •
~
I
I
I
I
2
3
4
,
x/d {d=0.425nm}
Ylpre 5.1. Graphs of the component volumetric charge densities, p+(x) and p_(x), based on Monte Carlo computer simulation (data points) and DDL theory (solid lines)."
I
I
162
THE SURFACE CHEMISTRY OF SOILS
by the computer simulation and the values of the volumetric charge density components, p+(x) = coexp(FIjJ(x)jRT) p_(x) = coexp(FIjJ(x)jRT)
(5.17)
calculated for Co = 100 molrn"? at 298 K with the help of Eq. 5.12 .. At this low concentration, the errors inherent in Eq. 5.1 appear to be mutually compensating.f At higher concentrations (e.g., Co = 103 mol, m 3 ) , the computer simulation results deviate significantly from the predictions of Eq. 5.17, in that DDL theory underestimates the extent of negative anion adsorption and fails to reproduce the oscillation in p + (x) produced by fluctuations in the true electric potential about its mean value, ljJ(x). 7 For the 2: 1 electrolyte, these inadequacies of DDL theory are apparent even at Co = 50 molrn ":', as shown in Fig. 5.1. In this case, the DDL model predictions of ion distribution have only qualitative significance, even when corrected for finite ion size by restricting them to the region x > dj2, where d is the ionic diameter. The results of computer simulation indicate that the PoissonBoltzmann equation does not provide an accurate description of ion swarms containing bivalent species."
5.2. SURFACE COMPLEXATION MODELS: STATISTICAL MECHANICS Consider a solid surface on which a single ionic species has been adsorbed from an aqueous solution phase through the mechanism of either innersphere or outersphere surface complex formation. The solid surface is assumed to bear only one kind of reactive functional group, there being M of these groups per unit area, and it is further assumed that only one group participates in a complex with an adsorbed molecular unit. The geometric properties of the surface do not have to be prescribed more closely than by this requirement of a onetoone complexation reaction with adsorptive ions and by the condition that it be reasonable to speak of at least a welldefined average of z nearestneighbor reactive functional groups for each such group on the surface. These simplifying assumptions concerning ionic adsorption mediated by a surface complexation reaction make it possible to give a straightforward foundational discussion of the principal moleculartheoretic features of several recent surface complexation models. These models, whose specific properties are considered in Sees. 5.3 to 5.6, have as their overall objective the quantitative description of adsorption phenomena in terms of the structure of the interfacial region imparted by the formation of inner and outersphere surface complexes. Just as the DDL model attempts to give quantitative significance to the term O'D in the balance of surface charge through a specification of the spatial distribution of surfacedissociated
". .! "
CHEMICAL MODELS OF SURFACE COMPLEXATION
163
ions, the surface complexation models attempt to give quantitative meaning to the terms (TIS and (T as in the balance of surface charge through predictions of the speciation of surfacecomplexed ions. The combination of these two models then leads to a computerbased algorithm for the estimation of adsorption isotherms and related surface chemical data." The fundamental molecular attributes of the leading surface complexation models can be revealed by pursuing a statistical mechanical description of the chemical system introduced in the first paragraph. Recall that statistical mechanics is the branch of physical chemistry that applies the concepts of probability to interpret the behavior of matter in stable states. 10 For the present discussion, the relevant probability postulate from statistical mechanics is embodied in the Gibbs factor for a single molecular system: P(system)
=
Q exp(Np,/ k B T)
(5.18)
where N is the number of molecules in the system, each of which has the chemical potential (per molecule) u: kB = 1.38054 X 10 23 J. K 1 is the Boltzmann constant; T is absolute temperature, and Q is the partition function for the system. The partition function can be viewed as the relative probability that the system is in any of the numerous states of differing energy available to it, whereas the Gibbs factor, P(system) , represents the relative probability that the system exists with N identical molecules in any of these states.l" Thus P(system) is interpreted as the relative likelihood of observing a chemical system in equilibrium with a thermal reservoir, at temperature T, that regulates the internal energy, and with a matter reservoir, at chemical potential p" that regulates the number of molecules. When the chemical system is an array of surface complexes, the matter reservoir is just the contiguous aqueous solution phase that contains the adsorptive ions. Suppose that the surface complexes and the remaining uncomplexed surface functional groups in the prototypical chemical system under consideration do not interact with one another, except "geometrically" through the constraints
= N SR + NSR'c zNSR 2Nc c + NRC = zNSR'c
M 2NR R + NRC =
(5.19a) (5.19b)
where SR designates an uncomplexed surface functional gro~p, SR'C designates a surface complex, Ni(i = SR or SR'C) is the number of species (per unit area) of type i, and Nj k = Nk j (j, k = Rand C) is the number of pairs of nearestneighbor surface species (per unit area) in which one species is of type j and one is of type k, with R designating a surface functional group and C a surface complex. Equations 5.19 represent conditions imposed by the geometric requirements of a fixed total number of surface functional groups M and a onetoone surface complexation reaction.!" Because these M groups are assumed to react independently, it
164
THE SURFACE CHEMISTRY OF SOILS
is sufficient to formulate a statistical mechanical description of them by considering the two chemical options available to a single surface functional group. The relative probability that an uncomplexed group exists on the surface is (5.20a) and the relative probability that a surface complex exists instead is PSR'C =
QSR'C
exp(Pc/ kBT)
(5.20b)
according to Eq. 5.18. The relative probability that either an uncomplexed group or a complex will be found on the surface at a given location is the sum of the relative probabilities in Eq. 5.20: {(T,PR,Pc) =
QSR
exp(PR/kBT) +
QSR'C
exp(pc/kBT) (5.21)
The function {(T, P R ,pc) provides the basis for calculating any property of the system comprising M independent surface functional groups. If the surface functional group on a solid particle is electrically charged (e.g., the siloxane ditrigonal cavity on montmorillonite), or if an innersphere surface complex formed on it bears a net charge (e.g., a phosphate anion complexed on goethite), it is not reasonable to assume no interactions among the surface species. The same conclusion applies to any outersphere surface complex as well, since the mere physical separation of a complexed, charged species (e.g., a metal cation) from an ionized functional group (e.g., a dissociated surface hydroxyl) leads to a nonvanishing resultant electric field, even in the case of a neutral complex. At the very least, one expects that relatively longrange, although partially screened, coulomb forces will operate among charged functional groups Or complexes on a surface, just as they do in an aqueous solution phase. These electric forces can be envisioned, in a first approximation, to be of a nonspecific character that produces a kind of background potential field that mediates the interactions among the surface species. Taking the simplest case, one can estimate the strength of the background potential by the product of the average number of like nearest neighbors of a central surface species and the average energy of interaction between the central species and one of its neighbors.P Ziet/Ji == (zNJM)ei = average number of nearest neighbors x average interaction energy per neighbor where Z, is the species valence and t/Ji is the average electric potential created by z nearest neighbors of the surface species i. However, the potential field, ,pi, should not be limited to the coulomb effects produced by nearest neighbors, since it pertains to longrange interactions. A more appropriate expression for t/Ji can be obtained by assuming that its van der Waals limit exists. This limit refers to the mathematical process of letting z become infinite while F/ goes to zero in such a manner that their product.
CHEMICAL MODELS OF SURFACE COMPLEXATION
165
1jJ? = UJZie, remains finite:
(5.22) in the van der Waals limit. Equation 5.22 represents the potential field obtained when the range of interaction tends to infinity and the strength of interaction tends to zero in a special way. The concept of a longrange average potential field is not limited to coulombic interactions. It also provides the physical basis for the wellknown van der Waals models of liquids, solutions, and ferromagnets.l" The effect of the average longrange potential field, IjJ(VW) , on P(systern) in Eq. 5.20 is to multiply Q by the Boltzmann factor, exp(  ZeljJ(vw) j «« T), where Z is the valence of the molecular species under consideration: 10 p(VW)(system) == Q exp(ZeljJ(vw)jkBT)exp(p,fkBT)
(5.23)
The Boltzmann factor acts to modify p(vw)(system) for the effect of the "external potential field", ljJ(vw), which acts on each surface species. The corresponding change in g in Eq. 5.21 is g(vw)(T,P.R,P.c)
=
QSR exp[(p.R  ZSR e ljJ~v;»)jkBT] +QsR'c exp[(p.c  ZSR'C e 1jJ~~DjkBT] (5.24)
Equation 5.24 can serve as an approximate relative probability expression for an array of interacting surface species. Note that only the longrange part of the interactions is given explicit consideration. For example, if the surface functional group bears no net charge (e.g., a surface hydroxyl group), then no lateral interaction among such groups appears in the van der Waals model since ZSR equals zero in this case. For the binary surface chemical system described by Eq. 5.24, the most important special cases of complexation reactions are SRZSR(S) + pMm+(aq) + qL1(aq) + xH+(aq)
+ yOH(aq)
= SR'Mp(OH)yHxL~SR'C
SRZSR(S) + qL1(aq) + xH+(aq)
+ pZp(aq)
= SHxL~sC
(5.25a)
+ Rr(aq) (5.25b)
Several examples of these two surface complexation reactions are listed in Table 5.2. The reaction in Eq. 5.25a describes either innersphere complexation of a cationic species or outersphere complexation of any ionic species. Electroneutrality requires that ZSR + pm + x  ql  y
=
ZSR'C + Zp
(5.26)
where m is the valence of the reacting metal M, I is the valence of the reacting ligand L (either inorganic or organic), and SR is assumed to comprise SR'(s), an undissociable moiety, and P. a dissociable molecular unit whose valence is Z,J' (The valence of SR must be equal to I
Table 5.2. Special cases of the reactions in Eq. 5.25
SoOSOH b SOH SOH SOH SOH SOH
Ll
Mm+
SRzsR a
Na+ Na+ Cu2+ Pb z+ 




H+

Cl
H+ H+
OHOH
FUL
C

P0,43Cit3
d

• Siloxane ditrigonal cavity. e
Inorganic surface hydroxyl group. Fulvic acid anion.
d
Citrate (2hydroxypropanel ,2,3tricarboxylate).
b
zm
a
i<
Rr 
pZp
" 'i;"ftf5ttb
,»
?~~~~~;o..
Reaction SoO(s) + Na+(aq) = SoONa(s) SOH(s) + Na+(aq) = SONa(s) + H+(aq) SOH(s) + Cqaq) + H+(aq) = SOHzCI(s) SOH(s) + Cu2+(aq) + FUL"(aq) = SOCuFUL(s) + H+(aq) SOH(s) + Pbz+(aq) + OH(aq) = SOPbOH(s) + H''{aq) SOH(s) + POl(aq) + 2H+(aq) = SHZP04(s) + OlF'(aq) SOH(s) + Cit3(aq) + H+(aq) = SHCiC(s) = OH(aq)
CHEMICAL MODELS OF SURFACE COMPLEXATION
167
ZSR  Zp.) Equation 5.25b describes the innersphere complexation of an anionic species through the ligand exchange mechanism. In this reaction, actually a special case of Eq. 5.25a, SR comprises a permanent structural moiety S and an exchangeable ligand R; the entity R' in the general surface complex SR'C does not exist, and so the symbol for the complex is shortened to SC, where C == HxL q • More generally, one could substitute any cationic species (or set of species) for the proton in Eq. 5.25b. Equations 5.25 can be modified without difficulty to describe the case wherein several surface functional groups are involved simultaneously in a complexation reaction.V The conditional equilibrium constant for the reaction in Eq. 5.25a can be expressed in the form 13 (5.27) where x is a mole fraction, ( ) is an activity in the aqueous solution phase, and
An expression for "K can be derived in the context of the van der Waals model with the help of Eq. 5.24 and the definition 10 p~vw) Ni xi = ' =  ~vw)  M (5.28) of the mole fraction of species i in a binary mixture. Equation 5.28 states that the expected value of the mole fraction is equal to the ratio of the relative probability that i exists in the mixture to the sum of relative probabilities for all components in the mixture. With this equation and the two explicit expressions for P}YW), one derives from Eq. 5.27 the equation C
_
K 
exp[(JLc  ZSR'C e t/J~V;:~/ kBT](pzp) QSR exp[(/LR  ZSR e t/J~i")/kBT](C)
QSR'C
(5.29)
According to thermodynamics, at equilibrium, 10
/Lc  /LR = /L[C(aq)]  /L[pzp(aq)] =
/LO[C(aq)]  /LO[pZp(aq)] + kBT In
[(~~)]
(5.30)
where /LO[C(aq)] == p/LO[Mm+(aq)] + q/LO[LI(aq)] + Y/LO[OH(aq)] and /Lo is a StandardState chemical potential. (In Eq. 5.30, when P exists, /LR is taken to be the chemical potential per molecule of P in the solid adsorbent.) The combination of Eqs. 5.29 and 5.30 produces the model result "K .. (K~R'C/ KSR)exp[ (ZSR'C" e t/J~R~~'  ZSR e t/J~V;»/ k n T] (5.31)
THE SURFACE CHEMISTRY OF SOilS
168
where
KSR'c = QSR'C exp(p,o[C(aq)]/ kBT) K SR = QSR exp(JLO[pZp(aq)]/ kBT)
(5.32)
Finally, wi th the help of Eqs. 5.19a, 5.22, and 5.28, Eq. 5.31 Can be written in the more explicitly compositiondependent form cj(
= (KSR'c/ KSR)exp( + ZSR e l/JgR/ kBT) x exp]  (ZSR'Cl/JgR'C + ZSR l/JgR) e XSR'C/ k B T]
(5.33)
According to the van der Waals model, the conditional equilibrium constant fc1r the reaction in Eq. 5.25a is an exponential function of the mole fracti.on of the surface complex species SR'C. A similar derivation can be given for the conditional equilibrium constant pertaining to the ligand exchange reaction in Eq. 5.25b by deleting R' and settingp = y = and pZp = R r  in Eqs. 5.27, 5.30, 5.31, and 5.32. The thefIllodynamic properties of the reaction in Eq. 5.33 follow immediately from Eq. 5.27 and standard methods of quadrature.P For example, atter equating the right sides of Eqs. 5.27 and 5.33 and forming the common logarithm of all terms, one has the result
°
log (p Zp ) + Iog [XSR'C]    Iog (C) _ Iog [KSR'C. exp(+ZSR e l/JgR/kBT)] XSR K SR (ZSR'C l/JgR'C + ZSR l/JgR)e (In lO)k BT XSR'C (5.34) Equation S.34 shows how measurements of the composition of the adsorbent surface and of the activities in the aqueous solution phase can be used to determine certain combinations of the constant parameters in the van der w~als model. A graph of the left side of Eq. 5.34 versus XSR'C should produce a straight line (at constant temperature) whose y intercept and slope are related to the K and l/Jo parameters of Eqs. 5.22 and 5.32. The standard quadrature formulav' In K =
fa! In « dXSR'C
for the thertllodynamic equilibrium constant pertaining to Eq. 5.25a shows that, in the van der Waals model,
K
=
(KSR'c/ KSR)exp[ (ZSR'Cl/JgR'C  ZSRl/JgR)e/2k BT]
(5.35)
Therefore, the algebraic sum of the y intercept and one half the slope in Eq. 5.34 is equal to the common logarithm of the equilibrium constant, K. The rational activity coefficients of the two solidphase species, SR and SR'C, can also be calculated with standard quadrature formulas, J:l but it is
169
CHEMICAL MODELS OF SURFACE COMPLEXATION
sufficient here only to note that their ratio is fSR'c fSR
K
0
0
= cK = exp[(ZSR'Co/SR'C  ZSRo/SR)ej2k BT] x exp[+(ZSR'Co/~~~  ZSRo/~V;)e/kBT]
(5.36)
according to Eqs. 5.31 and 5.35. Equation 5.36 shows that the exponential factors in the van der Waals model equations for CK and K represent the longrange coulomb contribution to the rational activity coefficients of the surface species. The essence of the van der Waals model is that it provides an estimate of how coulomb interactions among the surface species affect the equilibrium constants for surface complexation reactions and the activity coefficients of these species. The van der Waals model can be generalized to include the situation in which several kinds of surface complex coexist simultaneously or that in which surface complexation involves polydentate ligancies with respect to the surface functional groups (e.g., bidentate complexes with two groups bonded to a bivalent metal cation). 12 These kinds of generalizations of the model are not required explicitly in the present chapter, but their existence underscores the broad utility of the van der Waals model as a conceptual tool for elucidating the foundational aspects of surface complexation theories. 5.3. THE CONSTANT CAPACITANCE MODEL
The constant capacitance mode114 ,15 is a molecular description of surface complexation reactions involving the inorganic hydroxyl group. The chemical basis of the model can be developed from its three principal assumptions concerning the interfacial region: 1. Inorganic hydroxyl groups form only innersphere surface complexes with adsorbed species. 2. The chemical reactions that describe surface complexation are
aSOH(s) + pMm+(aq) + qL1(aq) + xH+(aq) • + yOH(aq) = (SO)aMp(OH)yHxLg(s) + aH+(aq)
(5.37a)
bSOH(s) + qL1(aq) + xH+(aq) = SbHxLJ(s) + bOH(aq)
(5.37b)
where 5 = pm + x  a  ql  y and 'Y = x + b  ql are valences of the solid phase products. Equations 5.37 are the same as Eq. 5.25 (with R = OH, ZSR = 0; P = H, Zp = +1; R' = 0, ZSR'C:; 5; Zsc:; 'Y, r = 1) when b, the number of moles of reactive OH groups, equals unity. In the constant capacitance model, the conditional equilibrium constants for the reactions in Eq. 5.37 use the Constant Ionic Medium Reference State for the activity coefficients of the aqueous species. 16 Because of this convention, the species Mm+(aq) and U(aq) in Eq. 5.37 never refer to the metal cation and the ligand making up the
170
THE SURFACE CHEMISTRY OF SOILS
background electrolyte. By analogy with Eq. 5.27, the conditional equilibrium constant for the reaction in Eq. 5.37a can be written in the form x [H+:r C K I = _s,,o;..:c=__ (5.38) xSOH [C] where and the square brackets refer to concentration in moles per cubic decimeter. Equation 5.38 is written under the assumption that the concentrations [H+] and [C] are enough smaller than the concentration of the background electrolyte to justify setting the aqueous phase activity coefficients equal to 1 on the scale of the Constant Ionic Medium Reference State.l" 3. When the total particle charge is small in absolute magnitude, it is proportional to the inner potential at the particle surface:
=
c»,
(5.39)
where
~CjZ7T/2t/J
(5.40)
which is consistent with Eqs. 3.3a and 5.39 when t/J == t/Js and IZjFt/Js!RTI is small enough to justify replacing the exponential function in Eq. 5.15 by its first three terms in a MacLaurin expansion. In the constant capacitance model, the surface complexation reactions that involve H+ or OH alone are special cases of Eq. 5.37a: 14 SOHt(s) = SOH(s) + H+(aq) (5.41a) THE NET PROTON CHARGE.
SOH(s) = SO(s) + H''{aq)
(5.41b)
The conditional equilibrium constants for these two reactions are 15 KS
=
al 
xsoH[H+] +
XSOH 2
K" _ "so[H+] liZ
(5.42a)
" SOH
(5.42b)
CHEMICAL MODELS OF SURFACE COMPLEXATION
171
(Note that Eq. 5.41a is written in the reverse of the special case of Eq. 5.37a corresponding to a = x = 1, P =q = Y = 0, and that K~l in Eq. 5.42a is the inverse of "K' in Eq. 5.38 applied to this special case.) Besides the conditional constants in Eq. 5.42, the constant capacitance model specifies two intrinsic equilibrium constants for the proton reactions'f K~l(int)
= K~l exp(  Ft/lsiRT)
(5.43a)
K~2(int)
=
(5.43b)
K~2
exp( Ft/lslRT)
The intrinsic equilibrium constants are postulated to be independent of the composition of the solid phase (although they remain conditional in the sense of the Constant Ionic Medium Reference State). They can be determined experimentally on the basis of the linear expressions that result from combining Eqs. 5.39, 5.42, and 5.43: XSOH ) [+] _ s . F log ( xSOHi  log H  log Ka1(mt)  (In 10)CRT log[H+]  10g(:::J
=
log
K~2(int) 
(In
1~CRT
UH
UH
(5.44a) (5.44b)
where up has been set equal to UH, the net proton surface charge density, because of Eq. 3.2. Equations 5.44 can be applied to proton titration data under the assumption that'" pH < PZNPC pH> PZNPC
(5.45)
where U max == FM/N A is the maximum absolute value of UH, M is the total number of reactive OH groups per unit area of adsorbent, N A = 6.023 X 1023 mol"! is the Avogadro constant, and PZNPC is the point of zero net proton charge (Sec. 3.2). Equations 5.45 are equivalent to assuming that the species SO(s) does not exist below the PZNPC and the species SOHt(s) does not exist above the PZNPC; i.e., in general, (5.46) according to Eq. 1.24. The combination of Eqs. 5.44 and 5.45 permits the calculation of log K~i(i = 1 or 2) and the parameter C from the y intercept and slope of a plot of the left side of Eq. 5.44 against either xSOHi or XSo, as illustrated in Fig. 5.2 for yAlz0 3 Y Once the values of the common logarithms of K~l(int) and K~2(int) and of the capacitance density C have been determined in this way, they can be used with Eqs. 5.39,5.42, and 5.43 to calculate UH and the distribution of SOH, SOHt, and SO at any pH value. The conformity of the proton titration data for ,...A1 203 to the constant capacitance model (within experimental precision) is evident in Fig. 5.2.
8
~
0'
0
5
log K~I (int) = 7.2
r
I
_o~
~
~o. ~
yA1 20 3
.~
If
~ I
O.IM NaCI04
10.0
~
6
9.5~ :::: log
21 0
I
0.08
I
I·
I
0.24
I
I
I
0.40
0.56
XSOH+2
I
I
0.72
I
I
9.0 0
 . • 6
0.08
Kg
6
6
6
6 6 6 6
6
(int) =9.5
2
0.24
0.40
0.56
XSO
Ipre 5.2. Plots of the left side of Eq. 5.44 against either xsoH! or XSo for yA1203 suspended in 0.1 M NaCI04 (3.2 kg'm 3 IISpCDSion).17 The different symbols represent separate experiments.
__~
'~
;
 ".~ ~ ;;;...,~. ~_=".."":;,,
.
  .
'.
<:..::0 ....... ••• 
6
173
CHEMICAL MODELS OF SURFACE COMPLEXATION
Equations 5.44 can be recognized as special cases of the van der Waals model expression in Eq. 5.34 obtained by setting ZSR 0 and IZsR'c1 == 1. Equation 5.44a corresponds exactly to Eq. 5.34 after the identifications
=
K:al (iInt)
= 
SO H KK
C
SOH!
= 
CTmax 0 l/JSOH!
(5.47a)
have been made, and the same kind of result follows for Eq. 5.44b with the definitions S'
Kdmt)
K so K SO H
_
=
U max
C=o
l/Jso
(5.47b)
where tIP is the van der Waals potential. These correspondences show that the intrinsic equilibrium constants are related closely to the partition functions of the surface species (Eq. 5.32) and that the capacitance factor is related to the ratio of the maximum absolute value of CTH to the maximum absolute value of the van der Waals mean electric potential (Eqs. 5.22 and 5.45). Thus the intrinsic equilibrium constants provide a quantitative measure of the strength of the chemical bonds between a surface OH group or a surface complex and the remainder of the solid adsorbent. The capacitance parameter is seen to be the capacitance per unit of adsorbent surface area associated with either a fully protonated or a fully dissociated hydroxyl surface. This relationship is consistent with the special case of Eq. 5.39 that occurs when ICTHI = CTmax and ll/Jsl is equal to its maximum value. The intrinsic equilibrium constants have thermodynamic significance, in that they determine the PZNPC through the condition XSo = XSOH! (pH = PZNPC) applied to Eq. 5.42: 14 PZNPC =
!
(pK~1(int)
+ pK~2(int»
(5.48)
However, the intrinsic constants are not the same as the thermodynamic equilibrium constants for the reactions in Eq. 5.41. The thermodynamic constants can be calculated with the help of Eq. 5.35 and the correspondences in Eq. 5.47:
K1 =
K~1(int)exp(FCTmax/2CRT)
K2 == K: 2(int)exp( FCTmax/2CRT)
(5.49a) (5.49b)
where Ki(i = 1,2) is a thermodynamic constant. Equations 5.49 reflect the fact that the intrinsic equilibrium constants refer to a Standard State in which the species SOH{(s) or SO(s) are at unit mole fraction but create no surface charge density,12.14.18 i.e., K1 = Kai(int) (i = 1,2) only if O'max = O. This unconventional Standard State deprives the intrinsic constants of ordinary thermodynamic significance, although they are directly proportional to thermodynamic cquilibrlum constants.
174
THE SURFACE CHEMISTRY OF SOilS
Figure 5.2, with its two lines of unequal slope (in absolute value), illustrates another typical feature of applications of the constant capacitance model. The value of the capacitance parameter C inferred from each slope is not the same above and below the PZNPC. 14,15,17 This result is in conflict with the nonspecific, coulombic nature of t/J~vw) indicated in Sec. 5.2; with the DDL theory relation between aD and t/Jin Eq. 5.40; and with the general thermodynamic requirement that t/JgOH! = It/JgoI in a ternary system comprising SOH(s), SOHt(s), and SO(S).19 Therefore, the lack of uniformity in the experimental value of C for pH values above and below the PZNPC must be regarded as an inherent shortcoming of the constant capacitance model. METAL CATION ADSORPTION. The formation of innersphere surface complexes involving metal cations is typically described in the constant capacitance model with the chemical reactions 15,17,20 SOH(s) + Mm+(aq) = SOM(m1)(s) + H+(aq) 2S0H(s) + Mm+(aq)
(5.50a)
= (SOhM(m2\s) + 2H+(aq) (5.50b)
The conditional equilibrium constants for these reactions are 15
{SOM(m1)}[H+] *Ki == {SOH}[M m+]
*
s _
f32
=
{(SOh M(m2)}[H+]2 {SOH}2[M m+]
(5.51a) (5.51b)
where { } denotes concentration in moles per kilogram of adsorbent. Equations 5.50a and 5.51a are special cases of Eqs. 5.25a and 5.27, respectively, obtained by setting pZp == H+, [C] == [M"'"], SR = SOH, and SR'C == SOM. The conditional constants *Ki and *f3'2 are usually evaluated by graphic methods that employ measured concentrations of M in surface complexes and calculated values of {SOH} based on experimental determinations of the acidity constants K~l and K~ .15,17,20 If M is a metal in oxidation state II, then both surface species in Eq. 5.50b are electrically neutral and the van der Waals model predicts that *f3'2 is independent of surface charge, i.e., that *f3'2 = *f32(int). However, since the surface complex SOM+ is positively charged, the definition'f *KWnt)
= *Ki exp(Ft/JslRT)
(5.52)
should be applied by analogy with Eq. 5.43. In practice,15,17,20 it is found that *Ki either does not depend significantly on the total particle charge or shows a much smaller dependence than the exponential one in Eq. 5.52. Unless this result is caused by a lack of sensitivity in the methods used to determine *Ki, it implies an additional problem of selfconsistency in the constant capacitance model.
175
CHEMICAL MODELS OF SURFACE COMPLEXATION
100
o w
Cu(II)
CO
0:::
g o
60
<{
~
•
Z W
()
0:::
•
SILICA GEL 3M NaCI0 4
W
Q.
2
3
4
5
6
7
8
9
pH Figure 5.3. Adsorption edges for Fe (III) , Cu(II), Cd(II) on silica gel suspended in 3 M NaCI0 4 . The solid lines represent calculated values based on the constant capacitance model. (After Schindler et al. 20 )
Despite these difficulties with internal consistency, the constant capacitance model can provide an excellent quantitative description of the dependence of metal adsorption on pH, as exemplified in Fig. 5.3., and it gives a prediction of the pH dependence of 0" p in the presence of adsorptive bivalent meta! cations that is in complete qualitative agreement with the surface charge behavior implied in Fig. 4.7. 15 The increase in metal adsorption with increasing pH value occurs in the constant capacitance model solely because of an increase in the concentration of the 80 species and in the strength of the innersphere complexes between this species and the metal cation, as reflected in the conditional constants in Eq. 5.51. Hydrolysis of the adsorbed metal cation is not usually invoked in the constant capacitance model because significant adsorption occurs at pH values well below the PZNPC of the adsorbent and below the onset of hydrolysis of the adsorptive metal in the aqueous solution phase. 14,15 With respect to the reversals of surface charge implied in Fig. 4.7, the constant capacitance model provides a mechanism based on a competition between the reactions in Eq. 5.41 and those in Eq. 5.50, In the absence of an adsorptive metal cation, the model predicts a single charge reversal at the PZNPC (cf. the lowest curve in Fig. 4.7). When the metal cation is present, an increase in pH value contributes to a negative surface charge
THE SURFACE CHEMISTRY OF SOilS
176
through Eq. 5.41b and a positive surface charge (for m > 1) through Eq. 5.50a. If the concentration of metal cations in the aqueous solution phase and the value of *K~ are large enough, the reaction in Eq. 5.50a eventually dominates and the surface charge increases with increasing pH value, as indicated in Fig. 4.7. However, as the pH value becomes high enough to induce significant hydrolysis of the adsorptive metal cation in the aqueous solution phase, the surface charge again decreases, according to the constant capacitance model, because the concentration of the SOM(m1) species is reduced sharply by the decline in the value of [M"."] in Eq. 5.51a. This mechanism of surface charge decrease does not predict that the total surface charge at high pH values will emulate that of a hydroxypolymer coating of the adsorbed metal cation; instead it predicts that the change at high pH values will be similar to that expected in the absence of the adsorbed metal. 21 The constant capacitance model postulates that anions react with surface hydroxyl groups through the ligand exchange mechanism embodied in Eq. 5.37b. 14 ,22 In typical applications, the value of b in Eq. 5.37b is either 1 or 2 and the corresponding conditional equilibrium constants have the form ANION ADSORPTION.
(5.53a)
s =
{S2HxL~Y+1)}[OHY
f32  {SOHf[HxL~Xql)]
(5.53b)
where in each case the equilibrium constant for the formation of HxL~ql)(aq) from H+(aq) and L'(aq) has been incorporated. By analogy with Eq. 5.43, an intrinsic equilibrium constant that corresponds to K~ can be defined as Ki(int) ==
K~
exp( "IFl/JsI RT)
(5.54)
and the analog of Eq. 5.44 can be derived: 10g[OH] + 10g(XSHL) . XSOH =
log Ki(int)  (In
10g[HxL~ql)]
1~;CRT up
(5.55)
If experimental conditions are arranged such that SOH and SHxL q are the only surface species, then up = "I U max XSHL, where XSHL is the mole
fraction of SHxL q, and Eq. 5.55 becomes a special case of the van der Waals model expression in Eq. 5.34. In particular, the identifications pZp _ OH, SR'C  SHxL q , SR  SOH, ZSR = 0, ZSR'C = "I. and
177
CHEMICAL MODELS OF SURFACE COMPLEXATION
[C] == [HxL q(xql)] can be made. It also follows that KWnt) == K SH L
C ==
K SO H
'Y~max ~SHL
(5.56)
in complete analogy with Eq. 5.47. The constant capacitance model has been applied successfully to describe the adsorption of both inorganic and organic anions by hydrous oxides.F Both adsorption isotherms and adsorption envelopes like those illustrated in Fig. 4.8 are accounted for quantitatively, except in the case of sulfate adsorption. It is possible, however, that this anion adsorbs through outersphere instead of innersphere complex formation, as discussed in Sec. 4.4. Aside from sulfate, anion adsorption envelopes are predicted in the constant capacitance model on the basis of an increase in [OH], which causes the concentrations of the surface complexes in Eq. 5.53 to decrease, and a decrease in up'
5.4. THE TRIPLE LAYER MODEL
The triple layer modee3 ,24 offers a molecular description of surface complexation reactions that differs from the constant capacitance model in several fundamental respects. These differences can be brought into clear relief through a comparative listing of the principal chemical assumptions that underlie the triple layer model: 1. The proton and the hydroxide ion form innersphere surface complexes.
All other adsorbed metal cations and inorganic or organic anions form outersphere complexes. 2. If the reacting surface functional group is an inorganic hydroxyl group, the chemical reactions that describe surface complexation are special cases of Eq. 5.37a. However, except for the protonationproton dissociation reactions in Eq. 5.41, the solid phase product, (SO)aMp(OH)yHxL;(s), is understood to always represent an outersphere complex. Therefore, when metal cations or cationic complexes adsorb, a water molecule separates them from the (SO)a unit. When anionic complexes adsorb, they, too, are separated from the protonated (SO)a unit by a water molecule. The ligand exchange mechanism of Eq. 5.37b is not invoked as the basis for surface complexes with anions. Conditional equilibrium constants in the triple layer model use the Infinite Dilution Reference State for the activity coefficients of aqueous species. 16 With this convention, the species M m + (aq) and L l  (aq) in the reaction in Eq. 5.37a can refer to the metal cation and the anion of the background electrolyte. The conditional equilibrium constant for this general reaction takes the form cK
= "sodH + )a "~Cl"(C)
(5.57)
THE SURFACE CHEMISTRY OF SOilS
178
which is the special case of Eq. 5.27 in which SR' = SO, pZp = H+, and SR = SOH. 3. The relationship between surface charge and inner potential is specified through the following equations:
O'd
=
O'H = C1(o/s  0//3)
(5.58a)
O'd = CZ(o/d  0//3)
(5.58b)
sgn(o/d){ 2eoDRT:t Cj[exp(ZjFo/d/RT) 1Jf/Z (5.58c)
where C 1 and Cz are integral capacitance densities and the inner potentials o/s,· .0//3, and o/d are identified with the three planes labeled "s," "{3," and "d" in Fig. 5.4. Equation 5.58c is the same as Eq. 5.15 applied to the d plane, i.e., DDL theory is assumed to apply to the aqueous species that neutralize surface charge, with the diffuse region beginning at the outer periphery of the water molecules that solvate ions adsorbed in outersphere surface complexes. It is evident from Fig. 5.4 that the net charge density in the {3 plane, 0'/3' corresponds to
Figure 5.4. A schematic portrayal of an inorganic hydroxyl surface, showing planes associated with surface hydroxyl groups ("s"), innersphere complexes ("a"), outersphere complexes ("{3"), and the diffuse ion swarm ("d").
s a
OXYGEN
d
CHEMICAL MODELS OF SURFACE COMPLEXATION
179
and that surface charge balance (Eq. 3.36) is expressed mathematically by the equation (TOS
(5.59) in the triple layer model. By contrast with the constant capacitance model, the linear relationships in Eqs. 5.58a and 5.58b are assumed valid whatever the magnitudes of the inner potentials, 0/.. o/f3, and o/d' Moreover, the chargebalance condition, Eq. 5.59, is imposed explicitly and the full DDL theory expression for (T d ==' (TD is used. Note that Eqs. 5.58 and 5.59 are not consistent for arbitrary values of the surface charge densities and inner potentials unless ions are present in the {3 plane under all circumstances. THE NET PROTON CHARGE. In the triple layer model, the protonation and proton dissociation reactions in Eq. 5.41 are described by the conditional equilibrium constants xSOH(H+)
Qal == ::'=,'''
(5.60a)
XSOHt
Qa2 ==
xso(H+)
(5.6Ob)
=.=..;'...:..
XSOH
Besides the use of the Infinite Dilution Reference State with respect to the activity of H+(aq), the Qa,U = 1,2) in Eq. 5.60 differ from the K~, U = 1,2) in Eq. 5.42 through the stipulation that XSOHt and xsoare mole fractions of the uncomplexed solid phase species SOHt(s) and SO(s). Thus complexed species like SOH 2L<1 1)(S) and SOM(ml)(s) are excluded from Eq. 5.60 even though SOHt and SO form part of their structure on the molecular level. Instead, special cases of Eq. 5.37a, such as Eq. 5.50 and the sum of Eqs. 4.44a and 4.44c, are assumed to apply to the background electrolyte and contribute to (TH' The conditional equilibrium constants for these latter reactions are, for the common example of a 1: 1 background electrolyte ML(aq)
*QL == xsoH(H+)(L)
(5.6Oc)
XSOH2L
*Qw== XSOM (H+) XSOH (M+)
(5.6Od)
Corresponding to these four conditional constants are the triple layer model intrinsic equilibrium constants."
K::r
iIE
Qal exp(eo/s/kBT)
"'K~l. "'Qa exp[e(lP"  o/(3)/kBT]
(i
=
1,2)
(5.61a)
(a = L  ,M+) (5.61b)
The four intrinsic constants are postulated to be independent of the
180
THE SURFACE CHEMISTRY OF SOilS
composition ofboth the solid and the aqueous solution phase. They can be determined experimentally on the basis of linear expressions that follow from the combination of Eqs. 5.58a, 5.60, and 5.61: , (XSOH)' , e"'f3 pH log' , = logK~~t  e UH XSOHt (In 1O)C1kBT (In 1O)kBT
pHlog
(XSO) _ logKint XSOH
a2 

e (In1O)C
pH IOg(x::::J log(L) = log * pH _IOg(x
SO M
)
1kB
TuH

e"'f3 (Inl0)k T B
Kt~  (In 1O)eC~::'~ u~'>:
(562a) .
(5.62b) (5.62c)
e
+ 10g(M+) = log * Kk1\ 
XSOH
where
UH = (FM/NA)(xSOHt +
XSOH 2L 
xso 
XSOM)
(5.63)
Under the assumption that experimental conditions have been arranged to make one of the surface species that contribute to UH dominant, precise graphic extrapolation methods can be applied to determine the intrinsic equilibrium constants in Eq. 5.62 from measurements of the conditional constants and UH over a range of concentrations of the background electrolyte. 25 The linear relationship implied in Eqs. 5.62c and 5.62d is illustrated in Fig. 5.5 for rutile suspended in LiN03 . 26 It is assumed in this application that the concentration of LiN0 3 and the pH are high enough to justify the approximation of neglecting all mole fractions except XSOM in Eq. 5.63. The y intercept of the line through the data equals 7.2 and corresponds to log *Kb\, according to Eq. 5.62d. The slope of the line equals 25 and therefore
_. eFM _ 1 .2 Ct  4'25(ln 1O)NAkB T' .30 F m 1""_,,,,1
at 298.15 K, where M = 1.2 X 1019 m 2 has been used in the calculation.r'' These two parameters can be related to the van der Waals models parameters by setting SR'C = SOM and SR = SOH in Eq. 5.34 and comparing the resulting expression with Eq. 5.62d. In this application, ZSOH = 0 but ZSOM = 1 because the van der Waals average potential is created by the solvated M+ cations in the f3 plane. Therefore, with the correspondences pZp = H+ and (C) = (M") inserted into Eq. 5.34, the triple layer model parameters can be expressed by the equations'f *Kint _ M+ 
KSO M K SO H
C
_
1 
FM 0
N A "'SOM
(5.64)
where "'~OM is the maximum van der Waals electric potential created by
CHEMICAL MODELS OF SURFACE COMPLEXATION
181
I I r,.rr,,,,...,
Rutile in LiN03
+ ...J
o
*o0LiT .. 1M •
O.IM
6
__
5 ~
~
_
__JL.___
0.02
__JL.___
___I_ ____I_ ____I_ _.......L_ _.......L_..J
0.04..
0.06
0.08
uH I(FM/.¥A)
Figure 5.5. A graph of log *Qu+ (Eq. 5.60d) versus uH/(FMNA ) (Eq. 5.63) for rutile suspended in LiN0 3 . The line through the data conforms to Eq. 5.62d. (After Davis et al. 23)
the complexed M cations and FM/N A is the maximum absolute value of (TH' The molecular interpretation of Eq. 5.64 is similar to that of Eq. 5.47, with the parameter C 1 being the capacitance, per unit of adsorbent surface area, of an array of solvated M+ complexed by SO. The thermodynamic equilibrium constant for the reaction SOH(s) + M+(aq) = SOM(s) + H''{aq)
(5.65)
can be calculated in the triple layer model with the help of Eqs. 5.35 and 5.64: (5.66) Just as in the constant capacitance model, the intrinsic equilibrium constant in the triple layer model refers to an unconventional standard state wherein the complexed species create no coulombic effects, i.e., *K~~ = K when c/1~OM = O. Equations 5.62c and 5.62d provide the basis for two independent determinations of the .capacitance parameter C 1 in the triple layer model. However, the check on internal consistency that these two separate evaluations of C, could furnish has never been performed in any published study.2:l,24,27.,o In fact, C 1 has been taken universally as an adjustable
182
THE SURFACE CHEMISTRY OF SOilS
model parameter along with the truly adjustable capacitance factor Cz in Eq. 5.58b. For this reason, no conclusion is possible as to the accuracy of the triple layer model in selfconsistently representing the molecular structure of the inorganic hydroxyl surface, notwithstanding its widespread success in reproducing surface charge data for hydrous oxides suspended in electrolyte solutions. Z4 The formation of outersphere surface complexes involving metal cations has been described typically in the triple layer model by the reactions z3,z4 METAL CATION ADSORPTION.
SOH(s) + Mm+(aq) SOH(s) + Mm+(aq) + H zO(l)
=
SOM(ml)(s) + H+(aq)
(5.67a)
= SOMOH(s) + 2H+(aq) (5.67b)
Equation 5.67b is obtained from Eq. 5.25a (SR = SOH, ZSR = 0, P = Y = 1, q = x = 0, SR' = SO, ZSR'C = 0, pZp = H+) by adding the ionization reaction of water. The conditional equilibrium constants for these reactions are Z3 (5.68a) (5.68b) Reactions involving two SOH to form (SOhM(mZ) are excluded because . they invariably lead to serious disagreement between measured and calculated adsorption edges for metal cations. z3,z4 Moreover, the values of * KMm+ determined in applications of the triple layer model usually are small enough to preclude the dominance of the outersphere complex SOM(ml) except at pH values well below the PZNPC. This behavior is in direct contradiction with that typically observed in applications of the constant capacitance model, where the innersphere complex SOM(ml) tends to be dominant even above the PZNPC. The conditional constants in Eq. 5.68 are related to triple layer model intrinsic equilibrium constants through the equationz3,z4 *K~nt
==
*Ka exp[ e(l/Is  (m  l)l/I~)/kBT]
(a = Mm+,MOH(ml»
•
(5.69)
When M'?" represents a metal cation not in the background electrolyte, the intrinsic constants are determined by fitting the triple layer model to adsorption edge data. This fitting entails a surface speciation calculation with previously measured values of the intrinsic constants in Eq. 5.61, the capacitance parameters C\ and C2 , and the parameter M. The computation includes Eqs. 5.58, 5.59, and 5.69, as well as surface charge and mole balance equations imposed as constraints. 23 •31
183
CHEMICAL MODELS OF SURFACE COMPLEXATION
The triple layer model has been shown to provide quantitative descriptions of both adsorption edges and uwpH relationships for a variety of hydrous oxide adsorbents suspended in aqueous solutions ranging in composition from single, 1: 1 electrolytes to majorion seawater. 23,24,2730 The increase in adsorption with pH commonly observed for bivalent metal cations (Fig. 4.6) is interpreted in the triple layer model as the result of an increase in the concentration of the SO species and in the formation of the outersphere complex SOMOH. This effect is illustrated in Fig. 5.6 for the adsorption edge of Pb(II) on yA12 0 3 suspended in 0.1 M NaCI0 4 . 32 The model curve, which follows the experimental data closely reflects almost entirely the contribution of complexed PbOH+ cations, since the SOPb + species never accounts for more than 20 per cent of the adsorbed lead and the PZNPC of yA120 3 is about 8.3. Thus a kind of surfaceinduced hydrolysis of the adsorptive metal cation plays a major role in the triple layer model, whereas in the constant capacitance model it plays no role at all. This difference is made all the more striking by the fact that the data in Fig. 5.6 have been described with equal quantitative accuracy by the constant capacitance model. 17 ,33 The charge reversal behavior shown in Fig. 4.7 also can be described by the triple layer model. 34 The mechanism relies on the competition between the reactions in Eq. 5.41 and that in Eq. 5.67b. When an adsorptive, bivalent metal cation is present, an increase in pH value causes the
Figure 5.6. The adsorption edge for Pb(II) on yAl z0 3 suspended in 0.1 M . NaCl0 4 • The solid line represents the contribution of SOPb+ alone. (After Davis and Leckie z3) 100 rrr.rra::::;==,
80 "0 CI.l X CI.l
a. E
.""
60
50 _Pb 2+ and 50  PbOH+
o
o
... cCI.l::
40
u
CI.l
0..
20 _____     
,50Pb 2 + only
...... .... 7.0
OL......I.....L.....I......I..~
3.5
4.0
4.5
5.5
5.0
pH
6.0
6.5
THE SURFACE CHEMISTRY OF SOilS
184
formation of the SOMOH species to increase sharply. At a given pH value, this species increases the particle charge (i.e., a decrease of the net charge in the d plane) relative to its value when the adsorptive, bivalent metal cation is absent. This point is made clearly through a consideration of charge balance in Eq. 5.59: at a fixed pH value UH remains constant while uf3 increases when MOH+ appears in the (3 plane. The increase in particle charge through outersphere surface complexation can be large enough, if * Kkitow is large enough, to reverse the negative particle charge expected from an increase in uncomplexed SO as the pH value increases. At very high pH values, if the concentration of MOH+(aq) is reduced through the formation of more hydrolyzed species, e.g., M(OH)g(aq), there could be a loss of SOMOH on the adsorbent and a return of the particle charge to negative values. Like the constant capacitance model, the triple layer model does not predict that the ultimate particle charge will emulate that of a hydroxypolymer coating of the adsorbed, bivalent metal cation. The triple layer model postulates that anions react with surface hydroxyl groups according to the general equation ANION ADSORPTION.
aSOH(s) + L1(aq) + xH+(aq)
= (SO)aHxL 8(S) + aH+(aq) (5.70)
which is a version of Eq. 5.37a. In most applications.P the stoichiometric coefficient a in Eq. 5.70 is set equal to unity but x can vary from 0 to I  1. The conditional and intrinsic equilibrium constants for the surface complexation reactions have the form (5.71a) (5.71b) in analogy with Eqs. 5.6Oc and 5.61b. The values of *K~:L are determined by fitting the model to adsorption envelope data following procedures similar to those outlined for metal cation adsorption.P A striking confirmation of Eq. 5.70 for SOH on goethite and L = CI or CI0 4 has been found through a kinetic study of the adsorption of these two anions in acidic suspensions" The kinetics data revealed that, after protonation of the SOH group, the anion diffuses to the {3 plane, where it is bound temporarily as a species with twodimensional mobility. Shortly thereafter, the anion moves about in the {3 plane until it locates an SOHt site where it can form an outersphere complex. The initial protonation step involves a time constant of the order of milliseconds, the diffusion of the anion to the {3 plane involves a time constant near 0.1 JLS, and the surface complexation reaction involves a time constant in microseconds. The value of '" KWb calculated from the rate constants" for the surface complexation reaction agreed with the static value determined from adsorption experiments. 24 Reasonable agreement with experimental adsorption envelopes, like those
CHEMICAL MODELS OF SURFACE COMPLEXATION
185
in Fig. 4.8, has been obtained even when the triple layer model is applied to strongly adsorptive oxyanions. However, except for SO~, this agreement is likely to be a model artifact since the mechanism of strong oxyanion adsorption is ligand exchange, as discussed in Sec. 4.4. 5.5. THE OBJECTIVE MODEL
The objective model'" derives its name from a pluralistic conceptualization of the species possible on an inorganic hydroxyl surface. This conceptualization, as will emerge clearly from the following list of model hypotheses, includes features of both the constant capacitance and the triple layer model. 1. Surface complexation involves all four of the planes depicted in
Fig. 5.4. Complexed protons and hydroxide ions reside in the s plane, innersphere complexes containing trace metal cations or oxyanions are assigned to the a plane, outersphere complexes with the ions of a background electrolyte are assigned to the 13 plane, and the d plane marks the beginning of the aqueous solution phase, where the diffuse ion swarm is found. 2. The activity of a species i located in the plane A(A = s,a, or 13) is equal to the ratio of the surface excess of i (Eq. 4.5) to moles of i per unit area that can still be accommodated in the plane A:36 r~w) I
(5.72)
where ail.. is the activity of i in the plane A, r}w) is the surface excess of i, M A is the maximum number of surface species possible per unit area in the plane A, and the sum is over all species adsorbed in the plane A. The activity of species i in the plane Ais assumed further to be related to the activity in the aqueous solution phase through the equatiorr" (5.73) where K'A is an empirical parameter representing the interaction between i and a surface functional group, a, is the activity of i in the aqueous solution phase, Z, is the valence of the adsorbed species, and !/JA is the inner potential at the plane Aexpressed relative to a potential in the aqueous solution phase far from the surface. The combination of Eqs. 5.72 and 5.73 provides the basic adsorption equation of the objective model:
r}W)
= [(MAIN..... ) 
:t rjW)]
KIA
a, exp(Z,F !/JAIRT)
(5.74)
Equation 5.74 represents a set of coupled algebraic equations (one for each adsorbed species in the plane A) that is subject to the molebalance
186
THE SURFACE CHEMISTRY OF SOILS
constraint (5.75) 3. The relationships between surface charge density and inner potential are specified by expressions similar to Eq. 5.58: UH
= G sa( l/Js
 l/Ja)
UH
+ Ua = Gaf3 (l/Ja  l/Jf3)
(5.76a) (5.76b)
where the G parameters are capacitance densities and U a is identified with UIS in Eq. 3.2. The surface charge density Ud is also given by Eq. 5.58c as a function of l/Jd' and the balance of surface charge takes the form of Eq. 3.3: (5.77)
Equations 5.58c, 5.76, and 5.77 define the chargepotential relations in the objective model for any set of adsorbed species in any plane or in the diffuse ion swarm. Although surface complexes are considered in the objective model in the spirit of Fig. 5.4, no complexation reactions or equilibrium constants are used. Instead, the activity relations in Eqs. 5.72 and 5.73 are invoked to .describe complex formation. Equation 5.72 is identical with the equation for the activity of an adsorbed species that experiences no lateral interactions on a surfacer" On the other hand, Eq. 5.73 can be derived by applying Eq. 3.20 to an adsorbed species under the assumption that the inner potential, cf>, can be equated to l/JA:
jL[i] = go + RT In aiA + ZjFl/JA
(5.78a)
ji[i] = JL[i(aq)] = JL°[i(aq)] + RT In a,
(5.78b)
and (d. Eq. 5.30)
for equilibrium with respect to the transfer of species i across the interfacial region. Equation 5.73 follows from Eq. 5.78 after making the definition
KiA == exp{(JLO[i(aq)]  go)/RT} As pointed out in Sec. 3.3, Eq. 5.78a has no thermodynamic significance when l/JA is an inner potential and Eq. 5.73 must be regarded as an ad hoc model assumption. • Equation 5.72 can be applied successively to the species SOH and SOHt in the s plane to derive the expression r(w) a K SO H S K~1 = ;~~ w = K exp(Fl/Js/RT) (5.79) SOH!
SOHiS
where K SO H S ... exp(€o/RT). Equation 5.79 is the same, formally, as Eq, 5.43a and is a special case of the van der Waals model expression in
CHEMICAL MODELS OF SURFACE COMPLEXATION
187
Eq. 5.34. Thus the protonation (and proton dissociation) of the inorganic hydroxyl surface is described in the objective model just as it is in the constant capacitance model. However, in the objective model, aH is given the explicit mathematical representation  F(r(w) r(w) ) aH SOH~ so = as _ (Ms / NA)[KsoH}saw exp( F«/Js/ RT)  KsosaoH exp(F«/Js/ RT)] 1 + KSOH~SaWexp(F«/Js/RT) + KSOSaOHexp(F«/JslRT) (5.80) which follows from Eqs. 5.74 and 5.75 applied to SOH, SOHt, and SO.36 Equation 5.80 is a special case of the surface charge density relationship applied to each plane A: aA = F ~
zjrt)
(A = s,a, or f3)
(5.81)
j
where the sum extends over all species j in the A plane. Equations 5.81 are subject to the constraints implied in Eqs. 5.58c and 5.77. The objective model considers the parameters MA , KiA' and GA>..' (A,A' = s, a, or f3; A 1= A') to be adjustable curvefitting parameters. The constants pertaining to the sand f3 planes are determined by fitting the model to potentiometric titration data (aH as a function of pH) obtained in the presence of a background electrolyter" An additional check on this fit 'can be made if one assumes that «/Jd is the same as the zeta potential and measured values of ( as a function of pH are available. Once the parameters for the sand f3 planes have been established, adsorption isotherm, adsorption edge or adsorption envelope, and surface charge data pertaining to the reaction of the inorganic surface hydroxyl group with trace metal cations or with oxyanions can be used to determine the parameters in the a plane from curvefitting algorithms.39 It should be apparent even from this brief discussion that the objective model is essentially a parameteroptimization procedure for speciating the interfacial region near an array of inorganic surface hydroxyl groups. The model exhibits some features of a hybrid between the constant capacitance and triple layer models in that its "binding constants," KiA, can be related in pairs to the intrinsic equilibrium constants of the constant capacitance model whereas its "surface potentials," «/JA' are used like the inner potentials in the triple layer model and assigned to specific planes containing adsorbed species. Chemical reactions and their, concomitant equilibrium constants play no role in the objective model. In this respect, the model is close in spirit to the classical GouyChapmanSternGrahame picture of the electrical double layer.t" with the a plane identified as the inner Helmholtz plane and the f3 plane as the outer Helmholtz plane. This mixture of classical double layer theory and the surface complexation concept is not a fully selfconsistent chemical model, however, because it does not reduce to the triple layer model when no species are present in the
a plane.
188
THE SURFACE CHEMISTRY OF SOILS
To see this point in detail, consider a hydrous oxide surface bathed by an aqueous solution containing only the electrolyte ML(aq). In this case, Eqs. 5.76 and Eq. 5.58 prescribe identical surface chargeinner potential relationships (with G;'l= G~l + G;;rl = C1 and G(3d = C2 ) and Eqs. 5.77 and 5.59 are the same. The surface charge density in the s plane, according to the objective model, is given by Eq. 5.80. This equation indicates that O"H is determined by the activity of the proton in the aqueous solution phase and by the inner potential, l/Js' On the other hand, according to the triple layer model, O"H is given by Eq. 5.63, which, through Eqs. 5.60 and 5.61, depends explicitly on the activity of H+, M+, and L  in the aqueous solution phase, as well as on the inner potentials l/Js and l/J(3' Indeed, Eqs. 5.60a, 5.61a, and 5.79 are in direct conflict, since the quantity Qal contains XSOH!, the mole fraction of uncomplexed SOH~, whereas r~~Ht in Eq. 5.79 comprises the sum XSOHt + xSOH2L, the total mole fraction of SOH~ , both complexed and uncomplexed. The root cause of this difference is the inconsistent use of a f3 plane in the objective model to allow adsorption of the background electrolyte without then partitioning O"H to reflect this adsorption. Therefore, despite the very good description of experimental data possible with the objective model,36,39 it does not have the same status, as a chemical model, accorded the constant capacitance and triple layer models. 5.6. THE STRUCTURE OF SURFACE COMPLEXATION MODELS The intent of the present chapter has been to elucidate the molecular structural features of several models of the interfacial region that enjoy widespread application. It should be apparent from the discussion that these models are only qualitatively accurate at the molecular level, even though good quantitative descriptions of potentiometric titration data and ion adsorption isotherms can be obtained by curvefitting techniques. The conclusion that should be drawn from these facts is that titration and adsorption experiments are not sensitive to the detailed structure of the interfacial region. Given the typical number of adjustable parameters in a surface complexation model, it is possible to fit most data on proton, metal cation, and oxyanion adsorption without having an accurate picture of surface speciation." More severe constraints on a model, however, might be imposed by data obtained for aqueous systems comprising several adsorptive ions involved in competitive surface reactions." but the most direct sources of information concerning the' molecular structure of the interfacial region are Xray, optical, magnetic resonance, and neutron spectroscopy experiments.F These experiments offer probes of molecular energy transfer that are responsive to the details of structure and bonding at an interface. They can be expected to be reliable guides in the future development of surface chemical models. It is possible to distill from the discussion in Sees. 5.1 to 5.5 a set of general properties for surface complexation models. These properties
CHEMICAL MODELS OF SURFACE COMPLEXATION
189
divide naturally into two categories: constraint equations and molecular hypotheses. An illustration of the two categories is now made with the inorganic surface hydroxyl group taken as an example. For each class of reactive surface hydroxyl groups, there is an equation of mole balance. This equation has the general mathematical form CONSTRAINT EQUATIONS.
~S = L L L a{(S(i)O)aM;P(OH)yHxL~k)} a j,k p,y,k,q
A
+
LL L b
j,k p,y,x,q
b{S~)M;,n(OH)yHxL~k)}
(5.82)
where M, is the total number of reactive hydroxyl groups of type i, S(i)OH, per unit area, S is a specific surface area, and { } refer to a solidphase concentration in moles per kilogram. The species in the first sum in Eq. 5.82 include as special cases the innersphere proton and hydroxide ion complexes in Eq. 5.41, the innersphere metal complexes in Eq. 5.50, the outersphere metal complexes in Eq. 5.67, and the outersphere ligand complex in Eq. 5.70. The species in the second sum in Eq. 5.82 are generalizations of the innersphere ligand complex in Eq. 5.37b. For each of the surface charge densities UH, UIS, and Uos, an equation that includes the relevant surface complexes can be established. The surface density of net proton charge is given by. the expression UH
= (FjS)
~ I
[L {S(')(OH)xL~k)} ,L 
k,q,x
j,p,y
{S(i)OMi/\OH)y}] (5.83)
where F is the Faraday constant. Equation 5.83 is the same as Eq. 5.46 with the one difference that here the species that contribute to XSOH! and XSo are shown explicitly. The surface density of innersphere complex charge is given by the equation UIS
= (FjS)
LLL
j,k p,y,x,q
i
+
[ZIs{(S(i)O)aM~j)(OH)yHxqk)}
ZIs{Sbi)M~j)(OH)yHxqk)}]
(5.84)
where, in the notation of Eq. 5.37, ZIS = pm + x  ql  y is the valence of a complexed species bound directly to (S(i)O)a or S~). The first term in the sum in Eq. 5.84 refers only to innersphere complexes with metallike species; the second term refers to innersphere complexes with ligandlike species." The surface density of outersphere complex charge is given by the equation Uos = (FjS)
LL L I
where Zos .. pm
+x
l,k
".y.x.t{
Zos{(S(i)O)aM~j)(OH)yHxL~k)}
(5.85)
 ql  y is the valence of a metallike or ligandlike
190
THE SURFACE CHEMISTRY OF SOilS
species with at least one water molecule interposed between it and the surface anion, (S(i)O)~. Equations 5.83 to 5.85 are subject to the chargebalance expression (Eq. 3.3b) + aH + aIS + aos + aD + 0 (5.86) This equation and Eq. 5.82 provide the mass and charge balance constraints on any surface complexation model. Since each of the solid phase species in Eq. 5.82 can be regarded as one of the products in a chemical reaction, as in Eq. 5.37, there exist chemical equilibrium constraints for each class of reactive surface hydroxyl groups: «S(i)O) M(j)(OH) H L(k»(H)ax K(i) a pyx q (5 87 ) soc  (S(i)OH)"(M(j)P(OH)Y(L(k»q . a ao
.
(S(i)M(j)(OH) H L(k»(OH)b y b Pyx q sc (S(i)OH)b(M(j»)p(HY(L(k»q
K(') 
(5 87b) .
where K~bc and K~b are thermodynamic equilibrium constants. The reduction of the activities in Eq. 5.87 to products of activity coefficients with either solid phase mole fractions or aqueous phase molalities requires a choice of reference state. Either the Constant Ionic Medium Reference State (as in the constant capacitance model) or the Infinite Dilution Reference State (as in the triple layer model) may be chosen, and this choice determines whether the ions in the background electrolyte are included in Eqs. 5.82 to 5.85. Regardless of the choice of reference state, the left sides of Eqs. 5.87 are independent of the composition of the solid and aqueous phases and in this way act as constraints in addition to those of mass and charge balance. MOLECULAR HYPOTHESES.
If experimental methods exist for measuring the
composition of the solid and aqueous solution phases in a suspension of adsorbent particles, then Eqs. 5.82 to 5.85 constitute a description of the surface chemistry that requires no additional molecular hypotheses. 12 . Surface complexation models represent molecular theories that try to calculate the composition of the solid phase in a suspension, given the composition of the aqueous solution phase and a set of hypotheses concerning the detailed structure of the interfacial region. The specific focus of these models is the equilibrium constants in Eq. 5.87. Consider, for example, Eq. 5.87a. The equilibrium constant K~bc can be expressed (')
K(i) _ cK;oc fsoc soc fa
.
(5.88)
SOH
where CK(I)
_
soc 
xsodH)a xS'OH(C)
(5.89)
is the conditional equilibrium constant, in the notation of Eq. 5.27, and
191
CHEMICAL MODElS OF SURFACE COMPLEXATION
fsoc and fSOH are rational activity coefficients.P Given that K~bc can be measured, the task of a surface complexation model is to develop a method for calculating the rational activity coefficients. Once this is accomplished, the value of «a: can be calculated and the composition of the solid phase predicted through a prediction of Krbc and introduction of the results into Eqs. 5.82 to 5.85. The prediction of the solid phase composition proceeds in exactly the same way as a speciation calculation for the aqueous solution phase." In Sec. 5.2 it is shown that the van der Waals model in statistical mechanics leads to a specific prediction of the functional dependence of ratios like fsoc/HoH on the molecular properties of an interfacial region (d. Eq. 5.36). The surface complexation models discussed in the present chapter are related to the van der Waals model and therefore also make specific predictions of the dependence of rational activity coefficients on molecular parameters. As an example, consider the constant capacitance model and, in particular, Eqs. 5.41b, 5.42b, and 5.43b. Equation 5.42b is a special case of Eq. 5.89 (a = 1; P = Y = x = q = 0), and Eq. 5.43b is analogous to Eq. 5.88. With the help of Eqs. 5.47 and 5.49b, one can write the exact analog of Eq. 5.88: C
C
K 2 = K~2 exp[F(!o/go  o/s)/RT]
(5.90)
since K 2 in Eq. 5.49b is a special case of K~~c in Eq. 5.87a. It follows from a comparison of Eqs. 5.88 and 5.90 that
fsof:SOH
0 = exp [ F (120/S0
/] O/S )RT
(5.91)
in the constant capacitance model. Equation 5.91 is a fundamental molecular hypothesis in the model. Since the inner potential, o/s' cannot be determined independently, the model must make the additional assumption contained in Eq. 5.39. Once this is done, only the capacitance parameter C remains to be determined from measurements of the dependence of K~2 on up, as described in Sec. 5.3. In the case of the triple layer model, the formation of the species SO is described by two equilibrium constants and Eqs. 5.60b and 5.60d are the relevant special cases of Eq. 5.89. Equations 5.61, for i = 2, a = M+ are analogous to Eq. 5.88. Taking Eq. 5.61b with a = M+ in combination with Eq. 5.66, one can drive the expression
K = *Qm+ exp[ e(!o/goM
+ O/S ""' o/(3)/kB T ]
(5.92)
since Kin Eq, 5.66 is a special case of K~bc in Eq. 5.87a. The ratio of rational activity coefficients, fSOM/fsOH' then follows from a comparison of Eqs. 5.88 and 5.92: f:f:SOM so...
= exp[

e(~o/~OM + o/M 
o/(3)/k BT]
(5.93)
This equation expresses a fundamental molecular hypothesis in the triple
Table 5.3. Constraint equations and molecular hypotheses in the constant capacitance and triple layer models for a hydrous oxide suspended in a 1: 1 electrolyte solution. Constraint equation
Molecular hypothesis
Constant capacitance model = f~oc exp(ZsocFr/JslRT) aH = Cr/Js for aH near zero No outersphere surface complexes
XSOH{ + XSO + XSOH = 1 aH ~ (FM/ N A)(XSOW2  XSO) aH + aD = 0
fsoc
Triple layer model xSOHi + XSOH2L + xso + XSOM + XSOH = 1 aH = (FM/NA)(xsOHi + XSOH2L  xso  XSOM) aos = (FM/NA)(xsOM  XSOH2d aH + ,aos + aD = 0
fil'
= f;~ exp(Z;er/JA/kBT)
(A
=s
or (3)
aH = C1(r/Js  r/Jf3) aH + aos = C 2(r/Jf3  r/Jd) aD
=
(8E ODRTC Md l / 2 sinh(Fr/Jd/2RT)
Note the following: Zsoc = valence of the surface complex SOc. M = reactive hydroxyl groups per unit area. IiA = rational activity coefficient of surface species i in plane A. I~ = constant determined by the reference state assumed. Z, = valence of surface species i (e.g., SO; M+ complexed by SO; H+ complexed by SOH) located in the plane .1.(.1. CM L = concentration of ML(aq).
= s or f3).
CHEMICAL MODELS OF SURFACE COMPLEXATION
193
layer model. Because the inner potentials are not determinable independently, Eqs. 5.58a and 5.64 must be invoked, leaving C1 to be determined by measurements of the dependence of * QM+ on UH' The general pattern that can be extracted from these two examples comprises two steps: 1. A molecular interpretation of the equilibrium constants in Eq. 5.87 is initiated by stating whether the surface species in the numerators form innersphere or outersphere complexes. 2. Consistent with the hypotheses made in step 1, the rational activity coefficients of the surface species are expressed mathematically in terms of molecular parameters. If these parameters cannot be related directly to measurable quantities, additional molecular equations are invoked to provide such a relationship.
Thus the molecular hypotheses in a surface complexation model provide a detailed interpretation, in terms of an assumed structure for the interfacial region, of the concentrations, surface charge densities, and equilibrium constants in the constraint equations. These features of the models are illustrated in Table 5.3 for an adsorbent bearing a single class of surface hydroxyl group and suspended in a 1: 1 background electrolyte solution. Note that the expression given for the rational activity coefficient in the triple layer model is consistent wth Eqs. 5.61, 5.69, and 5.71b when applied to surface species, not surface complexes. Equation 5.93 results from applying the expression in Table 5.3 to SO and complexes M+ individually, then setting (f~osf~+{3) = exp( e«/JgoM/2kBT). The same general considerations apply to an adsorbent bearing other kinds of surface functional group, e.g., the siloxane ditrigonal cavity.t" It is evident from an examination of Table 5.3 that the basis for improvement in the development of surface complexation models lies with more accurate specifications of inner and outersphere surface complexes and more comprehensive expressions for the rational activity coefficients of surface species. NOTES 1. Introductory discussions of the PoissonBoltzmann equation can be found in Sec. III of K. L. Babcock, Theory of the chemical properties of soil colloidal systems at equilibrium, Hilgardia 34: 417 (1963); in Chap. 6 of G. Sposito, The Thermodynamics of Soil Solutions (Clarendon Press, Oxford, 1981); and in Chap. 1 of G. H. Bolt, Soil Chemistry. B: PhysicoChemical Models (Elsevier, Amsterdam, 1979). 2. See, e.g., D. C. Grahame, The electrical double layer and the theory of electrocapillarity, Chern. Rev. 41: 441 (1947); C. W. Outhwaite, Modified PoissonBoltzmann equatiorl in electric double layer theory based on the BogoliubovBornGreenYvon integral equations, J. C. S. Faraday 1/74: 1214 (1978); and the references cited therein. 3. The situation in which this condition is not met (i.e .. interacting double layers) is discussed in E. C. Childs. The splice charge in the Gouy layer between two
194
THE SURFACE CHEMISTRY OF SOILS
plane, parallel nonconducting particles, Trans. Faraday Soc. 50: 1356 (1954) and in F.A.M. de Haan, The negative adsorption of anions (anion exclusion) in systems with interacting double layers, J. Phys. Chern. 68: 1970 (1964). See also Chap. 1 and 7 in G. H. Bolt, op. cit.' These more complicated DDL theories are not required for the chemical models discussed in the present chapter. 4. D. C. Grahame, Diffuse double layer theory for electrolytes of unsymmetrical valence types, J. Chern. Phys. 21: 1054 (1953). See also Chap. 1 in G. H. Bolt, . 1 op. elf. 5. See, e.g., G. H. Bolt, op cit. ,1 pp. 1417: Most often, the absolute magnitude of r/J(O) is set arbitrarily equal to + 00 and the DDL model is calibrated instead by introducing (T(x) = (Tin into Eq. 5.5, where (Tin is a measured value of the intrinsic surface charge density. The adjustable parameter in the model is thereby shifted from r/J(O) to the value x = 5 that satisfies Eq. 5.5, with an appropriate formula for r/J(x) used in calculating the derivative on the left side. The effect of this substitute calibration is to place the plane to which (Tin refers at some positive value of x instead of at x = 0 and to restrict the application of the DDL model to the region x > 5. However, aside from the advantage gained by forcing (T(x) to have a reasonable value at the particle surface, the physical aspects of this renormalized DDL model visavis surface complexes are the same as those of the unrenormalized model having the surface plane at x = O. 6. The first unequivocal demonstration of this important, wellknown constraint appears in O. Stern, Zur Theorie der elektrolytischen Doppelschicht, Z. Elektrochem. 30: 508 (1924). The Stern model of the interfacial region was the first chemical model in the spirit of the present chapter. 7. G. M. Torrie and J. P. Valleau, Electrical double layers. 1: Monte Carlo study of a uniformly charged surface, J. Chern. Phys. 73: 5807 (1980).4. Limitations of the GouyChapman theory, J. Phys. Chern. 86: 3251 (1982). The second paper also gives references for recent attempts to modify DDL theory to take into account finite ion size and potential fluctuations. 8. Theoretical calculations that anticipated this result are summarized in Chap. 7 of M. J. Sparnaay, The Electrical Double Layer. Pergamon Press, Oxford, 1972. 9. The development of computerbased algorithms from surface complexation models is discussed in J. Westall, Chemical equilibrium including adsorption on charged surfaces, in Particulates in Water (M. C. Kavanaugh and J. O. Leckie, eds.). American Chemical Society; Washington, D.C., 1980. 10. An introduction to statistical mechanics that is adequate for a comprehension of the present discussion is given in Chap. 6 of G. Sposito, op cit.: Full details are provided in Chap. 7 and 14 of T. L. Hill, An fntroduction to Statistical Thermodynamics. AddisonWesley, Reading, Mass., 1960. 11. The method of deriving Eq. 5.23 presented here follows the discussion on p. 252 in T. L. Hill, op. cit. 10 More general (and more rigorous) methods for deriving partition functions in the van der Waals limit are given in Sec. 16 of E. A. Guggenheim, Statistical thermodynamics of mixtures with nonzero energies of mixing, Proc. Royal Soc. (London) 183A:213 (1944). 12. G. Sposito, On the surface complexation model of the oxideaqueous solution interface, J. Col/oid Interface Sci. 91:329 (1983). 13. Conditional equilibrium constants for reactions in heterogeneous chemical systems are discussed fully in Chap. 5 of O. Sposito, op. cit. I
CHEMICAL MODELS OF SURFACE COMPLEXATION
195
14. W. Stumm, C. P. Huang, and S. R. Jenkins, Specific chemical interaction affecting the stability of dispersed systems, Croatica Chern. Acta 42: 223 (1970).
15.
16. 17. 18.
19.
20.
21.
22.
23.
W. Stumm, H. Hohl, and F. Dalang, Interaction of metal ions with hydrous oxide surfaces, Croatica Chern. Acta 48:491 (1976). W. Stumm, R. Kummert, and L. Sigg, A ligand exchange model for the adsorption of inorganic and organic ligands at hydrous oxide interfaces, Croatica Chern. Acta 53: 291 (1980). Comprehensive recent discussions of the constant capacitance model are given in P. W. Schindler, Surface complexes at oxidewater interfaces, in Adsorption of Inorganics at SolidLiquid Interfaces (M. A. Anderson and A. J. Rubin, eds.; Ann Arbor Science, Ann Arbor, Michigan, 1981) and in H. Hohl, L. Sigg, and W. Stumm, Characterization of surface chemical properties of oxides in natural waters, in M. C. Kavanaugh and J. 0. Leckie, op. cit.9 A computerbased algorithm for the constant capacitance model is described by J. Westall, . 9 op. Cit. The Constant Ionic Medium Reference State is compared with the more common Infinite Dilution Reference State in Chap. 2 of G. Sposito, op. cit." H. Hohl and W. Stumm, Interaction of Pb2+ with hydrous yAl z0 3 , J. Colloid Interface Sci. 55: 281 (1976). The standard state to which conventional thermodynamic equilibrium constants refer is that of unit mole fraction for each solid phase component in a reaction and unit molality without coulomb interactions for each aqueous phase ion in a reaction. See p. 32 in G. Sposito, op. cir? S.Y. Chu and G. Sposito, The thermodynamics of ternary cation exchange and the subregular model, Soil Sci. Soc. Am. J. 45: 1084 (1981). The discussion given on p. 1088 of this paper, particularly Eq. 35, shows that the van der Waals potentials Zjel/Jp must be independent of the index i for surface complexes of a given kind (e.g., innersphere). c.P. Huang and W. Stumm, Specific adsorption of cations on hydrous yAlz0 3 , J. Colloid Interface Sci. 43:409 (1973). P. W. Schindler, B. Furst, R. Dick, and P. U. Wolf, Ligand properties of surface silanol groups. I. Surface complex formation with Fe3+, Cu z+ , Cd z+ , and Pb2+, J. Colloid Interface Sci. 55:469 (1976). C.P. Huang and Y. T. Lin, Specific adsorption of Co(II) and [Co(III)EDTA] complexes on hydrous oxide surfaces, in Adsorptionfrom Aqueous Solution (P. H. Tewari, ed.). Plenum, New York, 1981. A similar interpretation of the data in Fig. 4.7 is given in D. W. Fuerstenau, D. Manmohan, and S. Raghavan, the adsorption of alkalineearth metal ions at the rutile/aqueous solution interface, in P. H. Tewari, op. cit. zO R. Kummert and W. Stumm, The surface complexation of organic acids on hydrous yAl z0 3 , J. Colloid Interface Sci. 75: 373 (1980). L. Sigg and W. Stumm, The interaction of anions and weak acids with the hydrous goethite (aFeOOH) surface, Colloids Surfaces 2: 101 (19801981). D. E. Yates, S. Levine, and T. W. Healy, Sitebinding model of the electrical double layer at the oxide/water interface, J.es. Faraday 170: 1807 (1974). J. A. Davis, R. 0. James, and J. 0. Leckie, Surface ionization and complexation at the oxide/water interface. I: Computation of electrical double layer properties in simple electrolytes, J. Colloid Interface Sci. 63: 480 (1978). J. A. Davis and J. 0. Leckie, Surface ionization and complexation at the oxide/water interface. II: Surface properties of amorphous iron oxyhydroxide and adsorption of metal ions, J. Colloid Interface Sci. 67: 90 (1978). 3: Adsorption of IInionl, J. Colloid Interfufe Sci. 74: 32 (1980).
196
THE SURFACE CHEMISTRY OF SOilS
24. Comprehensive recent surveys of the triple layer model are to be found in J. A. Davis and J. O. Leckie, Speciation of adsorbed ions at the oxide/water interface, in Chemical Modeling in Aqueous Systems (E. A. Jenne, ed.; American Chemical Society, Washington, D.C., 1979) and in R. O. James and G. A. Parks, Characterization of aqueous colloids by their electrical doublelayer and intrinsic surface chemical properties, Surface Colloid Sci. 12: 119 (1982). A computerbased algorithm for the triple layer model is described by J. Westall, op. cit. 9 25. R. O. James, J. A. Davis, and J. O. Leckie, Computer simulation of the conductometric and potentiometric titrations of the surface groups on ionizable latexes, J. Colloid Interface Sci. 65: 331 (1978). A complete discussion of the graphic extrapolation methods, with examples, is given on pp. 167170 in R. O. James and G. A. Parks, op. cit. 24 26. J. A. Davis, R. O. James, and J. O. Leckie, op. cit.23 27. R. O. James, P. J. Stiglich, and T. W. Healy, The Ti0 2/aqueous electrolyte system: Applications of colloid models and model colloids, in P. H. Tewari, op. cit.2o 28. L. Balistrieri and J. W. Murray, Surface of goethite (aFeOOH) in seawater, in E. A. Jenne, op. cit. 24 The surface chemistry of goethite (aFeOOH) in major ion seawater, Am. J. Sci. 281: 788 (1981). The adsorption of Cu, Pb, Zn, and Cd on goethite from major ion seawater, Geochim. Cosmochim. Acta 46: 1253 (1982). The surface chemistry of 8Mn02 in major ion seawater, Geochim. Cosmochim. Acta 46: 1041 (1982). 29. A. E. Regazzoni, M. A. Blesa, and A. J. G. Maroto, Interfacial properties of zirconium dioxide and magnetite in water, J. Colloid Interface Sci. 91: 560 (1982). 30. M. M. Benjamin and N. S. Bloom, Effects of strong binding of anionic adsorbates on adsorption of trace metals on amorphous iron oxyhydroxide, in ·20 PHT . . ewan,' op. cit. 31. Surface speciation calculations are analogous to speciation calculations for aqueous solution phases, as pointed out by J. Westall, op. cit. ,9 in a detailed review. 32. See Part II of the series by J. A. Davis and J. O. Leckie, op. cit. 23 33. Other examples of surface chemical data that are described equally well by the triple layer and constant capacitance models are given in J. Westall and H. Hohl, A comparison of electrostatic models for the oxide/solution interface, Advan. Colloid Interface Sci. 12: 265 (1980). 34. See R. O. James et aI., op. cit. 27 35. See Part 3 of the series by J. A. Davis and J. O. Leckie, op. cit. 23 ; J. A. Davis and J. O. Leckie, op. cit.24; L. Balistrieri and J. W. Murray, op. cit28 36. M. Sasaki, M. Morlya, T. Yasunaga, and R. D. Astumian, A kinetic study of ionpair formation on the surface of aFeOOH in aqueous suspension using the electric field pulse technique, J. Phys. Chem. 87: 1449 (1983). 37. J. W. Bowden, A. M. Posner, and J. P. Quirk, Ionic adsorption on variable charge mineral surfaces: Theoreticalcharge development and titration curves, Aust. J. Soil Res. 15: 121 (1977). N. J. Barrow, J. W. Bowden, A. M. Posner, and J. P. Quirk, An objective method for fitting models of ion adsorption on variable charge surfaces, Aust. J. Soil Res. 18:34 (1980). A. M. Posner and N. J. Barrow. Simplification of a model for ion adsorption on oxide surfaces, J. Soil Sci. 33: 211 (19H2). Reviews of the objective model are given in
CHEMICAL MODELS OF SURFACE COMPLEXATION
38. 39.
40. 41.
42. 43. 44.
197
F. J. Hingston, A review of anion adsorption, in M. A. Anderson and A. J. Rubin, op. cit.,15 and in J. W. Bowden, A. M. Posner, and J. P. Quirk, Adsorption and charging phenomena in variable charge soils, in Soils with Variable Charge (B.K.G. Theng, ed.; New Zealand Society of Soil Science, Lower Hutt, New Zealand, 1980). The objective model is compared briefly with the constant capacitance and triple layer models by J. Westall and H. Hohl, op. cit. 33 See, e.g., Eq. 78 in T. L. Hill, op. cit. lO J. W. Bowden, S. Nagarajah, N. J. Barrow, A. M. Posner, and J. P. Quirk, Describing the adsorption of phosphate, citrate and selenite on a variablecharge mineral surface, Aust. J. Soil Res. 18: 49 (1980). N. J. Barrow, J. W. Bowden, A. M. Posner, and J. P. Quirk, Describing the adsorption of copper, zinc and lead on a variable charge mineral surface, Aust. J. Soil Res. 19: 309 (1981). See, e.g., D. C. Grahame, op. cit.,2 for a discussion of the classical electrical double layer. This central point is made cogently by J. Westall and H. Hohl, op. cit.33 Even the diffuse double layer model can be made to fit adsorption data by using the value aD as an adjustable parameter! See, e.g., J. W. Stucki and W. L. Banwart, Advanced Chemical Methods for Soil and Clay Minerals Research. D. Reidel, Dordrecht, Holland, 1980. A complexed species is metallike if ZIS > 0, ligandlike if ZIS < O. The constant capacitance model has been applied, in essence, to the adsorption of monovalent cations by montmorillonite in 1. Shainberg and W. D. Kemper, Ion exchange equilibria on montmorillonite, Soil Sci. 103: 4 (1967). The triple layer model is applied to the same phenomenon by R. O. James and G. A. . 24 Par k s, op. elf.
FOR FURTHER READING
M. A. Anderson and A. J. Rubin, Adsorption of Inorganics at SolidLiquid Interfaces. Ann Arbor Science, Ann Arbor, Michigan, 1981. Chapters 1, 2, 5, 6 and 7 provide specialized introductions to surface complexation models. G; H. Bolt, Soil Chemistry. B: PhysicoChemical Models, 2nd rev. ed. Elsevier, Amsterdam, 1982. Chapter 2 surveys diffuse double layer theory as applied in soil chemistry, and Chap. 13 surveys surface complexation models. R. O. James and G. A. Parks, Characterization of aqueous colloids by their electrical doublelayer and intrinsic surface chemical properties, Surface and Colloid Science 12: 119 (1982). Perhaps the most complete review of the triple layer model from the perspective of GouyChapmanSternGrahame double layer theory. M. C. Kavanaugh and J. O. Leckie, Particulates in Water: Characterization, Fate, Effect, and Removal. Advances in Chemistry Series 189. American Chemical Society, Washington, D.C. 1980. Chapters 1 and 2 give excellent accounts of the constant capacitance model in theory and application. Chapter 2 also contains a discussion of the computational aspects of the triple layer model.
6 SURFACE CHEMICAL ASPECTS OF SOIL COLLOIDAL STABILITY
6.1. THE SMECTITE QUASICRYSTAL
In Sec. 1.4 the concept of the smectite quasicrystal was introduced as a means of interpreting data on the specific surface area of montmorillonite. This concept, which describes the heterogeneous smectite particle formed by stacking hydrated unit layers along the crystallographic c axis (Fig. 1.11),1 is discussed in more detail in the present section. The discussion is intended to fill out the conceptual basis for understanding the behavior of soil clay suspensions containing smectites. Fundamentally, for any colloidal suspension, an operational meaning must be given to the terms particle and interparticle forces in order to describe the structure and stability of the suspension. The present section addresses the nature of the particles in smectite suspensions, taking as an illustrative example the clay mineral montmorillonite. Perhaps the first clear indication of the existence of montmorillonite quasicrystals appeared 30 years ago with the finding that Camontmorillonite suspensions exhibit a d(001) spacing of 1.91 nm that persists even as the electrolyte concentration is reduced to zero.f This invariant d(001) spacing is consistent with the formation of an outersphere surface complex between exchangeable Ca2+ ions and a pair of opposing siloxane ditrigonal cavities. In this surface complex, the octahedral solvation unit, Ca(H20)~+, would be arranged in the interlayer region with its principal symmetry axis parallel to the crystallographic caxis. Four of the solvating water molecules then would lie in a central plane that is parallel with the opposing siloxane surfaces, while the remaining two water molecules would reside in planes between the siloxane surfaces and the central plane (see Fig. 6.1). Supporting evidence for this structural arrangement can be found in the results of quasielastic neutron scattering experiments. which point to the existence of a rigid EQUILIBRIUM STRUCTURE.
SURFACE CHEMICAL ASPECTS OF SOIL COLLOIDAL STABILITY
199
Figure 6.1. An exploded view of the threelayer hydrate of Camontmorillonite.
octahedral solvation shell for Ca2+ in the 1.91 nm hydrate of Camontmorillonite, and in electron spin resonance spectra of exchangeable Cu2+ and Mn2 + in the threelayer hydrate of montmorillonite, which show that the principal symmetry axis of the octahedral solvation shell is perpendicular to the siloxane surface." Thus it may be concluded that a stable, outersphere surface complex that brings together two unit phyllosilicate layers in facetoface association is a characteristic molecular structure in suspensions of montmorillonite bearing bivalent exchangeable cations. A variety of experimental methods has been applied to determine the equilibrium number of unit layers in a montmorillonite quasicrystal. The results of some of these experiments are summarized in Table 6.1. Although variability exists among the experimental estimates for a given homoionic form of the clay mineral, a clear consensus emerges as to the absence of quasicrystals in dilute Namontmorillonite suspensions (1.2 ± 0.2 unit layers) and to the presence offour to eight unit layers per quasicrystal in dilute Camontmorillonite suspensions. Perhaps none of the determinations summarized in Table 6.1 is conclusive by itself, but taken as a group the set of data is quite convincing. A brief review of the five techniques listed in Table 6.1 can serve as a guide to estimating the reliability of the individual results. Smallangle neutron or Xray scattering" from dilute (less than 20 kg of clay per cubic meter) suspensions of montmorillonite can be used to infer the average thickness of the scattering particles, which are assumed to be discshaped aggregates consisting of unit layers in facetoface association with water layers interspersed between them. The intensity of the neutrons or Xrays scattered through small angles by one of these aggregates depends on the radius of gyration, which in turn can be related to the
Table 6.1. Experimental estimates of the number of unit layers in facetoface association in a particle of montmorillonite Exchangeable cation
Neutron scattering"
Li+ Na+ K+ Cs+ Mg 2+ Ca 2+
1 2 3 
Xray scattering"
Electron microscopy' 

1 

68
1.4 ± 0.5 
16 ± 2
Viscosity"

1.0
1.0 1.3 1.4 1.7 2.9 4.2 5.0 
Light scattering7
Chloride exclusions
1.0 1.0 1.0 1.2 1.7 1.2 1.5 2.7 2.8 3.0 5.5 4.2 6.2 7.0 2.7
1.0 1.0 1.2 1.1 1.5 2.1 4.2 8.8 5.9 6.5
SURFACE CHEMICAL ASPECTS OF SOil COllOIDAL STABILITY
201
particle thickness through standard geometric formulas. Smallangle scattering data interpreted in this way for cold neutrons led to aggregate thickness estimates of 1.1, 2.6, and 4.2 nm, respectively, for Li, K, and Csmontmorillonite." Within the experimental precision of 0.2 nm, these results are consistent with particle structures comprising one, two, and three unit phyllosilicate layers, respectively (e.g., in Kmontmorillonite, 2.6 ± 0.2 nm compared with 0.96 + 0.29 + 0.96 = 2.2 nm for a twolayer quasicrystal). The same kind of approach with Xrays led to estimates of one unit layer per particle in dilute suspensions of Namontmorillonite and six to eight unit layers per particle for Camontmorillonite." Highresolution transmission electron microscopy' can be used to make a direct estimate of the number of unit layers in a montmorillonite aggregate. A critical factor in this method is sample preparation. If the solidification and ultimate dehydration of a clay suspension (required in order to present the suspension to an electron beam) do not alter the aggregate structure, then the average number of layers in an aggregate can be determined accurately through a microscopic examination of its cross section. In practice, some alteration in aggregate structure is expected during sample preparation, and there is a possibility that ultrasectioning the sample will lead to an overestimate of the number of layers in thick quasicrystals whose outermost clay platelets are only partially intact." For these reasons, the estimate for Camontmorillonite in Table 6.1 should be regarded as an upper limit. Measurements of the specific viscosity of a very dilute (less than 2 kg of clay per cubic meter) montmorillonite suspension can be used to determine the average thickness of the suspended clay particles if the relationship" 71sp =
k 1Jp
(6.1)
is observed to represent the specific viscosity, 71sp, as a function of the volume fraction of clay particles, 1Jp • In Eq. 6.1, 71sp
=
71su 
71so
(6.2)
71so
and
1Jp = (c/Pc)(l + 0)
(6.3)
where 71su is the viscosity of a suspension containing c kilograms of clay per cubic meter of suspension volume, 71so is the viscosity of the aqueous solution in which the clay is suspended, Pc is the mass density (in kgrn P) of the clay, and 0 is the ratio of occluded water volume to clay volume in an aggregate. If it is assumed that the aggregates are thin discellipsoids of semimajor axis a and semiminor axis b (b ~ a), then kin Eq. 6.1 can be interpreted geometrically:" k = 0.849a h
(6.4)
202
THE SURFACE CHEMISTRY OF SOILS
The application of Eq. 6.1 to the estimation of the number of unit layers per clay aggregate involves the additional assumptions that (1) the parameters a, fJ, and Pc do not depend on the type of exchangeable cation on the clay and (2) each aggregate of either Na or Limontmorillonite comprises a single unit layer. With these two assumptions, the slopes of linear plots of 1]sp against c can be compared for several homoionic montmorillonites and used to calculate the number of unit layers, as given in Table 6.1. These estimates are relative values based on a number of simplifying assumptions. The use of light scattering to estimate the number of unit layers per clay aggregate in a montmorillonite suspension is analogous to the method of smallangle neutron or Xray scattering. The intensity of light scattered by an aggregate depends on the refractive index characteristics of the aggregate, the concentration of clay in the suspension, and the number of unit layers in facetoface association within the aggregate." Under the assumption that the refractive index characteristics and the mass density of the clay do not depend on the type of exchangeable cation, the turbidity of a series of homoionic montmorillonites is proportional to the number of unit layers per aggregate. With the convention that Limontmorillonite suspensions contain only singlelayer aggregates, relative estimates, as given in Table 6.1, are possible. Graphs of the volume of chloride exclusion against the inverse square root of chloride concentration can be used to estimate the specific surface area of the aggregates in a montmorillonite suspension, according to Eqs. 1.17 and 1.19. If it is assumed that the entire suspension comprises quasicrystals with n unit layers each, thenf = 1.0 in Eqs. 1.19 and 1.20. If it is assumed also that no complexes form between exchangeable cations and siloxane ditrigonal cavities on the external surfacesof quasicrystals, then Eq. 1.20 leads to the conclusion that the specific surface area measured by chloride exclusion is proportional to n, With the convention that n = 1 for Limontmorillonite, the relative estimates of n in the last two columns of Table 6.1 can be made." These estimates are naive in that surface complexes on the external surfaces are ignored despite the evidence for their existence discussed following Table 1.8. However, measurements of Vex for Ca and Mgmontmorillonite suspensions do indicate a limiting value, equal to about 0.3 dnr' kgI, as the inverse square root of the chloride concentration is extrapolated to zero." This limiting value is in agreement with the y intercept in Eq. 1.19: Sod/2 = 7.51 x 105 m2 kg 1 x (1.91  0.96)nm/2 = 0.357 dnr' kgI, the volume inside the quasicrystals from which chloride is assumed to be completely excluded. Although the estimates of n in Table 6.1 also reflect differences in the extent of external surface complexation on the homoionic montmorillonites, the good agreement of the measured Vex values with those predicted by Eq. 1.19 indicates that chloride exclusion data do give evidence for quasicrystal formation.
SURFACE CHEMICAL ASPECTS OF SOIL COLLOIDAL STABILITY
203
The estimates in Table 6.1 clearly are not truly quantitative since they are based on both model assumptions and computational simplifications that cannot be substantiated a priori. Nonetheless, they do show unanimity for a given homoionic form of montmorillonite and it does seem justifiable to infer from them that, in relatively dilute suspensions, the structure of Namontmorillonite particles is different from that of Carnontmorillonite particles. By induction one would conclude also that there should be some kind of continuous transition from more or less singleunitlayer particles to quasicrystals as one observes changes in the properties of suspensions of montmorillonite bearing both Na + and Ca2+ on the basal planes. This conclusion is verified experimentally by the data in Fig. 6.2.10 The ordinate of the graph represents the ratio of the value of some suspension property P to the value of P for Namontmorillonite; the abscissa refers to values of the charge fraction of exchangeable Na+ on the clay. Both the intensity' of the light transmitted (not scattered) by a suspension and the electrophoretic mobility of its constituent particles are expected to be directly sensitive to particle dimensions. The intrinsic viscosity (the ratio of T/sp to c in Eqs. 6.1 and 6.3) and the chloride exclusion volume are dependent on
Figure 6.2. Scaled value P/ PN a of four montmorillonite suspension properties versus the charge fraction on Na+ on the clay.lOThe curves through the data points are meant only as guides to the eye. 1.0
r:::~.I
•
0.8
0.6
•o
o
o
TRANSMITTED LIGHT INTENSITY
•
ELECTROPHORETIC MOBILITY
o
INTRINSIC VISCOSITY
•
CHLORIDE EXCLUSION VOLUME
oOl....~......L_L.~ 0.2
0.4
0.6
0.8
1.0
204
THE SURFACE CHEMISTRY OF SOILS
particle shape and external surface area, respectively. That these four properties show sharp increases when the charge fraction of Na + on the clay lies between 0.15 and 0.30 indicates that, in this range, the quasicrystals of Camontmorillonite are largely being broken up in favor of more or less singleunitlayer aggregates. Evidently, when E N a < 0.3, the quasicrystals are stable entities with exchangeable Na+ cations residing principally on their external surfaces, as discussed in connection with Fig. 3.4. The mixing together of Na and Camontmorillonite suspensions to produce an overall charge fraction of Na + on the clay particles below 0.1 results in a very rapid (less than 1 min) formation of quasicrystals from conversion of the Namontmorillonite particles.!' This rapid conversion is necessarily mediated by a redistribu: tion of the exchangeable cations such that Na + ions are relocated, as required, to the external surfaces of alreadyformed quasicrystals that contain Ca2+ ions on their internal surfaces. The relocation probably involves replacement by Na+ of Ca2+ already on external surfaces since the latter ions are likely to have a higher mobility than Ca2+ adsorbed inside a quasicrystal. 12 On the other hand, if the mixing together of two homoionic montmorillonite suspensions produces an overall charge fraction of Na + larger than 0.6, then there is a gradual decomposition of the initial set of quasicrystals, with the final result being a suspension whose physical properties resemble closely those of a collection of singleunitlayer clay particles.!' This slower process of quasicrystal conversion to single unit layers reflects both the lower mobility of Ca2+ in the interlayer region and the difficulty Na+ has in replacing these bivalent cations in the initial step of quasicrystal destruction. In keeping with this point of view, the decomposition is aided by maintaining a low electrolyte concentration, since interlayer swelling is thereby enhanced. 13 These characteristics of quasicrystal formation and breakdown are consistent with the trends in Fig. 6.2. When E N a is less than 0.1, for example, the properties of a mixed Na/Camontmorillonite do not differ much from those of Camontmorillonite and the quasicrystal should remain a stable entity. When E N a is larger than 0.6, however, the mixed Na/Camontmorillonite exhibits properties that are indistinguishable from those of a Namontmorillonite and a quasicrystal should be an inherently unstable structural unit. When Na and Camontmorillonite are mixed together and quasicrystal formation is favored, it is likely that the thermodynamic driving force is a negative enthalpy change (heat release). Since the quasicrystal represents a more ordered local arrangement of unit montmorillonite layers than what exists in a dilute suspension of Namontmorillonite , the entropy change accompanying quasicrystal formation should be negative. This result in turn means that the entropy contribution to the Gibbs energy change for QUASICRYSTAL
FORMATION.
SURFACE CHEMICAL ASPECTS OF SOIL COLLOIDAL STABILITY
205
quasicrystal formation is positive and that the required negative Gibbs energy change (because the quasicrystal is stable) must derive from a negative enthalpy change. This enthalpy change can be measured by comparing the heat of immersion from mixing Na and Camontmorillonite in water to produce a given value of E N a with the heat of immersion of an Na/Camontmorillonite with the same charge fraction E N a already on its surfaces.!" The heat of immersion that accompanies the mixing of the two homoionic clays is the larger by about 5.9 kJ . mol,", which means that the enthalpy change for quasicrystal formation is about  5.9 kJ· mol,". This enthalpy change can also be measured by subtracting the enthalpy of NaCa exchange (+ 1.7 ± 0.2 kJ molj ') from the total enthalpy change observed when a CaCl z solution is added to a suspension of Namontmorillonite. IS The result is 4.9 ± 0.2 kJ . mol.,", which is in reasonable agreement with the first estimate. That both values are negative substantiates the conjectured thermodynamic driving force for quasicrystal formation.
6.2. INTERPARTICLE FORCES IN PHYLLOSILICATE SUSPENSIONS The particles in a stable phyllosilicate suspension can be envisioned, in an ideal geometric sense, as comprising one or more unit layers stacked along the crystallographic c axis (Sec. 1.4 and Fig. 1.11). If the stacking is not extensive, the particles resemble thin wafers and it is reasonable to imagine the forces they exert on one another as emanating from planar surfaces. The nature of these interparticle forces is discussed in the present section after this geometric simplification is adopted. Actual interparticle forces no doubt are more complicated than the model interactions described below, but the essential physical features of the true forces should be represented adequately. If the net charge on a phyllosilicate particle is not zero, an electric field and a nonvanishing net volumetric charge density are produced in the aqueous solution near the surface of the particle. These two effects combine to produce an electric force that in turn can act on a neighboring charged clay particle to accelerate it, unless the particle is restrained by an external force. If the two charged particles and the aqueous solution between them are quiescent, the restraining external force is manifest simply as a pressure gradient that balances the net electric force in a unit element of volume anywhere in the aqueous solution phase. Consider two identical opposing planes arranged geometrically as in Fig. 3.3, with the origin of coordinates set in one of them and with the other located at the point x = d (replacing the plane of shear) along an outward normal from the first. Each plane is to represent the surface to which up in Eq. 3.2 refers. Within the aqueous solution between the planes, the volumetric charge density of species i is, according to the diffuse double layer theory. equal to the ith term on the right side of THE ELECTROSTATIC FORCE.
206
THE SURFACE CHEMISTRY OF SOILS
Eq. 5.9. In differential form this charge density obeys the equation
RT zpdpj
=
cjZjFexp(ZjFl/J/RT)dl/J
=
pjdl/J
I
(6.5)
where pj is the charge density at some point x and l/J is the corresponding inner potential. Upon summing both sides of Eq. 6.5 over all species and making use of the wellknown relation for the osmotic pressure of an ideal electrolyte solution,
P
RT}2 (pJZjF)
=
(6.6)
i
one can derive the forcebalance expression.'"
dP + pdl/J
(6.7a)
= 0
where p is given by Eq. 5.9. Since l/J(x) is related to the volumetric charge density, p(x), through the Poisson equation (Eq. 3.26), Eq. 6.7a can be transformed, with the help of Eqs. 3.26 and 5.4b, to the expression 1 (dl/J) d [ P(x)  eoD dx 2 dx
2] = 0
(6.7b)
where eo is the permittivity of vacuum and D is the dielectric constant of the water between the planes. Equation 6.7b is equivalent to the equation
P(x)  2"1 eoD (dl/J)2 dx
=
P«
(6.7c)
where Pm = P(d/2) is the pressure at the point x = d/2, halfway between the two planes. Equation 6.7c includes the condition that the net electric field, dl/J/dx, be zero at this halfway point. A practical application of Eq. 6.7c cannot be made until the constant of integration Pm is expressed in terms of molecular properties. This can be done by rewriting Eq. 6.7a as the integral expression pm
i
dP
= 
Po
fc"'m
p(l/J)dl/J
(6.8)
0
where Po is the pressure in the aqueous solution far from the two planes, where l/J(x) may be set equal to 0, and l/Jm == l/J(d/2). Equation 5.9 can be introduced into Eq. 6.8 to yield the result
r;
= Po
+ RT}2 cj[exp(ZjFl/Jm/RT)  1]
(6.9)
i
where all of the symbols in the following Eqs. 1.11 and 5.1. pressure required to maintain density O'p a distance d apart
second term on the right side are as defined This model expression gives the applied the two planar surfaces bearing the charge at equilibrium.
SURFACE CHEMICAL ASPECTS OF SOIL COLLOIDAL STABILITY
207
The full specification of either P(x) or Pm as a function of position between the planes cannot be made without solving Eq. 5.1 subject to the conditions dl/J) ( dx x=d/2 0
l/J(d/2) = l/Jm
(6.10)
A first integration of Eq. 5.1 under these conditions produces an equation analogous to Eq. 5.8: dl/J {2RT dx = sgn(l/J) 8 D ~ cj[exp( ZjFl/J(x)/RT)  exp( ZjFl/Jm/RT)]
}1/2
0
(6.11) Equation 6.11, like Eq. 5.8, can be solved analytically for a single symmetric electrolyte that dissociates completely. 17 However, the result is only a formal expression in terms of elliptic integrals that must be evaluated from mathematical tables." Alternatively, one can transform Eq. 6.11 into an analog of Eq. 5.11a: dy dx
= sgn(Y)K[2(cosh
Zy  cosh ZYm)]1/2
(6.12)
and use an iterative, computerbase algorithm to solve it numerically. 18 (In Eq. 6.12, y = Fl/J/RT and K = (3co, as in Table 5.1.) With either approach, Eq. 6.12 is integrated between x = 0 and x = d/2 to produce a relationship between l/Jm' l/J(O) , and the interplane separation d. The integration can be done with l/J(O), the particle surface potential, fixed at a predetermined value, in which case u(O) follows from Eqs. 5.5 and 6.12:
J
u(O) = sgn(yo)
8 0 DRTK
F
[2(cosh ZYo  cosh ZYm)]I/2
(6.13)
where Yo = Fl/J(O)/RT. Since u(O) = UD in the DDL model and UD = up by Eq. 3.3a, the condition of fixed l/J(O) implies that up depends on l/Jm and d. If the integration of Eq. 6.12 is done with up = u(O) fixed instead, then the boundary condition (6.14) must be applied and Eq. 6.13 is used to calculate l/J(O), which clearly depends on l/Jm and d. It is possible that neither up nor l/J(O) should be held fixed in the integration of Eq. 6.12 if surface complexation phenomena are important as the interplane separation is varied.l" In this case, Eqs. 6.13 and 6.14 collapse into a single expression (because of Eqs. 3.3a and 5.5) that relates a variable surface charge density to a variable surface potential. Another relationship between these two parameters is needed in order to make the algebraic problem determinate. This relationship can be taken from any of the surface.complexation models described in Chap. S. For
208
THE SURFACE CHEMISTRY OF SOILS
example, Eqs, 5.42, 5.43, 5.44, and 5.46 can be used to connect O"p with 1/1(0), given that measured values of O"max and the K~(int) (i = 1,2) are available. ' The mathematical effort to solve Eq. 6.12 is reduced dramatically if the condition ZKdj2 ~ 1 obtains. In this case, the approximate equation for I/I(x) in Eq. 5.14 can be applied immediately to calculate I/Im as the superposition of I/I(dj2) for each charged planer'?
RT
I/Im = 8 ZF a exp(  ZKd/2)
(6.15)
where a = tanh (ZFI/I(0)/4R T). Since ZKd/2 is very large, I/Im is very small in this approximation and Eq. 6.9 must be expanded in a MacLaurin series in I/Im to the lowest nonvanishing order to be consistent: Pm = Po + cRT(ZFl/lm/RT)2 = Po + 64a 2cRT exp( ZKd)
(6.16)
In this approximation, Pm is an exponentially decreasing function of the interplane separation. The potenial energy per unit area, 'Pm' corresponding to the force per unit area, Pm' can be calculated readily by a standard integration: 16 'Pm = 2
j:
12
[Pm(g)  Po]dg = 128a
64a 2 = ZK cRT exp(ZKd)
2cRT j:12 exp(2ZKg)dg (6.17)
where 2g has been substituted for din Eq. 6.16 as a dummy variable of integration. Calculated values of Pm based on Eq. 6.9 and the integration of Eq. 6.12 agree semiquantitatively with experimentally determined reversible curves of the swelling pressure of Namontmorillonite versus the interplane separation.j" These curves, which apply to the clay mineral suspended in dilute solutions of NaCl, agree fairly well with the theoretical prediction obtained with either O"p(= 0.118 C'm 2) or 1/1(0) (= 0.25 V) held fixed. The two theoretical curves are identical for d > 1 nm. A more direct test of the DDL model of the electrostatic force is shown in Fig. 6.3. 21 The graphs are semilogarithmic plots of the repulsive force per unit radius (potential energy per unit area) between two muscovite cylinders in contact with a solution of KN0 3 . The force between the two mica planes is measured through the deflection of a spring attached to one of them, and the interplane distance is measured by interferometry. The lines through the data points in Fig. 6.3 represent Eq. 6.17 (with Z = 1). The excellent agreement between experiment and theory is convincing evidence for the applicability of DDL theory in 1: 1 electrolyte solutions at low concentrations. At higher concentrations of KN0 3 (above 10 mol, m'3), however,
209
SURFACE CHEMICAL ASPECTS OF SOIL COLLOIDAL STABILITY
104 .___.....,....,."""T""~_,__..,._,.___~_r_...,
MUSCOVITE IN KN0 3 20°C pH6 • O.lmol m 3 o I mol m 3
10
o
10
20
30
40
50
60
70
80
90
100
110
120
d (nrn) Figure 6.3. Measured values of the force F between two muscovite cylinders of radius R as a function of their separation d in aqueous solutions of KN0 3 • The ratio F/2TrR equals the potential energy per unit area for the interaction between the two mica surfaces. 21
and even at low concentrations (0.1 mol, m3) in 2: 1 electrolyte solutions, the DDL model predictions fail to describe the observed force curves.P This failure can be traced to the inherent inadequacy of Eq. 5.1 for phyllosilicates suspended in moderately concentrated 1 : 1 electrolyte solutions and in any asymmetric electrolyte solution, as discussed in Sec. 5.1 (see Fig. 5.1). When considered over a time interval much longer than 10 s, the distribution of electronic charge in a nonpolar molecule is geometrically spherical. However, on a time scale comparable to or shorter than 10 16 s (approximately the period of an ultraviolet light wave), the charge distribution of a nonpolar molecule exhibits significant deviations from spherical symmetry, taking on an evanescent dipolar (or higher multipole) character. These deviations fluctuate rapidly enough to average to zero when observed over, say, 10 14 s, but they persist long enough to induce distortions in the charge distributions of neighboring molecules. If two nonpolar molecules are brought close together, each induces in the other a fluctuating dipolar character and the correlations between these induced dipole charge distributions do not average to zero over a long time period, even though the individual dipole distributions themselves average to zero. On a very short time scale. a nonpolar molecule creates a dipolar electric field of intensity E ... fJ..I R'\ where fJ.1 is the magnitude of the instantaneous THE VAN DER WAALS DISPERSION FORCE. 16
THE SURFACE CHEMISTRY OF SOilS
210
dipole moment of the molecule and R is the distance between the center of the molecule and the point at which E is evaluated.P This electric field in turn induces a dipole moment JL2 = aE = aJLdR 3 in another nonpolar molecule separated from the first by the distance R, where a is the polarizability of the second molecule. The correlation between the two instantaneous dipole moments produces the potential energy V =  JLIJL2/R 3 according to classical electrostatics. Therefore, the average potential energy of interaction is V =  aJLilR 6 and the corresponding force is F = 6aJLIIR 7 . This force is known as the van der Waals dispersion force. For small values of intermolecular separation, this force can be large, although it cannot compete with the much stronger covalent interactions. At large intermolecular separations it is much smaller than the coulomb force. Suppose that a nonpolar molecule confronts the planar surface of a solid comprising N of the same molecules per unit volume. The van der Waals dispersion potential energy for the interaction between the single molecule and the solid can be calculated with the equatiorr'" (6.18) Equation 6.18 is interpreted as follows. The single molecule is positioned a distance z from the planar surface and a distance R = [(z + ()2 + p 2F/2 from a point within a ringshaped element of the solid (Fig. 6.4). The volume of this element of solid is dr = pd({Jdpd( in cylindrical polar coordinates. The van der Waals potential energy between the single molecule and the molecules in the volume element is C dV(z) = R 6 N dr
C
(ex> (ex>
V(z)
=
2TTNC
Jo Jo
TTNC (ex>

2
pdpd( [(z + ()2 + p2j3
d(
Jo (z + ()4
TTNC

6z 3
Now suppose that the single molecule is embedded in a solid just like the one it confronts. Within a thin slab of thickness dz that lies parallel to the planar surface of the solid. there are Ndz molecules per unit area. and so
SURFACE CHEMICAL ASPECTS OF SOIL COLLOIDAL STABILITY
211
ATOM
SOLID Figure 6.4. Cylindrical polar coordinates to define the spatial relationship between an atom located a distance R away from a ringshaped element of volume located a distance ( inside a solid with a planar surface.
the potential energy per unit area between two opposing solids a distance d apart is23 CPvw(d)
=N 
f
d""
7r:
2
V(z)dz
A 121Td 2
=
C L"" ::
(6.20)
where A == (1TN)2C is called the Hamaker constant. Equation 6.20 shows that the van der Waals dispersion potential energy (per unit area) falls off as the inverse square of the distance separating two opposing planar surfaces. Because it is additive for all molecules in the two solids, this attractive interaction decreases with distance of separation much more slowly than the interaction between an isolated pair of molecules. A tacit assumption in the derivation of Eq. 6.18 is that the response of one molecule to the distorted charge distribution of the other is effectively instantaneous. If the intermolecular separation is small enough, this approximation does not affect the calculation of V(z), but at some distance of separation its effect is significant. In broad terms, this distance is reached when the time required for the ftuctuating dipolar field of one molecule to
212
THE SURFACE CHEMISTRY OF SOILS
propagate to the other molecule and be returned becomes comparable with the period of the fluctuation itself. Under these conditions, the correlations between the two induced dipole distributions weaken and the potential energy of interaction eventually becomes proportional to the inverse seventh power of the intermolecular distance instead of the inverse sixth power.P This potential energy corresponds to a force depending on the inverse eighth power of the distance, the retarded van der Waals dispersion force. The transition between the nonretarded and retarded van der Waals forces is not usually abrupt, but occurs gradually over distances on the order of tens of nanometers. The retarded van der Waals force between the two planar surfaces a distance d apart can be calculated following the procedures in Eqs. 6.18 to 6.20, with the result
B
'PRvw(d)
=  3d 3
(6.21)
where B is the retarded Hamaker constant. The theoretical calculation of the Hamaker constants in Eqs. 6.20 and 6.21 for the case of two opposing planar solid surfaces with an aqueous solution between them is a difficult area of current research. 22 ,24 An approximate equation for A pertaining to this physical situation can be derived under the assumptions that the solids are dielectrics, that only the liquid water between them affects the van der Waals force, and that the solids and the water absorb ultraviolet radiation at a single characteristic frequency. The resulting equation is22 3(n~  n;)2hWo
(6.22)
where n, (i = w or s) is a refractive index of water or solid, lU o is the characteristic angular frequency of absorption, and h = 1.0546 X 10 34 J . s is the Dirac constant. With nw = 1.33, ns = 1.6 (typical for phyllosilicates), and Wo = 2 X 1016 rad s 1 as a typical angular frequency, Eq. 6.22 leads to the estimate A = 1.9 X 10 20 J. Theoretical estimates of B can be developed in a similar fashion.P with the result B = 10 28 J. m. Figure 6.5 shows measured values" of the van der Waals potential per unit area for muscovite surfaces contacting aqueous solutions of KN0 3 or Ca(N03h at concentrations between 10 and 103 mol· m 3. The experimental method was the same as described in connection with Fig. 6.3, but with conditions arranged to suppress the electrostatic force. The line through the data points represents Eq. 6.20 multiplied by 27T on both sides, with A = 2.2 ± 0.3 x 10 20 J. The good agreement for d < 7 nm between theory and experiment with respect to the d dependence suggests that the van der Waals force does not depend on the type of electrolyte present or, in the range examined, on its concentration. Further support for the conclusion that A does not depend on the type of electrolyte comes from the agreement between the
SURFACE CHEMICAL ASPECTS OF SOIL COLLOIDAL STABILITY
213
o ......::............0
50

( \J
IE
100
"'?
::l 
o
"'C
~
ft
150 MUSCOVITE
I:::
C\J
•
KN0 3
o
Co(N0 3)2
200
250 L.._ _'..L o 5
....L.
10
I
15
d (nrn) Figure 6.5. Measured values of the van der Waals potential energy per unit area, 'Pvw(d) , for opposing muscovite surfaces separated by a distance d in aqueous solutions of KN0 3 and Ca(N03h at concentrations from 10 to lcP mol· m ~3 and at pH 6. 21
measured value and the theoretical estimate (Eq. 6.22) of this parameter, since the latter is based on the properties of water alone in the aqueous phase. For interplane separations larger than 7 nm, Fig. 6.5 suggests that the retarded van der Waals force is important. The scatter in the experimental data prevented a conclusive test of Eq. 6.21, however. The electrostatic and van der Waals dispersion forces retain the common attribute of depending on the nature of liquid water in the aqueous solution phase only through the macroscopic dielectric constant. In the case of the electrostatic force as exemplified in Eq. 6.16, the only dependence on the properties of liquid water comes through the parameter 1<, which, as shown in connection with Eq. 5.11, is a function of the bulk (zerofrequency) dielectric constant, D. Similarly, for THE SOLVATION FORCE.
214
THE SURFACE CHEMISTRY OF SOilS
the nor.retarded Hamaker constant represented by Eq. 6.22, the standard equality between the square of the refractive index and the dielectric constarst at optical frequencies'f can be applied to show that the van der Waals dispersion force also depends only on the properties of liquid water as a boll: dielectric continuum. The @bsence of any parameters referring directly to the molecular nature of liqui,d water is certainly a simplifying feature of the electrostatic and van der w.als dispersion forces, but it is evident that this simplicity ceases to be realistic at some point as two planar phyllosilicate surfaces are brought closer 2lnd closer together. For example, during quasicrystal formation by unit layers of montmorillonite bearing exchangeable Ca2+ cations, one can imagine that the competition between the repulsive electrostatic force and the att ractive van der Waals force will, along with random thermal motions. determine the behavior of two siloxane surfaces approaching one another from a distance of separation larger than 10 nm. However, at the interplelIlar separation distance of 0.95 nm, which is characteristic of the outersf'bere surface complex in Fig. 6.1, it can be expected that the force require d to bring the particle surfaces closer together must have a compooent that reflects the effort necessary to desolvate the exchangeable Ca 2 + ctltions. Indeed, at distances between 10 nm and 0.95 nm, the force bringing the siloxane surfaces into close proximity must displace water molecules from the second solvation shell of Ca2+ cations (Sec. 2.2). When the two surfaces collapse into the quasicrystal configuration, almost all of these outermost solvating water molecules will have been ejected from the interlayer region (Fig. 2.4), and the force required to accomplish this task must tD some extent depend on the structure of the cation solvation complex at the molecular level. 25 Based on qualitative arguments only, it is not possible to derive an explicit relationship between the additional force required to desolvate exchangeable cations and the interplanar separation distance. Since most of the metal cations encountered on the surfaces of natural phyllosilicates tend to form octahedral primary solvation complexes in aqueous solutions (Sees. :2.2 and 2.3), it is likely that the additional force increases markedly as the ioterplanar separation decreases below 1 nm, the characteristic diameter of octahedral solvation complexes. For separations larger than 1 nm, it is possible that the additional force drops rapidly to zero if the van der Waals dispersion force is strong enough to overcome the electrostatic force and displace water molecules from secondary solvation shells of the cations in the aqueous solution between the opposing phyllosilicate surfaces. The effect of the finite diameter (0.29 nm) of the water molecules on the decay of the additional force with distance should be to superimpose an oscillatory feature that exhibits relative maxima at the mean positions of the molecules projected along a normal extending from one opposing surface to the other. 25 Qualitative evidence for the existence of a solvation force between siloxane surfaces has been adduced from experiments on the compression
215
SURFACE CHEMICAL ASPECTS OF SOIL COLLOIDAL STABILITY
of Namontmorillonite particles aligned perpendicularly to their crystallographic c axes in a NaCI background solution.j" In a solution of 0.1 mol, m 3 NaCl, the reversible experimental compression curve (pressure applied versus interplanar separation) for Namontmorillonite was observed to always lie significantly above the theoretical compression curve, based on Eqs. 6.9 and 6.11 and the derivative of 'Pvw(d) in Eq. 6.20, when the interplanar separation decreased from 5.0 to 1.8 nm. This positive deviation of the experimental compression curve became even larger after the clay adsorbed ndodecyl hexaoxyethylene glycol monoether, a nonionic surfactant compound that reduces both the electrostatic and the van der Waals force. The conclusion drawn was that an additional force must be significant at interplanar separations below 5 nm. As with the electrostatic and van der Waals dispersion forces, a more precise characterization of the solvation force has come from direct experimental measurements of the net force per unit radius (energy per unit area) between opposing muscovite surfaces.j? Figure 6.6 shows this
Figure 6.6. The net force per unit radius between muscovite surfaces in contract with an aqueous solution of KBr at pH 6.2. 28 The solid line represents the contribution of electrostatic and van der Waals forces.
MUSCOVITE 0.5 mol m 3 KBr
a:: <, LL.
ELECTROSTATIC ~ PLUS VAN DER WAALS FORCES
102
o
10
20
30
d(nm)
40
50
216
THE SURFACE CHEMISTRY OF SOILS
net force as a function of interplanar separation for two mica surfaces in contact with a solution of 0.5 mol, m 3 KBr at pH 6.2. 28 The solid line in the figure represents the combination of the electrostatic and van der Waals forces according to Eqs. 6.9, 6.11, and 6.20, with 1/1(0) = 0.1 V taken as a fixed surface potential. For separations of the planes smaller than about 6 nm, there is a marked positive deviation of the experimental data from the theoretical curve. The difference between the data and the curve can be fit by regression to the equatiorr" 'Psolv(d)
=
a 21T exp( dj8)
(6.23)
where a and 8 are empirical constants. From this kind of curve fitting, it is found that a = 0.03 to 0.05 N 'm 1 and 8 = 0.3 to 1.0 nm. 27 ,29 The solvation force decays approximately exponentially with a decay length, 8, near 1 nm, in agreement with the qualitative expectations outlined above. Several qualitative properties of the solvation force between the siloxane surfaces of muscovite have been determined experimentallyr" 1. In the temperature range 20 to 65°C, there is no change in either a or 8 in Eq. 6.23. This lack of temperature dependence ofthe solvation force is consonant with the very small temperature dependence of the Gibbs energy change for cation solvation in aqueous solutions. 2. The solvation force diminishes as the concentration of the aqueous solution between the mica surfaces decreases. When the concentration drops below 0.1 mol, m 3, the solvation force begins to disappear altogether. 3. The solvation force is not detectable when the principal cation in the aqueous solution between the mica surfaces is the proton. 4. In the presence of 1: 1 electrolyte solutions at pH 5 to 6, the solvation force makes an appearance at a threshold concentration, whose value depends on the metal cation in the electrolyte. These threshold concentrations are 60 (Li), 10 (Na), 0.04 (K), and 1 (Cs) mol· m 3 for Group IA metals. Thus a in Eq. 6.23 is both cation and concentrationdependent. These experimental properties of the solvation force are consistent with the hypothesis that exchangeable cations, either in outersphere surface complexes or in a diffuse swarm, determine the nature of the solvation force between siloxane surfaces. (Exchangeable cations in innersphere surface complexes can also playa role if they are partially solvated.) If the proton is the principal exchangeable cation (e.g., when the pH or the electrolyte concentration is very low), desolvation seems to require no more than the presence of the van der Waals force. For monovalent metal cations, the threshold concentration at which the solvation force appears increases as the selectivity of the siloxane surface for the cation relative to
SURFACE CHEMICAL ASPECTS OF SOIL COLLOIDAL STABILITY
217
potassium ions decreases (Fig. 4.4). This inverse correlation suggests that a certain fraction of the K+ cations in the siloxane ditrigonal cavities of the muscovite surface must be replaced by metal cations in outersphere complexes and/ or the diffuse ion swarm in order for the solvation force to be manifest. Since the proton is always a third exchangeable cation when K+ ~ M+ (M = Li, Na, or Cs) exchange occurs, the appearance of the solvation force should also depend on the selectivity of muscovite for the proton in the ternary system K+M+H+muscovite. Clearly, the chemical master variables that determine the appearance of the solvation force are the composition of the aqueous solution between the mica surfaces and the selectivity coefficients for K+M+, K+H+, and M+H+ exchange. Since the solvation force is defined as the difference between the observed net force and the net van der Waals plus electrostatic force, as calculated with Eqs. 6.9,6.11, and 6.20, it follows from the foregoing discussion that Eq. 6.12 should be integrated in the context of an appropriate surface complexation model (e.g., the triple layer model) to provide the most accurate theoretical estimate of the electrostatic force. 30 6.3. THE STABILITY OF SOIL COLLOIDAL SUSPENSIONS
A suspension of soil colloids is said to be stable if the average particle size of the colloids does not increase at a significant rate to the point when gravitational settling can occur.P If a soil colloidal suspension is unstable, it is said to undergo coagulation as its constituent particles interact to form larger particles. When coagulation produces a relatively loose, open network of linked particles in a structure that is often ephemeral, the process is called flocculation. When more permanent, compact structures are produced instead, the process is called aggregation. The smallest concentration of electrolyte, in moles per cubic meter, at which a soil colloidal suspension begins to undergo rapid coagulation is called the critical coagulation concentration (ccc). The value of the ccc, in general, depends on both the nature of the colloidal particles and the composition of the aqueous solution in which they are suspended. The measurement of the ccc entails the preparation of dilute (less than 3 kg' m 3 solids concentration) suspensions in a series of solutions of increasing electrolyte concentration. After 1 hour of shaking and a standing period of 24 hours, the coagulated suspensions show a clear boundary separating the settled solid mass from an aqueous solution phase, and the ccc can be bracketed between two values determined by the largest electrolyte concentration at which coagulation does not occur and the smallest at which it does. 32 Colloidal stability plays an important role in the maintenance of the soil aggregate structures on which the penetrability of the soil surface and the permeability of the soil profile depend." The study of soil colloidal stability has not yet produced exact, quantitative theories, but there have begun to emerge general relationships between stability, interparticle forces, and surface chemistry that are of predictive value.
218
THE SURFACE CHEMISTRY OF SOILS
The empirical relationship concerning the ccc first suggested by Schulze 100 years ago and generalized by Hardy in 1900 can be statedr'" THE SCHULZEHARDY RULE.
The critical coagulation concentration for a colloid suspended in an aqueous electrolyte solution is determined by the ions with a charge opposite in sign to that on the colloid and is proportional to an inverse power of the valence of the ions.
The SchulzeHardy rule is illustrated in Table 6.2 for five important soil minerals." Mean values of the ccc extracted from published studies, together with standard deviations reflecting the range of ccc values reported, are presented in the table for ions whose absolute valence is equal to 1 or 2. For the hydrous oxides, the particle charge is positive and the coagulating ions are anions; for the phyllosilicates, the particle charge is negative and the coagulating ions are cations. The ratio of ccc values for IZI = 2 and !ZI = 1 is given in the fourth column of the table. These ratios may be compared with a theoretical value of r 6 = 1/64 = 0.0156, which is derived below. It is evident from Table 6.2 that the SchulzeHardy rule provides a semiquantitative prediction of relative ccc values for soil colloidal suspensions. The inverse sixth power of the coagulating ion valence appears to be a reasonable factor for relating ccc values. A theoretical derivation of the SchulzeHardy rule can be developed on the basis of the interparticle forces described in Sec. 6.2. Each of the three forces is associated with a potential energy that contributes additively to the total potential energy between two planar particle surfaces a distance d apart. If
a
+ 27T exp( d/ 13) (6.25)
according to Eqs. 6.17,6.20, and 6.23. It is assumed in Eq. 6.25 that dis Table 6.2. Critical coagulation concentrations for colloidal suspensions of soil minerals35 Soil mineral Al hydrous oxide Fe hydrous oxide Illitic mica Kaolinite Montmorillonite
ccc (121 = 1), molrn ? 50 11 48 10 8
± ± ± ± ±
9 2 11 4 6
ccc (121 = 2), molm ? 0.5 ± 0.2 0.21 ± 0.01 0.14 ± 0.02 0.3 ± 0.2 0.12 ± 0.02 Simple DLVO theory:
ccc(121 = 2) ccc (121 = 1) 0.010 0.019 0.003 0.030 0.015 0.0156
SURFACE CHEMICAL ASPECTS OF SOIL COLLOIDAL STABILITY
219
large enough to make Eq. 6.17 applicable but not so large as to require a retarded van der Waals dispersion force (Eq.6.21). Since Eq.6.17 approximates 'Pm(d) within about 20 per cent for d > I/ZK and 'Pvw(d) begins to take on retarded character for d above 7 nm, 17 ,21 the range of dvalues over which Eq. 6.25 should be applicable is (at 298 K) 9.6/ zJC < d < 7 nm, where c is the electrolyte concentration in moles per cubic meter. If the ccc values in the second column of Table 6.2 are substituted for c, the lower limit of d lies between 1 and 4 nm. If the ccc values in the third column of the table are used, the required lower limit of d generally exceeds the upper limit of 7 nm (e.g., for c = 0.5 mol· m 3, the lower limit of d is 6.8 nm). Therefore, 'Pvw(d) is better represented by Eq. 6.21 than by Eq. 6.20 in this case. On the other hand, 'Pm(d) calculated from the PoissonBoltzmann equation is not very accurate for bivalent ions, and the value of the retarded Hamaker constant in Eq. 6.21 is not known accurately for soil minerals. These facts suggest that Eq. 6.25 can serve as well as any available expression to illustrate the relationship between the ccc and ionic valence in a simple and qualitative fashionr'" Since 'P(d) comprises both positive and negative terms, it is expected to show a relative maximum at some d value for many possible choices of Z, K, a, A, a, and 8. This kind of mathematical behavior is illustrated in Fig. 6.7 for the case Z = 1, K = 0.329 nm", a = 0.462, A = 2.210 20 J, a = 0.05 J . m 2, and 8 = 1 nm. These values are appropriate for a stable suspension of illitic mica in 10 molrn"? NaCI at 298 K. 29 Figure 6.7 Figure 6.7. Total potential energy per unit area for the interaction of two charged parallel phyllosilicate surfaces, with 10 mol· m 3 NaCl interposed between them, according to Eq. 6.25. See also the solid curve in Fig. 6.6.
Interplanar separation,
4
THE SURfACE CHEMISTRY OF SOilS
220
shows the characteristic behavior of ({J(d) , wherein a pronounced minimum occurs for very small values of d followed by the maximum and at least one more relative extremum. (See also the solid curve in Fig. 6.6.) If two more extrema occur, the one at a finite d value is a shallow minimum termed the secondary minimum. (The primary minimum is the very deep one at small d values.) Sometimes flocculation is associated with the secondary minimum and aggregation with the primary minimum.V On the hypothesis developed by Derjaguin, Landau, Verwey, and Overbeek (DLVO),38 a colloidal suspension becomes rapidly unstable if the maximum value of ({J(d) is small relative to the random thermal energy of the colloidal particles. This hypothesis forms the basis of the DLVO theory of colloidal stability. With the approximate expression for ({J(d) in Eq. 6.25, one can apply the DLVO hypothesis in the form
({J(d)
=
0
(a({Jjad)ccc
=0
(c = ccc)
(6.26)
to derive a relationship between the ccc and Z. Equations 6.26 state that both ((J(d) and its first derivative with respect to d vanish when c in Eq. 6.25 equals the ccc. The first condition implies the equation
64a2 A ZK ccc RT exp( ZKcd) = 127Td 2 c
a 
127T exp( dI5)
(6.27a)
whereas the second condition on ((J(d) yields the expression A
64 a2 ccc RT exp( ZKcd) = 67Td3

al5 27T exp( dl({J)
(6.27b)
where Kc = J {3 ccc = 0.1041 Jccc nm " at 298 K with the ccc in moles per cubic meter. The right side of Eq. 6.27a must be positive in order that the value of the ccc remain positive. This requirement is met for sufficiently small values of d (since a? grows arbitrarily large and exp( dl 5) remains finite as d goes to zero) as well as for sufficiently large values of d (since d 2 approaches zero more slowly than exp( dl 5) as d goes to infinity. In some intermediate range of d values, the right side of Eq. 6.27a can be negative if the hydration force dominates the van der Waals dispersion force. The colloidal particles maintain a stable suspension so long as this condition persists. In DLVO theory, it is customary to assume that the electolyte concentration and suspended particle configuration are such that the van der Waals dispersion force dominates the hydration force to the extent that the latter can be neglected.l" Under these conditions of electrolyte concentration and particle configuration (which differ for different kinds of soil colloid and background electrolyte), the second term on the right side of Eq. 6.27 is dropped and the two expressions are divided to derive the result
z,« =
2
(6.28)
The substitution of Eq, 6.2H into Eq. 6.27u (without the term in u) thcn
SURFACE CHEMICAL ASPECTS OF SOIL COLLOIDAL STABILITY
221
gives the equation
.3/ _ (30721T a RT) 3 KC eee e2 A Z 2
or
2RT)2 _(30721Ta eee Z 2
e f3
3/2
A
6
(6.29)
Equation 6.29 represents the SchulzeHardy rule according to a simplified application of the DLVO theory. It follows from this equation that eee(Z = 2)/eee(Z = 1) = 2 6 = 0.0156, in good agreement with the trend in the fourth column of Table 6.2. However, this good agreement must be considered in large measure the result of a fortuitous cancellation of the effects of the physical factors neglected when Eq. 6.25 is invoked without the term in fPsolv(d). Although the interplay of electrostatic and van der Waals dispersion forces as represented in Eqs. 6.17 and 6.20 is sufficient to derive a proportionality between the ccc and a power of the ionic valence via the DLVO hypothesis in Eq. 6.26, the detailed numerical relationship found in Eq. 6.29 is not accurate (it predicts impossibly large ccc values) and is not improved by a better representation of fPm(d) based on the exact solution of the PoissonBoltzmann equation. 17 The derivation of an equation to predict the ccc values in Table 6.2 awaits greater precision in the determination of both the parameters and the distance dependence in the component potentials of fP(d). According to the DLVO theory, the rapid coagulation of a colloidal suspension is induced by a reduction in both the magnitude and the range of the repulsive electrostatic force as the concentration of electrolyte increases. The essential physical soundness of this conceptual view has been demonstrated experimentally in studies of the behavior of montmorillonite suspended in either Liel or NaC!. The colloidal particles in this case are individual unit layers (Table 6.1), and the principal electrostatic force between them emanates from their siloxane surfaces. When the electrolyte concentration is very low (less than 0.01 molrn"), the decay length ofthe electrostaticforce, K 1 in Eq. 6.17, is very large (greater than 60 nm), even in suspensions whose clay concentration is around 40 kgrn", Under the conditions, both the van der Waals dispersion force and the hydration force are negligible and the electrostatic force is powerful enough to order the montmorillonite particles into parallel stacking along a direction perpendicular to their crystallographic e axis. This arrangement of the clay particles, known as a tactoid, has been found through smallangle neutron scattering experiments on suspensions of Limontmorillonite.r" The interplanar separation distances varied from about 40 nm at a clay concentration of 68 kg· m 3 to about 120 nm at a clay concentration of 20 kg m 3. These large interplanar separations and the repulsive force that produces them distinguish the tactoid clearly from the quaslcrystal, which is produced by attractive forces COMPLEXATION REACTIONS.
• !
£
•
I
I'
••
..
222
THE SURFACE CHEMISTRY OF SOILS
The characteristic behavior of the electrostatic force in bringing about parallel arrangements of montmorillonite particles has also been verified at electrolyte concentrations approaching and exceeding the ccc of Namontmorillonite suspended in NaCl. 40 However, a different situation exists when the coagulating ions have a valence different from unity or, in general, when these ions can engage significantly in complexation reactions, either with surface functional groups or with other ions in the aqueous solution phases. Complexation reactions in the aqueous solution phase tend to produce what is termed the antagonistic effect;" wherein the ccc increases as the concentration of an added complexing ion increases. For example, if Ca2+ cations alone produce the coagulation of a negatively charged colloid according to the DLVO conceptualization, then the ccc, defined conventionally in terms of the total concentration of the metal." must increase as the concentration of an added anion that can form soluble complexes with the metal increases. In other words, the presence of a complexing anion, say SO~, reduces the concentration of the free ionic species, Ca2+, through the formation of the complex CaSO~, and a larger total calcium concentration is required to bring the concentration of the species Ca 2+ up to the level required to produce coagulation." This effect, of course, occurs equally well with complexing cations added to a suspension of positively charged colloid and coagulating anions. The formation of soluble complexes by coagulating ions reduces the effectiveness of these ions in diminishing the electrostatic force, but the fundamental mechanism that brings about coagulation is not changed. On the other hand, if the coagulating ions can form surface complexes with the suspended colloidal particles, the nature of the coagulation process does change and the DLVO hypothesis becomes inappropriate. The formation of surface complexes alters the total particle charge density, up, directly, whereas the formation of the compact diffuse double layer inherent to the DLVO hypothesis only screens the total particle charge density to reduce its longrange effect. If the surface functional group is the siloxane ditrigonal cavity, innersphere complex formation with monovalent metal cations can reduce the total particle charge sharply. Since this type of surface complex formation is more likely, it follows that, as the soft Lewis acid character of the metal cation increases (Sec. 4.3), Cs+ should be more effective than Na+, for example, at reducing up and thereby promoting coagulation. Experimental evidence supporting this hypothesis comes from the observation that the ccc of a dilute Namontmorillonite suspension (0.25 kg' m 3) at pH 6 is 2.1 mol, m 3 in NaN0 3 , whereas the ccc of a Csmontmorillonite suspension at the same clay concentration and pH is 0.79 mol· m 3 in CsN0 3 •42 The lower cccfor Csmontmorillonite evidently reflects a larger number of innersphere surface complexes formed per unit area and, therefore, a lower up' In the case of bivalent metal cations, siloxane ditrigonal cavities tend to form outersphere surface complexes leading to quasicrystals, as described in Sec. 6.1. Since two ditrigonal cavities are involved, quasicrystal forma
SURFACE CHEMICAL ASPECTS OF SOil COllOIDAL STABILITY
223
tion also produces an electrically neutral surface, but it is the internal surface of a quasicrystal that has its total charge density reduced. Experiments on the coagulation of Camontmorillonite suggest that outersphere complexation of Ca2+ is an aggregation process that follows a flocculation process induced by Ca2+ cations participating in the surface chargescreening mechanism hypothesized in the DLVO theory.P In this case, outersphere complexation is a gradual particle rearrangement phenomenon that may require several days' time. When initiated from a stable suspension, however, outersphere complexation and quasicrystal formation can be very rapid, as pointed out in Sec. 6.1. When the principal surface functional group is the inorganic or organic hydroxyl group, colloid stability can be affected strongly by the pH value, since innersphere complexes with protons and hydroxide ions are formed. A soil colloidal suspension containing particles bearing surface hydroxyl groups (e.g., hydrous oxides or kaolinite) tends to coagulate at the PZC regardless of the background electrolyte concentration. In the absence of surface complexes involving ions other than H+ or OH, the PZC coincides with the PZNPC and coagulation depends on the balance of surface charge between protonated and dissociated functional groups as expressed through O"H; In the presence of other complexforming ions, O"p is the determining property for rapid coagulation and the effects of the ions in the aqueous solution phase must be evaluated as described in Sees. 3.1 and 3.2. As a general rule, the existence of ions that can form surface complexes significantly can be detected by examining the ccc as a function of the colloid concentration in the suspension. If the DLVO mechanism is the principal cause of coagulation, the ccc is essentially independent of the colloid concentrationat least over a severalfold changewhereas if surface complexation is the principal cause, the ccc tends to increase with the colloid concentration, since the surface complexation capacity is also increased.t" If the complexed ion is multivalent, surface complexation can result in a reversal of the sign of O"p, as described in Sec. 4.3 for metal cations. When this happens, the ions in the aqueous solution phase that previously were of the same charge sign as the colloidal particles become potential coagulating ions. The mechanism of any subsequent coagulation induced by these ions can be either surface chargescreening or surface complexation. When polymer ions form surface complexes with soil colloidal particles, stability depends on stereochemistry as well as on surface charge density. 45 If the extent of polymer adsorption is small, a soil colloidal suspension may be coagulated at a lower concentration of an added noncomplexing electrolyte than in the absence of the polymer. In this situation, the addition of electrolyte brings the colloidal particles closer and closer together until the polymer chains can form bridges among them, inducing coagulation. Since the polymer bridging can occur with the particles farther apart than the separation required to make the particles' own van der Waals forces effective. coagulation can occur at lower electrolyte
· 224
THE SURFACE CHEMISTRY OF SOILS
Table 6.3. Factors affecting the stability of soil colloidal suspensions Factor Electrolyte concentration pH value Surface complexes with small ions Surface complexes with polymer ions
Effects
Promotes stability
Promotes coagulation
Extent of diffuse double layer; solvation force Changes UH Changes up
When increased
When decreased
pH = PZC up = 0
pH
Changes up and/or particle association
With polymer bridges
By electrostatic repulsion
up
=f PZC =f 0
concentrations. If polymer adsorption is significant, coagulation by polymer bridging may take place at extremely low electrolyte concentrations or the colloidal suspension may be stabilized by the electrostatic force between the coatings of adsorbed polymers. Which phenomenon occurs depends on pH, on electrolyte concentration, and on the configuration of the adsorbed polymer ion. The principal surface chemical factors that determine the stability of soil colloidal suspensions are summarized in Table 6.3. Surface reactions affect colloid stability through changes in the strength of the repulsive electrostatic and solvation forces and, if macromolecules are involved, through changes in particle association mechanisms. Coagulation is the result of a reduction in the efficacy of the repulsive electrostatic and solvation forces, whether through chargescreening, surface complexation, or stereochemically induced particle bridging. NOTES 1. The concept of the quasicrystal is distinguished from that of the tactoid in J. P. Quirk and L.A.G. Aylmore, Domains and quasicrystalline regions in clay systems, Soil Sci. Soc. Arn. I. 35: 652 (1971). 2. K. Norrish and J. P. Quirk, Crystalline swelling of montmorillonite, Nature 173: 225 (1954). A. M. Posner and J. P. Quirk, The adsorption of water from concentrated electrolyte solutions by montmorillonite and illite, Proc. Royal Soc. 278A:35 (1964). A. M. Posner and J. P Quirk, Changes in basal spacing of montmorillonite in electrolyte solutions, I. Colloid Sci. 19: 798 (1964). 3. See, e.g., G. Sposito and R. Prost, Structure of water adsorbed on smectites, Chern. Rev. 82: 553 (1982). 4. D. J. Cebula, R. K. Thomas, and J. W. White, Smallangle neutron scattering from dilute aqueous dispersions of clay, l.eS. Faraday 176: 314 (1980). R. Hight, W. L. Higdon, and P. W. Schmidt, Smallangle scattering study of sodium montmorillonite clay suspensions, J. Chern. Phys. 33: 1656 (1960). R. Hight, W. T. Higdon, H.C.H. Darley, and P. W. Schmidt, Smallangle Xray scattering from montmorillonite clay suspensions: II, J. Chern. Phys. 37: 502 (1962).
SURFACE CHEMICAL ASPECTS OF SOIL COLLOIDAL STABILITY
225
5. I. Shomer and U. Mingelgrin, A direct procedure for determining the number of plates in tactoids of smectites: The Na/Ca montmorillonite case, Clays and Clay Minerals 26: 135 (1978). 6. I. Shainberg and H. Otoh, Size and shape of montmorillonite particles saturated with Na/Ca ions (inferred from viscosity and optical measurements), Israel J. Chem. 6:251 (1968). L. L. Schramm and J.C.T. Kwak, Influence of exchangeable cation composition on the size and shape of montmorillonite particles in dilute suspension, Clays and Clay Minerals 30: 40 (1982). 7. A. Banin and N. Lahav, Particle size and optical properties of montmorillonite in suspension, Israel J. Chem. 6:235 (1968). L. L. Schramm and J.C.T. Kwak, op. cit." J. E. Dufey and A. Banin, Particle shape and size of two sodium calcium montmorillonite clays, Soil Sci. Soc. Am. J. 43: 782 (1979). 8. D. G. Edwards, A. M. Posner, and J. P. Quirk, Repulsion of chloride ions by negatively charged clay surfaces. Part 2. Monovalent cation montmorillonites, Trans. Faraday Soc. 61: 2816 (1966). Part 3. Di and trivalent cation clays, Trans. Faraday Soc. 61:2820 (1966). L. L. Schramm and J.C.T. Kwak, Interactions in clay suspensions: The distribution of ions in suspension and the influence of tactoid formation, Colloids Surfaces 3: 43 (1982). 9. D. G. Edwards et al., op. cit.,s Part 3, Fig. 1. 10. Light transmission: L. L. Schramm and J.C.T. Kwak, op. cit:" Electrophoretic mobility: P. BarOn, I. Shainberg, and I. Michaeli, Electrophoretic mobility of montmorillonite particles saturated with Na/Ca ions, J. Colloid Interface Sci. 33:471 (1970). Intrinsic viscosity: I. Shainberg and H. Otoh,op. cit.6 Chloride exclusion volume: J. E. Dufey, A. Banin, H. G. Laudelout, and Y. Chen, Particle shape and sodium selfdiffusion coefficient in mixed sodiumcalcium montmorillonite, Soil Sci. Soc. Am. J. 40: 310 (1976). 11. I. Shainberg and A. Kaiserman, Kinetics of the formation and breakdown of Camontmorillonite tactoids, Soil Sci. Soc. Am. J. 33: 547 (1969). 12. I. Shainberg and W. D. Kemper, Electrostatic forces between clay and cations as calculated and inferred from electrical conductivity, Clays and Clay Minerals 41: 117 (1966). I. Shainberg, J. D. Oster, and J. D. Wood, Electrical conductivity of Na/Camontmorillonite gels, Clays and Clay Minerals 30: 55 (1982). 13. G. A. O'Connor and W. D. Kemper, Quasicrystals in NaCa systems, Soil Sci. Soc. Am. J. 33:464 (1969). 14. R. Keren and I. Shainberg, Water vapor isotherms and heat of immersion of Na/Camontmorillonite systems. II: Mixed systems, Clays and Clay Minerals 27: 145 (1979). 15. L. L. Schramm and J.C.T. Kwak, Thermochemistry of ion exchange and particle interaction in clay suspensions, Can. J. Chem. 60: 486 (1982). 16. That ideal solution behavior is essential to the derivation of Eq. 6.7a has been shown in W. Olivares and D. A. McQuarrie, Interaction between electrical double layers, J. Phys. Chem. 84: 863 (1980). 17. See Chapter IV in E.J.W. Verwey and J.T.G. Overbeek, Theory of the Stability of Lyophobic Colloids. Elsevier, Amsterdem, 1948. E. P. Honig and P. M. Mul, Tables and equations of the diffuse double layer repulsion at constant potential and at constant charge, J. Colloid Interface Sci. 36: 258 (1971). 18. D. Y.C. Chan, R. M. Pashley, and L. R. White, A simple algorithm for the calculation of the electrostatic repulsion between identical charged surfaces in electrolyte, J. Collotd lnterfac« Sci. 77:2H3 (1980).
226
THE SURFACE CHEMISTRY OF SOilS
19. T. W. Healy, D. Chan., and L. R. White, Colloidal behaviour of materials with ionizable group surfaces, Pure Applied Chem. 52: 1207 (1980). 20. L. M. Barclay and R. H. Ottewill, Measurement of forces between colloidal particles, Spec. Disc. Faraday Soc. 1: 138 (1970). See also B. P. Warkentin, G. H. Bolt, and R. D. Miller, Swelling pressure of montmorillonite, Soil Sci. Am. J. 21:495 (1957). I. Shainberg, E. Bresler, and Y. Klausner, Studies on Na/Ca montmorillonite systems. 1. The swelling pressure, Soil Sci. 111:214 (1971). 21. J. N. Israelachvili and G. E. Adams, Measurement of forces between two mica surfaces in aqueous electrolyte solutions in the range 0100 nm, J.C.S. Faraday Trans. 174: 975 (1978). 22. J. N. Israelachvili and D. Tabor, Van der Waals forces: Theory and experiment, Prog. Surface Membrane Sci. 7: 1 (1973. See also J. N. Israelachvili and D. Tabor, The measurement of van der Waals dispersion forces in the range 1.5 to 130 nm, Proc. Royal Soc. (London) 331A:19 (1972). 23. This kind of standard calculation is described in Chap. 10 of P. C. Hiemenz, Principles of Colloid and Surface Chemistry. Marcel Dekker, New York, 1977. 24. J. N. Israelachvili, The calculation of van der Waals dispersion forces between macroscopic bodies, Proc. Royal Soc. (London) 331A:39 (1972). See also Chap. 7 in J. Mahanty and B. W. Ninham, Dispersion Forces. Academic Press, London, 1976. 25. Similar concepts of the solvation force are presented in B. W. Ninham, Longrange vs. shortrange forces. The present state of play. J. Phys. Chem. 84: 1423 (1980). 26. L. M. Barclay and R. H. Ottewill, op. cit.2o 27. J. N. Israelachvili and G. E. Adams, op. cit.21 28. R. M. Pashley, Hydration forces between mica surfaces in aqueous electrolyte solutions, J. Colloid Interface Sci. 80: 153 (1981). 29. R. M. Pashley, DLVO and hydration forces between mica surfaces in Li+, Na+, K+, and Cs+ electrolyte solutions: A correlation of doublelayer and hydration forces with surface cation exchange properties, J. Colloid Interface Sci. 83: 531 (1981). 30. A rudimentary form of the triple layer model has been applied in this way by R. M. Pashley, op. cit.29 31. See, e.g., D. H. Everett, Manual of Symbols and Terminology for Physicochemical Quantities and Units. Appendix II: Definitions, Terminology and Symbols in Colloid and Surface Chemistry. Butterworths, London, 1972. 32. See, e.g., p. 23 in H. van Olphen, An Introduction to Clay Colloid Chemistry, 2nd edn. Wiley, New York, 1977. 33. J. P. Quirk, Some physicochemical aspects of soil structural stabilityA review, in Modification of Soil Structure (W. W. Emerson, R. D. Bond, and A. R. Dexter, eds.) Wiley, Chichester, U.K., 1978. Y. Chen and A. Banin, Scanning electron microscope (SEM) observations of soil structure changes induced by sodiumcalcium exchange in relation to hydraulic conductivity, Soil Sci. 120:428 (1975). Y. Chen, J. Tarchitzky, J. Brouwer, J. Morin, and A. Banin, Scanning electron microscope observations on soil crusts and their formation, Soil Sci. 130:49 (1980). 34. J.T.G. Overbeek, The rule of Schulze and Hardy, Pure Appl. Chem. 52: 1151 (1980). 35. E.J.W. Verwey and J.T.G. Overbeek, op. cit. ,Itt p. 9. S. L. SwartzenAllen
SURfACE CHEMICAL ASPECTS Of SOIL COLLOIDAL STABILITY
36. 37.
38.
39. 40.
41.
42. 43.
44. 45.
227
and E. Matijevic, dolloid and surface properties of clay suspensions. III. Stability of montmorillonite and kaolinite, J. Colloid Interface Sci. 56: 159 (1976) J. D. Oster, I. Shainberg, and J. D. Wood, Flocculation value and gel structure of sodium/calcium montmorillonite and illite suspensions, Soil Sci. Soc. Am. J. 44:955 (1980), and the references cited in these papers. Somewhat more refined derivations of this relationship are presented in E. P. Honig and P. M. Mul, op. citY and in J.T.G. Overbeek, op. cit.34 R.S.B. Greene, A. M. Posner, and J. P. Quirk, A study of the coagulation of montmorillonite and illite suspensions by calcium chloride using the electron microscope, in W. W. Emerson et aI., op. citY B. V. Derjaguin and L. Landau, A theory of the stability of strongly charged lyophobic sols and the coalescence of strongly charged particles in electrolytic solutions, Acta Phys.Chim. USSR 14:633 (1941). E.J.W. Verwey and J.T.G. Overbeek, op cit.16 D. J. Cebula and R. H. Ottewill, Neutron diffraction studies on lithium montmorillonitewater dispersions, Clays and Clay Minerals 29:73 (1981). I. C. Callaghan and R. H. Ottewill, Interparticle forces in montmorillonite gels, Faraday Disc. Chem. Soc. 57: 110 (1974). E. Frey and G. Lagaly, Selective coagulation and mixed layer formation from sodium smectite solutions, Proc. Int. Clay Conf. 1978, p.l31 (1979). B. Rand, E. Pekenc, J. W. Goodwin, and R. W. Smith, Investigation into the existence of edgeface coagulated structures in Namontmorillonite suspensions, J.C.S. Faraday 176: 225 (1980). The effect of complexation reactions on colloid stability is described, with many examples, in E. Matijevic, Colloid stability and complex chemistry, J. Colloid Interface Sci., 43:217 (1973). See also E. Matijevic, The role of chemical complexing in the formation and stability of colloidal dispersions, J. Colloid Interface Sci. 58: 374 (1977). See Figs. 2 and 6 in S. L. SwartzenAllen and E. Matijevic, op cit.35 R.S.B. Greene, A. M. Posner and J. P. Quirk, Factors affecting the formation of quasicrystals of montmorillonite, Soil Sci. Soc. Am. J. 37: 457 (1973). R.S.B. . 37 1 op. cit. G reene et a., W. Stumm, C. P. Huang, and S. R. Jenkins, Specific chemical interaction affecting the stability of dispersed systems, Croatica Chem. Acta 42: 223 (1970). For an introductory review, see Sec. 2.4 in B.K.G. Theng, Formation and Properties of ClayPolymer Complexes. Elsevier, Amsterdam, 1979.
FOR FURTHER READING W. W. Emerson, R. D. Bond, and A. R. Dexter, Modification of Soil Structure. Wiley, Chichester, U.K., 1978. The first five chapters of this symposium publication provide details on many aspects of the surface chemical features of soil colloidal stability. J. N. Israelachvili, Forces between surfaces in liquids, Advan. Colloid Interface Sci. 16:31 (1982). An advancedlevel summary covering the topics discussed in Sec. 6.2 of the present book. B. W. Ninham, Longrange vs, shortrange forces: The present state of play, J. Phys. Chem, 84: 1423 (1980). This lively account of the current state of understanding of interparticle forcefl is mUflt reading to follow Sec. 6.2.
228
THE SURFACE CHEMISTRY OF SOILS
B. W. Ninham, Hierarchies of forces: The last 150 years, Advan. Colloid. Interface Sci. 16: 3 (1982). Another mustreading article, this one dealing with the limitations of interparticle force theories that assume the liquid phase to be a continuum dielectric. H. van Olphen, An Introduction to Clay Colloid Chemistry, 2nd edn. Wiley, New York, 1977. Chapters 2, 3, 4, and 7 of this standard monograph form a useful adjunct to the present chapter as regards phyllosilicate suspensions. J.T.G. Overbeek, Strong and weak points in the interpretation of colloid stability, Advan. Colloid Interface Sci. 16: 17 (1982). An overview of the status of DLVO theory by one of the Starting Four. E.J.W. Verwey and J.T.G. Overbeek, Theory of the Stability of Lyophobic Colloids. Elsevier, Amsterdam, 1948. Part II of this classic monograph should be read by the mathematically minded as a comparison to Sec. 6.2.
SELECTED PHYSICAL CONSTANTS*
Avogadro constant
NA
6.02252 x 1023 mol"!
Boltzmann constant
kB
1.38054 x 10 23 J K 1
Diffuse double layer constant
f3
1.084 x 1016 m mol"!
Faraday constant
F
9.64870 x 104 C mol "
Molar gas constant
R
8.3143 J K 1 mol"!
Permittivity of vacuum
£0
8.85419 x 10 12 C2
r '
m 1
• D. D. Wagman, W. H. Evans, V, B, Parker, R. H. Schumm, I. Halow, S. M. Bailey, K. L. Churney, and R. L. NUllall, The NBS tables of chemical thermodynamic properties, J. Phy«. Chem. Rr!. DUlu II,Supp. 2:1 (19H2).
INDEX
Adsorbate, 26 Adsorbed water, 58, 69 excess acidity, 71 phyllosilicates, 70 relation to ionic potential, 28 Adsorption, 25,29, 113, 122 defined, 113 isotherm, 116117,122 kinetics, 12728, 140 metal cations, 128 negative, 31,106,109 organic matter, 143 oxyanions, 138 pH effect, 134 precipitation versus, 12228 surface excess, 113 Adsorption edge, 135, 139, 175, 183 Adsorption envelope, 13940 Adsorption isotherm, 11617 Adsorptive, 26 Aggregation, 217 Aluminol group, 18, 40 Anion exchange, 14344 Anion exchange capacity, 36, 80
Babcock model, 109 Balance of surface charge, 17881 general equation, 79 model equation, 179,18990,192 BET equation, 2728
Cation bridalna, 143,14546 Cation exchanae capacity, 36, 80 C·curve taotherm, 117
Chlorite, 67 weathering sequence, 21 Coagulation, 217 Colloidal stability, 21724 and complex formation, 22124 DLVOtheory, 220 factors affecting, 224 Constant capacitance model, 16977 anion adsorption, 17677 metal adsorption, 17476 protonation, 17074 PZNPC, 173 Coprecipitation, 8, 125 CPB method, 29 Critical coagulation concentration, 217, 222 complexation effects, 222 DLVO theory, 22021 measurements, 218 polymer effects, 223 SchulzeHardy rule, 218
Diffuse double layer (DDL) theory, 15462 analytical solutions, 158 electrostatic force, 206 Monte Carlo simulations, 16062 triple layer model, 178 Diffuse layer charge, 79,81,98,100,159, 178,207 Distribution coefficient, 27, 11819 DLVO theory, 220 Donnan potential, 91 D·.truclure, 48,54,59,67
232 Electrochemical potential, 8890, 186 Electrokinetic phenomena, 94106 convection current, 95 general equation, 97 Electrokinetic plane of shear, 94, 105 Electroosmosis, 101, 103 Electrophoretic mobility, 83,97,99100 defined, 97 quasicrystal formation, 203 relation to PZC, 98 surface complexes, 99100,17576 surface hydrolysis, 13637, 18384 Electrostatic force, 2059 DDL model, 2069 measurements, 2089 Elovich equation, 12728,14041 Exclusion volume, 31,107,202 calcium montmorillonite, 202 defined, 31, 107 diffuse double layer theory, 3133 molecular interpretation, 107 quasicrystal formation, 3435,2023 relation to specific surface area, 32, 107 sodium montmorillonite, 3334
Flocculation, 217
Galvani potential, 9192 Gibbs factor, 16365 Gibbsite, 45 PZC, 84 surface charge, 40 surface hydroxyls, 5, 17 Goethite, 45 adsorption envelope, 140 ligand exchange, 140 surface area, 24 surface charge, 40 surface complex, 1617 surface hydroxyls, 1617
Halloysite, 58 Hamaker constant, 21112 model equation, 212 retarded, 212 Hcurve isotherm, 11617 HSAB principle, 129 Humic substance, 9 adsorption mechanisms, 14347 functional groups, 1819 metal adsorption, 135 Hydrogen honding, 14~
INDEX
lAP (ion activity product), 12427 Illitic mica, 6 metal adsorption, 13334 specific surface area, 30, 34 Inner potential, 9091,15455,206 model dependence, 93 Poisson equation, 95 PoissonBoltzmann equation, 154 Innersphere complex, 13,1516,145, 178
adsorption selectivity, 129 defined, 13, 178 effect on coagulation, 222 surface charge, 79, 189 Interparticle forces, 20517 total potential energy, 21820 Intrinsic surface charge, 36 Ionic potential, 28,63,71,13738 and interlayer hydration, 28 and organic matter adsorption, 146 and surface protonation, 71 Ionic radii, 3 Isoelectric point, 81,110 Istructure, 48,52 Kaolinite, 67 metal adsorption, 18, 13334 PZC, 84 surface area, 24,30 surface charge, 40 surface complex, 18 surface hydroxyls, 1718 water structure, 5861 weathered, 22 Kurbatov plot, 135 Langmuir equation, 27, 118, 124 phosphate precipitation, 124 twosurface, 118 Layer charge, 6,8,3839,61 Lcurve isotherm, 11617 Lewis acid, 17 Lewis acid site, 1718 Lewis acid softness, 7172,12933,146 relation to cation exchange, 12933 relation to organic matter adsorption, 146 Lewis base, 14, 132 Ligand effects on metal adsorption, 13238 Ligandlike adsorption, 136, 139, 146, 197 Ligand exchange, 13841, 143, 14547 defined, 13H
233
INDEX evidencefor, 13941 organic matter adsorption, 147 surface complex model, 165,169 Liquid water, 54 dynamic structure, 4849
Metal adsorption, 12838 ligand effects, 132 selectivity, 129 Metallike adsorption, 136, 139, 197 Misono softness parameter, 71,130 defined, 130 relation to adsorption, 13031,146 Montmorillonite, 68 electrophoretic mobility, 99 metal adsorption, 12933,135 quasicrystal, 3435,198205 surface area, 2425,30,34 surface charge, 37 surface coating, 21 surface complex, 15 water structure on, 66
NavierStokes equation, 95 Negative adsorption, 31, 106 Babcock model, 109 DDLtheory, 107 Neutron scattering, 51, 199, 221
Objective model, 18588 Organic matter adsorption, 14347 mechanisms, 143 Outersphere complex, 13, 15, 18, 178 defined, 13, 178 effect on coagulation, 223 and metal adsorption, 132 and oxyanion adsorption, 139 quasicrystal, 199 surface charge density, 79,189
Packing area, 2627, 29 CPB, 28 nitrogen, 27 water, 27 pH effect, metal adsorption, 135,175, 183 organic matter adsorption, 146 oxyanion adsorption, 140 pH,(» 135, 137 Phyllosilicates, 4 groups, 6 intentratlflclltion, 11121
layer charge, 6,8 layer types, 68 surface area, 30,34 surface complexes, 15, 18,21 water structure, 5769 weathered, 22 Point of zero charge, 81, 8384, 86 Poisson equation, 95 PoissonBoltzmann equation, 154 analytical solutions, 158 assumptions, 15455 asymptotic solution, 158,208 integrated form, 156, 207 Polarizable interface, 92 Polymer bridging, 22324 Potentialdetermining ion, 93 Precipitation, 122 adsorption versus, 12228 ion activity product, 124 kinetics, 128 Proton surface charge, 39 measurement, 4142 PZC, 81,83,86 electrokinetic measurement, 98 mixtures, 87 oxyanion adsorption, 85,139 PZNC, 81,83 relation to PZC, 82, 86 relation to PZNPC, 86 PZNPC, 81,83 relation to PZNC, 86 PZSE, 41,83 relation to PZC, 83,86 shift from adsorption, 85
Quasicrystal, 22,2425,34,100,198205 defined, 24, 198 enthalpy effect, 2045 equilibrium structure, 198204 formation, 2045 neutron scattering data, 200201 smectite, 198199
Relative surface excess, 106,11315 Reversible interface, 91 Rotational correlation times, 49
SchulzeHardy rule, 218 Scurve isotherm, 11617 Sedimentation potential, 104 Selectivity sequence, 129 Self·diftlcusion coefficient, 49, S3, 56, 6567
234
Sheet structure, dioctahedral, 23 tetrahedral, 23 trioctahedral, 3 Silanol group, 18,40 Siloxane ditrigonal cavity, 1316 cation exchange, 129 Lewis base, 1416 organic matter reactions, 146 quasicrystal, 19899 weathering sequence, 19 Smectite, 6 interstratification, 20 quasicrystal, 198 surface coating, 21 weathered, 22 Solvation force, 21317 measurements, 21516 swelling pressure, 21415 Solvation shell, 54,5657,214 bivalent ions, 56,62 monovalent ions, 55,67 Sorption, 122 Specific adsorption, 79,85 effect on PZSE, 85 Specific surface area, 2325 chloride exclusion, 34 CPB adsorption, 2930 negative adsorption methods, 29 nitrogen adsorption, 28,30,34 phyllosilicates, 30, 34 physical methods, 23 positive adsorption methods, 25 water adsorption, 2830 Streaming potential, 102 Structural surface charge, 37 heterogeneity, 3839 Structure, 112, 47 allophane, 9 amorphous, 1 crystalline, 1 humic substances, 912 oxides, 35 phyllosilicates, 4,68 sheet, 23 water, 4754 Surface charge density, 3542 alkylammonium method, 38 balance law, 79 dissociated, 79 innersphere complex, 79 intrinsic, 36 outersphere complex, 79 particle, 79 proton, 39, 189 structural, 37,86
INDEX
Surface complex, 13, 15, 16, 18 and specific surface area, 34 Surface complexation model, 16269 activity coefficients, 192 reactions, 165, 190 structure, 18893 Surface functional group, 12 Lewis acid site, 1718 orangic, 1819 oxide, 1618 siloxane sheet, 1316 weathering sequence, 19 Surface hydroxyl, 1619 Surface protonation, 3942,7172, 138139,143144 and adsorption, 144 model calculations, 170, 179 Surface speciation, SO, 163, 16985 Swelling pressure, 208,21415 Tactoid, 221 Triple layer model, 17785 anion adsorption, 18485 metal adsorption, 18284 protonation, 17982 van BernmelenFreundlich equation, 12022 van der Waals interactions, 14547, 20913 interparticIeforce, 21011 measurements, 213 van der Waals model, 16469 conditional equilibrium constant, 167 equilibrium constant, 168 rational activity coefficients, 169, 192 Vermiculite, 68 layer charge, 6,61 surface area, 30 surface coating, 21 surface complex, 15 water structure on, 61 Vstructure, 48,5253 Water bridging, 14345 Water structure, 4754 Dstructure, 54 electrolyte solutions, 5457 experimental methods, 49 Istructure, 52 Vstructure, 5254 Zeta potential,
96