ADVANCES IN CATALYSIS VOLUME 11, Volume 11

ADVANCES IN CATALYSIS AND RELATED SUBJECTS

VOLUME XI

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ADVANCES IN CATALYSIS AND RELATED SUBJECTS VOLUME XI

EDITED BY

D. D. ELEY Noltingham, England

P. W. SELWOOD

PAULB. WEISZ

Euanalon, Illinois

Paulaboro, N . J .

ADVISORY BOARD

PETERJ. DEBYE Zthaca, N . Y .

W. JOST

P. H. EMMETT

W. E. GARNER

Baltimore, Md.

Bristol, England

E. K. RIDEAL

Cfdtlingen, Germany

Londm, England

H. S. TAYLOR Princeton, N . J .

1959

ACADEMIC PRESS INC. NEW YORK AND LONDON

COPYRIW~T @ 1969, BY ACADEMIC PRESSINC. ALL RIGHTR RESERVED NO PART OF THIS BOOK MAY B E REPRODUCED I N ANY FORM B Y PHOTOSTAT, MICROFILM, OR A N Y OTHER MEANS, WITHOUT WRITTEN PERMISSION FROM THE PUBLISHERS.

ACADEMIC PRESS INC. 111 FIFTHAVENUE NEWYORE3, N. Y.

llnited Kingdom Edition

Published by

ACADEMIC PRESS INC. (LONDON)LTD. 40 PALLMALL,LONDONS.W.1

Library of Congress Catalog Card Number 40-7766

PRINTED I N T H E UNITED STATES OF AMERICA

CONTRIBUTORS TO VOLUME XI

L. G. AUSTIN,Fuel Technology Department, The Pennsylvania State University, University Park, Pennsylvania J. J. CHESSICK, Surface Chemistry Laboratory, Lehigh University, Bethlehem, Pennsylvania

R. V. CULVER, Department of Metallurgical and Chemical Engineering, University of Adelaide, Adelaide, South Australia J. HALPERN, Department of Chemistry, University of British Columbia, Vancouver, B.C., Canada G. KEMBALL, Department of Chemistry, The Queen’s University of Belfast, Belfast, North Ireland G. NATTA, Istituto d i Chimica Industriale del Politecnico, Milan, Italy

I. PASQUON, Istituto d i Chimica Industriale del Politecnico, Milan, Italy

FRANK RUSINKO, JR., Fuel Technology Department, The Pennsylvania State University, University Park, Pennsylvania F. C . TOMPKINS, Chemistry Department, Imperial College of Science and Technology, London

P. L. WALKER, JR., Fuel Technology Department, The Pennsylvania State University, University Park, Pennsylvania A. C. ZETTLEMOYER,Surface Chemistry Laboratory, Lehigh University, Bethlehem, Pennsylvania

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Catalysis remains a fascinating meeting ground of knowledge and experience, of theories and of experimentation belonging to various disciplines of science. Catalysis is not a science, it is a phenomenon. It may arise in connection with a vital biochemical process, an industrially important chemical reaction, an interesting intramolecular rearrangement, a mesoninfluenced nuclear change, a combustion process, an atomic spin transmutation, or innumerable other rate processes. The phenomenon of catalysis arises in connection with many scientific endeavors, and it involves many and diverse scientific principles. In this volume of the Advances in Catalysis and Related Subjects, we have continued our attempt to collect progress and integrated knowledge toward a better scientific understanding of catalyzed rate processes. A major area of catalytic experience has evolved in the discoveries and observations of man-made stereospecijic chemical reactions (The Kinetics of the Stereospecific Polymerization of a-Olefins), a field of human endeavor which approaches closely on nature’s ability to synthesize macromolecules with great specificity. On the other end of the molecular weight spectrum, the activation of hydrogen dominates as a basic phenomenon a variety of inorganic, organic and bio-organic rate processes, and recent advances make an integrated review appropriate (The Catalytic Activities of Hydrogen in Homogeneous, Heterogeneous, and Biological Systems). Exchange reacticms using (isotopic) hydrogen, have long been important tools in the study of catalytic molecular interchanges, and a review of such exchange phenomena with hydrocarbons is made in the article on Catalytic Exchange of Hydrocarbon with Deuterium. The electronic properties of solid catalytic surfaces have been the subject of much attention in recent years. The importance of the electronic phenomena in the interaction of reactants with catalyst make it imperative to follow, from year to year, at least some of the important developments in this field (Surface Potentials and Adsorption Process on Metals). Furthermore, there is a constant need and a search by the catalytic researcher for tools to examine the locus and sites of heterogeneous catalysis, viz. the surface, and its physical-chemical nature; an examination of new methods of examination and of the type of information it may produce, appears to us to be an important function of this publication (Immersional Heats and the Nature of Solid Surfaces). One elemental solid which has been important in relation to rate processes occurring on its surface is carbon. It has played roles as catalyst, as catalyst vii

viii

PREFACE

support, and as a reactant. Even as a reactant, it may play a catalytic role in relation to individual steps of its self-reaction and many basic phenomena are common to gas-solid rate processes and the solid catalyzed gas conversion process (Gas Reaction of Carbon). The Editors always face the imposing boundary condition of a practical and finite size for each volume, which always makes the ratio of material that could be covered to that which should be covered smaller than unity. They face therefore a constant but inevitable obligation to express regret concerning the accomplishments and areas of interest which could not be included in the present volume.

P. B. W. September, 1969

CONTENTS CONTRIBUTORS TO VOLUMEXI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . PREFACE ....................................................................

v vii

The Kinetics of the Stereospeciflc Polymerization of a-Oleflns

BY G . NATTAA N D I . PASOUON

I . Introduction to Anionic Coordinated Polymerization of a-Olefins . . . . . . . . I1. Over-All Kinetics of Polymerization Process ............................ I11. Chain Transfer, Termination Processes, and Molecular Weight of the Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV . Steric Composition of Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V . Determination of the Number of Active Centers . . . . . . . . . . . . . . . . . . . . . . . . VI . Mean Lifetime of the Growing Polymeric Chains . . . . . . . . . . . . . . . . . . . . . . . VII . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 10 23 46 50 60 64 65

Surface Potentials and Adsorption Process on Metals

BY R . V . CULVERA N D F . C . TOMPKINS I . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I1. The Surface Properties of Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I11. The Modification of Surface Properties by Adsorbates . . . . . . . . . . . . . . . . . . IV . The Preparation of Clean Metal Surface V . The Measurement of Work-Function Changes . . . . . . . . . . . . . . . . . . . . . . . . . . V I . Adsorption and Work-Function Studies . VII . Surface-Potential Data ............................................ VIII . Electron Transfer and Bond Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I X . The Kinetics of Desorption and Surface Migration . . . . . . . . . . . . . . . . . . . . . . . X . Surface Reaction Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X I . Heats of Adsorption .................... X I 1. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

68 73 77 82 101 106 111 118 127

Gas Reactions of Carbon

BY P . L . WALKER.JR., FRANK RUBINKO.JR., A N D L . G . AUSTIN I . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I1. Thermodynamics of Gas-Carbon Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I11. Review of General Mechanisms for the Gas-Carbon Reactions . . . . . . . . . . IV . Review of Kinetics for the Gas-Carbon Reactions . . . . . . . . . . . . . . . . . . . . . . V . Role of Mass Transport in Gas-Carbon Reactions . . . . . . . . . . . . . . . . . . . . . . VI . Use of Density and Area Profiles on Reacted Carbon Rods for Better Understanding of Gas-Carbon Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII . Some Factors, Other than Mass Transport, Which Affect the Rate of GasCarbon Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

134 135 138 153 164 178 201

X

CONTENTS

Appendix.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

212 217

The Catalytic Exchange of Hydrocarbons with Deuterium

BY C. KEMBALL

I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11. General Aspects of Exchange Reactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. The Exchange of Molecules Possessing a High Degree of Symmetry.. . . . IV. The Exchange of Molecules Possessing 8 Low Degree of Symmetry.. . . . . V. Some Results with Unsaturated Molecules.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI. Concluding Remarks.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

223 228 239 250 257

259 261

lmmersional Heats and the Nature of Solid Surfaces

BY J. J. CHESSICKA N D A. C. ZETTLEMOYER

I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

263

. . . . . . . . . . 268

VII. Site Energy Distribution.. . . . .............. VIII. Solution Adsorption. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References. . . . . . . . . . . .................

291

The Catalytic Activation of Hydrogen in Homogeneous, Heterogeneous, and Biological Systems

BY J. HALPERN I. Introduction.. . ............................. 11. Homogeneous .......................... 111. Heterogeneous IV. Biological Systems. . . . . . . . . . . . . . . ..................... V. Concluding Remarks.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ......... References. . . . . . . . . . . . . . . . . . . . ....................... AUTHORI N D E ,X , , ,. . SUBJECT INDEX, ............................. ........................

358 363 365 381

The Kinetics of the Stereospecific Polymerization of a-Olefins G. NATTA

AND

I. PASQUON

Ialiluto di Chimica Induelriale del Politecnico, Milan, Italy Pw 2

I. Introduction to Anionic Coordinated Polymerization of a-Olefins . . . . . . . . A. Generalities.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Stereospecificity of Catalyst .......................... C. Mechanism of Stereospecific merization. . . . . . . . . . . . . . . . . . . . . . . . . . D. Influence of the Crystalline Substrate on the Stereospecific Polymerization. . . . . . . . . ................................................... 11. Over-All Kinetics of Polymerization Process ..... ... A. Catalytic Systems Used. ...................................... B. Influence of the Sizes of 8 Crystals on the Polymerization Rate. Adjustment Period.. . . . . ..................................... C. Catalytic Behavior of aStereospecific Propylene Polymeriza.................................... itions on the Polymerization Steady..................................... State Rate . . . . . . . . . . . . . . 111. Chain Transfer, Termination Processes, and Molecular Weight of the Polymers ......................... A. Catalysts Used and Their B. Independence of the Molecular Wei Polymer of Reaction Time for, Long Reaction Times.. . . . . . . . . . . . . . . . . C. Chain Transfer Process Depending on Alkylaluminum Concentra-

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

6

9 10 10 11 16

17

26

26

D. Chain Transfer Process Depending on the Amount of Titanium Com-

................................................ 32 E. Chain Transfer Process Depending on the Propylene Partial Pressure.. 34 F. Influence of the Temperature on the Single-Chain Transfer and Termina....................................... tion Processes. . . . . . G. Comparison betwee trinsic Viscosity and Specific Radioacti the Polymer Obtained in the Presence of I4C-Labeled Trialkylalumi...... ........... num H. Relative Importance of the Different Chain Transfer Processes. . . . . . . I. Relation between Intrinsic Viscosity and Number Average Polymerization Degree for Polypropylene.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. Remarks on the Catalytic Nature of the Coordinated Anionic Catalysis ............ ............... IV. Steric ................................. V. Determination of t ............. 1

41 43 44 46

46 50

2

G. NATTA AND I. PASQUON

Pwe

A. Adsorption of W-Labeled Alkylaluminums on a a-Titanium Trichlo................................................ ride Number of Active Centers by a Kinetic Method.. . B. n e t VI. Mean Lifetime of the Growing Polymeric Chains. . . . . . . . . . . . . . . . . . . . . . . . A. Determination of the Mean Lifetime from the Number of Active Centers ...................... ....... B. Variation of the Molecular Weight during the Polymerization. . . . . . . . . . C. Block Copolymers (Hetero ). .......................... VII. Conclusions. . . . . . . . . . . . . . . . . . ............................ References... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50 56

60 60 61 64 64 65

1. Introduction to Anionic Coordinated Polymerization of a-Olefins A. GENERALITIES Considerable interest has been shown in the new processes of stereospecific polymerization, not only so far as they concern the production of new classes of polymers, having unusual characteristics and improved properties, but also because they are representative of a peculiar new type of heterogeneous catalysis, of great interest from the practical and the theoretical points of view (1-5). The discussion of kinetic work will be here preceded by a summarized description of the chemical nature of the polymerization, to which we have attributed a mechanism of anionic coordinated type. Such a definition of the reaction mechanism depends upon the fact that the catalyst is a complex in which, generally, a transition metal acts as a coordinating agent and that a carbon atom, which belongs t o the extremity of a growing polymeric chain, is coordinated to such a complex and, in the activated state, it possesses a negative charge. The stereospecific polymerization of a-olefins takes place only in the presence of heterogeneous catalytic systems, including a crystalline substrate (formed by halides of transition metals, such as T i c & , TiCb , VCh , CrCL , CoClz , etc.) and a suitable metallorganic compound ( 5 ) . Such metallorganic compound or coordination complex contains an electropositive metal for which the carbon-metal bond may be considered a t least partly polarized, so that the carbon atom has a partially ionic character and behaves as a carbanion. The above-mentioned metallorganic compounds must have the property of forming complexes with the halides of transitions metals. It is required, in order to get catalytic complexes, that the metal of metallorganic compounds be able to create a strong localized electric field; therefore, metals having a very small ionic diameter (below 1 A.) jointly with a very electropositive character are to be used. For such reasons, metals such as Cu,

KINETICS OF POLYMERIZATION OF LU-OLEFINS

3

Ba, Sr, K, Rb, Cs, although they have high electropositivity, cannot be employed, their ionic radius being too large, whereas other metals such as B, with a small ionic radius, are not so suitable, because they show an insufficient electropositivity (6, 6). The most suitable metallorganic compounds are those of A1 or Be, since these metals are characterized by small ionic radius [for instance, Al(CzHa)3, A1C1(CzH& , Al(iCdH&, Be(CzH&]. Less efficiency is shown by certain metallorganic complexes containing Zn, Li, etc. (6, 6.) The formation of prevailingly electron-deficient complexes between transition metals of low valency and metallorganic compounds of metals having small ionic radius has been clearly shown. The electron-deficient metallorganic compounds I

R

R

R

\ / \ / \ / \ / Be

Be

Be

Be

I1

where R is an nlkyl group, polymerize ethylene to low-molecular-weight polymers (’7). Crystallizable complexes containing transition metals of the following general formula have been isolated : I11

where R1 is a halide or an alkyl group and Rz is an alkyl group. They polymerize ethylene to high-molecular-weight polymers (8).

B. STEREOSPECIFICITY OF CATALYSTS The metallorganic compounds (I, 11) employed in presence of a heterogeneous phase containing an amorphous compound of a low-valency, strongly electropositive transition metal, generally polymerize a-olefins to amorphous polymers. In a similar fashion, the soluble reaction products of such metallorganic compounds with compounds of transition metals, chemisorbed on amorphous substrates, polymerize a-olefins to amorphous polymers (6, 9). The same compounds (I, 11) employed in presence of solid crystalline halogenated compounds of some transition metals behave as stereospecific

4

0. NATTA AND I. PASQUON

TABLE I 8lereospeci$city of Cala~!ylicSystems: a-Tic1&(CZ&.),, t = 75", PC,H, 2.4 atm.)

-

Metal of the metal alkyl compound

Ionic radii of the metal, A.

Polypropylene not extractable in boiling n-heptane yo

Be A1 Mg Zn

0.35 0.61 0.60 0.74

94-90

80-90 78-86 30-40

catalysts and polymerize the a-olefins to crystalline polymers (6, 9). A greater stereospecificity is shown by catalysts containing metallorganic compounds of metals with very small ionic radius (see Table I) (6, 6 ) . Complexes of type I11 and also traces of soluble halides of strongly electropositive transition metals, being able to form complexes with metallorganic compounds of the type I, 11, increase the activity of the stereospecific catalysts formed by the action of metallorganic compounds on crystalline substrates (10, 11). They can also polymerize in a stereospecific way in the presence of crystalline substrates of transition metals (for instance, CoC12) which are not by themselves sufficiently electropositive, (when used in the presence of metallorganic compounds) to polymerize the a-olefins (10, 11). The stereospecific catalysts polymerize a-olefins, giving linear polymers, by head-to-tail addition containing long sequences of monomeric units, whose carbon atoms show the same relative steric configuration. The nonstereospecific catalysts, on the contrary, give chains whose monomeric units follow each other in a random or not ordered way as far as it concerns the relative steric configuration. Each molecule of a-olefin, at the moment of polymerization, may give rise to two types of monomeric enantiomorphous units, which differ only for the steric configuration, one being the mirror image of the other one (Fig. 1). Only the heterogeneous catalysts, and in particular those acting on a crystalline substrate, contain active centers, each of which makes an asymmetric synthesis, as it converts the monomer molecules which do not yet contain atoms of asymmetric carbon, at the moment of the polymerization, into monomeric units having all the same steric configuration (19,6). An asymmetric structure has been ascribed to such active centers, that justifies their behavior as catalysts of asymmetric synthesis (6). In a heterogeneous not optically active catalyst there is the same probability that an active center shows a given steric structure or the enantiomorphous one; it follows that one half of the present active centers will cause a given configuration of monomeric units (for instance, right-handed) and the other half will cause the opposite configuration (left-handed).

KINETICS OF POLYMERIZATION OF a-OLEFINS

5

monomer having planar srruc ture

k monomeric enantiomorphous units

FIQ.1.

There will be in a raw polymer the same number of chains, whose monomeric units show, with regard to a certain terminal group, a given structure (for instance, right-handed) and the eame number with the opposite steric structure (left-handed). The raw polymers of this type have been called isotactic and may in general crystallize (1).They differ for this reason from atactic polymers, in which the monomeric units follow in the same chain with random steric configuration and are unable to crystallize. In an isotactic chain having a very great length (considered as being of infinite length), there will be no more asymmetric carbon atoms because the asymmetry of the tertiary carbon atoms, which was due to the different structure or length or configuration of the two parts of the chain linked to it, disappears (6). Such carbon atoms show, however, the same steric configuration of the tertiary carbon atoms which follow or precede them, and this makes them different from atactic polymers (6, 13, 14). Before the discovery of stereospecific catalysis, all the known polymers of a-olehs were unable to crystallize, because their structure was chemically irregular (for instance, not rigorously linear or not rigorously head-to-tail) and because it was sterically irregular (16). A difference of structure between isotactic and atactic polymers exists independently of their physical state. If we could, in fact, stretch on a horizontal plane a sterically regular segment of the main chain of an isotactic polymer of the type (CHR-CHs), the R groups linked to the tertiary carbon atoms would range themselves all over or under such plane, whereas in an atactic polymer they would be arranged in a random way, partly over and partly under it (Fig. 2). The chains of isotactic polymers (in which the dimensions of R are much greater than those of the hydrogen atom) have the tendency to assume a helicoidal configuration with a pitch which depends on the dimensions of the R group. There is evidence that a helicoidal structure has the tendency to exist also (at least partially) in the amorphous state. It is detectable,

6

G. NATTA AND I. PASQUON

H

R

H

Fro. 2. Chains of stereoisomeric poly-a-olefins supposing the main chain stretched on a plane. I. Isotactic. 11. Syndiotactic. 111. Atactic.

however, in the crystalline state. In the crystals we may find macromolecules of isotactic polymers with a helix-shaped arrangement, which is ternary (in the case of polypropylene, polystyrene, modification I of polybutene, etc.), quaternary (in the case of poly-3 methyl-butene-I), or heptenary (in the case of poly-4-methylpentene-1, etc. (Fig. 3) (18, 1 7 ) . The helices may show a right- or left-handed winding (independent of the steric configuration of the tertiary carbon atoms. In the crystal lattice of many isotactic polymers, there may be found a chain packing, characterized by the fact that each right-handed chain is surrounded by lefthanded chains and vice versa (Fig. 4) (18, 19). To the high regularity of structure must be ascribed the exceptional properties of isotactic polymers (high melting point, high mechanical characteristics, possibility to form films or fibers made of oriented crystals having high tensile strengths). To them is attributed the great interest arisen in the fields of plastics and synthetic fibers (6).

C. MECHANISM OF STEREOSPECIFIC POLYMERIZATION The process may be ascribed to the coordinated anionic type. Such a process which leads to the addition of a molecule of monomer in a polymeric chain, may be considered as divided into several consecutive steps.

KINETICS O F POLYMERIZATION OF (U-OLEFINS

0

R

I R = - c H ~ . - ~ H.-CH-CH* , -CH*-CH~-CH-(CH& -o-cH,: ~-c~-cH-(cH,),

n

7

UI

R.c~-cH-(cH,)-c,H,

-cH~-cH-wI,)~

R* -CH-bb)*.

-0

FIG.3. Chains of isotactic polymers.

The electron-deficient catalytic complex, containing a transition metal, has the tendency to attract the olefin molecule, whose ?r-electrons tend to compensate the deficiency of electrons of the complex. The catalytic complexes may possess a type of structure as follows:

8

a.

NAWA AND I. PASQUON

Rr

R8

\ / \

Ra/M’\

/

Rs

/”.\ Re where M t is the transition metal and Mp is the strongly electropositive metal to which the alkyl groups are bound. Only when such a complex is chemisorbed or lies on the surface of a crystalline lattice made of a compound of a transition metal does the catalyst act in a stereospecific way in the polymerization of a-olefins. In the first reaction step, the olefin is strongly polarized by the catalyst, as follows: RHC=CH,

R4

00 -, RH&--CH~

At the same time, a dissociation of ionic type of the bridge bond takes place. The bridge bond M-R-M is, in fact, weaker, as demonstrated by

FIG.4. Projection of the crystalline polypropylene lattice, on a plane perpendicular to the axis of the polymeric chains.

KINETICS OF POLYMERIZATION OF (r-OLEFINS

P

R

9

P

e

-

I+!..’

CH2 {.yR

(-I 1+1 CH2-CHR ’ I-(\

RinM!.

,CH2P

__c

Rkfl{.;

,*

.‘/c$?.

‘?l2 R i

.

.\R----M*R 2 n

.

a

I

‘R’

FIQ.6. Hypothesis of addition of a monomer molecule on the bond between the catalytic complex and the growing chain, in the anionic coordinated polymerization.

the greater length of this bond between metal and R group compared with the bonds between side groups R and the metal. This was observed by X-ray examination of different complexes, containing bridge bonds (20, 21). The introduction of a monomeric unit occurs between the electronegative -CH2 at the chain end and the electropositive metal. A new -CH2 group deriving from the new monomeric unit, comes and substitutes in the complex the -CH2 group of the previous monomeric unit (see Fig 5). The reaction of polyaddition is represented by the following equation: (+I (-) [Cat]--CH2P

+ CH,=CHR

(+)

(-1

+ [Cat]--CHd3HRC&P

The termination of the growing polymeric chain may occur through several different processes, mostly by chain transfer. Either the process of chain transfer with the monomer, or the reaction of dissociation to hydride, leads to the formation of terminal vinylidenic groups, whose presence was noticed in the olefin polymers, obtained with the previously described catalysts (22)*

The chain termination processes will be described in detail in the following sections, dealing with the kinetic study of polymerization process.

CRYSTALLINE SUBSTRATE ON THE STEREOSPECIFIC POLYMERIZATION The stereospecificity depends not only upon the electropositivity and the ionic radius of the metal which belongs to the metallorganic compound, used for the preparation of the catalyst, but also upon the lattice structure of the crystalline substrate made of the transition metal compound (6). Besides the chemical composition, the crystalline structure of the substrate exerts a great influence on the stereospecificity of the catalyst. For instance, the halides of the type MX,,which crystallize with layer

D. INFLUENCE OF

THE

10

0. NATTA AND I. PASQUON

FIQ.6. a-TiCls and TiC12crystalline lattices.

lattice (a-TiC13, T i c & , vc13, etc.) (Fig. 6) (23, 24) are all suitable for the preparation of stereospecific catalysts (9,5,25,26'). In the case of TiC13 the less crystalline forms obtained a t low temperature by precipitation from solution of Tic14 and alkylaluminum are less stereospecific than the well-crystallized forms obtained a t high temperature ( 5 ) .TiCl3 crystallizes in three forms at least (27), and the greatest stereospecificity is given by the a-form. For this reason the catalytic systems, which we have mostly employed for studies of stereospecific polymerization of a-olefins, are those made using a-TiCls. II. Over-All Kinetics of Polymerization Process

A. CATALYTIC SYSTEMS USED As already stated in the first chapter, several catalytic systems show n certain stereospecificity in the a - o l e h polymerization.

KINETICS O F POLYMERIZATION O F a-OLEFINS

11

These systems may be differentiated either by the nature of the compound of the transition metal or by the type of the metallorganic compound used for their preparation. The behavior of the different catalytic systems (containing transition metal crystalline compounds) in the a-olefin polymerization, except for the different degree of stereospecificity,may be connected with a definite kinetic scheme. This was shown by experimental work performed a t the Institute of Industrial Chemistry of the Milan Polytechnic. When the compound of the transition metal is changed (e.g., a-TiC13, &Ticla), generally, the molecular weight of the resulting polymer changes. Also the nature of the alkyl group of the metallorganic compound influences the stereospecificity and the molecular weight of the polymer obtained (28). The nature of the olefm exerts a certain influence on the rate constant of the over-all polymerization. This is connected with factors of steric character and to the more-or-less enhanced electron-releasing character of the alkyl group bound to the vinyl group which may influence several steps of the over-all polymerization process. Although the catalysts containing beryllium alkyl are more stereospecific than those with alkylaluminum (6, S ) , nevertheless the greater part of our kinetic measurements were performed using alkylaluminum compounds, since they represent a special practical interest due to the higher availability, and lower toxicity compared with the corresponding beryllium compounds. The results summarized in this paper have been obtained using the catalytic systems: Al(CnHs)t-a-TiCla-n-heptane or

A1(CzH&C1-a-TiCls-n-heptane.

The kinetic measurements reported in the following sections are concerned with the polymerization of propylene; the results obtained with this monomer can, however, be extended to other olefins (e.g., normal: butene-1, pentene-1, or branched). For this reason, although we limit ourselves to recording measurements made with one monomer only and with two types of catalytic system, we have given the most general title to this paper.

B. INFLUENCE OF THE SIZESOF a-Tic13CRYSTALS ON THE POLYMERIZATION RATE.ADJUSTMENT PERIOD The a-TiClr (violet modification), prepared by reduction of Tic14 with flowing hydrogen at high temperature (29), generally shows hexagonal lamellae whose sizes, depending on the method of preparation, lie in the range from 1 p to several hundred microns (see for instance the sample of Fig. 7). Sometimes the a-TiC13lamellae do not show any defined geometric shape, and their dimensions may reach a millimeter (see for instance the sample of Fig. 8).

12

Q. NATTA AND I. PASQUON

.-t t

0, 0

5

i0

15

20 25 h 30 polymerization time

FIG.9. Propylene polymerization rate at constant pressure and temperature as function of polymerization time ( p o , ~ = , 1,460 mm. Hg, 1 = 70"). 1

2 ~~

a-TiCli (sample A ) , g , / l . [A1(C2H1)8]mol./l.

0.80 4.46

x

1.00 10-3

2.94 X 10-1

In Fig. 9 the characteristic behavior of propylene polymerization rate is plotted us. polymerization time. The data were obtained by operating at constant pressure with a catalytic system containing a-TiCls crystalshaving initial sizes between 1 and 10 p (a-TiCls sample A). It may be noticed that during the initial polymerization period (adjust-

KINETICS OF POLYMERIZATION OF O-OLEFINS

13

51 0 Fro. 10. Propylene polymerization rate at constant pressure and temperature 1,450 mm. Hg, t = 70°C) obtained with two samples of unground a-TiClr whose crystals have different sizes (seeFigs. 7 and8). (a-TiC1, : 1.64 g./l., [AI(CIH~)~]: 2.94 X 10-1 mol./l.). ( ~ c , R= ~

ment period) the activity of the catalyst increases until it has reached a value which remains, afterwards, practically constant in the time. This adjustment period has been explained on the assumption that crystals and aggregates of a-TiC1, are smashed and cleaved under the mechanical action of growing polymeric chains, so that we have a consequent increase up to a constant value, in the number of active centers which directly participate in the polymerization. This assumption has been proved by the following experimental data: 1. The polymerization rate, under steady-state conditions, appeared to be almost independent of the initial size of the a-TiC13crystals (Fig. 10). 2. By operating with ground a-TiC13(sizes 5 2 p ) the adjustment period was definitely affected. The initial period, characterized by an increasing rate which might otherwise last for 7-8 hrs., was greatly shortened and modified (see Fig. 11) (SO, 31). 3. The rate that can be reached under steady-state conditions (for instance, by operating at 70") seems to be practically unaffected by a moderate amount of grinding (see Fig. 11). The effect of a moderate degree of grinding on the extent of a-TiCla active surface leads to a final result similar to that resulting from the mechanical disaggregation caused by the action of the growing polymeric chains. It may be assumed that in any case the final size of the cu-TiC13particles reaches approximately the same limiting value. On the other hand, it is most likely that the exceptionally small and active a-TiCla particles, obtained during the grinding, are unstable and lose their activity on ageing. In fact, at the beginning of the reaction, when using ground a-TiC13, the

14

Q. NATTA AND I. PASQUON

6

m 2

C

k

li

0 3

0 4

polymerization time

FIG.11. Effect of previous physical treatments on a sample of a-TiClo on the propylene polymerization rate, at constant pressure and temperature ( t = 70" pc,~,= 1,450 mm. Hg). 1 and 2: ground cuTiCls (sample A ) (sizes 5 2 p ) . 3 and 4 : unground aTiCla (sample A) (sizes within 1 to 10 p ) .

polymerization rate very quickly reaches a maximum and decreases nfterwards, more or less slowly, until attaining the steady-state condition. The presence of such a maximum may be ascribed to very small a-TiC13 particles which lose their activity during the polymerization, either by recrystallization, by reaction with Al(CzH&, or by occlusion in the solid polymeric product. In particular, it may be observed that the maximum disappears when operating with Al(CZH&Cl instead of Al(C*H& (32). 4. By operating with unground a-Tic13 the time ( t 3 1 4 ) which is necessary of the value of polymerization rate in steady-state condito reach the tions varies inversely with the polymerization rate measured under steadystate conditions (SO, 31). In fact, by comparing the polymerization carried out at different temperatures and pressures, referred to the same amount of a-TiC13, we observe different values of t314 mainly depending upon the overall polymerization rate, and consequently upon the value reached by the rate under steady-state conditions (Fig. 12) (31). 5 . The use, in the propylene polymerization, of unground a-TiC13 that had been previously maintained, for many hours, in the presence of solutions of A1(C2H6)3 a t temperatures lower than 80°, does not substantially modify the observed reaction rate and its variation during the adjustment period (31). 6. It has been observed by microscopic examinations that the a-TiC18 lamellae are very thin and brittle. 7. In some tests it has been observed that the polymerization rate at

15

KINETICS OF POLYMERIZATION OF a-OLEFINS

3 1

0.3

0.1

FIQ.12. Dependency of the t a l , index of the adjustment period, on the reciprocal of the propylene polymerization rate in Ateady state conditions. Tests performed with unground a-TiCla (sample A ) .

t , "C PCaHa

,mm. Hg

1

2

3

4

5

6

7

32 1,680

43 1,640

32 2,680

56 1,570

70 750

70 1,450

2,450

70

zero time is not zero; it keeps the initial value for several minutes before starting to increase (see, for instance, the lowest curve of Fig. 11). 8. It has also been found that the polymer formed from the beginning of the reaction is already prevailingly isotactic. This means that, from the start of the reaction, there exist a certain number of active centers on the solid a-Tic13 surface which immediately yield isotactic polymer; consequently, it can be excluded that, a t least for the active centers present on the initial free surface of a-titanium trichloride, there is an initial activation process, whose rate is slow enough to be observed even when operating a t low temperature (30"). The above statements are in good agreement with the fact that, after the reaction has been carried out in steady-state conditions and has been stopped by taking off the monomer, thereafter, when the initial value of monomer concentration has been re-established (Fig. 13), the reaction starts

16

G . NA'M'A

0

20-

1

1 I

I

AND I. PASQUON I,

mohtaincd for 14 t~a t 70% and pc$64

I

16

17h

j

again a t once and at the same steady-state rate. The lowest curve of Fig. 13 shows that the steady-state rate at a given temperature (below SOo) is the same also if the steady-state conditions had been previously reached a t lower temperature (30,31). C. CATALYTIC BEHAVIOR OF a-TiCl3 IN STEREOSPECIFIC PROPYLENE POLYMERIZATION

From the curve reported in Fig. 9, we may observe that the polymerization rate, obtained by operating at constant pressure, after the initial udjustment period, remains practically constant for many hours. This occurs only when operating with pure reagents and solvents, with not too finely ground cr-TiC13, and under such conditions as to get limited polymerization rates per unit volume solvent (some g. of C3Halhr. per liter of solvent) (SO, 33). This time-constant rate is proportional to the a-TiCla amount which proves that, at least formally, the over-all polymerization process is really a catalytic one, with regard to the a-TiCla. The catalytic behavior of a-TiCls is, in any case, connected with the existence on its surface of metallorganic complexes which act in the polymerization only if a-TiC13 is present. This makes stereospecific polymerization processes (of coordinated anionic nature) very different from the better known polymerization processes, initiated with free radicals. In the latter process, the initiator is not a true catalyst, since it decomposes during the reaction, forming radicals which are bound to the dead polymer; on the contrary, in the case of stereospecific polymerization, each molecule of polymer, at the end of its growing period, can be removed from the active center on the solid surface of the catalyst which maintains its initial activity. There is evidence that each active center which initiates a polymeric chain (coordination complex between the titanium salt and a metal-dkyl

KINETICS O F POLYMERIZATION OF (U-OLEFINS

17

compound) retains unaltered its ability to form macromolecules, independent of the number of polymer molecules produced. Many homogeneous catalytic processes, in particular of anionic nature, are known, in which the polymerization takes place by stepwise addition (polymerization of ethylene oxide (34) of ethylene at low pressure and temfor which perature with AIRa (7, 36),of styrene by Szwarc catalysts (M), the growth of the macromolecule can last for a very long time). This led some researchers to talk of a life of macromolecules and of living molecules (37). This attribute is justified by the fact that the growth of the macromolecules does not show any termination; it stops when the monomer is removed, but is resumed immediately at the same rate when the monomer concentration is restored to its initial value. In some cases (e.g., the case of “living polymers” of Szwarc, obtained with anionic catalysts), it is exactly the same macromolecule which continues to grow, yielding polymers whose molecular weight increases with the polymerization time. In the case under examination (heterogeneous catalysis in the presence of coordinated polymetallic complexes) the molecular weight of the polymer is generally almost independent of the polymerization time, whenever the polymerization lasts for more than about 10 min. The macromolecules bound to the catalytic complex can be detached from the active center, but their detachment leaves unchanged the activity of the catalytic center which can initiate the formation of another macromolecule.

D. INFLUENCE OF

THE OPERATINGCONDITIONS ON THE TION STEADY-STATE RATE.

POLYMERIZA-

1. Experimental Apparatus and Operating Conditions. The polymerization of propylene in the presence of a heterogeneous catalyst and a solvent occurred at a relatively low partial olefin pressure and was carried out in an apparatus continuously fed during the reaction with the olefin in the gaseous state at constant pressure (Fig. 14). The amount of olefin consumed was determined by the decrease of pressure with time, measured on the feed vessel, kept at constant temperature by water circulation, where the olefin was maintained in the gaseous state, It has been said that the polymerization rate observed under steady-state conditions, with a given sample of a-TiC1, is practically independent of the initial sizes of the crystals. It is, moreover, convenient to point out that not all samples of o-TiCls prepared by the different methods we have examined, lead in all cases to rates equal to each other. The most active samples of a-TiCla have an activity that does not exceed three times the value given by less active samples which we have here examined. As the initial sizes of a-TiCla crystals seem to have very little influence

18

Q. NATTA AND I. PASQUON

FIG.14. Apparatus used for kinetic measurements of propylene polymerization (reaction vessel rocking 45 times per min. through a 45' angle). PI = pressure gage, PC = pressure control, FI = flow indicator, TC = temperature control.

on the steady-state rate, such differences could be ascribed to the degree of purity of a-titanium trichloride. The most frequent impurities of commercial a-titanium trichloride are generally other chlorides (Tic14 ,TiC12),metallic titanium, titanium nitride, and the products resulting from oxydation or hydrolysis of the titanium chlorides, the latter being unstable at air and moisture. Some of these impurities have opposite effects on the catalytic activity and stereospecificity,depending on their concentration. As we shall show below, the stereospecificity of the catalytic system can be influenced by impurities contained in the a-titanium trichloride. The larger part of the results reported in this paper, have been obtained with an old sample of a-titanium trichloride called a-TiCl,--sample A. This sample is neither one of the most active nor one of the most stereospecific products we have studied. The analytical tests carried out on the product, have given the following results: Methanol insoluble residue: 1%

Ti :C1 ratio

= 1:2.96 in g. atoms

Kinetic data have been obtained with unground a-titanium trichloride, operating at constant temperature and pressure of olefin, during the whole polymerization.

KINETICS OF POLYMERIZATION OF a-OLEFINS

19

In some preliminary tests an examination was made of the influence of some physical factors on the reaction rate in the apparatus employed, such as mass and heat transfer depending on the degree of filling and stirring of the reaction vessel (33). It has been found that, for a given temperature, with the equipment used (see Fig. 14), there is a limiting rate, depending on the volume of the solvent, at which the mass and heat transfer phenomena become determining; operating, for instance, at 70°, in 250 cc. of solvent, the limiting rate is almost equal to 20 g. of polymerized CSHe per hour (33). All kinetic tests have been carried out at polymerization rates lower than this value. The order in which the components of the catalytic system (a-titanium trichloride and trialkylaluminum), the solvent (n-heptane), and the olefin are brought together has no practical influence on the polymerization rate. The rate values are independent of the temperature at which the catalyst is prepared by the action of alkylaluminum solution on a-titanium trichloride, provided that this temperature is not higher than 70" and the concentration of the alkylaluminum in solution is not too low (above 0.5 X mol/l. n-heptane) (30, 33). Most of the kinetic results reported in this study refer to concentrations of trialkylaluminum in solutions higher than 1.4 X mol/l. of solvent. On account of the sensitivity of the catalysts to traces of moisture or oxygen, it is generally not suitable to operate with lower concentrations of alkylaluminum, because the latter acts also as a protector of the solid catalyst. However, by operating with very pure solvents and reagents, the concentration of AlR3 can be reduced to lower values mol/l.). Triethylaluminum/a-TitaniumTrichloride Ratio. Many tests have been carried out with different trialkylaluminum/titanium trichloride molar ratios (from 1 to 8.5) without any considerable difference in the kinetic results obtained with the considered a-Tic13 sample (Fig. 15). For ratios lower than 0.4, the data obtained are of uncertain interpretation, owing to the degree of purity of the solvents and reagents which have been used (33).For such low values of the ratio, the reaction rate against time initially increases, goes through a maximum, and then decreases rapidly without attaining a stationary value. The decrease of the catalytic activity is due to a consumption of A1R3 and, in fact, the activity can be restored with the addition of small amount of A1R3. Overlooking the anomalies due to the lack of absolute purity of the reagents, one must assign a zero reaction order with respect to aluminumalkyl concentration, in the range of the above reported conditions. The result is due to the fact that the alkylaluminum, in the concentrations considered above, is always in excess with respect to the number of active centers existing on the surface of the solid catalyst. [TriethylaZuminum]/[CaH6] Ratio. Using a triethylaluminum concentra-

20

G . NATTA AND I. PASQUON

1

2

3

4

5

1.64 u-TiCls (sample 3.80 4.36 3.80 0.80 A ) , g./l(Al(C2Hs)3],mol./l.2.95 X 10-'8.65 X 10-z11.80 X 10-z4.45 X 10-a5.90 X 10P 5.50 Al/Ti, mol. 1.18 3.10 4.80 8.50 [A1(CzHa)$1 0.048 0.143 0.190 0.072 0.095 [CsHsl

tion higher than about 1.4 X lo-' mol/l. and a triethylaluminum/a-titanium trichloride ratio higher than about 1, the value of this second ratio does not influence the kinetics of the over-all polymerization process. Therefore, in the range of variables tested: [triethylaluminum]/[CaHs] = 0.015 to 0.4,the formation of possible soluble alkylaluminum olefin complexes is not kinetically detectable (SO, 33). This is confirmed by the independence of the olefin solubility in solutions of alkylaluminum in hydrocarbon on the alkylaluminum concentration (58). Amount of a-TiC13.In Fig. 15 the polymerization rate, obtained a t constant pressure of olefin with different amount of cr-TiCL , is plotted US. time. The steady-state rate is found to be proportional to the amount of a-TiCla present in the reaction system (Fig. IS), in agreement with the heterogeneous nature of the catalysis (30, 33). Propylene Partial Pressure. The polymerization rate, under steady-state conditions (Figs. 17 and 18) is proportional to the partial pressure of propylene (SO, $3). Polymerization Temperature. Apparent Activation Energy Based on the Steady-State Rate.* The rates observed at different temperatures, referred

* I n our kinetic calculations, we refer t o the directly observed partial pressure of propylene, rather than to its fugacity, because over the temperature and pressure range examined, we can assume that partial pressures and fugacities are pructicully proportional. I n fact, from the literature data, the variation in propylene fugacity coefficient, in the range of our kinetic tests, is small (about 0.97 a t 30" and 2700 mm. Hg; about 0.99 a t 70"and 450 mm. Hg of propylene partial pressure).

KINETICS OF POLYMERIZATION OF a-OLEFINS

21

FIG.16. Dependency of propylene polymerization rate in steady-state conditions on the amount of a-TiCla (sample A ) in the catalytic system.

FIG.17. Propylene polymerization rate at constant temperature (70") and at different pressures as function of polymerization time (a-TiC13: sample A : 3.60 g J . ; [AI(CZH~)~]: 5.88 X mol./l.).

to a given amount of a-TiCla and to a given partial pressure of propylene, are reported versus polymerization time in Fig. 19. The diagram shown in Fig. 20, which gives the log of the polymerization rate under steady-state conditions, plotted us. the reciprocal of the absolute temperature, was drawn from the above data. The activation energy calculated from the data reported in Fig. 20 is about 10,000 cal./mol. The activation energy referred to the concentration of the olefin in the liquid phase can be deduced from the one referred to the pressure in the gaseous phase, by adding the solution heat of the propylene in n-heptane,

1500

1000

500

2000

2!

m m Hg

FIQ.18. Dependency of propylene polymerization rate in steady-state conditions on the propylene partial pressure (a-TiClr:sample A ) .

FIQ.19. Propylene polymerization rate at constant pressure ( p c , ~ = , 1,500 mm. Hg) at different temperature, as function of polymerization time. a-TiClr (Sample A ) ,

IAl(CaHs)iI, mol. 11.

g./l.

Al/Ti, mol. ~~

1 2

3 4 5 6 7 8 9

3.80 0.80 7.60 1.60 7.60 10.80

1.18 8.50 1.50

5.90

10-9

5.60

10-' 10-* 10-' 10-'

3.60 1.05

x

17.70 X 7.36 X 7.36 X 17.70 X 7.36 X

20.20

12.16 12.10 22

~

2.96 X 10-a 4.45 x lo-' 7.36 X 10-*

lea

0.52 2.20 0.94

KINETICS OF POLYMERIZATION OF &OLEFINS

23

FIG.20. Log of propylene polymerization rate in steady-state conditions as function of 1/T ( p c , ~ = , 1,500mm. Hg, a-TiCl8 : sample A ) .

equal to about 4000 cal./mol. Consequently, the activation energy measured from the steady-state rate and referred to the olefin concentration in the liquid phase corresponds to 14,000 cal./mol. (SO, 31). If we consider the results reported so far, the polymerization rate of propylene under steady-state conditions, catalyzed by the catalytic system Al( CoH6)3-a-TiC13-n-heptane, shows the following relation: =

~~-10,0001RT

GT~PC~H~

For the sample of a-TiC13to which the above data are referred = 2 x 107 e--lO,OOO/RT GTipca H 6

(1)

(2)

where r = polymerization rate under steady-state conditions (g. CaHa/h) pCaHe= partial pressure of propylene (atm.) GTi = g. a-TiC13in the catalytic system. Equation (1) is applicable to other samples of a-TiC13 by varying the value of A . For instance, the sample ( B ) shown in Fig. 7 shows a value A = 3.4 X lo'.

111. Chain Transfer, Termination Processes, and Molecular Weight of the Polymers

The chain transfer and termination processes have been studied by the following methods: Intrinsic viscosity measurements on the resulting polymer. Analysis of end groups of polymeric chains by chemical, radiochemical and physical methods ( I R examination). By operating particularly at 70" it has been observed that every transfer and termination process of polymeric chains involves in the same way

24

Q. NATTA AND I. PASQUON

(from a qualitative point of view) the growing macromolecules, independently of their steric structure. We must, however, notice that the molecular weight of the atactic polymers which are always present in small amount in the crude polymer, is generally much lower than that of the isotactic polymer. In fact, while the intrinsic viscosity of the isotactic polymer generally ranges from 2 t o 5, we found correspondingly 0.5-1 for the atuctic polymer. We shall examine in detail the influence of thedifferent factors controlling the intrinsic viscosity of the isotactic polymers during the polymerization. A. CATALYSTS USEDAND THEIRSTEREOSPECIFICITY The steric composition of the polypropylenes depends on the degree of purity of cu-TiCl3 used in the polymerization. It has been observed, for instance, that the so-called isotacticity index of polypropylene (polymer residue after extraction in boiling n-heptane ) can attain values ranging from 75 to YO%, depending on the catalytic properties of the samples of a-TiC13. Also the average molecular weight depends on the purity of the a-TiCl3 samples used. For instance, the same sample of a type of a-TiC13 which, in the raw state, during a 2-hr. polymerization test of propylene, gives polymers having an intrinsic viscosity equal to 1.5 after a series of washings with anhydrous hydrocarbons (before the polymerization tests) leads to polymers having intrinsic viscosities which increase with the number of washings, until they reach an asymptotic value of about 3.3. For that reason, the study of chain transfer and termination processes in propylene polymerization has been performed by using a standard type of a-TiC13 (sample A ) which is the same as that used in the previously performed kinetic tests, but treated as follows (31): Grinding in a stainless steel bottle, containing spheres of stainless steel (the dimensions of a-TiC13after grinding are 1 2 M ) . Washing with anhydrous n-heptane several times. The a-TiCls treated in this way gives reproducible results for the kinetic behavior, the molecular weights, and the steric composition of the polymer. The atactic amorphous portion (9-16% of the total) contained in the obtained polypropylene has been separated by treating the raw polymer with n-heptane a t room temperature. When operating in such a way, we have not separated the stereoblock fraction (extractable in boiling n-heptane) from the isotactic (not extractable in boiling n-heptane) fraction of polymer. The results reported in this paper are generally referred t o the crystalline fraction, named non-atactic, which contains also some stereoblock polymers (at the considered polymerization temperatures, the latter generally correspond only to 5-7 % of the total) ( 9 )

25

KINETICS O F POLYMERIZATION OF (r-OLEFINS

B. INDEPENDENCE OF THE MOLECULAR WEIGHTAND STERICCOMPOSITION OF THE POLYMER OF REACTION TIME,FOR LONGREACTION TIMES Many polymerization tests have been carried out under different conditions (temperature from 30 to 70" and propylene partial pressure from 450 to 1,450 mm. Hg). When operating under such conditions, we never observed any effect of polymerization time, on the molecular weight and steric composition of the polymer, either after a few minutes of polymerization (e.g., in the interval in which the reaction rate with ground a-Tic13 shows a maximum) or after many hours (when a small decrease in the over-all polymerization rate occurs) (Table 11). This means that, under the tested conditions, the growing time of each polymeric chain is not slow enough to be measured, on the basis of the above reported kinetic data. For this reason, by operating particularly a t 70" and with a propylene partial pressure of about 1 atm. and assuming that all active centers which are present on the surface of cr-TiC13 have the same activity, the average TABLE I1 Polymerization of Propylene to Zsotactic Polymer. Zndependenee of the Molecular Weight and of the Steric Composition from the Polymerization Time

'9

OC

PCaHe s mm. €16

IAI(C*Ft) rl, mol./l.

o-Tic1 I, (sample

U/Ti, niol.

Ahdl.

Polymerization time, hr.

x

1.50

3

1450

2.94 X

3.00

1.5

31

1450

2.94 X

1.50

3

51

1110

1.47 X 10-2

0.30

7.5

70

450

2.36 X

1.20

3

70

450

2.94 X 10-2

1.50

3

70

450

7.36 X

11.30

1

!4

70

950

2.94 X 10-2

1.50

3

>6

70

1450

1.77 X 10-2

700

31

%"

Intrinsic viscosity of le non-atactic polymer: ?I, 100 cm.:,JK.

89 88.5 85 86 86 84 87 87 90 90 91 91 91 90 88.5 88.5 88 88 87

4.40 4.34 4.66 4.65 4.70 4.90 4.50 4.45 3.56 3.47 3.28 3.14 2.18 2.13 3.84 3.78 3.84 4.16 4.20

~-

_______

31

Nonatactic polymer,

2.94

14 31 1 4 8 17 8 24 10 15 4 7 1

0.91

3

2 6 4 7

The data am related to the polymers insoluble in n-beptane at room temperature and include the stereoblock polymers soluble in boiling n-heptane ( b 7 % of the whole polymer) and the isotactic polymer.

26

Q. N A W A AND I. PASQUON

growing time of each macromolecule must not be longer than a few minutes (89, 40).

C. CHAINTRANSFER PROCESS DEPENDING ON ALKYLALUMINUM CONCENTRATION We have separately studied the nature of end groups and the dependence of the molecular weight of the polymeric chains, on the alkylaluminum concentration in the catalytic system. 1. Intrinsic Viscosities The measurements of intrinsic viscosity [q] have been carried out at 135' in tetralin. Under these conditions, the relationship between [q] and viscosimetric molecular weight M , for isotactic polypropylene is (41): [q] =

KMO."

In fig. 21, the values of l/[q]1'0.74= l/[q]1.36(this factor can be assumed as being proportional to the reciprocal of the degree of polymerization 2,) of the considered polypropylene fraction, are plotted vs. the square root of alkylaluminum concentration. The data plotted in Fig. 21, corresponding to constant quantities of a-titanium trichloride, can be assumed to give straight lines and the straight lines obtained for several values of CTi can be assumed to be parallel. The limiting line for CTi = 0 has been calculated from the data plotted in Fig. 22. The dependence of the intrinsic viscosity of the polymer (and consequently of its molecular weight) on the alkylaluminum concentration

*

,

I

0

02 0.3 (mots At (CpH&/I bheptme)"p

01

FIQ.21. Dependency of the reciprocal of the polymeriration degree (proportional to l/[q]lJb) of the non-atactic polypropylene fraction, on the square root of the aluminum alkyl concentration ( t = 70°, %,a, 9W mm. Hg, ground a-TiCla: sample A ) .

-

KINETICS OF POLYMERIZATION OF (r-OLEFINS

27

FIQ.22. Specific radioactivity (and corresponding values of -C2Hs mol. per mol. of polymerized CsHa) of the non-atactic polypropylene fraction, aa function of the square root of the alkylaluminum concentration. (Tests performed with "C-labeled A l ( C ~ H at ~ )1~= 70°, pcla, = 460 mm. Hg, ground cr-TiCls: sample A ) .

shows that this compound takes part (directly or indirectly) in a transfer or termination process of the growing polymeric chains. 2. Radiochemical Determination of End Groups

An attempt was made to determine whether the variations of the molecular weight with the alkylaluminum concentration are due to a chain transfer, with participation of the alkyl groups of alkylaluminum. Polymerization tests were performed, using 14C-labeled ethylaluminum and detecting the radioactivity of the polymer. Careful preliminary tests were necessary to demonstrate the suitability of these methods for the present study. In particular, it was necessary to verify that the radioactivity detectable in the polymer may not be caused by contamination or other processes different from the ones taken into consideration. It was then found that it is possible to remove throughly from the polymer the last traces of unreacted ethylaluminum or of its soluble complexes with titanium compounds by washing with anhydrous hydrocarbon. No alkylation of the preformed polymer caused by triethylaluminum or its derivatives has been observed (4.2). There is evidence that sometimes a permanent radioactive contamination of the polymer appears when one adds to a suspension of the polymer in n-heptane 14C-labeled triethylaluminum and certain samples of a-titanium trichloride (particularly when the a-TiClr contains Tic14 or other compounds of Ti( IV) , as impurities).

28

0. NATTA AND I. PASQUON

V'

-II, E

lXlU4

200 0:1 0:2 0.3. [mols A I [C~H~)J/I n- h ept ane] 'I2

Fxa. 23. Specific radioactivity (and corresponding values of -C1H6 mol. per mol. of polymerized C3Hd of the atactic polypropylene fraction, as function of the square root of the alkyl-aluminum concentration. (Tests performed with W-labeled Al(CnH6)a at t = 70", P C ~ H=~ 460 mm. Hg, ground a-Ticla: sample A ) .

This contamination remains after purification of the polymer from alkylaluminum by washing. Other samples (such as that shown in Fig. 7 ) are not contaminated. The amount of this contamination is in any case limited. This point will be discussed in one of the next paragraphs. All the reported data relating to radioactivity measurements have been corrected for radioactive contamination. The use of "C-labeled triethylaluminum allowed us to demonstrate that the quantity of -C2H6 groups [deriving from A1(C2H6)3]which is bound to the non-atactic polymer a t the end of the polymerization, when operating with a constant amount of titanium trichloride, is a linear function of the square root of the alkylaluminum concentration (Fig. 22), in the considered range of expeiimental conditions (42). Similar results have been obtained by analyzing the fraction of amorphous polymer (Fig. 23) (38). 3. Polymeric Isotactic Chains Bound lo the Aluminum

Determinations of aluminum have been carried out on fractions of polymeric product containing isotactic chains deriving from the polymerization. These measurements were performed in an attempt to establish whether the chain transfer process, depending on the alkylaluminum concentration, leads to the formation of macromolecules which remain bound to the aluminum. The polymer has been therefore purified by physical methods from the unreacted ethylaluminum and from the heterogeneous catalyst. The above determinations were carried out by taking into consideration

KINETICS OF POLYMERIZATION OF (Y-OLEFINS

29

a fraction of the polymeric product containing isotactic chains that may be easily separated from the catalyst in the following way (@) : The unreacted alkylaluminum and the atactic polymer were removed from the vessel in which the polymerization was carried out, by means of decantation and repeated washings with anhydrous n-heptane a t 50'; the separation of most of the polymer from the a-TiC13 was then made by washing a t 100" with anhydrous xylene. The polymer contained in the xylene solution was further purified by repeated precipitations and washings of the polymer precipitated with anhydrous xylene at - 70'. The aluminum was determined spectrophotometrically using 8-hydroxyquinoline in a known quantity of polymer obtained from the xylene solution and previously purified. The absence of titanium from the polymeric product, isolated in this fashion, was checked by conventional analytical methods. The results obtained are plotted in Table 111. I n the same table, for purposes of comparison, are recorded the amounts of ethyl groups derived from the Al(C?H5)3, as found in certain fractions of the polymer by the radiochemical methods. The amount of aluminum bound in the polymer is higher in the test performed with higher triethylaluminum concentrations. A comparison with the tests performed with the same alkylaluminum concentrations, but with different amount of a-TiC13, shows, on the contrary, that the amount of aluminum bound to the polymer decreases remarkably TABLE I11 End Groups i n the Isotactic Polypropylene, Deriving from the Chain Transfer Processes Depending on the Catalyst Concentration (Catalytic System: a-TiCl $-A1(C2H6)-n-Heptane) I

a-TiCIa (sample

4, g.

0.11 0.15 0.50 0.50 0.50

I

AI(CzHd:, mol.

250 cm.8

I , "C.

--Gbend groups/CaHo mol A1 atoms(CaH6 in the mol. In polymer fraction polymer fraction, insoluble in soluble in xylene n-heptane at at loOo room temperature*

x x x x x

Heptane Heptane Heptane Heptane Xylene

70 70 70 70 100

0 . 5 x 10-3 0 . 6 x 10-3 1.35 X 2.7 x 10-3 2 . 2 x 10-3

Polymerization conditions

9.9 9.9 9.9 39.6 9.9

10-3 10-3 10-3 10-3 10-3

Solvent,

2 . 3 x 10-3 2.3 x 10-3 2 . 7 X lo-' 4 . 9 x 10-3 -

-Cab end ~~OUPS/C:HS mol in the isotactic polymer fraction not extractable in boiling n-heptanec

1.4 X 10-3 1 . 4 X 10-3 1 . 7 x 10-3 3.0 X -

Average of the values (which lay in the range 1.3-1.4) obtained in four polymerization tests. Thia fraction contains the isotactic and stereoblock polymers. These data were calculated from the preceding ones, taking into account the percentage and the moleeular weight of the stereoblock polymers contained in the fraction extractable in boiling n-heptane. (I

30

0. NATTA AND I. PABQUON

decreasing the amount of a-TiC13. Probably some soluble titanium compounds act catalytically in the transfer of alkyls from the aluminum to the polymeric chains.

4. Mechanism of the Chain Transfer Process Depending on the Triethylaluminum Concentration The results reported in the preceding paragraphs indicate that the triethylaluminum molecules present in solution take part in a chemical process which affects the molecular weight of the polymers. In polymerization tests carried out in a relatively short time, the amount of reacted ethylaluminum is very small; this is proved also by the fact that the results obtained in these tests are not dependent on the reaction time. Furthermore, it has already been found that in the considered range, the over-all reaction rates do not seem to be affected by the concentration of ethylaluminum. It may be pointed out, therefore, that the ethylaluminum takes part in a chain transfer process. An almost linear dependence of l/[g]'.*' and of the number of -CzHs groups found in the polymer was found on the square root of the ethylaluminum concentration. The number of aluminum atoms chemically bound to the unpurified polymer decreases with the ethylaluminum concentration in the catalytic system. These results make us believe that the rate of the chain transfer process under examination is given by the relation: r3

= k&*C!I

(3)

where C A I = molecular concentration of triethylaluminum C* = number of active centers This dependence on the square root of the ethylaluminum concentration may be interpreted by assuming that the triethylaluminum acts in dissociated form in the chain transfer process. It is in agreement with the wellknown dimeric structure of triethylaluminum which is dissociated as follows : AIz(CnHa)a

2Al(C*Hs)a

(4 )

It has been also related by Bonitz ( 4 )that besides the homopolar dissociation, A12(CnHK)amay be partially dissociated in a heteropolar way: AI?(CzHs)s

+

[AI(C*Ha)al(+) [AI(C*Ha)r](-)

(5)

To explain the results obtained in our researches, we could take into consideration a chain transfer mechanism, such as the following one (at

31

KINETICS OF POLYMERIZATION OF (r-OLEFINS

least in initial stage) : [Cat](+)(-)CHICH(CHZCH),R

I

CH3 [Cat](+)

+ [AI(CZHK)Z](+)

.--)

AH8

(6)

+ (C2HK)zAlCHzCH(CH&H)nR AH3

+ [A1(C2HK)r](-)

[Cat](+)

4

AH1

+

[Cat](+)(-)CH2CH3 Al(CzH&

(71

It is possible that in the later stages of polymerization there may occur transfer processes involving more than one ethyl group per aluminum atom. I n this way, the catalyst will be regenerated while the monomer alkylaluminum takes part in the equilibrium of association with other alkyls in solution. Another interpretation that may be taken into consideration, kinetically equivalent t o the former one, is a total substitution of the polymeric alkylaluminum compound which is bound to a catalytically active complex containing the transition metal, as follows: TiCl.AZYzP

+ A1(CZH&

4

TiCI,A1(C?H6)3

+ AlYzP

(8)

where P = polymeric chain

Y = alkyl group (e.g., ethyl or polymeric chain-one can be substituted by a chlorine atom).

of the two Y

It has been observed that other metallorganic compounds (e.g., Zn(C2H&, which is not associated as A1(C2Ha)3)can be involved in chain transfer processes (46).In this case presumably alkyl groups are exchanged as follows: [CatIP

+ Zn(CzHK)2

-+

[Cat] C2HK

+ CzHIZnP

(9)

The rate of this chain transfer process is of first-order with regard to the Zn(C2H& concentration ($8). The kinetics of the above reported chain transfer reactions seem to be also catalytically affected by the titanium compound present in the reaction system. In fact we have observed (Table 111) that both the numbers of ethyl groups and aluminum atoms bound to the polymeric chains decrease with decreasing amount of titanium compound in the catalytic system. The above-recorded chain transfer processes and the processes of exchange between alkylaluminum in solution and alkylaluminum bound to the catalytic complex could also be effected by soluble polymeric alkylaluminum of the type (C2H6)A1P2or (C2Ha)2A1P(where P = polymeric chain). This

32

G. NAT'FA

AND I . PASQUON

will involve more than one ethyl group per atom of aluminum brought into the polymeric chains. In any case, such chain transfer processes lead to a continuous increase of the molecular weight of the alkylaluminum compounds during the polymerization. It is, however, possible that alkylaluminum molecules having a low molecular weight are regenerated by a mechanism similar to those reported in the study of the kinetic behavior of ethylene polymerization, in the presence of trialkylaluminum ( 3 6 ) or through a dissociation to a hydride: (CzHa)2AlCHzCH(CHzCH)nR ~ H s

-+

(C2Ho)zAIH

+ CHz=C (CH*-CH)nR bHa

AH3

&Hs

(10)

or through a transfer reaction with the monomer: (CzHo)zAlCHzCH(CHzCH).R &HI (CpHs)zAlC& CHZCHs

+ CHz=CHCHs

+

AHs

+ CHz=C (CHZCH)nR AHs

(11)

AH3

In the case of ethylene polymerization with AIRl alone, however, the transfer reaction with the monomer which is thermodynamically displaced towards the right, depends on the temperature (36) and, practically, does not occur any more a t low temperature ( 5oz+ 2e

with the previously bound electrons returning to the metal. A further insight may be obtained into the mechanism of the Hz Dz exchange reaction as a result of recent S.P. investigations which have revealed the presence of adsorbed atomic and molecular H a on a W suiface (124). Interrupting the flow of Hz t o a W film at -190' gave rise to a positive drift in potential characteristic of molecular H Zadsorption. Further, it was found that (1) adsorption was competitive (and activated), in that H atoms were replaced by Hz molecules before the surface was covered with H atoms, and ( 2 ) an increase in pressure favored the adsorption of molecular H2 . Similar results were obtained by Wortman et a2. ( 6 3 ) ,who noted a field-dependent transformation in the adsorbed film between 2" and 4" K. during the low-temperature spreading of large doses of Hz on a Ni surface in the F.E.M. This was accounted for by a shift in the equilibrium between adsorbed Hz molecules and the terminal fraction of the adsorbed H atoms. These experimental results lead to two significant deductions. I n the first place, the presence of a stable adsorbed layer of molecular HZat low temperature on a W surface lends support t o the Rideal mechanism (166)for the Hz Dz exchange reaction, aiz.,

+

+

since the exchange may proceed via H and H2 adsorbed at temperatures too low to permit mobility of the H atoms within the monolayer proper. Secondly, since the exchange process proceeds through substitutional adsorption and the rate of catalytic H, exchange with D2has been shown to be pressure-dependent ( l o o ) , the available evidence does not favor the original Bonhoeffer-Farkas mechanism (166), H

k-4

D

+ HD

+

2w.

XI. Heats of Adsorption In an adsorption process involving ionic or covalent bonding, the adsorption heats of principal interest are -AH,,, the heat of adsorption a t zero coverage and 6( - A H ) , the decrease in the heat of adsorption with coverage. It is in connection with the latter that the role of the work func-

120

R. V. CULVER AND F. C. TOMPKINS

tion is most significant, but it is desirable to consider the evaluatioii of - AHo before dealing with the variation in - A H with coverage.

HEATOF ADSORPTION A. THEINITIAL 1, - AH0 for the Adsorption of Alkali Metals. If an alkali metal atom is located at an infinite distance from a metal surface at zero potential, then the heat of adsorption comprises the work done in ( 1 ) transferring an electron from the atom to the metal, and (2) bringing the positiveion to its equilibrium distance from the metal surface (la?‘).In the first step, the energy change is (e4 - e I ) , where I$is the work function of the metal and I is the ionization potential of the alkali metal atom. In the second, the force of attraction on the positive ion at a distance d from the metal surface, i.e., the electrostatic image force, is e2/4d;hence, the heat liberated is e2/4do, where do is the equilibrium distance of the adsorbed ion from the metal surface. This distance is often assumed t o be equal to the ionic radius, which is 1.83 A. for the Na ion. The initial heat of adsorption, therefore, is -AH0 = @ - e l

+ e2/4do

(9)

The significance of the terms in Equation (9) is readily appreciated by referring to Fig. 2, which shows the potential energy curves for the adsorption of Na ions on W metal. Here the difference between the work function of the metal and the ionization potential of the Nu atom is given by the difference between the potential energy levels C and D, while the difference between the minimum A in the potential energy curve and the energy level C corresponds t o e2/4do, the interaction energy between the ion and its image. Some initial heats of adsorption are shown in Table X. In calculating 3te2/4do (3t = Avogadro’s number), it has been assumed that the distance of the adsorbed ion from the surface is equal to the ionic radius, and since TABLE X Initial Heals of Adsorption, kcal./g. atom“ System

9

I

W-Na

104 104

118 89.4

w-cs

xe’/4do 44.5 31.1

-AHo (calc.) -AH0 (exptl.) 30.5 45.7

32* 64c

a Trapnell, B . M. W., in “Chemieorption”, Chapter 6. Butterworths, London, 1955. * Boaworth, It. C. L., Proc. Roy. Sac. (London) A162,32 (1937); Eley, D. D., Trans. Faraday Sac. 49, 643 (1953). c Taylor, J . B., and Langmuir, I . , I’hlls. Rev. 40. 463 (1932); 44, 423 (1933).

SURFACE POTENTIALS A N D ADSORPTION PROCESS O N METALS

121

the value of e2/4do may be modified by polarization forces, van der Waals' forces, and repulsion forces, the agreement between the calculated and experimental data is regarded as satisfactory. 2 . Calculation of -AH0 from Bond Energies and Dipole Moments. Several attempts have been made to calculate the initial heat of adsorption from bond energies and dipole moments. Recently Higuchi et al. (106, 107) have shown that by approximating the complex formed between a metal atom and an adsorbate atom to a diatomic molecule, the bond energy E of the surface complex M-A may be calculated from a knowledge of the energy of pure covalent and ionic bonds and the dipole moment of the complex, as derived from work-function measurements. For a monatomic gas the evaluation of - AH0 for adsorption on a nearly bare surface follows immediately, as under these conditions - AH0 = E. The bond energy for the complex M-A is related to the energies of the ideal ionic and covalent bonds, H i and H , , respectively, and the fraction Ci' of the ionic bond in the adsorption bond, by the expression (128)

E - Hi - I - = 1 ~E - Hc To a good approximation,

and

H,

=

[E'(M-M)

+ E'(A-A)]/2

where a is the electron affinity of the metal M , and I is the ionization potential of the adsorbate A when an electron is transferred from A t o M . If the direction of electron transfer is reversed, then a is the electron affinity of A , and I is the ionization potential of M . E ( M - M ) and E ( A - A ) are the bond energies of the single bonds ( M - M ) and (A-A ) ,respectively ; E ( M - M ) is calculated from the heat of vaporization of the metal, A, and has the value 2A/12 for f.c.c. metals and 2A/8 for b.c.c. metals. The fraction Ci" of the ionic bond in the adsorption bond is expressed in terms of the dipole moment by the relation

C? = M/edyA where d y A is the sum of the atomic metal radius and the covalent bond radius of the adsorbed atom except for alkali metal atoms when d y A is replaced by the monovalent ionic radius. The dipole moment M is evaluated from the work function change observed during adsorption, viz., M = A1$/2?r300u for covalent adsorption, u being the number of dipoles per

122

R. V. CULVER A N D F. C. TOMPKINB

cm? of surface. A value of M for an almost bare surface is required, but as the experimentally determined work functions usually refer to a fully covered surface, it is necessary to disregard the possible effects of mutual depolarization a t high coverage and assume that M8-o = Me-1 . Finally for a homonuclear gas which chemisorbs dissociatively, -AH0 = 2E - E ( A - A )

Initial heats of adsorption have been calculated in this way for various systems including (1) Ba and Sr on W, (2) H2 on Ni, Fe, Ta, Rh, Cr, Cu, Co, and Pt, ( 3 ) O2 on W, Ni, and Fe, (4) N2 on W, Ta, and E'e and ( 5 ) CO on Fe and Ni. With the exception of the system Ni 0 2 , where oxidation may have occurred, there is fair agreement between calculated and experimental values of - AHo , as shown in Table XI. . The initial heat of adsorption of H 2 on a number of metals can be predicted (Eley, 129) with a fair degree of accuracy from the equation

+

-AH0 = H c

+ 23.06M2

(10)

which was based on Pauling's empirical relation (104) -AH0

=

Hc

+ 2 3 . 0 6 ( 2 ~-

~

4

)

~

Here z M and x4 are the respective electronegativities of thc metal and t)hc adsorbate atoms and the difference ( x M - z A )may bc approximated to the dipole moment M at 0 = 0. Trapnell (127)has extended these calculations to other adsorbates such as 0 2 , N2 , CO, and C2H4, but the agreement between experimental and calculated values of - AH0 is less satisfactory for a molecule such as C2Ha than for 02,owing to the uncertainty of the nature of the surface bonds. If, however, Equation (10) is applied t o the adsorption of alkali metals, it is found that the calculated values of -AH0 TABLE XI Initial Heats of Adaor lion Calculated from Bond Energies and Dipole Moments"

I

I System M-A

Dipole Dipole moment Length M(D) d ~ , A d.

mole

mole

Initinl heats

= E

mole

W-Be W-H w-0 Ni-CO 4

~ _ _ _ _ _ ~ _ ---~ 87.0 104.2 87.0 aa.7 iao.1 18.4 a.eo 64.4 0.212 0.778

0.610

1.67 1.m a.oi

64.4 64.4

103.4 ma/a

16.1

68.6

183.9 183.9 176.1

16.4 60.7 31.6

80.9

68.4

117.2 61.1

118.2 61.1

Higuchi I.. Rae, T., and Eyring, H., J . Am. Chsm. Soc. T9, 1330 (1967); ibid. ? 4969 I , (19666). Cham. Phus. za, 1808 (1966). Roberta, J. K.,Prw. Roy. Soc. (London) A l l , 446, 464 (1836). Beeak, O.,Aduancss in Calalums 2, 161 (1960)

* Moore, 0.E., and Alliaon, H.W., J

mole

_

83O 4.5c IW 3Kd

_

SURFACE POTENTIALS AND ADSORPTION PROCESS ON METALS

123

are too high, e.g., for the adsorption of Ba on W, -AH0 (calc.) is 4,280 kcal./mole, as opposed to a value of 83 kcal./mole for - AH0 (exptl.) (106, 107).Thus, the method appears to be limited to cases where the bonding is essentially covalent and the resulting dipole moment comparatively small. The procedure of Eyring, which has a quantum-mechanical basis is, however, equally applicable to both ionic and covalent adsorption.

B. THEVARIATION IN

THE

HEATOF ADSORPTION WITH COVERAGE

The change in the work function which accompanies adsorption on a metal surface has an effect on the heat of adsorption. In the formation of a dipole layer which is negatively charged outwards, the work done in transferring an electron from a point inside the metal to the region of the adsorbed atom is given by (eA+) e. v., as considered in Sec. 111. Furthermore, as the value of A+ increases with adsorption, the work of transferring electrons will increase correspondingly. Alternatively, if the double layer is positive outwards, as in cationic adsorption, eA+ is the work done in transferring an electron from a point outside the metal to a surface of diminishing electron affinity. Thus, the heat of adsorption-comprising the heat of binding, i.e., the initial heat - AH0 ,and the change in the work functiondecreases with coverage irrespective of the sign of the double charge layer. Accordingly, -AH

=

- A H o - eA+

and if - AHo is independent of coverage, 6(-AH)

=

-AHo+

=

2r~,,,OMe

AH = eA+

(for covalent adsorption)

(11)

where 6( - A H ) is the decrease in the differential heat of adsorption. De Boer (130)first drew attention to the contribution of the “workfunction effect” to the heat of chemisorption of alkali atoms on a metal surface. With Cs on W, for example, the heat of adsorption is described by the equation, - A H = -AH0 - eA+

=

-AHi - e l

+ e+ - eA+

which may be written in terms of the dipole moment by introducing the relation eA+ = 4rumOMe (for ion adsorption) as -AH

=

- AHi - e I

+ a$ - 4 ~ ~ , e M e

so that if - A H i , the heat of adsorption of the Cs ion, ( -e2/4d0), is constant and the dipole moment, M , does not vary during the adsorption process, the heat of adsorption, - A H , should decrease linearly with cover-

124

R. V. CULVER A N D F. C. TOMPKINS

age. Such a relationship is not observed experimentally, however, and the discrepancy is attributed to the discontinuous nature of the charge distribution of the surface dipoles and their mutual depolarixation. With regard to the former, de Boer has shown that if the dipole layer formed by the chemisorbed Cs ions consists of a double layer of discrete charges, then the potential gradient extends to the region outside the double layer (14, 180). As a result, Cs ions are adsorbed more strongly by a partly covered W surface than by a bare one and the heat of adsorption of the Cs ion increases with coverage. The mutual depolarixation of the dipoles becomes important at high coverage and leads to a decrease in the dipole moment. For several metal H2 systems, it has been found that the experimental heat of adsorption is a linear function of the surface coverage (24,131). This implies that for these systems the distribution of dipoles approximates to a continuous layer of charge and that Equation (11) correctly describes the change in the heat of adsorption when an electron is moved through the double charge layer. Originally Boudart (108) used the relation

+

6( - A H )

=

>4eA$

to account semiquantitatively for the observed decrease in the d8erenti:il heat of adsorption for the systems W Cs, W H2 ,W 0 2 , W N2, and Ni H2 in terms of the change in work function. This relation was derivcd for a double layer with a homogeneous charge distribution in which the binding electrons spent most of their time in the region midway between the bound atoms-a situation which has been criticized (16) on the grounds that the electrons must form part of the double layer. Further, the assumption of a continuous charge distribution for adsorbates other than H2 may not be justified. If the charge distribution is discrete, rather than continuous, the potential energy curves evaluated by Gomer (41) show that at low coverage the potential at the midpoint in the double layer is very much less than >4A+. In considering the magnitude of this work function effect Mignolet (16) has pointed out that in moving an electron work is done against both electrostatic and quantum mechanical forces and not against the electrostatic field alone as frequently assumed. For this reason, he prefers t o derive a relation between the decrease in the differential heat of adsorption 6( - A H ) and the change in the work function eat$ in accordance with a model for the formation of a covalent bond involving the excitation of an electron from the conduction band of the metal into a vacant adsorbate orbital. The electron shift reduces the height of the highest occupied level and gives rise to a double charge layer with a negative sign. Accordingly, the increase in the work function is given by

+

+

4 = AE/e

+

+

+

SURFACE POTENTIALS AND ADSORPTION PROCESS ON METALS

125

where A& is the decrease in energy attending an electron transfer, and it follows that there will be an increase in the excitation energy for the transfer of succeeding electrons. Then assuming that the decrease in the heat of adsorption 6( - A H ) may be entirely attributed to the reduction in the height of the highest occupied level, i.e., 6( - A H ) = A&, he obtains the expression 6( - A H )

=

eAq5

which is identical with Equation ( 11) derived from electrostatic considerations. An examination ( 1 6 ) of a few metal-gas systems for which reliable data are available, viz., W H2, Ni Hz , and Fe H2 has shown that there is reasonable agreement between 6( - A H ) referring to the difference in the differential heat of adsorption a t 8 = 0 and 8 = 1 and A4 corresponding to the change in work function, as disclosed by S.P. measurements, over the same range of coverage. It would appear, however, more satisfactory to restrict such investigations to a limited range of coverage, such as 0 = 0.2 t o e = 0.8, and so avoid the effect of surface heterogeneity at 8 2 0 and lateral interactions between adsorbed atoms at 8 2 1 on the heat of adsorption. The analysis of S.P. and heat of adsorption data has been extended by Higuchi et al. (106,107) to the systems Ni Hz , Ni 0 2 , W H2, and Hz . They used Equation (11) t o express the difference between the Fe initial heat of adsorption, -AH0 , and - A H , the heat of adsorption a t a coverage 8, in terms of the change in work function over the range of coverage 0 t o 8. Aq5 was calculated for various values of 0 on the assumption that a linear relation existed between the S.P. and the coverage, and while it has been shown that this is only approximately true (77) , the divergence from linearity is normally not serious. A comparison between the calculated and experimental plots of 6( - A H ) against 8 showed that the relation of 6( - A H ) to 8 was correctly described, although there was considerable deviation from the experimental 6( - A H ) data in the systems W H2 and W O2for coverages above 8 = 0.5. Figure 21a and b shows 6 ( - A H ) against 8 curves for the chemisorption of H2 on Ni and Fe, respectively. In Fig. 21a, 6 ( - A H ) values were calculated from the data of Eeeck ( 3 2 ) and Schuit and de Boer (131 ), and the value of Aq5 at 0 = 1 was taken as 0.33 v. ( 1 6 ) ; in Fig. 21b, the respective values of - A H and - AHo were selected from the data of Bagg and Tompkins (is,%'), - AH0 = 31 kcal./mole being obtained by extrapolating the adsorption heats from 0 = 0.2 to 8 = 0, and A+ a t 8 = 1 was taken as 0.43 v. (77). An inspection of Fig. 21 reveals that the agreement between the experimental and calculated data for 6 ( - A H ) is satisfactory in both cases; it is significant,

+

+

+

+

+

+

+

+

+

126

R. V. CULVER AND F. C. TOMPKINS

0

1.0

e

0

8

1.0

(b)

(a)

FIG.21. The decrease in the differential heat of adsorption with coverage (a) for Ni-H1 and (b) for Fe-H2

.

however, that the experimental values of 6( - A H ) are less than those calculated from the change in work function. In the system Ni Hz , de Boer (133)has recently offered an explanation for the difference between the calculated and the experimental heats of adsorption in terms of a model in which H atoms are chemisorbed on top of the Ni atoms-an arrangement which may account both for the negative S.P. (75) and the decrease in the electrical resistance of the metal film (114), as observed experimentally. The bonding is covalent, and the sharing of electrons between the metal and the adsorbate leads t o an array of n atoms per unit area containing m additional electrons ( m < n ) moving freely among the chemisorbed atoms; consequently the charge per atom is (m/n)e.An atom adsorbed on the surface has the probability m / n that it will take up an electron from the bulk metal, so that when an electron passes through the double layer (assumed homogeneous) at the metal surface, the decrease in the heat of adsorption is modified by the factor m/n; hence,

+

6( - A H ) = (m/n)eA+ Such a picture for the adsorption process leads to a linear decrease in the heat of adsorption with coverage and a value of 6( - A H ) essentially less than that computed from the relation 6( - A H ) = eA+.

C. ADSORPTION IN TERMS OF

SURFACE ELECTRON GAS While the decrease in the heat of chemisorption has been attributed t o a change in the electron distribution a t the metal surface, it is doubtful A

SURFACE POTENTIALS AND ADSORPTION PROCESS ON METALS

127

whether the transfer of electrons with consequent changes in the Fermi level would give rise t o the observed values of 6( - A H ) in covalent adsorption. An alternative mechanism has been proposed by Temkin (134). He suggests the presence of a two-dimensional surface electron gas which takes part in the chemisorption process, and derives an equation for changes in the kinetic energy of the electrons, viz.,

- AH

=

h2~,e/4~m

(12)

whcre h is Planck’s constant, m is the mass of the electron, and a,e is the number of adsorbed atoms per cm.’ of surface. Usually the calculated values of - A H are too large, so that it is necessary to replace m by an “effective mass.” There are few quantitative data available for testing the equation. Apart from the work of Federova and Frumkin ( 1 3 5 ) , which showed that the heat of solution of hydrogen in the p phase of the Pd H system (Pd containing GO at. % H ) was a function of the concentration of the dissolved hydrogen, other data in the literature point t o the nondependence of - AH with the concentration. The heat of solution of hydrogen in @ Ti (136), for example, does not fall with an increasing concentration of dissolved hydrogen, and it may be argued in this case that as the heat of solution of hydrogen in the metal is almost constant, it is unlikely that electronic interaction between chemisorbed atoms and surface electrons would produce a substantial change in - A H . Hence, a t the present time it is difficult t o accept the validity of Equation (12) ; should it be so, then work-function changes would be related to changes in the energy levels of the electron gas, and it follows that the concepts of dipole moments and surface potentials would need to be revised (133).

+

XII. Conclusions The tabulated S.P. values show that there is a need for more precise experimental measurements, employing modern high-vacuum techniques and the use of more refined methods of preparing clean metal surfaces, e.g., ion bombardment with subsequent examination of the surface by electron diffraction. However, the results obtained by a variety of measuring techniques, including the F.E.M., are generally consistent with regard t o the sign of the S.P. and the approximate magnitude. An advance from an experimental viewpoint has been made by Eisinger ( 7 8 ) , who used the “flash filament” method of Becker (137) to determine the coverage (molecules per cm.2) of a monocrystalline W ribbon with its surface normal in the 11131 direction and measured the work function change photoelectrically. Thus, he was able t o directly relate the change in S.P. t o the density of metal atoms in a particular crystal plane. The S.P. values cannot be generally interpreted in terms of a simple

128

R. V. CULVER AND F. C. TOMPKINS

model for the adsorption bond. For ionic adsorption the work fiiiictioii change is usually attributed t o the modification of the surface double layer by the deposition of dipoles. For covalent adsorption, however, this mechanism may not apply and consequently the change in work function may not be correctly expressed by the relation A4 = 2ru,OM. Clearly, the complete interpretation of the work function change for simple gases and radicals must await the results of a more critical analysis of the bonding process at a metal surface. Turning now t o the applications considered in Secs. IX, X, and XI, we note that the activation energies of desorption and migration are conveniently measured by S.P. methods, while the results obtained for the adsorption of NZO on Pt show that there is considerable scope for the application of work-function measurements in investigating catalytic renctions at metal surfaces.

REFERENCES 1 . Lennard Jones, J. E., Trans. Faraday SOC.a8, 333 (1932). 2 . Dowden, D. A., J . Chem. SOC.p. 242 (1960).

3. Richardson, 0. W., and Robertson, F. S., Phil. Mag. [7] 43, 162 (1922).

4. Langmuir, I., and Kingdon, K. H., Phys. Rev. 21, 380 (1923).

6. Bosworth, R . C. L., J. Proc. Roy. SOC.N . S. Wales 79, 63, 166, 190 (1945). 6 . Herring, C., and Nichols. M. H., Revs. Modern Phys. 21, 185 (1949). 7. Chalmers, J . A., Phil. Mag. [7) 99, 399, 416, 496, 506, 599, 608 (1942). 8. Hulburt, H. M., in “Catalysis” (1’. H. Emmett, ed.), Vol. 11, p. 200. Reinhold, New York, 1961. 9. Parsons, R., i n “Modern Aspects of Electrochemistry’’ (J. O’M HockriN, cd.), Chapter 111. Butterworths, London, 1954. 10. Lange, E., and Miscenko, K. P., 2.physik. Chem. (Leipzig) A149, 1 (1!)30). 1 1 . Bardeen, J., Phys. Rev. 49, 663 (1936); Oldekop, W., arid Sunter, P.,%. Z’hysik 136. 534 (1964). 1%. Lewis, T. J., Proc. Phys. SOC.(London) B67, 187 (1954). 13. Becker, J. A,, Revs. Modern Phys. 7 , 95 (1935). 1.6. de Boer, J. H., and Veenemans, C. F., Physica 1, 960 (1934). 16. Langmuir, I., Chem. Revs. 18, 147 (1933). 16. Mignolet, J. C. l’., Bull. soc. chim. Belg. 64, 126 (1955). 17. Coulson, C. A., “Electricity.” Oliver, London, 1951. 18. Johnson, R . P., and Shockley, W., Phys. Rev. 49, 436 (1936). f9. Muller, E. W., 2.Physik 106, 541 (1937). 20. Porter, A. S., and Tompkins, F. C., PTOC. Roy. SOC.(London) A217, 544 (1953). 21. Becker, J. A., Advances i n Catalysis 8 , 135 (1957). 2%.Alpert, D., J. Appl. Phys. 24, 860 (1953). 23. Thomas, L. B., and Schofield, E. B., J. Chem. Phys. 2S, 861 (1955). 24. Roberts, J . K., Proc. Roy. SOC.(London) Al62, 446, 464 (1935). 26. Allen, J. A., Revs. Pure and Appl. Chem. (Australia) 4, 133 (1954). $6. de Boer, J. H., Koninkl. Ned. Akad. Wetenschap. Proc. 49, 1103 (1946). BY. Beeck, O . , Smith, A. E., and Wheeler, A,, Proc. Roy. SOC.(London) A177, 62 (1940).

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28. de Boer, J. H., and Kraak, H. H., Rec. trav. chim. 66, 941 (1936). 29. Shishakov, N. A,, J . Exptl. Theoret. Phys. U.S.S.R. 22, 241 (1952). 30. Mignolet, J. C. P., Rec. trav. chim. 74, 685 (1955). 91. Wheeler, A., i n “Structure and Properties of Solid Surfaces,” (R. Gomer and C. S. Smith, eds.), p. 439. Univ. of Chicago Press, Chicago, 1952. 32. Beeck, O., Advances i n Catalysis 2 , 151 (1950). 33. Hickmott, T. W., Advances i n Catalysis 9, 167 (1957). 34. Farnsworth, H. E., Schlier, R. E., George, T. H., and Burger, R. M., J . Appl. Phys. 26, 252 (1955). 36. Dillon, J. A , , and Farnsworth, H. E., Phys. Rev. 99, 1643 (1955). 36. Schlier, R. E., and Farnsworth, H. E., i n “Semiconductor Surface Physics” (R. H. Kingston, ed.), p. 5. Univ. of Pennsylvania Press, Philadelphia, 1957. 37. Autler, S. H., and McWhorter, A. L., i n “Semiconductor Surface Physics” (R. H. Kingston, ed.), p. 47. Univ. of Pennsylvania Press, Philadelphia, 1957. 38. Bridgman, P. W., “The Thermodynamics of Electrical Phenomena in Metals.” Macmillan, New York, 1934. 39. Reimann, A. L., “Thermionic Emission,” Chapter 111. Chapman & Hall, London, 1934. 40. Fowler, R. H., and Nordheim, L. W., Proc. Roy. SOC.(London) A119, 173 (1928). 41. Gomer, R., J . Chem. Phys. 21, 1869 (1953). 42. Fowler, R . H., Phys. Rev. 38, 45 (1931). 43. Suhrmann, R . , and Sachtler, W. M. H., Proc. Intern. Symposium on Reactivity of Solids, Gothenburg, 1962, p. 601 (1954). 44. Oatley, C. W., Proc. Roy. SOC.(London) A166, 218 (1936); Proc. Phys. SOC. (London) 61, 318 (1939). 46. Hull, A. W., P h y . Rev. 18, 31 (1921). 46. Weissler, G. L., and Wilson, T. N . , J . Appl. Phys. 24, 472 (1953). 47. Mignolet, J. C. P., Discussions Faraday SOC.8 , 326 (1950). 48. Zisman, W. A., Rev. Sci. Znstr. 3, 367 (1932). 49. Gysae, B., and Wagener, S., Z. tech. Physik 19, 264 (1938); 2. Physik 116, 296 (1940). 60. Taylor, J. B., and Langmuir, I., Phys. Rev. 40, 463 (1932); 44, 423 (1933). 61. Becker, J. A., Phys. Rev. 28, 341 (1926). 62. Becker, J. A , , Phys. Rev. 33, 1082 (1929); Trans. A m . Electrochem. SOC.66, 155 (1929). 63. Brattain, W. H., and Becker, J. A., Phys. Rev. 43, 428 (1933). 64. Moore, G. E., and Allison, H. W., J . Chem. Phys. 23, 1609 (1955). 66. Becker, J. A., Trans. Faraday SOC.28, 148 (1932). 66. Kingdon, K . H., Phys. Rev. 24, 510 (1924). 67. Reimann, A. L., Phil. Mag. (71 20, 594 (1935). 68. Klein, R., J . Chem. Phys. 21, 1177 (1953). 69. Gomer, R., and Hulm, J. R., J . Chem. Phys. 27, 1363 (1957). 60. Becker, J. A., and Brandes, R. G., J . Chem. Phys. 23, 1323 (1955). 6 f . Gomer, R . , Wortman, R., and Lundy, R., J . Chem. Phys. 26, 1147 (1957). 62. Muller, E. W., Ergeb. exakt. Naturwiss. 27, 290 (1953). 69. Wortman, R., Gomer, R., and Lundy, R., J . Chem. Phys. 27, 1099 (1957). 64. Ives, H. E., and Olphin, A. R., Phys. Rev. 34, 117 (1929). 66. Bosworth, R. C . L., Proc. Roy. SOC.(London) A160, 58 (1935); A164, 112 (1936). 66. Bosworth, R . C. L., Trans. Faraday SOC.32, 1369 (1936). 67. Mayer, H., Ann. Physik 33, 419 (1938). 68. Suhrmann, R., Advances in Catalysis 7, 303 (1955).

R. V. CULYER AND F. C. TOMPKINS

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69. Suhrmann, R., and Csech, H., Z. physik. Chem. (Leiptig) B28, 215 (1935). 70. Suhrmann, R., and Sachtler, W. M. H., Arbeitstagung Festkorperphysik,

Dresden, 1952. 71. Suhrmann, R., J. chim. phys. 64, 15 (1957). 78. Suhrmann, R., Z. Elektrochem. 60, 804 (1956).

73. Mignolet, J. C. P., Discussions Faraday SOC.8 , 105 (1950). 74. Sachtler, W.M. H., and Dorgelo, G. J. H., J . chim. phys. 64, 27 (1957). 76. Sachtler, W.M. H., J. Chem. Phys. 26, 751 (1956). 76. Baker, M. McD., and Rideal, E. K., Nature 174, 1185 (1954). 77. Culver, R. V., Pritchard, J., and Tompkins, F. C., i n “Surface Activity” (J. H. Schulman, ed.), Vol. 2,p. 243. Academic Press, New York, 1958. 78. Eisinger, J., J. Chem. Phys. 27, 1206 (1957). 79. Eisinger, J., J . Chem. Phys. 28, 165 (1957). 80. von Duhn, J. H., Ann. Physik 43, 37 (1943). 81. Ogawa, I., Doke, T., and Nakada, I., J. Appl. Phys. (Japan) 21, 223 (1952). 88. Giner, J., and Lange, E., Nalurwiss. 40, 506 (1953). 83. Hackerman, N., and [Lee,] E. H., J . Phys. Chem. 69, 900 (1955). 84. Mignolet, J. C . P., J. chim. phys. 47, 172 (1950). 86. Mignolet, J. C. P., J . Chem. Phys. 20, 341 (1952). 86. Mignolet, J. C. P., J. Chem. Phys. 21, 1298 (1953). 87. Mulliken, R.S . , J . A m . Chem. SOC.71, 600 (1960);74, 811 (1952). 88. Bloyaert, F.,D’Or, L., and Mignolet, J. C. P., J. chim. phys. 64, 53 (1957). 89. Mignolet, J. C. P., J . chim. phys. 64, 19 (1957). 90. Handler, P., i n “Semiconductor Surface Physics” (R. H. Kingston, ed.), p. 23. Univ. of Pennsylvania Press, Philadelphia, 1957. 91. Brattain, W. H., and Bardeen, J., Bell System Tech. J . 32, 1 (1953). 98. Pratt, G.W., and Kolm, H. H., in “Semiconductor Surface Physics” (R. 1%. Kingston, ed.), p. 297. Univ. of Pennsylvania Press, Philadelphia, 1957. 93. Langmuir, I., and Kingdon, K. H., Phys. Rev. 34, 129 (1929). 94. Reimann, A. L., Proc. Roy. Soc. (London) A163, 499 (1937). 96. Bosworth, R.C.‘L., and Rideal, E. K., PTOC. Roy. SOC.(London) A162, 1 (1937). 96. Bosworth, R. C. L., and Rideal, E. K., Physica 4, 925 (1937). 97. Bosworth, R. C . L., Proc. Cambridge Phil. SOC.59, 394 (1937). 98. Bosworth, R. C. L., Trans. Faraday SOC.36, 397 (1939). 99. Copley, M. J., and Spence, R. W., J . A m . Chem. SOC.61, 3027 (1939). 100. Eley, D. D., and Rideal, E. K., Proc. Roy. SOC.(London) A178, 429 (1941). 101. Burshtein, R., J . chim. phys. 64, 106 (1957). 108. Bourion, R.,J. phys. radium 12, 930 (1951). 103. Mignolet, J. C. P., i n “Chemisorption” (W. E. Garner, ed.), p. 118.Butterworths London, 1957. 104. Pauling, L., “The Nature of the Chemical Bond.” Oxford Univ. Press, London and New York, 1948. 106. Trapnell, B. M. W., “Chemisorption,” Chapter VII. Butterworths, London, 1955. 106. Higuchi, I., Ree, T., and Eyring, H., J. A m . Chem. SOC.79, 1330 (1957). 107. Higuchi, I., Ree, T., and Eyring, H., J. Am. Chem. Soc. 7 7 , 4969 (1955). 108. Boudart, M., J . A m . Chem. SOC.74, 3556 (1952). 109. Eischens, R . P., Pliskin, W.A., and Francis, 8. A., J . Chem. Phys. 22,1786 (1954). 110. Eischens, R . P., Francis, 8. A., and Pliskin, W. A., J. Phys. Chem. 60,194 (1956). 111. Broeder, J. J., van Reijen, L. L., Sachtler, W. M. H., and Schuit, G. C. A., Z. Elektrochem. 60, 838 (1956). 118. Mulliken, R. S., J . Chem. Phys. 2 , 782 (1934).

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113. Mignolet, J. C. P., Bull. SOC. chim. Belg. 66, 837 (1956). If.&. Suhrmann, R.,and Schulr, K. Z., 2. physik. Chem. (Frankfurt) [N.F.] 1, 69 (1954. 116. Moore, L. E., and Selwood, P. W., J . Am. Chem. SOC.78, 697 (1956). 116. Suhrmann, R.,i n “Chemisorption” (W. E. Garner ed.), p. 108. Butterworths, London, 1957. 117. de Boer, J. H., i n “Chemisorption” (W. E. Garner, ed.), p. 171.Butterworths, London, 1957. 118. Johnson, M., and Vick, F. A., Proc. Roy. SOC.(London) A161, 308 (1935). 119. Bosworth, R. C. L., Proc. Roy. SOC.(London) A162, 32 (1937). 180. Eley, D.D., Trans. Faraday SOC.49, 643 (1953). 181. Elovich, S.Y., and Zhabrova, G. M., J. Phys. Chem. (U.S.S.R.) 13, 1761, 1775 (1939). 188. Langmuir, I., J. Am. Chem. Soc. 64, 2798 (1932). 183. Gomer, R.,J. Chem. Phys. 28, 168 (1958). 1.84. Mignolet, J. C. P., Rec. Irao. chim. 74, 701 (1955). f86. Rideal, E. K., Proc. Cambridge Phil. Soc. 36, 130 (1939). 186. Bonhoeffer, K.F., and Farkas, A., Z. physik. Chem. (Leipzig)Bl2, 231 (1931). f87. Trapnell, B. M. W., i n “Chemisorption” (W. E. Garner, ed.), Chapter VI. Butterworths, London, 1955. 188. Ree, T., and Muroyama, N., PTOC. Imp. Acad. Japan 20.93 (1944);Chem. Abstr. 43, 5240 (1949). 189. Eley, D . D., Discussions Faraday SOC.8, 34 (1950). 130. de Boer, J . H., “Electron Emission and Absorption Phenomena.” Cambridge Univ. Press, London and New York, 1935. 131. Schuit, G. C. A., and de Boer, N. H., Rec. trau. chim. 72, 909 (1953). 138. Bagg, J., and Tompkins, F. C., Trans. Faraday SOC.61, 1071 (1955). 133. de Boer, J. H., i n “Chemisorption” (W. E. Garner, ed.), p. 27. Butterworths, London, 1957. 134. Temkin, M. I., “Symposium on Problems of Chemical Kinetics, Catalysis, and Reactivity.” Akad. Nauk, S.S.S.R., 1955. 136. Federova, A. J., and Frumkin, A. N., J. Phys. Chem. (U.S.S.R.) 27, 247 (1953). 136. McQiiillan, A. D., Proc. Roy. SOC.(London)A204, 309 (1950). 137. Becker, J. A., and Hartman, C. D., J . Phys. Chem. 67, 157 (1953).

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Gas Reactions of Carbon P. L. WALKER, JR., FRANK RUSINKO, JR., AND L. G. AUSTIN Fuel Technology Department, The Pennsylvania State University, University Park, Pennsylvania Page

I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 11. Thermodynamics of Gas-Carbon Reactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 A. Heats of Reaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 B. Equilibrium Constants and Product-Reactant Ratios. . . . . . . . . . . . . . . . 136 111. Review of General Mechanisms for the Gas-Carbon Reactions. . . . . . . . . . . 138 A. General Remarks.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 B. Mechanisms.. . . . . . . . . . . . . . . . . ............. IV. Review of Kinetics for the Gas-C A. Orders of Reactions. . . . . . . . . . 156 B. Activation Energies of Reactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Relative Rates of Gas-Carbon Reactions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 V . Role of M:tss Transport in Chs-CtLrbon Reactions, . . . . . . . . . . . . . . . . . . . . . . 164 A. General Remarks.. . . . . . . . . . . . . . ................................. 161 B. Three Temperature Zones in (;a rliori Reactions. . . . . . . . . . . . . . . . . . 165 C. General Discussion of Zone I1 for the Gas-Carbon Rc?actions... . . . . . . . 167 D. Comprehensive Rate l 1. At low temperatures, the production of carbon monoxide is small and the first inequality is satisfied. At high carbon dioxide pressures, the second inequality is satisfied. On the other hand, it is seen from Equation (2) that the carbon-carbon dioxide reaction will be first order when k2pc0 where dIIis the value of 4 for the start of Zone I1 and is 2, 4,or 6 for a plane, cylinder, or sphere, respectively. I n all cases, the specimens approach uniform internal reaction, that is chemical control, when 4 is I#Q~. The rate of reaction per unit external surface area in Zone I1 is given by

C R d K D Z or C I t d i i T i , irrespective of the geometric shape of the sample.

170

P. L. WALKER, JR., FRANK RUSINKO, JR., AND L. G . AUSTIN

TABLE IV Criteria for the Prediction of Gas-Carbon Reactions Entering Zone Varioue Geometrically Shaped Samples

Geometric shape

4

for

Rate of reaction v for 4 per unit area of > A 4'1 exterior surface Rate of reaction per unit area of exterior surface when 4 > concentration

1

sample

I

Plane: thickness R Cylinder: radius R Sphere: radius R

2. The transition region between Zones I and I1 will occur over a temperature range sufficient to increase 4 by ca. 20. Since 4 = RZ/k,/Derrand

where n = 1 for a plane = 2 for a

cylinder

= 3 for a sphere

Thus, 4'7 a dw/dt, and since over the transition region t#~ increases by ca. 20 while 7 goes from 1 to the over-all reaction rate, d w l d t , must increase by ca. 200 over the transition range. This implies, as discussed by Weisz and Prater (IOS),that the transition region between Zones I and I1 can cover a considerable temperature range. 3. Equation (25) can be used to determine whether a reaction is proceeding in Zone I or 11. Since Zone I is closely approximated when4 < 0.3 and 7 is close t o 1, if 4 ' is ~ $-in. i.d. Carbon samples 2 in. long by W in. in diameter with a %-in. hole through their center (the rods weighing ca. 8.8 g.) were suspended in the reactor by connecting them through a %-in. mullite rod to a balance. Reaction at the top and bottom of the carbon rods was minimized by >$in. diameter mullite plates. Following reaction to ca. 11% burnoff (1 g.) at temperatures of 925, 1O00, 1200, and 1305", density and surface area profile data were determined. The area data were determined in a conventional

GAS REACTIONS OF CARBON

179

B.E.T. apparatus ( l a l ) ,using nitrogen as the adsorbate at liquid nitrogen temperatures. Reactivity data were also determined at a number of other temperatures between 900 and 1350°, but subsequent profile data are lacking. The experimental results obtained from the measurement of surface area remaining after each lathe cut can be plotted as cumulative surface area against radius. If S,' is the surface area per cm. of radial distance at radius T , the cumulative surface area is given by

S, =

\

72

S,'dr

(43)

TI

If S, is the specific surface area at T in cm.2/cc., S,' = S , ( r / R ) A , where A is the external surface area of the rod (excluding the ends) in cm.2 and R is the external radius. Therefore,

or

Thus, the specific surface area at any radius in the rod can be estimated from the dimensions of the rod and the slopes of the cumulative surface area curve. In a similar manner, the porosity at any radius in the rod can be estimated from the corresponding slopes of the curve of cumulative weight vs. radius by the equation Pr =

R

where pr is the apparent density of the carbon at T and w eis the cumulative weight. Then

where 8, is the porosity of the carbon at r and p t is the true density of carbon, which, in this case, equals 2.268 g./cc.

PROFILE DATATO DETERMINE RATE OF REACTION B. USE OF DENSITY AT ANY RADIUS IN THE CARBON ROD The most accurate way t o obtain the rate of reaction at any radius in the rod would be to react a series of identical rods under identical conditions to different burnoffs, followed by the clitting of each rod as described. The

180

P. L. WALKER, JR., FRANK RUSINKO, JR., AND L. Q. AUSTIN

1

1.0 I

porosity a t which particles blow off

at

i

c

I

v)

0

a

8

unreacted parosi t y

0

-!AR

0

I

1

R2

RI

RADIUS WITHIN RODFIG.10. Illustration of the porosity profile through a rod at two times, t~ and t 2 , when reaction is occurring at a constant rate in temperature Zone 11.

rate of reaction, ( d n l d t ) , , at any radius could then be estimated from the changes in porosity with time. This would be a tedious process. In this study, ( d n l d l ) , is determined more simply and probably about as accuratcly by an alternative method. At sufficiently high temperatures, the reaction in t,he rod will proceed so fast that the carbon dioxide concentration will be zero a t some point in the rod (Zone 11).After an initial burnoff, the porosity a t the surface will reach a value at which the carbon no longer has sufficient structural strength to remain attached t o the rod. Carbon then will be lost by particles blowing off in the reacting gas stream. When this point is reached, it is obvious by intuition that the rate of reaction will be constant for a small decrease in external radius; and the profile functions through the rod will be duplicated after a time interval At but moved in a radius AR (equilibrium burning). The condition of the rod a t two different times is illustrated in Fig. 10. Clearly, the over-all rate of reaction per cm.2 of external surface b is given by

b = -AR At

pu

(48)

where pu is the apparent density of the unreacted carbon and b is constant for a small change in external surface area. Considering I cm.' of e x t r r r d rod surface,

but

Therefore,

QAS REACTIONS OF CARBON

181

Determination of ( d n l d t ) , is possible, since ( d 0 / d r ) , can be found from the slope of the 0 us. r plot and b can be found from the experimental reactivity curve. It should be noted that (&/&), is the rate of reaction per cm. thickness of section, whereas the actual rate of reaction in an infinitesimal section of thickness dr is ( d n l d t ) , dr. From profile data t o be discussed shortly, it was found that Zone I1 was approximated only at reaction temperatures of 1305" and higher. The overall rate of reaction curve for this temperature is given in Fig. 11. If it is assumed that the abrupt change in reaction rate after 4-min. reaction time occurs at the onset of equilibrium burning, the measured decrease in external radius of the rod can be assumed to have occurred between 4 and 8 min., and b can be calculated. The value of b is found to agree well with the rate calculated from Fig. 11. It is of interest to note that several workers (99, 116) have assumed AR/At to represent the rate of reaction of a carbon specimen only when the reaction is proceeding entirely on the external surface. The above reasoning shows that AR/At can be a constant and represent the over-all rate of reaction when the reaction is occurring internally and the utilized surface area is far greater than the external surface area. Graham and co-workers (116), studying the carbon-steam reaction under high-velocity conditions,

REACTION TIME, minutes

FIG. 11. Plot of weight loss vs. time for reaction of spectroscopic carbon rod with carbon dioxide at 1305" (Zone 11) to 11% burnoff.

182

P. L. WALKER, JR., FRANK RUSINKO, JR., AND L. G. AUSTIN

I-&+

REACTION TIME-

FIG.12. Typical plot of weight loss us. time for reaction of spectroscopic carbon rod with carbon dioxide at temperatures below Zone 11.

determine reaction rates from the change in external sample radius with time, using Equation (48). On the assumption that Equation (48) holds only when reaction takes place solely on the exterior surface, they calculate reaction probabilities, which they acknowledge to be about a thousandfold too high on the basis of other workers’ findings. Since they report that their reactant concentration at the exterior surface of the carbon does not go to zero but only to ca. C,/2, there is no doubt that some internal reaction is occurring. Using the formulas developed in Sec. V to estimate the degree of internal reaction and the true surface area undergoing reaction, reaction probabilities some thousandfold lower are calculated, in agreement with accepted values. At temperatures below Zone 11, equilibrium burning (as illustrated in Fig. 10) obviously is not obtained. It is found, however, that after some burnoff (usually less than 5 %) the reaction rate is essentially constant over a wide burnoff range. A typical reactivity plot is shown in Fig. 12. If it is assumed that the porosity measured at the close of the run is derived from uniform burning over time At, then

where Aer is the increase in porosity above the unreacted porosity at r . This estimation can only be used where the rate of reaction has been constant over most of the reaction time.

C. MASSTRANSPORT AND REACTANT CONCENTRATION PROFILES THROUGH THE ROD From a knowledge of the rates of reaction through the rod and the effective diffusion coefficient at any radius, it is possible t o determine the con-

GAS REACTIONS OF CARBON

183

centration profile through the rod without making any assumptions regarding the order of the reaction or the surface areas taking part in the reaction. Three limiting cases are possible depending on the manner in which mass transport is occurring through the rod. Equations for the three cases for the carbon-carbon dioxide reaction are derived in the Appendix and presented below. 1. Knudsen diffusion only is occurring (Case 1 ) :

where

At high rates of reaction, the reactant concentration in the center of the specimen, Co , approaches zero closely. 2. Bulk diffusion occurring but pores too fine to allow Poiseuille flow (Case 2) :

where Co/CR = L, p = C R

+ CR’ in g. of carbon per cc. of gas, and

[see Appendix for definition of (D:ff)r].CR‘ is the concentration of carbon monoxide at the surface. When the reaction is not in the stagnant filmcontrolled zone, C R = p ; and a t sufficiently high reaction rates, L ‘v 0. Therefore, Equation (53) can be simplified t o

cr= 2CR(1 -

e-F(‘)’CR)

(54)

3. Bulk diffusion occurring with a maximum of Poiseuille flow under conditions where Co ‘v 0 and p = C R (Case 3 ) :

Cr = C R ( eF ( r ) / C R - 1 ) where

(55)

184

P. L. WALKER, JR., FRANK RUSINKO, JR., AND L. Q. AUSTIN

D. DISCUSSION OF EXPERIMENTAL RESULTS 1. Density and Area Projiles. Figure 13 presents porosity profiles for the original carbon rod and for the carbon rods after reaction to ca. 11% burnoff at four different temperatures. The samples could only be cut down to a radius of ca. 0.35 cm. Attempts a t cutting to a smaller radius resulted in breaking through the thin carbon wall. The porosity point a t ca. 0.25 cni. represents the mean porosity of the carbon remaining after the last cut. At 1305", reaction occurred a t a considerable penetration into the rod, even though equilibrium burning was obtained. Reaction was effectively zero 0

.

6

as0.64-

0.62-

-

0.60

0.50-

A A

- UNAEACTED

- 9 2 5 * C. 0 - 1000 0 -1200 0 - 1305

I, 0

III

4

PIG.13. Porosity profiles through spectroscopic carbon rods before and after ra. 11% burnoff at different temperatures.

~

GAS REACTIONS OF CARBON

185

towards the center of the rod. Extrapolation indicates that the porosity a t the external surface is ca. 0.7 to 0.8. Since the external radius was decreased significantly during reaction, this suggests that the maximum porosity reached a t the surface before carbon particles dropped from the rod ranged from 0.7 to 0.8. In this experiment, carbon deposits were found in the top of the reaction tube. Apparently only about 70 % of the total weight loss a t this temperature was a direct result of carbon gasification. At 1200", no decrease in external radius occurred, with the surface porosity reaching a value of only 0.56. At this temperature, there wasa significant increase in porosity even near the center hole in the rod; consequently, it may be assumed that the carbon dioxide concentration was not zero in this part of the rod. Therefore, reaction was in the transition region between Zones I and 11. The reaction should be in Zone I1 when 4'7 = (R/CRD,rf)dw/dt> 4, as previously discussed. Since R is ca. 0.48 cm., and a t 1200", C Ris 1 X lo-' g. of carbon per cc., dw/dt is 0.22 X lo-' g. of carbon/min./cm.' and the mean Deff (as discussed shortly) is ca. 0.1 cm.'/sec., ~ + ~=q 1.7. Thus, the reaction should be near, but not in, Zone 11, in agreement with the interpretation of the porosity profile. It is seen that at 1000" the reaction is much more uniform through the rod but is still not in the chemical control zone. At this low rate of reaction, it appears that carbon dioxide is diffusing sufficiently rapidly between the inner wall of the carbon rod and the ceramic support rod to maintain : ~ n apprcciable concentration of reactant at the inner exposed surface of the rod. As expected, the minimum porosity (smallest amount of reaction) is found about half-way between the inner and outer radius, that is, at 0.4-cm. radius. Even at 925", the reaction is not uniform through the rod. This is difficult t o explain because the criterion for chemical control indicates that for the reaction rate at this temperature, the reaction should be well within Zone I. It can hardly be ascribed to a temperature gradient within the rod, since heat-transfer calculations show that the gradient through the rod t o supply the necessary heat of reaction at this low reaction rate is negligible ( 8 5 ) .Furthermore, since heat is being supplied to the sample from the outside, a minimum in temperature at an intermediate radius ( t o explain the minimum in reaction rate at a radius of ca. 0.4 cm.) is not conceivable. Possibily, the assumption of a complete interconnection of the pores within carbon rods is not correct. If the interior of the carbon rod was being supplied with reactant gas through both large and small pores which are not greatly interconnected, the nonuniformity of the profile a t 925" could be caused by the reaction still being in Zone I1 in the small pore system. The experimental Deff used to estimate the reaction zone would be determined almost entirely by diffusion through the large pores in the system and would

186

P. L. WALKER, JR., FRANK RUSINKO, JR., AND L. G. AUSTIN

be considerably too high to be used t o calculate the temperature zone operative for the small pore system. If it is postulated that the gas-carrying pore system within the rod behaves as a series of pores with effective diffusion radii ranging over a complete distribution from small to large, with effective diffusion coefficients for the smallest radii group of diffusing pores being, perhaps, one-hundredth of that for the largest, then the nonuniform porosity found at low rates of reaction is clearly explained. Much of the work described in the following pages would need to be recalculated using distributions of surface area and porosity with diffusion coefficients and integrating the effects of the systems. It should be emphasized, how-

0 1 0.2 int rrna I radius

I

0.3

I

0.4 RADIUS, cm.

I

0.5

I

0.6 external radius

FIG.14. Specific surface area profiles through spectroscopic carbon rods before and after ca. 11% burnoff at different temperatures.

GAS REACTIONS OF CARBON

187

ever, that it is difficult on the basis of our present understanding of the physical structure of carbon rods (106) to envision anything but an interconnected pore system. Figure 14 presents specific surface area profiles on the same carbon rods on which porosity profile data were determined. Aa expected, the specific surface areas of the samples reacted at 1305 and 1200" decrease markedly as the radius decreases. For the rod reacted a t 1305", it is seen that a negligible increase in porosity at the internal radius results in a 60% increase in specific surface area at the same radius. This can be attributed to a significant amount of closed pore volume being opened up at small burnoffs (122, 123). The additional volume is negligible, but the additional surface area provided by the micropores is comparatively large. Again, looking at the profile for the rod reacted at 1305", it is seen that the specific surface area goes through a maximum at a radius of cu. 0.5 cm. This is in line with the findings of Walker and Raats (106) and Wicke (31) that the specific surface area goes through a maximum as a function of burnoff or sample porosity. The area profiles for the rods reacted at 925 and 1000"are, in general, as expected. They show relatively little variation in area with radius. By cross-plotting the data in Figs. 13 and 14,the relation between the specific surface area and the porosity of the carbon rods after reaction at different temperatures can be presented, as in Fig. 15. It is seen that the surface area developed in the rods is not only a function of the porosity developed but also a function of the reaction temperature. The development

POROSITY,

FIQ.15. Relation between specific surface area and porosity for spectroscopic carbon rods after ca. 11% burnoff at different temperatures.

188

P. L. WALKER, JR., FRANK RUSINKO, JR., AND L. G. AUSTIN

01 0.3

I

0.4

I 0.5 POROSITY,

I 0.6

g,

(

7

FIQ.16. Variation of effective diffusion coefficient of carbon dioxide through carbon monoxide at N.T.P. with porosity of spectrosropic rarbon rods. PoroHit y developed by reaction with carbon dioxide at 950".

of an increasing surface area after constant burnoff as the reaction temperature is increased in the range of about 900 to 1200"has been previously discussed (106,124). It has been shown that variation in the over-all specific surface area developed in rods after reaction at different temperatures cannot be attributed only t o variations in porosity, as again shown in Fig. 15. 2. Variation of Doffwith Porosity of Carbon Rods. Before being able to calculate reactant concentrations through the rods at different reaction temperatures, it was necessary to determine experimentally values for Dell in the rods as a function of porosity. It has not been established that Dell is only a function of porosity for a given carbon material and independent of the temperature a t which this porosity is produced, but for simplicity this has been assumed t o be the case. Carbon rods % in. in diameter and in. long were cut from the original rods (the axis of the small rods being perpendicular to the axis of the original rods, since Detf perpendicular to the axis is the value desired) and reacted at 950" to various degrees of burnoff. The samples were then mounted in the diffusion apparatus described by Weisz and Prater (103)and Defffor hydrogen through nitrogen were determined at room temperature.* Deff values for three samples a t each burnoff were determined, and the values agreed within f 3 % at burn-

* The writers are indebted to P. B. Weisz of the Socony-Mobil Laboratories for determining the D.,r data.

GAS REACTIONS OF CARBON

0

0.1

0.3

0.2

0.4

(POROSITY I*

FIG.17. Relation between effective diffusion coefficient of carbon dioxide through carbon monoxide at N.T.P. and square of porosity for spectroscopic carbon rods.

offs below 33%. At higher burnoffs, the agreement between values was within *lo%. The diffusion coefficients, corrected t o carbon dioxide through carbon monoxide by multiplying by m 4 , are presented in Fig. 16 as a function of porosity. At porosities greater than 65 %, the pellets become too fragile t o handle. Contrary t o expectations, it is found that initial, small amounts of burnoff do not greatly increase Deft.This indicates that the marked increase in surface area for small amounts of burnoff occurs primarily by unblocking of pores which are not part of the main system of macropores through which the majority of diffusion is occurring. Apart from the data a t very low burnoffs, it is found that Defris directly proportional t o the square of the porosity, as shown in Pig. 17, or

Deff = AB2

(56)

where A = 0.0'35 crn.'/sec. a t N.T.P. This can be compared with the wellknown formula Deff =

where

Dfree

-

Y

(57)

is the tortuosity factor.* Possibly after a small initial burnoff,

* It is relevant to note that tortuosity defined by Equation (57) is by no means the same as that defined by ( L , / L ) , where L, is the effective tortuous pat,h length

190

P. L. WALKER, JR., FRANK RUSINKO, JR., AND L. G. AUSTIN

y = l / e ( y = 1 w h e n 8 = 1) and Deff

=

Dfreeez

(58)

From Equation (58), D f r e e has the value of 0.095 cm.2/sec. at N.T.P., compared to the value of 0.14 cm.'/sec. found from free-diffusion experiments (126).As discussed, the values of Doff were obtained from diffusion of hydrogen through nitrogen converted to carbon dioxide through carbon monoxide by multiplying by m 4 . Since hydrogen is much smaller than nitrogen, carbon dioxide, or carbon monoxide, it is probably more accurate t o correct Deff using the factor

When this conversion factor is used, Dfmecalculated from Equation (58) is 0.147 cm.*/sec., in good agreement with the experimental value. Since porosity-radius curves have been obtained, it is possible t o plot curves of Dell against radius for the reacted rods. T o correct to the temperature of reaction, it is assumed that D,ff is proportional to T',*(128). 3. Reactant Concentration ProJile through Rod during Reaction at 1200". Equations (52), (54), and (55) are used to calculate the reactant concentration profile through the rod during reaction at 1200". Co is initially asbut as will be seen later, its value can be approximated. The sumed 4, most significant conclusion that can be drawn from the concentration data in Table VI is that there is no major difference in the decrease of concentration through the rod for the three different cases, even at high rates of reaction. At low rates of reaction, Equations (52), (54), and (55) all give the same result, since there is little pressure build-up or forced flow in the rod. As would be expected, Cases 2 and 3 require that the concentration gradient be somewhat steeper to diffuse in the required amount of carbon dioxide for reaction. I n Table VI, the concentration through the rods also is expressed as a percentage of the surface concentration. It is probable that the actual mass-transport process is a combination of all three cases. However, since the percentage falloff of concentration in the rod is not much different in the three cases, the results may be used on a and L the measured thickness of the sample. As discussed by Carman ( I d b ) ,it is difficult to justify theoretically values of ( L J L ) which depart much from G.The value of tortuosity defined by Equation (57) must be considered as a correction factor which includes ( L J L ) , but it is also a function of how the various-sized pores in a solid are interconnected. The tortuosity factor equals (L./L) only when the pores available for diffusion are not of widely different size and the interconnections between them are not constrictions. This can best be seen by noting that as the pore interconnections becomc small, Dell tends to zero; therefore, y tends to infinity even though the diffusion path and the porosity do not necessarily change very much.

QAS REACTIONS OF CARBON

191

comparative basis as long as it is remembered that the absolute magnitude of the concentrations is in doubt. It will be noted that the predicted concentrations of carbon dioxide at the surface of the rod ((2,) are 0.35,0.56,and 0.39 X g. of carbon per cc. for Cases 1, 2, and 3, respectively. Under the conditions of the reaction, C, is about 1.0 X lo-*. From Equation (27) (where 6 is calculated using Equation (40) with y5 = 2.0), it is estimated that C, - C R = 0.04 X lod4g. of carbon per cc. Therefore,

CR

N

1.0

x

indicating that the discrepancy between the values of carbon dioxide concentration calculated from concentration profiles and Equation (27 ) cannot be attributed to significant control of the reaction by mass transport resistance across the "stagnant film." A minor part of the difference can be attributed to COnot being zero, which can be seen by extrapolating the original rate-concentration curves t o zero concentration, as discussed shortly. The major part of the discrepancy is almost certainly caused by If the assumed variation between Dell and temperature (D.ff a Delf were to vary with temperature to about the 0.9 power, the correct carbon dioxide concentration at the outside of the rod would be calculated. Unfortunately, no data are available for this relation for these particulai carbon samples. 4. Variation of Reaction Rate with Temperature for Spectroscopic Carbon Reacting with Carbon Dioxide. Figure 18 presents the Arrhenius plot showing the variation in reaction rate with temperature for the spectroscopic carbon reacting with carbon dioxide. At temperatures below 950°, an activation energy of 93 kcal./mole is obtained, the value probably approaching E l reasonably closely (32, 68) . Between 950 and lOOO", there is an abrupt change in apparent activation energy, which might be interpreted as the entire transition region between Zones I and 11. However, this interpretation is not valid. The porosity profile for the carbon reacted at 1200" (Fig. 13) indicates that the reaction is still in the transition region. Further, using Equation (25), the start of Zone I1 is calculated to occur when dwldt is ca. 6 g. of carbon reacting per hour. Although this value is approximate, it is over 50 times the value of dwldt at 1000". Also presented in Fig. 18 is the ideal change in reaction rate of the spectroscopic carbon with temperature, assuming a true activation energy of 93 kcal./mole. Zone I1 should start at a reaction rate of ca. 6 g. of carbon per hour and knowing that 7 'v 0.5 at thestart of Zone 11, the temperature can be approximated. It is of interest to note that the ideal activation energy in Zone 11, 46.5 kcal./mole, is closely approximated by the change in experimental reaction rate with temperature above ca. 1250". It might be expected that the smaller values of experimental reaction

192

P. L. WALKER, JR., FRANK RUSINKO, JR., AND L. G . AUSTIN 100

I

I

low/ T.

I

I

j

OK.-'

FIG. 18. Arrhenius plot for reaction of spectroscopic carbon rods with carbon dioxide at 1 atm. pressure.

rate which are observed in the transition region between Zones I and I1 are a result of forced flow or pressure buildup in the rod opposing the entry of carbon dioxide. However, the concentrations listed in Table VI indicate that these factors cannot account for such a marked discrepancy in reaction rate. It is probable that the buildup of carbon monoxide concentration in the rod at temperatures above 10oO" results in retardation of the reaction.

GAS REACTIONS OF CARBON

193

5 . T r u e and Apparent Order of Reaction. From a knowledge of ( d n l d t ) , through the rod, the over-all rate of reaction can be determined by graphical integration. When this is done for the rod reacted a t 1200", it is found that the integrated rate of reaction in the rod (0.127 g. of carbon reacting per hour per cm.' of external area) agrees well with the total rate of reaction determined from the experimental rate curve (0.131), The corresponding values for the rod reacted at 1305" are 0.30 and 0.41, which indicates that 28 % of the over-all reaction is a result of carbon blowing from the external surface. This agrees well with the extent of mechanical loss of carbon predicted from the 1305" porosity profile (Fig. 13). At any radius r , the rate of reaction per unit area can be calculated from the quotient, ( d n / d t ) , / S , . Consequently, the specific rate of reaction and calculated carbon dioxide concentration (both taken a t the same value of r ) can be plotted to determine the true order of reaction, independent of diffusion control. Figure 19 presents such data for the carbon rod reacted at 1200", assuming the relative concentrations for Case 3 in Table VI to be applicable. From an auxiliary plot similar to Fig. 19, a finite reaction rate a t zero carbon dioxide concentration is found. Since the concentrations of carbon dioxide were calculated assuming COto be zero, it is clear that this reaction rate is due t80a finite Co concentration a t the center of the rod. The actual values of concentmtion at values of r were estimated by extrapolat-

C02 CONCENTRATION,

0. of carbon x 10' CC

FIG.19. Relation between specific reaction rate and carbon dioxide concentration in rod undergoing reaction at 1200".

194

P. L. WALKER, JR., FRANK RUSINKO, JR., AND L. a. AUSTIN

TABLE VI Concentrations of Carbon Diozide through Spectroscopic Carbon Rod Reacting at 1600" Baaed on Denaity Profile and Deft Data

C, , (9. of carbon in

0.35 0.40 0.45

0.60 0.55 0.60 R = 0.6225

C, as % of CR

C O * ) / ~x ~ . 104

Radius, cm. Case 1

Case 2

Case 3

Case 1

Case 2

Case 3

0.06 0.08 0.12 0.18 0.24 0.31 0.36

0.09 0.15 0.22 0.31 0.41 0.51 0.56

0.05 0.08 0.13 0.19 0.26 0.35 0.39

14 23 36 57 69 89 100

13 20 32 47 66 88 100

16 26 40 55 73 91 100

ing the rate vs. concentration plot to zero rate, taking the negative intercept on the concentration ordinate as CO, and adding this constant concentration term to the concentrations in Table VI, thereby arriving at Fig. 19. By this method, Cois estimated as 0.14 X lo-' g. of carbon per cc. at 1200". A similar plot for the rod reacted at 1305" is given in Fig. 20. Clearly, the reaction is not first order at either temperature, nor do the data fit a Langb C ) . The data fit an expresmuir expression of the form dn/dt = aC/( 1 sion of the form l/(dn/dt) = ( a / C ) - ( l / b ) , as seen in Fig. 21. Such an expression is consistent with the idea of carbon monoxide inhibition, as discussed below. Figure 22 presents the change of over-all reaction rate with change in partial pressure of carbon dioxide in the main gas stream. Nitrogen was used as the diluent, and the total flow rate was maintained constant. The over-all order of reaction is found to be ca. 0.5 from 950 to 1200". An overall order of reaction of cu. 0.5 close to the start of Zone I1 has been interpreted to mean a true reaction order of zero (70,79).In this case, however, as has been shown in Fig. 19, the true order is not zero at 1200".Therefore, the above reasoning is not valid. An over-all order of 0.5 would be expected (for reactionin Zone 11) if the mechanism of the reaction is represented by

+

as suggested by Ergun (46). Both a and b vary exponentially with temperature, a increasing and b decreasing with increase in temperature. By similar reasoning to that used to derive Equation (A18), it can be shown that for

GAS REACTIONS OF CARBON

195

o a0eo.w ~ 0 m 6 e aio QIZ a4 a16 0.18 QZO co, CONCENTRATION,W~* cc. carbon ~10' FIG.20. Relation between specific reaction rate and carbon dioxide concentration in rod undergoing reaction a t 1305".

reaction through a specimen,

cco= r ( p - cco,>

(60)

with r varying between 1 and 2 depending upon the pressure buildup which occurs in the material. Assuming I' = 1, for simplicity, cco cco,

-

Go,

- 1

(61)

The carbon dioxide concentration can be expressed as a fraction 'of the exterior gas concentration; that is, Cco,/p = f, with f varying from 1 to 0 from the exterior to the interior of the carbon. For any given value off, Cco/Cc,, is fixed, and therefore, dn/dt is a function off and not of CcOp alone, or

196

P. L. WALKER, JR., FRANK RUSINKO, JR., AND L. G . AUSTIN

I

I CO, CONCENTRATION 2 3

I I

-

0-

1200

- 1305

'

['.of carbon x IoI-' cc. 4

5

6

7

c.

0 -

I 0

p.

10 I

COI CONCENTRATION

'

I

20 of carbon x IOJ-' cc.

3

FIG.21. Relation between reciprocal of specific reaction rate and reciprocal of carbon dioxide concentration in rods undergoing reaction at 1200 and 1305".

Consider now a plane specimen of carbon (of uniform specific internal surface area and uniform D,ff) reacted in Zone I1 at two exterior carbon dioxide concentrations p1 and pz . For a given temperature, Equation (62) shows that the specific reaction rate a t a given value of Cco,/p is fixed. Therefore, in the two cases, since Cco,/p covers the same range of values, the specific reaction rates will cover the same range of values. However, in going from one fixed value of Cco,/p to another fixed value, the change in concentration and, therefore, the diffusional mass transport, will not be the samc in both cases even though the specific reaction rate covers the same range of values. Clearly, for the higher concentration case, penetration will occur deeper into the specimen and the given specific reaction rate range will apply over a larger section of carbon. The fall in Ccoz/p through

GAS REACTIONS OF CARBON

n

197

0 - 1000

0.5

0

0

K

- 1200

k z 0

I-

0.1 -

2 0.075LL

0.I Pco,

IN

0.25 Q5 0.75 1.0 GAS FLOW OVER ROD, otm.

FIG.22. Apparent order of reaction for whole rod at reaction temperatures between 950 and 1200".

the material is as illustrated in Fig. 23, where the curves are of the same shape, but the penetration scale at the higher external concentration is expanded uniformly. Consider the two infinitesimal sections AL and SL a t the same Cc,,/p value. Let SL = M L , then from Equation (62): Reaction in volume element SL = S , (dn/dt) SL

(63)

where 8,is the internal surface area per unit volume and the specimen is considered to be of unit cross sectional area. Also Reaction in volume element AL Therefore,

= S,

(dn/dt) AL

=

l/X (reaction in 6L) (64)

198

P. L. WALKER, JR., FRANK RUSINKO, JR., AND L. G. AUSTIN

AL 8L R ADlU S -+

0

L

FIQ.23. Illustrations of fractional carbon dioxide concentrations through reacting specimen, when exterior face is exposed to reacting gas of concentration P I or p~ , Pl

>PI.

That is,

Considering the gradient of Cco,/p at the external reacting face

[

d(Cco,lPi)

dx

1 d(C

=x[

"d","

/

) p2 1 2

That is,

Now the overall rate of reaction is equal to Deff

therefore

Eliminating X from Equations (69) and (66) and rearranging

GAS REACTIONS OF CARBON

199

Thus, the over-all rate should be proportional to the gas concentration in the main gas stream t o the half power. The above derivation applies to reaction completely in Zone 11. From Equation (59) it is seen that in Zone I, where Cco is small, the reaction should be zero order. Hence, over the transition region the apparent order of the over-all reaction should range from 0 to 0.5. This is not the case in the present work, as shown in Fig. 21, where the order is approximately 0.5 from 950 t o 1200".The discrepancy may be due to Equation (59) not being the correct equation for small values of carbon monoxide concentration. As was discussed in Sec. 111, the rate of the carbon-carbon dioxide reaction can be expressed as dt

1

+

+ c,, + il cco, '

33

33

which can be written in the form

by substituting for the Cco, Equation (60) with I' = 1. Equation (72) is of the form found to correlate the reaction rate us. concentration data presented in Fig. 21. When the pressure of carbon monoxide becomes appreciable, Equation (71) can take the form

which is of the form of Equation (59). Substituting for Cco Equation (60) with r = 1,

dn

x -e. + -

P

33

ilCC0,

cco,

[($>- (91

(74)

which again can be arranged in a form to satisfy the reaction rate versus concentration correlation presented in Fig. 21. Substituting K = i J j 1 and simplifying

200

P. L. WALKER, JR., FRANK RUSINKO, JR., AND L. 0. AUSTIN

-

COO CONCENTRATION WITHIN ROD Fro. 21. EfTcrt.of K [Eq. (75)j on the relation between the specific reaction rate m d carbon dioxide concentration in a rod. K < 1 (order > first) ; K = 1 (order = first) ; K > 1 (order < first).

The order of the reaction through the rod will depend on the value of K with respect t o 1, the various cases being illustrated in Fig. 24. In all ciises the order is approximately first when the carbon dioxide concentration is small. It should be kept in mind that all cases are derived from Equation (73), where the over-all order of reaction in the rod has been shown to be 0.5 when reaction is proceeding in Zone 11. At 1200 and 1305", K is found to be less than 1, whereas Ergun ( 4 6 ) quotes values of 1.8 and 2.4 (see Fig. 4) for reaction at 1200 and 130Oo, respectively.

E. SUMMARY The primary purpose of this section has been to show the possibilities for using density and area profile data to aid in the better understanding of gas-carbon reactions. In order to determine specific reaction rates and carbon dioxide concentrations a t given penetrations, it has been necessiiry to make assuinpt#ionswhich can only be approximations t o the truth. Several major anomalies in the results have been found, however. The calculated concentrations of carbon dioxide a t the external surface of rods rcacted a t 1200 (Table VI) and 1305" are not in agreement with the known carbon dioxide concentrations. Clearly, more information is required on the variation of Deff with temperature and its variation with porosity produced a t different reaction temperatures. It is feasible that a t high temperatures, considerable porosity may be produced without increasing D e f f to such a marked extent as found a t 900". Ariot,her anomaly is the nonuniformity of reaction found at 925O, when it, would be expected that the reaction should be in Zone I. The preliminary assumption of a completely interconnecting pore system may not be valid. It should also be noted that neither the value of K in Equation (75) nor the low-temperature activa-

GAS REACTIONS OF CARBON

201

tion energy of 93 kcal./mole agree with the values found by Ergun ( 4 5 ) . The activation energy value agrees much better with that suggested by Rossberg ( 3 2 ) and those found by Armington ( 6 2 ) .

VII. Some Factors, Other than Mass Transport, Which Affect the Rate of Gas-Carbon Reactions

The hope of attaining a quantitative understanding of the factors affecting the reactivity of carbons to gases has been the stimulus behind much work on gas-carbon reactions. At present, however, there is no clear understanding of why a given carbon reacts at a particular rate with a given gas under a fixed set of operating conditions. In this section, the possible effects on carbon reactivity of crystallite orientation, crystallite size, surface area, impurities in the carbon, heat treatment of the carbon, addition of halogens to the reacting gas, and irradiation are discussed briefly.

A. CRYSTALLITE ORIENTATION I n catalysis, one does not expect the activity of a catalyst t o be proportional t o its surface area, since there is good evidence that in many instarices cat,alytic action is limited to certain active regions which may constitute only a small fraction of the total surface area (129). As would be expected, the same reasoning holds true for gas-carbon reactions. Carbon is a multicrystallirie material, which can present varying degrees of surface heterogeneity depending upon the size and orientation of the crystallites. In the broadest sense, two main orientations of crystallites in the carbon surface need be considered-( 1) crystallites with their basal planes parallel to the surface and (2) crystallites with their basal planes perpendicular to the surface. According to Grisdale ( I S O ) , the rate of oxidation of carbon crystallites is ca. 17 times faster in the direction parallel to the basal planes (along their edges) than perpendicular to them. Therefore, it would be expected that the specific reactivity of a carbon would be at a minimum when its surface contains a maximum of crystallites with their basal planes parallel to the surface. Smith and Polley (131 ) showed this to be the case. They compared the oxidation rates of original and graphitized* (2700”) samples of Sterling FT carbon black, which have very close to the same surface areas (15.4 and 16.6 m.’/g.) and particle sizes (2,094 and 1,940 A. from electron micrographs). Figure 25 shows what they envision the orientation of the crys-

* It is to be emphasized that “graphitized” is used in this section to mean “heated to an elevated temperature above ca. 2200”.” This is in line with the popular usage of the word, and should not be interpreted to mean that after graphitization the carbon has a 100% graphitic structure. As discussed by Walker and Imperial (I%), artificial “graphite” approaches closely but does not have a 100% graphitic structure even after heat treatment to 3600”.

202

P. L. WALKER, JR., FRANK RUBINKO, JR., AND L.

0 RIGINAL CARBON BLACK

(f. AUSTIN

GRAPHITIZED CARBON BLACK

FIG. 25. Arrangement of crystallites in an original and graphitized (2700") particle of Sterling FT carbon black. [After W. R. Smith, and M. H. Polley, J . phy8. Chem.

80, 689 (1956).]

tallites in the two samples t o be. In the original carbon black, there are a number of exposed edges in the surface for reaction t o occur at a relatively high rate. On the other hand, they picture the graphitized carbon black as being in the shape of a polyhedron with its entire surface composed of crystallites with their basal planes parallel to the surface.* Smith and Polley find comparable rates of oxidation for the original and graphitized carbon blacks at temperatures of ca. 600 and BOO", respectively. If an activation is assumed for the oxidation of both carbons, energy of 50 kcal./mole ( 3 ) the ratio of reaction rates at the same temperature is ca. 200. Walker and co-workers (194)investigated the reactivity of a series of graphitized carbon plates to carbon dioxide in the apparatus previously described (86).The majority of the plates were fabricated from mixtures of 65 % petroleum coke (produced by delayed coking) and 35 % coal tar pitch, using standard techniques (136).Using X-ray diffraction, they determined the relative tendency of the different petroleum cokes to orient with their basal planes parallel to the surface of the carbon plates. A qualitative correlation is found showing that the reactivity of the plates decreases as the percentage of basal plane structure in the surface increases. Plates produced from a fluid coke (136, IS?') are found to have a gas reactivity lower than all plates produced from the delayed cokes, which is attributed to the fluid coke particles graphitizing in a manner similar to the Sterling FT carbon black, as previously discussed.

* The authors (131) and Kmetko (133) have confirmed definitely, from electron micrographs, that graphitization of carbon blacks of low surface area produces polyhedral particles.

GAS REACTIONS O F CARBON

203

B. IMPURITIES IN THE CARBON Much work has been done on the effect of the addition of impurities (salts and metals, chiefly) on the reactivity of carbon. Quantitatively, the effects are difficult to understand, since they are functions of the location of the impurity in the carbon matrix and the extent of interaction of the impurity with the matrix. Long and Sykes (94) suggest that impurities affect carbon reactivity by interaction with the r-electrons of the carbon basal plane. This interaction is thought t o change the bond order of surface carbon atoms, which affects the ease with which they can leave the surface with a chemisorbed species. Since the ?r-electrons in carbon are known to have high mobility in the basal plane, it is not necessary that the impurity be adjacent t o the reacting carbon atom. Indeed, it is thought that the presence of the impurity a t any location on the basal plane is sufficient for it t o affect the reaction. Impurities can either accelerate or retard carbon reactivity. Day (138) studied the effect of impurities on the oxidation of acetylene black by mixing equal weights of black and metallic oxides. He finds that a number of the impurities, including boron, titanium, and tungsten, inhibit oxidation, whereas iron, cobalt, nickel, copper, and manganese, among other metals, accelerate oxidation. Perhaps of greater significance is the finding that different methods of adding the impurity can affect markedly the degree of oxidation acceleration or retardation. For example, the addition of nickel originally as the nitrate is more effective than the addition of nickel originally as the hydroxide. Earp and Hill (99) find that the addition of salts t o graphite usually accelerates oxidation markedly; the notable exceptions being most of the borates and phosphates. Sat0 and Akamatu (139) report that alkali metals enhance the chemisorption of oxygen on carbon and weaken the carbon-carbon bonds a t the surface so as t o accelerate combustion. On the other hand, they report that phosphorus, while catalyzing the adsorption of oxygen on carbon, has a retarding effect on the release of the surface oxide. Nebel and Cramer (140) show that the addition of a series of lead compounds t o carbon at a concentration of ca. 5 wt. % lowers the ignition temperature (raises the combustion rate) of the carbon. Of importance is the finding that the extent of the catalytic effect depends on the particular salt. Lead acetate is the most effective, lowering the ignition temperature 293"; lead sulfate is the least effective, lowering the ignition temperature only 39". Lead pyrophosphate and lend orthophosphate are found not to lower the ignition temperature. Tuddenham and Hill (72) investigated the effect of addition of cobalt, iron, nickel, and vanadium to spectroscopic graphite on its gasification with

204

P. L. WALKER, JR., FRANK RUSINKO, JR., AND L. G . AUSTIN

steam at 1100". They added the impurities as the nitrate. They report that relative gasification rates increase from 19-fold for nickel to 32-fold for iron. Gulbransen and Andrew (141) investigated the effect of iron on the reactivity of spectroscopic graphite to carbon dioxide. The porous graphite was impregnated with an iron nitrate solution and then heated to a relatively low temperature t o convert the iron nitrate to iron oxide. In one run, mm. they then pretreated the sample by holding it at 850" for 1 hr. at Hg, prior to reacting the sample at 700" in 76 mm. Hg carbon dioxide pressure. Over the 10 min. of reaction time, the impregnated sample (contnining 0.078% iron) is reported t o have a reaction ratc 530 times that of the original graphite. In another run, they pretreated under similar vacuum conditions but at a temperature of 700" for 16 hrs. They find negligible change in gasification rate following this pretreatment. Gulbransen and Andrew conclude that the iron impurity must be present as either the re1

-

0 0 A -

0 A

I

ti

E! I

i

0" V

t

B

s 10 a

8

E +

-

I

E

h

I

I

-

ORIGINAL GRAPHITE 1.61 g./cc. APPARENT DENSITY I, I, 1.83 'I II ,I 1.99 'I HEAT TREATED GRAPHITE 1.41g./Cc. APPARENT DE!SITY ,I 1.63 " I1 II 1.76 "

\\-

=

-

-

--

Sa E a v) 10'4

I

0.75

I

0.80 1000 I T ,

I

0.85

I

0.90

0.95

OK.-'

FIQ.26. Arrhenius plots for reaction of raw and heat-treated rods of Ceylon graphite with carbon dioxide at 1 atm. pressure. [After F. Rnsinko, Jr., Ph.D. Thesis, The Pennsylvania State University, 1968.1

GAS REACTIONS OF CARBON

205

duced metal or as the carbide t o catalyze the carbon dioxide reaction. They suggest that their vacuum pretreatment at 700" did not effectively reduce the iron oxides. Rusinko (89)investigated the reactivity of pelletized natural graphite rods, before and after heat treatment at 2600", with carbon dioxide a t a series of temperatures from 800 to 1100".On heat treatment, the ash content is found to decrease from ca. 2 % to less than 0.1 %. The crystallite size and specific surface area are found to undergo negligible change. Figure 2G correlates reactivity data on rods of various densities with temperature using an Arrhenius plot. Heat treatment is seen to reduce the specific reactivity of the rods by a factor of ca. 10 but not to change the activation energy (42 kcal./mole). The implication in this case is that the removal of impurities decreases the number of carbon sites able to participate in the reaction, but the removal does not change the mechanism by which the active sites react. It is known that the activation energy obtained is less than E c , since the specific reactivity of the rods increases as the diameter of the rods reacted is decreased. It appears that reaction is proceeding in the transition region between Zone I and Zone 11.

C. CRYSTALLITE SIZE Usually it is difficult to separate the effect of crystallite size on carbon reactivity from the effects of crystallite orientation and impurity content. However, Armington ( 6 2 ) attempted t o do so by reacting a series of graphitized carbon blacks with oxygen and carbon dioxide, as discussed earlier in this article. Assuming that upon graphitization all the carbon blacks are converted t o polyhedral particles with the surface composed almost completely of basal plane structure, it is possible to eliminate crystallite orientation as a variable. Spectroscopically, the total impurity content of all the graphitized carbon blacks is quite low; and to a first approximation, the analyses of the individual constituents are similar. By selecting carbon blacks of a wide range of particle size, Armington was able t o control the extent of crystallite growth upon graphitization, since crystallites only grow t o a fraction (usually from $6 to > i o ) of the carbon particle size. The graphitized carbon blacks range in crystallite size from ca. 20 t o 130 A. and in particle size from ca. 130 to 2000 A. Particle sizes calculated from B.E.T. surface areas (assuming no internal porosity) agree well with particle sizes approximated from electron micrographs. Figure 27 presents data on the specific reactivity of the series of carbon blacks in 0.1 atm. of oxygen at 600"vs. the specific surface area of the blacks. Since the crystallite size is an inverse function of surface area, the conclusion t o be drawn from Fig. 27 is that the specific reactivity of carbons increases with increase in crystallite size. Armington reports similar results for the

206

P. L. WALKER, JR., FRANK RUSINKO, J R . ,

I

0

50

I

AND L. G . AUSTIN

I

100 150 SURFACE AREA, m 2 4 .

I 200

FIG.27. Relation between specific reactivity to oxygen and specific surface urea of a series of graphitized carbon blacks. [After A . F. Armington, P1i.D. Thesis, The Pennsylvania State University, 1980.1

reaction of the same graphitized carbon blacks with carbon dioxide. He suggests that catalysis of the reaction by the impurities still present in the blacks is responsible for this effect of crystallite size on reactivity. That is, assuming the same quantitative and qualitiative impurity content in all blacks, the larger the crystallite size the greater the number of edge carbon atoms which can be affected by a given impurity atom by ?r-electron transfer through the basal plane. Edges of crystallites will serve as zones of high resistance to electron flow. Consequently, an impurity atom associated with one crystallite will have little effect on the reaction rate of edge carbon atoms on other crystallites in the matrix.

D. EFFECT OF HEAT TREATMENT OF CARBONS ON THEIRSUBSEQUENT TO GASES REACTIVITY

Several cases of the effect of heat treatment on the subsequent reactivity of carbon have already been discussed. In both the work of Rusinko (89)

207

GAS REACTIONS OF CARBON

2.01

I

I

0

2

4

I

I

6 8 REACTION TIME, hours

I

10

I2

FIG.28. Effect of heat treatment on the reactivity of carbon derived from petroleum pitch. Reaction of 2 g. of 6 X 8-mesh carbon with carbon dioxide at 1100". [After P. L. Walker, Jr., and J. R . Nichols, "Industrial Carbon and Graphite," Society of Chemical Industry, p. 334. London, 1957.1

and Smith and Polley (lSI),heat treatment at elevated temperatures produces a marked decrease in reactivity of the carbon. It is to be emphasized, however, that heat treatment to elevated temperatures also can increase the subsequent reactivity of carbon. Walker and Nichols (142) investigated the reactivity of cokes produced from coal tar pitch and petroleum pitch. Particle samples (2 g. of 6 X 8-mesh material) having seen maximum temperatures of either 1100 or ca. 2750" were reacted with carbon dioxide at 1100" in the apparatus previously described (86). Figure 28 presents the reaction rate curves for the samples derived from the petroleum pitch. The graphitized sample has a reaction rate some fivefold higher than the sample which has not seen a temperature above 1100". Similar results are found for the samples produced from the coal tar pitch with the graphitized sample having a reactivity over threefold higher than the ungraphitized sample. For both materials, graphitization produced a marked increase in crystallite size, a marked decrease in impurity content, and only a minor change in surface area. As a follow-up to this work, Walker and Baumbach (143) investigated the effect of heat treatment on the reactivities of carbons produced from 20 different coal tar pitches and one delayed petroleum coke. Heat treatment again produced a marked increase in crystallite size, a marked decrease in impurity content, and only a minor change in surface area. They use the

208

P. L. WALKER, JR., PRANK RUSINKO, J I ~ . ,AND L. G. AUSTIN

1 000

1100

I 2000 HEAT TREATMENT TEMPERATURE, C.

I 2500

FIQ.29. Effect of heat treatment on the reactivity of carbons derived from coal tar pitch and delayed petroleum coke. Reaction with carbon dioxide at 1150'. [After P. L. Walker, Jr., and D. 0.Baumbach, unpublished results 1969.1

same apparatus and procedure as that used by Walker and Nichols ( I @ ) , while studying reactivities in carbon dioxide at 1150". Of the 20 samples derived from coal tar pitch, in 19 cases the graphitized sample (2660') has a considerably higher reactivity than the samples which have seen a maximum temperature of only 1150'. On the other hand, the reactivity of the graphitized petroleum coke is about one-half that of the coke having fieen a maximum temperature of 1150". Of even more interest is the effect of heat treatment to different elevated maximum temperatures on subsequent reactivity to carbon dioxide. In Fig. 29, results on a typical sample produced from coal tar pitch and a sample produced from delayed petroleum coke are given. Pronounced effects of graphitization temperatures in the range 2570 to 2680" are found. As noted, two separate heat treatment runs at temperatures of ca. 2655" were made on the sample from coal tar pitch to confirm the maximum in the reactivity. There is no doubt that the maximum exists. The relative values of temperatures reported agree well with the temperatures estimated from electrical resistivity data on the heattJreatedsamples. That is, room temperature electrical resistivities of carbons heated in this temperature range are known to increase with increasing heat treatment temperature.

GAS REACTIONS O F CARBON

209

The authors feel that these preliminary results of Walker and Baumbach on the effect of heat treatment of carbon on subsequent gas reactivity serve t o indicate the complexity of the problem. At the same time, the results indicate the necessity of much additional work in this area if an understanding of the factors decting the rate of gas-carbon reactions are t o be understood. These results emphasize that total impurity content in carbons is not the decisive factor determining gas reactivities. Of more importance is the location of the impurity in the carbon matrix and its particular chemical form. It is suggested that heat treatment can bring the impurity into more intimate contact with the carbon matrix through high-temperature reactions so that a small amount of impurity can serve as a more efficient catalyst. Also t o be kept in mind is the fact that the crystallite size of the carbon can increase with increasing temperature-at least up to a point. As discussed previously, the size of the crystallite determines, in part, how effectively the catalytic impurities are used. I t is suggested that a detailed cxaminat,ion of the effect of heat-treatment temperature on the gas reactivity of the carbons studied by Walker and Bauinbach (143) might show a series of reactivity maxima which correspond t o temperatures a t which different catalytic impurities first begin t o show sigiiificant solid state diffusion and reaction with the carbon matrix followed a t higher temperatures by their complete volatilization from the sample. The advent of significmt diffusion and reaction of the impurity with the carbon could result in a subsequent increase in gas reactivity. Complete volatilization of the impurity from the sample could result in a subsequent decrease in gas reactivity.

E. ADDITION OF HALOGENS TO

THE

REACTING GAS

The role which halogens play in raising the CO-CO2 ratio of the product gas in the carbon-oxygen reaction has been discussed in Sec. 111. Halogens can also affect markedly the rate of carbon burnoff. Day (24), for example, investigated the effect of chlorine on the carbon-oxygen reaction under high velocity conditions. The carbon was heated solely by the energy supplied by the reaction, and a t 20,000 ft./min. in pure oxygen, a surface temperature of lGG0" was maintained. The introduction of 0.15% chlorine t o the oxygen stream lowers the surface temperature by 280"; 0.25 % chlorine immediately extinguishes the reaction. The chlorine is thought to be dissociating and chemisorbing on the carbon sites preventing the formation of a carbon-oxygen complex. If the chlorine has not extinguished the reaction, subsequent removal of the chlorine from the oxygen stream results in the surface returning t o its original temperature. However, the return t o normal does not occur as rapidly as the poisoning, which is almost instantaneous. Wicke ( 3 1 ) investigated the effect of POCL on the carbon-oxygen reac-

210

P. L. WALKER, JR., FRANK RUSINKO, JR., AND L. G. AUSTIN

tion. He finds a normal ignition temperature of 650" in dry air. With 1 % by volume of POC1, added to the air, there is no reaction a t 650"; and it proves impossible to remove the inhibiting material from the carbon by subsequently passing in pure air. Even a t 900",the removal is found to take several minutes. The ignition temperature of the carbon is raised 200". Hedden (144) investigated the effect of the addition of POCla and chlorine on the rate of the carbon-carbon dioxide reaction at a temperature of 1100". After achieving a constant rate for the reaction in the absence of halogen-containing gas, he finds upon addition of impurity gas that there is an initial sharp increase in reaction rate. This is followed by a decrease in reaction rate. For POCL , the rate falls below the normal rate; for chlorine it remains above this rate. When the halogen-containing gas is stopped, the reaction rate in both cases increases sharply above the normal rate, followed by a continuing decrease back to the same value as that when no halogen-containing gas is added. The initial increase in reaction rate following halogen treatment t o a value greater than the normal value is ascribed to excessive surface roughening while the halogen is present in the reacting gas. The degree of surface roughening gradually decreases after the halogen gas flow is stopped until reaching the normal value. It can be concluded that the halogen-containing gases offer unusual possibilities for affecting the rate of attack of carbon surfaces by oxygen-containing gases.

F. IRRADIATION With the use of graphite as a moderator in nuclear reactors becoming of increasing importance, there is concern about the effects of irradiation on the rate of reaction of the graphite with gases. Aside from the practical importance of irradiation effects, high-energy irradiation of carbons provides a powerful tool for studying the relation between imperfections in the carbon lattice and rates of gas-carbon reactions. Relatively large and controlled concentrations of imperfections can be introduced into graphite by high energy particle bombardment, Kosiba and Dienes (146) investigated the effects of neutron irradiation on the rate of reaction of spectroscopic graphite rods with air. Figure 30 shows the effects of exposure of the graphite t o ca. 4 X 10" neutrons/cm.' at temperatures under 50" on its subsequent reaction rate over the temperature range 250 to 450". Prior irradiation increases the oxidation rate by a factor of ca. 5 to 6 at reaction temperatures of 300 to 350". The effect of irradiation decreases with further increase in reaction temperature, as evidenced by a larger activation energy of oxidation for the unirradiated graphite. Kosiba and Dienes estimate that at the reaction temperatures studied there is at most about 1% displaced carbon atoms remaining from the

GAS REACTIONS OF CARBON 470

4 7

3;)o

370

0 0

0.01

1.3

1.4

1.5

1.6

1000/T,

211

,

250 '1

- IRRADIATED - UNIRRADIATED

1.7

'K.-'

1.8

1.9

1

FIG.30. Arrhenius plots for the rate of oxidation in air of both unirradiated and previously irradiated spectroscopic graphite. [After W. L. Kosiba, and G. J. Dienes, Advances in Calalysis 9, 398 (1957).]

previous irradiation with neutrons. On the other hand, they observe that at W " ,for example, the higher oxidation rate of the irradiated sample persists even when 20 to 25% of the sample has been oxidized. They conclude, therefore, that the displaced carbon atoms are not themselves being oxidized preferentially but facilitate in some way the over-all oxidation. They further observe that this increase in reaction rate on irradiation is not brought about by an increase in surface area, since it is known from the recent work of Spalaris (1%') that the surface area decreases significantly upon irradiation at room temperature. Kosiba and Dienes (1.46)also investigated the effect of exposure of the graphite to gamma-irradiation during reaction on oxidation rates. On the

212

P. L. WALKER, JR., FRANK RUSINKO, JR., AND L. G . AUSTIN

unirradiated graphite, they find that the reactivity at 300" is hardly a1tered at a gamma-flux of 2 X 10' r./hr., whereas a significant increase in reactivity is observed at a flux of G X 10' r./hr. On an irradiated graphite, a flux of 2 X 10' r./hr, increases the reactivity at 300" by a factor of three over the irradiated graphite not reacted in a gamma-field. This means that the irradiated graphite subsequently reacted in a gamma-flux of 2 X 10' r./hr. at 300" had an over-all oxidation rate some 18-fold higher than the unirradiated graphite whether or not the unirradiated graphite was exposed to the above gamma-flux during reaction. Kosiba and Dienes conclude that the gamma-ray effect is probably due to the ionization of oxygen molecules, since gamma-rays have not been observed to have any effect on the properties of graphite at the exposures used. ACKNOWLEDGMENT We wish to express our appreciation t o the following groups for support of our studiccl on gas-carbon reactions either through direct financial assistance or through the supplying and processing of carbon materials: U.S. Atomic Energy Commission through Contract No. AT(30-1) -1710; The Commoriwealth of Pennsylvania through its continuing support, of r o d research; Consolidation Coal Co. ; Godfrey 1,. Cabot, Inc.; National Carbon Co.; Plastics and Coal Chemicals Division of the Allied Chemical Corp.; Socony Mobil Oil Co.; Speer Carbon Co.; and Stackpole Carbon Co. Their support has made the writing of this article possible.

Appendix A. SOLUTION OF DIFFERENTIAL EQUATION (21) Equation (21) is a Bessel equation of the general solution However, the function Y otends to infinity as r tends to zero, while the function Jo remains finite; and as C must be finite at r = 0, B must be zero. Thus

or

By computation or by using tables of Bessel functions, values of CIA can values. Let be found for a range of (r/2)4Then, by plotting loglo ( C / A) us. 9/2, it was found that for values of + > 4 loglo ( C I A ) = 0.84(+/2)

- 0.75

(A5)

GAS REACTIONS OF CARBON

213

Hence, loglo [5.62(C/A)l

= 2(4/2)

loglo e

(A61

or

5.62(C/A) = e'

(A7)

When C = C R , 4 = R d m i and, therefore,

A = 5.62CRexp - R d m i

(A8)

or

C, = CHexp r

d m

exp - R d m f

(A91

From the plot of log ( C / A ) against 4/2, it is found that C, is approximately constant throughout the rod for 4 < 0.2. (At 4 = 0.2, the concentration at the center of the rod is ca. 20%less than CI1.)

B. DERIVATION OF EQUATIONS FOR REACTANT CONCENTRATION PROFILE THROUQH CARBON RODSDEPENDING UPON TYPE OF MASSTRANSPORT 1. Knudsen Di$usion Only I s Occurring. For a very fine pore material in which the effective pore diameter is less than the mean free path of the molecules, bulk diffusion and Poiseuille flow do not occur. For this case, the change in volume given when C COz 2CO has no influence on the rate of diffusion of carbon dioxide into the rod, and Dpffis not dependent on the total pressure in the pores. Considering a wedge of carbon (Fig. A l ) ,

+

-

I

I I I

I

\ \ \ 'k-

i

I I

UNIT AREA

OF

EXTERNAL SURFACE EXPOSED TO I REACTING GAS AT I CONCENTRATION CR I

/ /'

- 0

FIG.A l . Section of rod of radius R undergoing reaction.

214

P. L. WALKER, JR., FRANK RUSINKO, JR., AND L. Q. AUSTIN

the amount of C02which diffuses through a plane at r must equal the C02 reacted from 0 to r. That is,

From the values of (dnldt), obtained experimentally,

can be obtained by graphical integration. Then

and integrating,

where C, is the concentration of COZat r in g. of carbon per cc. and COis the concentration of COS in the center of the rod. At high reaction rates, CoN 0. F ( r ) can be determined by graphical integration. 2. Bulk Di$USion Occurring But Pores Too Fine to Allow Poiseuille Flow. For bulk diffusion, Doffa (1/P) ,where P is the total pressure. If Poiseuille Row is negligible, then the concentration profiles of COz and CO through the rod can be shown as in Fig. A2. For the reaction C COZ+ 2C0,the increase in volume of CO over COZis two; and at any point, the diffusion gradient for CO must be double that for C o t . If C' is the concentration of CO at a point where the concentration of COz is C,

+

dC' - = -2- dC dr dr

a

v)

u)

W

RADIUS -e

FIQ. A2. Illustration of the pressure profiles through a rod when substantial bulk diffusion and negligible Poiseuille flow are occurring.

215

GAS REACTIONS OF CARBON

or

C'

+A

-2C

=

At the external surface, let the total pressure P R be made up of q inerts, Cg carbon dioxide and CfRcarbon monoxide. Then P R

= CR

+ +q

(A151

C'R

Therefore, CR

+

= p =

C'R

P R

-q

where p is in g. of carbon per cc. WhenC = CR C' )

p

- CR =

-2cR

c'

+

(A161 =

CIR = p -

+A

C R

and

(A171

or = p

C R

- 2c

(A181

At any point in the carbon, the total pressure P r is given by

Pr

= q

+ C + C'

= q

+p +

C R

-C

(A191

Now the diffusion coefficient Doifat this point under a pressure of P, is obtained from the diffusion coefficient Deli at the same point but measured nt P Rby the relation

If q

= 0)

or

or

If CO/C, = L, where L is clearly

< 1,

216

P. L. WALKER, JR., FRANK RUSINKO, JR., AND L. G . AUSTIN

t-

A CO, REACTED IN INTERIOR ‘ X - 2 CC. PER SEC. X cc. PER SEC OF CO

DIFFUSE OUT

CC. OF COO PER SEC DIFFUSE IN

X

Z CC. OF

COa PER SEC. SWEPT BACK IN POISEUILLE FLOW

1

X - 2 Z cc PER SEC. OF CO TRANSPORTED POISEUILLE FLOW BY

A

FIG.A3. Representation of flow conditions at a plane in a rod when bulk diffusion and a maximum of Poiseuille flow are occurring.

When the reaction is not in the stagnant film-controlled zone, C R = p and at high rates of reaction, L N 0. Therefore,

C,

=

2cR(1 -

e-P‘r)’CR)

( A25 1

3. Bulk Diflusion Occurring with a Maximum of Poiseuille Flow. The third limiting case is where the pores are so large that negligible absolute pressure differential builds up within the pores and Poiseuille flow carries the extra volume of CO to the exterior. Under these conditions, CO will diffuse out at the same rate as CO, diffuses in (that is, dC/dr = -dC’/dr), while CO is carried out by forced flow. It is clear, however, that the forced flow will also carry out some of the COz which diffuses in. This situation is represented by Pig. A3, where A A is a plane in the solid (after Thiele (100)). The total mass flow outwards in cc./sec. is given as Q = X - 22

+Z = X

-2

( A26 1

But Z = Q X C” where C” equals the concentration of COz in gas in cc. per cc. Therefore,

z

=

( X - Z)C

If

=

c”x

~

1

+ Cff

If 1 cc. of C o nweighs p g. of carbon a t the temperature and pressure applying, then considering 1 om.* of external surface of rod, the rate of reaction in g. of carbon per sec. is given by

i’g

dr = ( X - Z ) p =

(x - - -C”X )p 1

=

( - ) X P1 1

+ C”

+ C”

GAS REACTIONS OF CARBON

217

Now

Theref ore,

As C is in g. of carbon per cc., C” f(r)

=

=

C/p. Substituting from this and

1‘

(dn/dt),dr,

That is,

-dr

=

[‘-”dC 0

P+C

( A33

or (A34) For high rates of reaction, Co ‘v 0. If there is 100 % CO, in the reacting gas stream

c, = C , ( e

P(r)ICR

- 1)

(A35)

REFERENCES 1. Hougen, 0. A., and Watson, I