摘要:

AUTHOR INDEX * Allen, J. A., 309, 357, 360, 363. Anderson, J. S., 238, 305, 362. Baldock, G. R., 27. Barrer, R. M., 88, 206. Beeck, O., 93, 118, 159, 193, 314. Bevan, J. M., 238. Blekkingh, J. J. A., 200. Boer, J . H. de, 93, 206, 208, 363, 364. Bonner, Francis, 352. Bradley, R. S., 94. Bremner, J . G. M., 79, 92. Bruijn, H. de, 69, 95, 300. Chapman, P. R., 258. Colburn, C. B., 39. Cole, W. A., 314. Coulson, C. A., 27. Couper, A., 172. Denbigh, K. G., 83. Dixon, J. K., 290, 305. Dowden, D. A., 184, 203, 204, 206, 208, 210, 296, 305. Eggleton, A. E. J., 92, 195. Eley, D. D., 34, 99, 172, 191, 199, 205, 302, 363, 364. Eucken, A., 128. Evans, Alwyn G., 302. Evans, U. R., 296. Everett, D. H., 86. Eyring, Henry, 39. Garner, W. E., 194, 211, 246, 298. Given, P. H., 301. Goodeve, Charles, 192.Gray, T. J., 246,250,331, 364. Griffith, R. H., 258, 299. Guinier, A., 344. Halsey, Jr., J. E., 54, 88. Hillier, James, 348. Huang, K., 18. Hubbell, Harry H., 348. Huttig, G. F., 215. Irsa, Peter, 352. Johnson, Marvin, F. L., 303. Kemball, C., 94. Kropa, E. L., 290. Laidler, Keith J., 47, 90. Lindars, P. R., 258. Los, J. M., 321. Luft, N. W., 306. Lyon, Lorraine, 222. Maxted, E. B., 135. May, D. R., 290. Melik, John S., 303. Mignolet, J. C. P., 105, 326. Miller, A. R., 57, 80, 87. Milliken, Jr., T. H., 279. Mills, G. A., 279. Mitchell, J. W., 307, 309, 360, 363. Moon, K. L., 135. Morrison, J. A., 321. Oblad, A. J., 279, 302. Overgage, E., 135. Porter, A. S., 203, 358. Reynolds, P. W., 184. Rideal, Eric K., 96, 114. Ries, Jr., Herman E., 303. Ritchie, A.W., 159. Rowland, P. R., 196, 209, 363. Saunders, K. W., 290. Savage, S. D., 250. Schissler , Donald, 352. Schroyer, F. K., 337. Schuit, G. C. A., 205, 299. Schwab, G.-M., 79, 88, 89, 91, 166, Selwood, P. W., 222, 306, 337. Steiner, H., 264. Stone, F. S., 194, 246,254. Sykes, K. W., 82. Tamele, M. W., 270. Taylor, H. S., 9. Thomas, N., 80, 82. Tiley, P. F., 201, 202, 254, 362. Tompkins, F. C., 85, 92, 201, 202, 203. Trapnell, B. M. W., 114, 191, 193, Turkevich, John, 348,352. Twigg, G. H., 89, 90, 152. Ubbelohde, A. R., 203, 204. Uri, N., 207. Ward, A. F. H., 95. 365. Weiss, J., 302. Wheeler, A., 314. Wicke, E., 199. Winter, E. R. S., 231, 300. Wright, P. A., 194. Wyllie, G., 18, 82, 91. Young, D. M., 84, 85. Zawadzki, J., 140. Zwietering, P., 196. Zwolinski, Bruno J., 39.198, 205, 207, 298. 360, 365. * The references in heavy type indicate papers submitted for discussion.AUTHOR INDEX * Allen, J. A., 309, 357, 360, 363. Anderson, J. S., 238, 305, 362. Baldock, G. R., 27. Barrer, R. M., 88, 206. Beeck, O., 93, 118, 159, 193, 314. Bevan, J. M., 238. Blekkingh, J. J. A., 200. Boer, J . H. de, 93, 206, 208, 363, 364. Bonner, Francis, 352. Bradley, R. S., 94. Bremner, J . G. M., 79, 92. Bruijn, H. de, 69, 95, 300. Chapman, P. R., 258. Colburn, C. B., 39. Cole, W. A., 314. Coulson, C. A., 27. Couper, A., 172. Denbigh, K. G., 83. Dixon, J. K., 290, 305. Dowden, D. A., 184, 203, 204, 206, 208, 210, 296, 305. Eggleton, A. E. J., 92, 195. Eley, D. D., 34, 99, 172, 191, 199, 205, 302, 363, 364. Eucken, A., 128. Evans, Alwyn G., 302.Evans, U. R., 296. Everett, D. H., 86. Eyring, Henry, 39. Garner, W. E., 194, 211, 246, 298. Given, P. H., 301. Goodeve, Charles, 192. Gray, T. J., 246,250,331, 364. Griffith, R. H., 258, 299. Guinier, A., 344. Halsey, Jr., J. E., 54, 88. Hillier, James, 348. Huang, K., 18. Hubbell, Harry H., 348. Huttig, G. F., 215. Irsa, Peter, 352. Johnson, Marvin, F. L., 303. Kemball, C., 94. Kropa, E. L., 290. Laidler, Keith J., 47, 90. Lindars, P. R., 258. Los, J. M., 321. Luft, N. W., 306. Lyon, Lorraine, 222. Maxted, E. B., 135. May, D. R., 290. Melik, John S., 303. Mignolet, J. C. P., 105, 326. Miller, A. R., 57, 80, 87. Milliken, Jr., T. H., 279. Mills, G. A., 279. Mitchell, J. W., 307, 309, 360, 363. Moon, K. L., 135. Morrison, J. A., 321. Oblad, A. J., 279, 302.Overgage, E., 135. Porter, A. S., 203, 358. Reynolds, P. W., 184. Rideal, Eric K., 96, 114. Ries, Jr., Herman E., 303. Ritchie, A. W., 159. Rowland, P. R., 196, 209, 363. Saunders, K. W., 290. Savage, S. D., 250. Schissler , Donald, 352. Schroyer, F. K., 337. Schuit, G. C. A., 205, 299. Schwab, G.-M., 79, 88, 89, 91, 166, Selwood, P. W., 222, 306, 337. Steiner, H., 264. Stone, F. S., 194, 246,254. Sykes, K. W., 82. Tamele, M. W., 270. Taylor, H. S., 9. Thomas, N., 80, 82. Tiley, P. F., 201, 202, 254, 362. Tompkins, F. C., 85, 92, 201, 202, 203. Trapnell, B. M. W., 114, 191, 193, Turkevich, John, 348,352. Twigg, G. H., 89, 90, 152. Ubbelohde, A. R., 203, 204. Uri, N., 207. Ward, A. F. H., 95. 365. Weiss, J., 302. Wheeler, A., 314. Wicke, E., 199. Winter, E. R. S., 231, 300. Wright, P. A., 194. Wyllie, G., 18, 82, 91. Young, D. M., 84, 85. Zawadzki, J., 140. Zwietering, P., 196. Zwolinski, Bruno J., 39. 198, 205, 207, 298. 360, 365. * The references in heavy type indicate papers submitted for discussion.

ISSN:0366-9033    

DOI:10.1039/DF95008FX001

出版商:RSC    

年代:1950

数据来源: RSC

摘要:

AUTHOR INDEX * Allen, J. A., 309, 357, 360, 363. Anderson, J. S., 238, 305, 362. Baldock, G. R., 27. Barrer, R. M., 88, 206. Beeck, O., 93, 118, 159, 193, 314. Bevan, J. M., 238. Blekkingh, J. J. A., 200. Boer, J . H. de, 93, 206, 208, 363, 364. Bonner, Francis, 352. Bradley, R. S., 94. Bremner, J . G. M., 79, 92. Bruijn, H. de, 69, 95, 300. Chapman, P. R., 258. Colburn, C. B., 39. Cole, W. A., 314. Coulson, C. A., 27. Couper, A., 172. Denbigh, K. G., 83. Dixon, J. K., 290, 305. Dowden, D. A., 184, 203, 204, 206, 208, 210, 296, 305. Eggleton, A. E. J., 92, 195. Eley, D. D., 34, 99, 172, 191, 199, 205, 302, 363, 364. Eucken, A., 128. Evans, Alwyn G., 302. Evans, U. R., 296. Everett, D. H., 86. Eyring, Henry, 39. Garner, W. E., 194, 211, 246, 298. Given, P. H., 301. Goodeve, Charles, 192.Gray, T. J., 246,250,331, 364. Griffith, R. H., 258, 299. Guinier, A., 344. Halsey, Jr., J. E., 54, 88. Hillier, James, 348. Huang, K., 18. Hubbell, Harry H., 348. Huttig, G. F., 215. Irsa, Peter, 352. Johnson, Marvin, F. L., 303. Kemball, C., 94. Kropa, E. L., 290. Laidler, Keith J., 47, 90. Lindars, P. R., 258. Los, J. M., 321. Luft, N. W., 306. Lyon, Lorraine, 222. Maxted, E. B., 135. May, D. R., 290. Melik, John S., 303. Mignolet, J. C. P., 105, 326. Miller, A. R., 57, 80, 87. Milliken, Jr., T. H., 279. Mills, G. A., 279. Mitchell, J. W., 307, 309, 360, 363. Moon, K. L., 135. Morrison, J. A., 321. Oblad, A. J., 279, 302. Overgage, E., 135. Porter, A. S., 203, 358. Reynolds, P. W., 184. Rideal, Eric K., 96, 114. Ries, Jr., Herman E., 303. Ritchie, A.W., 159. Rowland, P. R., 196, 209, 363. Saunders, K. W., 290. Savage, S. D., 250. Schissler , Donald, 352. Schroyer, F. K., 337. Schuit, G. C. A., 205, 299. Schwab, G.-M., 79, 88, 89, 91, 166, Selwood, P. W., 222, 306, 337. Steiner, H., 264. Stone, F. S., 194, 246,254. Sykes, K. W., 82. Tamele, M. W., 270. Taylor, H. S., 9. Thomas, N., 80, 82. Tiley, P. F., 201, 202, 254, 362. Tompkins, F. C., 85, 92, 201, 202, 203. Trapnell, B. M. W., 114, 191, 193, Turkevich, John, 348,352. Twigg, G. H., 89, 90, 152. Ubbelohde, A. R., 203, 204. Uri, N., 207. Ward, A. F. H., 95. 365. Weiss, J., 302. Wheeler, A., 314. Wicke, E., 199. Winter, E. R. S., 231, 300. Wright, P. A., 194. Wyllie, G., 18, 82, 91. Young, D. M., 84, 85. Zawadzki, J., 140. Zwietering, P., 196. Zwolinski, Bruno J., 39.198, 205, 207, 298. 360, 365. * The references in heavy type indicate papers submitted for discussion.AUTHOR INDEX * Allen, J. A., 309, 357, 360, 363. Anderson, J. S., 238, 305, 362. Baldock, G. R., 27. Barrer, R. M., 88, 206. Beeck, O., 93, 118, 159, 193, 314. Bevan, J. M., 238. Blekkingh, J. J. A., 200. Boer, J . H. de, 93, 206, 208, 363, 364. Bonner, Francis, 352. Bradley, R. S., 94. Bremner, J . G. M., 79, 92. Bruijn, H. de, 69, 95, 300. Chapman, P. R., 258. Colburn, C. B., 39. Cole, W. A., 314. Coulson, C. A., 27. Couper, A., 172. Denbigh, K. G., 83. Dixon, J. K., 290, 305. Dowden, D. A., 184, 203, 204, 206, 208, 210, 296, 305. Eggleton, A. E. J., 92, 195. Eley, D. D., 34, 99, 172, 191, 199, 205, 302, 363, 364. Eucken, A., 128. Evans, Alwyn G., 302.Evans, U. R., 296. Everett, D. H., 86. Eyring, Henry, 39. Garner, W. E., 194, 211, 246, 298. Given, P. H., 301. Goodeve, Charles, 192. Gray, T. J., 246,250,331, 364. Griffith, R. H., 258, 299. Guinier, A., 344. Halsey, Jr., J. E., 54, 88. Hillier, James, 348. Huang, K., 18. Hubbell, Harry H., 348. Huttig, G. F., 215. Irsa, Peter, 352. Johnson, Marvin, F. L., 303. Kemball, C., 94. Kropa, E. L., 290. Laidler, Keith J., 47, 90. Lindars, P. R., 258. Los, J. M., 321. Luft, N. W., 306. Lyon, Lorraine, 222. Maxted, E. B., 135. May, D. R., 290. Melik, John S., 303. Mignolet, J. C. P., 105, 326. Miller, A. R., 57, 80, 87. Milliken, Jr., T. H., 279. Mills, G. A., 279. Mitchell, J. W., 307, 309, 360, 363. Moon, K. L., 135. Morrison, J. A., 321. Oblad, A. J., 279, 302.Overgage, E., 135. Porter, A. S., 203, 358. Reynolds, P. W., 184. Rideal, Eric K., 96, 114. Ries, Jr., Herman E., 303. Ritchie, A. W., 159. Rowland, P. R., 196, 209, 363. Saunders, K. W., 290. Savage, S. D., 250. Schissler , Donald, 352. Schroyer, F. K., 337. Schuit, G. C. A., 205, 299. Schwab, G.-M., 79, 88, 89, 91, 166, Selwood, P. W., 222, 306, 337. Steiner, H., 264. Stone, F. S., 194, 246,254. Sykes, K. W., 82. Tamele, M. W., 270. Taylor, H. S., 9. Thomas, N., 80, 82. Tiley, P. F., 201, 202, 254, 362. Tompkins, F. C., 85, 92, 201, 202, 203. Trapnell, B. M. W., 114, 191, 193, Turkevich, John, 348,352. Twigg, G. H., 89, 90, 152. Ubbelohde, A. R., 203, 204. Uri, N., 207. Ward, A. F. H., 95. 365. Weiss, J., 302. Wheeler, A., 314. Wicke, E., 199. Winter, E. R. S., 231, 300. Wright, P. A., 194. Wyllie, G., 18, 82, 91. Young, D. M., 84, 85. Zawadzki, J., 140. Zwietering, P., 196. Zwolinski, Bruno J., 39. 198, 205, 207, 298. 360, 365. * The references in heavy type indicate papers submitted for discussion.

ISSN:0366-9033    

DOI:10.1039/DF95008BX003

出版商:RSC    

年代:1950

数据来源: RSC

摘要:

5th SPIERS MEMORIAL LECTURE CATALYSIS : RETROSPECT AND PROSPECT BY HUGH S. TAYLOR The finest memorial to the first secretary of the Faraday Society is the maintenance of the General Discussioiis at the highest level of ex- cellence. Wherever physical chemistry is prosecuted, wherever students are acquiring physicochemical science, there the record of the discussions which Secretary Spiers initiated and organized for so many years will be found indispensable. There is a curious discrepancy in the archives of the Society concerning the General Discussions. In the index of Volume I11 for 1907 two general discussions are recorded, one on “ Osmotic Pressure,” one on “ Hydrates in Solution ”. In the index to the first twenty volumes of the Transactions the earliest recorded General Discussion is in Volume IV, on “ The Constitution of Water ”.I am at a loss to account for such a discrepancy unless it is a simple over- sight. The last General Discussion organized by Secretary Spiers was in October rg25 on “ Photochemical Reactions in Liquids and Gases ” and was held in Oxford. I was present on that occasion, which marked, as the General Discussions so frequently do, a milestone in the develop- ment of the particular phase of physical chemistry then under consider- ation. For such reasons, and with a peculiar sense of privilege and honour, I am happy on this occasion to introduce a general discussion on “ Hetero- geneous Catalysis’’ as the Spiers Memorial Lecturer, in my own Uni- versity, where, as a student in the departmental library, I first learned to appreciate how greatly these General Discussions can contribute to the definition of the present state of science and in what direction progress may develop.Sir Oliver Lodge was then President of the Society. The present Discussion is the third in a sequence which includes two famous predecessors. In 1922 the Discussion on Catalysis brought for- ward two basic concepts, that of Lindemann on the nature of unimolecular kinetics and that of Langmuir on reaction a.t surfaces betweep adjacently adsorbed reactants, with adsorption restricted to monolayers. The dis- cussion on “ Adsorption ” in 1932 was concerned, in the main, with slow processes of sorption and evoked, from our President, a definition of van der Waals’ and of chemisorption in terms of the potential energies between an impinging molecule and a surface.The diagram brought out clearly the manner in which activation energy of adsorption might be involved, and sharply differentiated physical and chemical processes of adsorption, the differences between which had been indistinct up to that time. It emerged that physical adsorption had little relevance to catalysis at surfaces ; the chemisorbed monolayers of Langmuir were the loci of such reactions. It is pertinent here to emphasize that the Langmuir formulation of surface kinetics was reFtricted to those surface reactions in which the velocity of interaction on the surface was the rate-determining process. This condition was indeed fulfilled in the classic researches of Langmuir and in further developments by Hinshelwood, Rideal, Schwab and others.A* 9I 0 RETROSPECT AYD PROSPECT It is useful, however, to recall an example which does not conform to this condition, the decomposition of ammonia on doubly-promoted iron synthetic ammonia catalysts as studied by Love and Emmett.1 They found a kinetic equation, d[NH3] [NH,]O dt LH,]O.~ -~ = k - which, on the Langmuir basis, would suggest a strong adsorption of hydro- gen on the iron surface and a moderate ammonia adsorption on the surface bare of hydrogen, with nitrogen an inert constituent. We now know that such a view is erroneous ; the slow step is the desorption of nitrogen from the surface, the slow sorption being rate-determining in synthesis. This example alone would have justified the emphasis on slow sorption in the monolager, first discussed by the Society in 1932.The availability of isotopic forms of a given molecular species has revealed the variation in temperatures at which these species will interact on surfaces which still further emphasizes the necessity for the concept of activation energy accompanying their chemisorption on catalyst surfaces. Some examples are cited in Table I. TABLE I.-INTERACTION OF ISOTOPIC MOLECULES ON SURFACES Catalyst Fe synthetic ammonia cata- lyst, doubly promoted . 2s * , ,, 8 Rhenium . NicGkl Osmium . , 9 , Isotope Reaction Temp. O C . for Measurable Rates - I95 + 25 +450 + 25 + I00 +500 - I95 +I50 + 250 1 Reference ?I Kummer and Emmett, Brookhaven Conference Report (Dec. 1948), p. I . Taylor and Jungers, J . Amer.Chem. SOL, 1935, 57, 660. McGeer, Thesis (Princeton, 1949). Sadek and Taylor, J . Amer. Chem. SOC., 1950, 72, 1168. Guyer, Joris and Taylor, J . Chem. Physics, 1941, 9, 287. 5 Wright and Taylor, Can. J . Bes. B, 1949, 27, 303. It is important for the further argument that these variations found with technical catalysts are also to be found with the idealized catalysts produced by the Beeck method of evaporating metals to form oriented or non-oriented films. IP these cases, also, where purity and cleanliness of surface have been raised to the highest attainable standards, similar variations in the temperature at which chemisorption occurs are found, although there will be differences between films and technical catalysts in the actual temperature range involved.Thus, on nickel films, Beeck has shown chemisorption of hydrogen even at 1 5 O K, but examines interaction between ethane and nickel films only in the temperature range 200-250° C. In contrast to Beeck's measurements on nickel films are those of Eucken and Hunsmann with reduced nickel from the oxide where the adsorption at zoo K shows a heat of van der Waals' adsorption. Chemi- sorption with 5 kcal. of heat of adsorption is found only at 50° K. While iron films chemisorb nitrogen (as molecules ?) at liquid-air temperatures Love and Emmett, J . Amer. Chem. SOC., 1941, 63, 3297. Eucken and Hunsmann, 2. physik. Chem. B, 1939, 44, 163.HUGH S. TAYLOR I 1 there is a slow activated adsorption of nitroga, with a much higher heat of adsorption, around room temperatures.This latter fact is to be con- trasted with the studies of Emmett and Brunauer with iron synthetic ammonia catalysts where the slow sorption of nitrogen was measured in the temperature interval from 224 to 449' C. This example takes us at once to the heart of a problem which it ought to be the objective of this Discussion finally to resolve. In 1925, a concept of the catalytic surface was formulated which emphasized heterogeneity or, as it came to be expressed, the concept of " active centres ". A variety of evidence on the properties of technical catalysts, which were the only catalysts then extensively studied, contributed to this concept of active centres. This evidence included observations on adsorption by catalysts both active and inactivated by heat treatment.It attempted to account for the great influence of poisons and promoters, present in t NITROGEN ISOTOPE EXCHANGE ON IRON CATALYST 9% I 1 1 1 ! ! 1 1 1 1 ! 1 1 1 1 ~ l 0 1 2 3 4 5 6 7 HOURS FIG. I minimal amounts, and invoked the existence of centres of high activity, very sensitive to poisoning. The quantitative measurements of poison- ing by Pease in the hydrogenation of ethylene and by Almquist and Black on the poisoning action of oxygen on water vapour irammonia synthesis on iron catalysts were conspicuous examples of such studies. Over the zs-year period, and largely due to the work of Balandin in Russia, of Roberts on the properties of a clean tungsten wire surface and of Beeck and his co-workers on evaporated films, a contrary view has emerged which has sought the interpretation of catalysis solely in terms cf the properties cf plane faces of crystalline materials, which, by specialized techniques, could be studied in a " clean " condition.It is my purpose to attempt a reconciliation of these two points of view in a more generalized and uni- fying concept. on the exchange reaction between light and heavy nitrogen on iron synthetic ammonia catalysis and on rhenium surfaces at 450°C provides a clue to such aa attempt. The velocity of Emmett and Brunauer, J . Amer. Chem. SOC., 1940, 62, 1732. McGeer, Thesis (Princeton, 1949). A recent research by McGeerI 2 RETROSPECT AND PROSPECT reaction was shown to be very sensitive to the reduction process t o which the catalyst was submitted prior to the velocity measurements.In Fig. I the slowest rate is that of an iron-alumina catalyst (No 954, 1-5 yo A1,0,) which had been prepared by reduction at 450' C with a fast stream of tank hydrogen containing 0-15 yo oxygen. The intermediate rate shows the rate of exchange when the same catalyst was subjected to re- duction in a stream of hydrogen from which oxygen and water vapour had been removed by the normal techniques of oxygen removal and drying of the gas stream. The residual water vapour was probably well below 0.01 yo. The fastest rate of exchange was obtained when excessive pre- cautions were taken to ensure dry, oxygen-free hydrogen for reduction. Similar findings resulted with the rhenium catalyst. The data suffice to show how very sensitive the exchange reaction is to the residual traces of oxygen that are left on an iron surface even with good reduction tech- niques.In the terminology of 20 years ago this is a typical example of " active centres " on a technical catalyst. It parallels entirely, as it should, the quantitative data obtained by Almquist and Black5 on an iron-alumina catalyst in ammonia synthesis in presence of water vapour as a poison. TABLE II.-AMMONIA YIELD AT A SPACE VELOCITY OF 25,000, 444°C AND The data in Table I1 recall some of these results. I ATM. PRESSURE Mg : 0, retained by catalyst . yo NH, produced The very marked effect of the first 5 mg. of oxygen retained is the mole striking since, from B.E.T. measurements of the surface area of this catalyst, only 10 to 15 yo of the total surface would be covered by this oxygen.Because the ammonia synthesis reaction is determined in rate by the slow step of chemisorption of nitrogen it is apparent that we must seek the interpretation of the " active centres " or quasi-heterogeneity in the effect of adsorbed oxygen on the surfaces of the iron crystallites. The presence of oxygen results in an incieased energy of activation of nitrogen adsorption on the iron surface. A generalization of this point of view for technical catalysts makes possible a reconciliation between the findings of those who have worked with clean tungsten wires and evaporated metal films and those whose attention has centred on the properties of technical catalysts. In each case one is concerned with the properties of one or more crystal faces of a particular catalytic species.In the case of technical catalysts, however, these properties may be profoundly modified by the presence of poisons as adsorbed oxygen or added ingredients such as alumina in the case just considered. Our knowledge in this area is being rapidly increased by reason of the studies of electron emission from hot wires and by studies of the properties of semi-conductors. One need only cite the beautiful studies of Miiller6 and of Jenkins relative to the emission of electrons from fine tungsten points as revealed by the field-emission projection electron microscope, and the influence of adsorbed oxygen, barium, thorium and sodium on the emission process. The varying activity of different crystal faces, the preferential adsorption of the poison on particular faces and the migration of poisons at definite temperatures can be visually demon- strated.Especially, however, the data accumulating on semi-conductors demonstrate how profoundly the conducting properties of a pure substance 5 Almquist and Black, J. Amer. Chem. SOC., 1926, 48, 2814. 6 Miiller, 2. physik., 1949. 126, 642. Jenkins, Reports Prog. Physics, 1943, 9, 177.HUGH S. TAYLOR 13 can be modified by traces of a prescribed impurity. One may cite in this respect the recent data of Pearson and Bardeen8 on the activation of silicon as a semi-conductor by additions of boron. The addition of 0.0013 atomic per cent of boron significantly changes the energy required to release an electron, whilst a concentration of 0.013 atomic per cent lowers this energy to zero. As Mott pointed out recently in the Kelvin Lecture @ impurity centres may be imagined as " gieat swollm ' atoms ' extending over 10-20 lattice parameters ',, a concept pertinent to the whole problem of interaction between adsorbed species on a surface.We must assume, in the case of the iron-synthetic ammonia catalyst already discussed, that the presence of impurity centres raises the activation energy of ad- sorption of nitrogen as oxygen would raise the activation energy ?f con- duction in zinc oxide semi-conductors. In this manner the findings of Beck on evaporated iron films can be correlated with those of Emmett and Brunauer and of McGeer with the technical iron catalysts. It is, on this basis, the impurity centre randomly distributed over the plane face of a crystal which would confer on such a crystal face quasi-heterogeneity.W7e can draw from the data on semi-conductors further analogies to problems of surface catalysis. VenVeyJ1O cited by Mott, has prepared semi-conducting NiO by dissolving in the lattice Li,O, the radii of the Li+ and Ni++ being practically identical. On heating in air, Li+ replaces Ni++ in the lattice and €01 each Li+ introduced a Ni+++ ion is formed. The latter are carriers of current by electron displacement. The magnetic measurements carried out by Selwood and his co-workers on valence induction in nickel and other oxides are illustrative of the same effect." Magnetic measurements, on nickel oxide impregnaked on y-alumina sup- ports, indicate that the nickel is present in the trivalent form.On mag- nesia, the isomorphous divalent oxide is present. On the rutile structure of titania the nickel assumes a valency of four, the oxide being bright yellow in colour. Manganese and iron oxides behave similady. The relation 01 valence induction to semi-conductors and to the whole problem of promoter action in catalysis is illuminated by such studies. Let us recall that the activation energy of adscrption of hydrogen by zinc oxide is markedly diminished by incorporating chromium oxide in the pre- paration. On the viewpoint here presented poisons and promoters become impurity centres in the normal lattice of the catalyst, the former tending to raise the activation energy of adsorption, the latter to lower it. A further factor which can be influenced by such impurity centres in a catalyst surface is the heat of adsorption.The data are scanty but what data are available tend to indicate that the measured heats of chemisorption are markedly less on technical catalysts than on the cor- responding evaporated films. The data of Beeck recorded for this Discussion on a variety of metal films for hydrogen, ethylene and nitro- gen are conspicuously higher heats of adsorption than have been recorded by Beebe, Eucken and others with technical catalysts. Indeed, the high heats of adsorption on evaporated films constitute a grave disadvantage of these films regarded as catalysts. They are, indeed, clean, but they " die " after brief experimentation because they are self-poisoned owing to the high heats of adsorption of one or more of the reactants.The technical cataljsts, though " dirty", at least " live ", largely because of the lower heats of binding to surfaces having " impurity centres ". From such circumstances it can result that a technical catalyst may have a higher activity than an evaporated film. has made one such Wright Pearson and Bardeen, Physic. Rev., 1949, 75, 865. Mott, Proc. Inst. Electr. Eng., 1949, 96, 253. 10 Verwey, Haayman and Romeyn, Chem. Weekblad, 1948, 4, 705. l1 Selwood, Bull. SOC. cham. France D, 1949, 489. l2 Wright, Thesis (Princeton, 1949).I 4 RETROSPECT AWD PROSPECT concrete comparison. With 27 mg. of a nickel-chromia (80 yo Ni) catalyst in a reaction volume of 350 cm.3, i.e. 0.077 mg. catalyst per ~ m . ~ gas, containing an equimolar hydrogen-ethylene mixture Wright found a half-life of tllz = 4 min.at -78’ C. From Beeck’s data and his temper- ature coefficient one computes a half-life of 45 min. at -78” C with 30 mg. nickel film in a reaction volume of 400 cm. or 0.075 mg. catalyst per ~ m . ~ of reacting gas. On this basis, the technical catalyst is 11 times as efficient as the evaporated film. The cause is obvious from an examin- ation of Beeck’s paper to this Discussion on the reactions of hydrocarbons. Most of his surface is covered with “ acetylenic residues ” by reason of the high heat of chemisorption of ethylene, thereby becoming ineffective for the catalytic interaction. Beeck’s data on the heat of adsorption of hydroen on clean tantalum, 45 kcal., and on a nitrided tantalum film, 27 kcal.are evidence for a lower heat of adsorption on metal surfaces covered in part with other constitnents. Another method of formulating the same idea is that, with technical catalysts, the areas responsible for the high initial heats of adsorption found with metal films are already occupied by impurity centres. Beeck’s data for heats of adsorption of hydrogen on his metal films vary directly with the change in d-band character of the metals. Boudart has recently l3 shown that Beeck’s measurements of activities in the hydrogenation of ethylene on metal films increase with increasing d-band character of the metallic bond as given by Pauling, with rhodium of maximum activity. This suggests that “ the lattice parameter is not to be considered solely as a cause but as an effect.The primary cause has to be sought in the electronic structure of the metal and a deeper insight into the latter may be obtained by means of Pauling’s theory.” From this point of view there is 9 notable discrepancy between the findings with films and technical catalysts in the case of copper. Beeck reports no hydrogen adsorption on films of copper whose d-band is filled. Technical copper catalysts have revealed chemisorption of hydrogen -from the eariiest studies of adsorption on catalysts, with a heat of adsorption of some 10 kcal. It is pertinent to ask whether this discrepancy is to be associated with the intrinsic nature of technical copper catalysts, to what extent it may be a function of a mixed Cu+-Cu++ structure deriving from impurity centres of a promoting character.Similar considerations, involving activation energy or heat of adsorption or both, animate the research work on catalysis by metal alloy systems. Schwab associates the catalysis in the decomposition of formic acid, on alloys of silver and of gold,l4 with a variety of metals giving both homo- geneous and heterogeneous phases, with an entry of protons into the interlattice planes and electrons dissolving in the electron gas of the metal, the required activation energy depending on the degree of com- pletion of Brillouin zones which define the allowed electron energies in the metallic stlucture. Similarly Couper and Eley l5 have associated the increase in activation energy of the hydrogen-deuterium exchange with the filling of the partly empty d-band of palladium by alloying with gold.Dowden l6 has treated the problem in detail theoretically and Reynolds l7 has applied the treatment to experimental findings on homo- geneous solid solution binary alloys of Group VIII metals with copper. In all such cases both activity and activation energy should be studied ; it is preferable also to study exchange reactions between isotopic mole- cules in order to minimize the influence of other factors such as displace- ment effects whcn two different molccular species are competing for a given surface. In this area there is a wealth of experimental opportunity. l3 Boudart, J . Amer. Chem. SOC., 1950, 72, 1040. l4 Schwab, Trans. Faraday SOC., 1946, 42, 689. l5 Couper and Eley, Nature, 1949, 164, 578.l6 Dowden, Chem. and Ind., 1949, 320 ; J. Chem. SOC.. 1950, 242. l7 Reynolds, Chem. and Ind., 1949, 320 ; J. Chem. SOC., 1950, 265.HUGH S. TAYLOR 1 5 Parallel studies with oxide systems will be equally interesting. In these, the properties of the catalytic oxide viewed as a semi-conductor will be useful aids to understanding. One example is copper oxide, recently examined by Garner, Gray and Stone,18 in terms of the electrical conductivities of thin films during formation, on reduction and after adsorption of gases. Oxygen enhances, hydrogen and carbon monoxide depress the conductivity of the Cu,O-CuO surface. The conductivity is interpreted in terms of a movement of electrons across an array of Cu+ and Cu++ ions. In contrast to cuprous oxide which is an oxidstion semi-conductor, zinc oxide is a reduction semi-conductor losing oxygen in a vacuum, the conductivity increasing and the excess zinc atoms enter- ing interstitially into the lattice as ions, the electron being held in the field of the positive charge.In this way the oxide acquires the characteristics of a metal, hydrogenating in character. Foreign ions can enter the lattice substitutionally and interstitially, electrons being trapped in their fields, the radius of the orbit of the trapped electron extending over several interatomic distances. The conductivity of the semi-conductors varies with the temperature and there is evidence that a whole spectrum of energies may be involved. Our knowledge of the properties of solid catalysts conferred by im- purity centres or admixtures of two or more constituents is still very much in the qualitative stage.It is known that the admixture of alu- minium oxide in magnetile increases considerably the difficulty of re- duction of the iron oxide. On the other hand the admixture of alumina has little influence on the dissociation pressure of copper oxide, but in- creases considerably the oxygen dissociation pressure with cerium oxide, CeO,. Chromium oxide admixture strongly increases the dissociation pressure of copper oxide. These findings on dissociation pressure are paralleled by the results of Rienacker l9 on the catalytic activity of such mixed oxides in the oxidation of carbon monoxide. The added oxide in- fluences both activity and activation energy of the basic catalyst, with marked lowering of the activation energy in those cases where admixture of the second oxide increases the oxygen dissociation pressure, and mith increase of activation when the added oxide decreases the reducibility of the basic catalyst.The old data of Kendall and Fuchs 2o on the influence of added oxides on oxygen release from barium peroxide, silver and mercuric oxides need to be recalled. The influence of added oxides on the slow sorption of hydrogen as illustrated by the accelerating influence of chromium oxide and the retarding effect of molybdenum oxide on the adsorption of hydrogen by zinc oxide is an example in another area. Such material should now be re-examined in the light of data revealed by Selwood on valence in- duction and with the newer techniques stemming from the study of semi- conductors.The catalyst itself, rather than the reactions which occur on it, seems to be the principal objective for future research in the coming years. This is not to deny the importance of a study of such reactions, since they, also, can reveal the nature and action of the catalyst surface. An excellent example in this respect is the recent work on the nature and functions of cracking catalysts, as exemplified by the recent con- clusions of Greensfelder, Voge and Good based on earlier work and newer investigations of the cracking of cetane, cetene and other hydro- carbons thermally and over catalysts such as activa.ted carbon, alumina, silica and alumina-silica commercial cracking catalysts. Two funda- mental types of cracking emerge, characteristic both as to the type of In the older literature there are many such examples.l8 Garner, Gray and Stone, Proc. Roy. SOC. A , 1949, 197, 294. 2o Kendall and Fuchs, J . Amer. Chem. SOC., 1921, 43, 2017. 21 Greensfelder, Voge and Good, Ind. Eng. Chem., 1949, 41, 2573. Rienacker, 2. anorg. Chem., 1949, 258, 280.16 RETROSPECT AXD PROSPECT primary and secondary reactions. Two types of mechanism are involved. The one involves free radical fragments and the pattern of cracking is described by the Rice-Kcssiakoff theory of cracking. This mechanism is characteristic of thermal cracking. The other mechanism is ionic in nature conforming closely to acid-activated, carbonium ion mechanism. Commercial acid -treated clays and synthetic silica-alumina catalysts are of the latter type.Activated carbon, an active, non-acidic catalyst gives a product distribution which can be interpreted as a free-radical type of cracking, quenched, as compared with thermal cracking, by reaction of free radicais with chemisorbed hydrogen on the catalyst to yield the corresponding normal paraffin, With silica-alumina, acidic- type catalysts, isomerization accompanies cracking to yield its particular spectrum of products. Such acidic surfaces are poisoned specifically by organic bases such as quinoline and by potash, ammonia and other alkalis, Oblad and his co-workers indicate that some 4 yo of the total surface is involved in such catdyses. Volkenstein 22 has recently analyzed the concepts of adsorption and of adsorption kinetics from the standpoint of the solid catalyst viewed as a structure containing a certain concentration of lattice defects, two-fold in nature.On the one hand, there are macro-defects, such as cracks, whose perturbations exceed those of the crystallographic unit. On the other hand, there are micro-defects which exercise perturbations of the order of the unit cell, the periodic structure being re-established at a distance of a few lattice parameters. In the terminology of semi- conductors, these defects include holes or vacant sites, interstitial atoms or ions, ions in a heteropolar lattice with normal position but anomalous charge, or foreign atoms in substitional or interstitial positions. Such defects deform a region of the lattice and it is the region which should be regarded as the defect.It is with the properties of such regions that catalysis may well be associated. Volkenstein introduces into his con- siderations the concept of mobility of micro-defects with an associated activation energy determined by the nature of the defect and the lattice and by the direction of migration. These micro-defects may react, attract or repel each other, dependent on the charges involved. Two defects may interact to produce a new defect with different properties, Volkenstein envisages the " disorder " in terms of the total number of defects which is small compared with the total number of unit cells. Eisorder may be " biographical ", that which is present at oo K and arising from the circumstances of the catalyst preparation or it may be " thermal " or that which results from the effect of temperature.The biographical disorder x, at oo K will increase progressively with temperature to a maximum y at T = 00, the thermal disorder a t any temperature varying from o at T = oo K to y - x at T = co. The relative importance of biographical and thermal disorder depends both on the temperature and the " biography ". In the older theories of adsorption one assumes (a) constancy' of ad- sorption centrts, (6) immobility of adsorption sites, and ( G ) invariance of sites with coverage. None of these assumptions enter necessarily into Volkenstein's treatment. Volkenstein assumes that adsorption occurs in the defect region. With one kind of defect the surface is energetically homogeneous.With differing defects there will be heterogeneity. Ad- sorption creates new centres. Increase of temperature increases the number of adsorption centres up to b u t not beyond the maximum, y. Volkenstein shows that the Langmuir isotherm results when the whole disorder is biographical. When, however, the defect is thermal involving an absorption of energy u, then, depending on the nature of the process producing the new defect whether unimolecular or by bimolecular inter- action of two defects, the mathematics shows that, with no heterogeneity 22 Volkenstein, Zhuw. Fiz. Khim., 1949, 23, 917.HUGH S. TAYLOR 17 of sites and without interaction between adsorbed atoms, the adsorption isotherm may conform to the Freundlich equation, uads = hpl/n, and the differential heat of adsorption can fall from an initial value q to a minimum q - u.The curve obtained is reverse sigmoid falling at first slowly, then rapidly and finally asymptotically to q - u at complete coverage. The adsorption centres on the crystal surface operate as a kind of plane gas the concentration of which increases on filling up and the change of energy of which is measured by the differential heat of adsorption. For the kinetics of adsorption the bimolecular production of sites can be shown to yield either a rapid Langmuir kinetics determined by the rate at which molecules strike the surface or an adsorption proportional to the square root of the time. For a unimolecular producticn of sites the kinetic expression for adsorption is that typical of the so-called activ- ated adsorption, k = k , exp (- E,,t/RT).In the theory of activated adsorption a potential bzrrier bntween adsorption sites and impinging molecule is assumed. In Volkenstein’s treatment it is the number of sites which increases with temperature and proportionally to exp (--u/RT). No potential barrier is assumed. An alternative method of stating the same is to say that the number of sites remains constant but the number of excited centres which are able to absorb increases as observed. There are several observations from the older literature on activated adsorption which can readily be interpreted on the bases of the Volkenstein concepts. In the General Discussion €or 1932 it was pointed out that the velocity of activated adsorption of hydrogen as measured on zinc oxide was very much smaller than the number of molecules striking the surface with the necessary activation energy.Our subsequent knowledge, from B.E.T. measurements, of surface area indicates that the discrepancy be- tween calculation and observation was of the order of IO*. A similar discrepancy was noted by Emmett and Brunauer in their careful measurements of the velocity and - activation energy of adsorption of nitrogen on synthetic ammonia catalysts. In this case the discrepancy was a t least of the order of IO~. From Volkenstein’s point of view these data would involve both the concentration of defect centres and the activation energy of adsorption of the molecule. In the case of doubly- promoted ammonia synthesis catalysts this might well be associated with the iron-potassium-oxide-aluminium oxide centres where the varying valency of iron, the univalent potassium and the trivalent aluminium ions suggest at once the possibility of lattice defects, as was pointed out to me by Boudart.Boudart has also emphasized in this regard the ob- servations of Pace and myself 23 on the identity in the velocities of adsorp- tion of hydrogen and deuterium on oxide catalysts which led to the con- clusion that “ the activation energy necessary is required by the solid adsorbent ’,. Other data on the influence of pressure on the velocity of chemisorption of hydrogen on oxides such as chromium oxide gel are also in agreement with the view that velocity is not determined by thz number of molecules striking the surface. To account for the slow sorptions ob- served it was earlier suggested that interaction must occur between the adsorbent and van der Waals’ adsorbed gas. The Volkenstein concept represents a mechanism by which such would be achieved. The apparent saturation capacity of an oxide surface for hydrogen adsorption at a given temperature and the large change to a new apparent saturation a t another temperature, facts familiar to a.11 who have studied the slow sorption processes on oxides, should be re-studied in reference to Volkenstein’s assumption that the sites available for adsorption, the “ thermal ” sites, vary with temperature. On this view the measure- ments of Shou-Chu Liang24 and the writer would gain new significance. In brief, measurements of slow sorption on oxide surfaces need to be 23 Pace and Taylor, J . Chem. Physics, 1934, 2, 578. 24 Taylor and Liang, J . Amer. Chem. SOL, 1947, 69, 1306.18 MOLECULE NEAR METAL SURFACE re-examined from the standpoint of the entropy as well as the energy of activation . In retrospect, three decades of scientific effort devoted to the science of catalytic phenomena have revealed a wealth of detail and understanding not available to the technologist in the empirical developments of the nineteenth and early twentieth centuries. The background of scientific theory and data that has been accumulated since Mr. Spiers first organized a General Discussion on Catalysis has led to a surer and swifter attack on any new catalytic problem that emerges. Out of the discussions which will ensue, here in Liverpool, we may anticipate a reconciliation of the several attitudes that sometimes have appeared to divide us, but are, in reality, a spur to further and continued effort towards the mastery of our science in an era which is of deep significance in all human affairs. In prospect, therefore, the future of our science is both challenging and bright. Chemistry Department, Princeton University, Princeton, N . J .

ISSN:0366-9033    

DOI:10.1039/DF9500800009

出版商:RSC    

年代:1950

数据来源: RSC

摘要:

18 MOLECULE NEAR METAL SURFACE I. THEORIES OF ADSORPTION AND PROPERTIES OF SURFACE LAYERS BEHAVIOUR OF A MOLECULE NEAR A METAL SURFACE BY K. HUANG* and G. WYLLIE Received 18th November, 1949 An account is given of the energy changes associated with electron transfer to or from a molecule a t distances from the metal surface such that quantum- mechanical tunnel effect may be neglected. A self-consistent treatment of the image field is used t o find the distribution of charge on a large adsorbed mole- cule. The modification in electronic structure of an adsorbed molecule in conse- quence of the formation of a weak covalent bond with the metal is treated in terms of a very simple model. A possible semi-empirical approach to treatment of the catalytically active surface is examined.It is of interest in a number of applications to consider the interaction between a molecule and a metal surface. At large distances, this inter- action is of the same nature as the van der Waals’ interaction between molecules, being attractive in character. This attractive potential has been discussed by a number of authors, especially Lennard- Jones, and Margenau and Pollard.2 The short-range interaction is of a more com- plicated character, and has only received a satisfactory discussion for the case in which the short-range forces are due to electron exchange and are purely repulsive.3 * Now a t Department of Theoretical Physics, Liverpool University. Lennard-Jones, Trans. Faraday Soc., 1932, 28, 334. Margenau and Pollard, Physic. Rev., 1941, 60, 128.Pollard, ibid., 1941, 60, 578.K. HUANG AND G. WYLLIE 19 Experimentally, it is usual to distinguish between physical adsorption and chemisorption, according as the binding energy between the adsorbed molecule and the solid surface is small or large. In physical adsorption the binding energy is of the order of the cohesive energy of a molec- ular crystal : in chemisorption it is of the order of the energy of an ionic or homopolar chemical bond. In the past, chemisorption has fre- quently been called " activated adsorption," since, in many cases it occurs comparatively slowly, and the temperature dependence of the rate corresponds to the necessity of a thermal activation energy. It seems, however, that chemisorption occurs instantly in those cases where experiments have been carried out with thoroughly clean metal surfaces (e.g.hydrogen on tungsten4), so it is at least possible that the observed activation characterizes the displacement of a previously chemisorbed layer rather than the simple process of adsorption. It is generally observed that heterogeneous catalysis is accompanied by chemisorption of at least one of the reactants on the catalyst surface. It is thus of interest to enquire what changes in molecular structure may be expected to accompany chemisorption. The object of the present paper is to outline the relevant considerations and draw some qualitative conclusions. I. A number of workers (e.g. Nyrop,5 Dowden,%') have suggested electron transfer in one direction or the other as the essential process in catalytic action. We shall consider first of all the energy changes associated with such transfer, where the separation of molecule and metal is such that we may neglect the influence of quantum-mechanical tunnel effect on this energy.Suppose that the work function, which is both the first ionization potential and the electron affinity of the metal, is x, that the electron affinity of the free molecule is A and that its first ionization potential is I. Then if molecule and metal are a t a great distance from each other, the work done in transferring an electron from metal to molecule is and from molecule to metal Typical values of the quantities concerned are x = z to 5 eV, A = o to I eV, I = g to 12 eV, so that in general W+ > W- > 0. Let us suppose an electron to have been transferred in one direction or other.There now exists an electrostatic attraction between metal and ionized molecule. We discuss first the simple case in which the mole- cule consists of a single atom. The ion will polarize under the influence of the charge induced by itself on the metal surface, and so long as its interaction with that charge is sufficiently described by the image field, the electrostatic energy of the system when the ion is at a distance Y from the surface is given by W - = x - A , w+ = I - x. where K is the polarizability of the ion in E.S.U. The approximation of the image field breaks down for static charges under two conditions, (i) if the surface charge density on the metal ap-- proaches the value of one electron per surface atom ; (ii) if the value of Y diminishes below the effective diameter of a metal atom or of the ion, whlchever is larger.The value of e 2 / 4 ~ is 2 eV for Y = 24A ; the second term in E, is gener- ally smaller. Thus, if W- has the rather small value of 2 eV, it is possible Roberts, Some Problems in Adsorption (Cambridge University Press, 1939). Nyrop, The Catalytic Action of Surfaces (Copenhagen, 1937). 6 Dowden, Research, 1948, I, 239. Nature, 1949, 164, 51.2 0 MOLECULE NEAR METAL SURFACE to form a negative ion near the surface a t such a distance that the exchange interaction is negligible, without expenditure of energy. The ion will, of course, only be in equilibrium at such a distance if there is already some sort of obstructing layer (e.g. of previously adsorbed atoms) between it and the metal surface.A larger molecule cannot be characterized electrostatically by a point charge and point dipole when i t is a t a distance from the surface compar- able with its own dimensions. We shall treat in some detail the case of a relatively large conjugated system, in which the charge transferred to the molecule is small compared with the total charge of the mobile electrons in the normal molecule, using a method developed by Coulson and his co-workers.* In a molecule of this type there are vacant molecular orbitals separated by only a small energy interval from the highest orbitals occupied by the mobile electrons in the ground state of the normal molecule. The charge transferred from the metal will enter such vacant orbitals.The molecular orbitals of the mobile electrons are constxucted as linear combinations of atomic orbitals #, s = I , . . . N ; we make the usual simplifying assumption that only one orbital on each atom need be considered. Coulson has defined polarizability coefficients (1) where q, is the number of mobile electrons on the atom s and ut is the Coulomb integral for the atom t . Under the condition mentioned above, i.e. that the fractional change in the q, is small, we may in a first approxim- ation treat these coefficients as having the same values in the adsorbed as in the normal molecule. In the final configuration of the molecule near the metal surface, there is an electrostatic field arising from the charge distribution on the molecule and its electrical image in the surface.This potential enters into the Coulomb integrals us, causing a change Au, as compared with the values in the normal molecule. If then E be the average number of electrons per atom (concerned in mobile orbital formation) transferred to the molecule, and E + Aq, the actual excess on atom s, we have from (I) in a first approximation where the repetition of the dummy index t implied summation. according to the atomic orbital 4,. Aq, = A%, - * ( 2 ) In the model used, the charge E + Aqr must be supposed distributed Thus we have the charge distribution - ( E + &s)e I +(y - Vr) I where r, is the position vector of the sth nucleus, and this together with its electrical image gives rise to a potential distribution which is every- where proportional to E + Aqs.The potential occurs linearly in the integrand of the Coulomb integral at, so we have the strictly linear relation, AM: = a t u ( ~ + A4u). * - (3) The a,, depend on the form of wave function involved and the geometrical configuration of the system. An example of their calculation €or a par- ticular simple case is given in the Appendix A. Eqn. (2) and (3) together determine Aq, and Au, for given E, for they can be combined to give the systems of linear equations and Longnet-Higgins and Coulson, Trans. Faruduy SOC., 1947, 43, 87 ; Proc. Roy. SOC. A , 1947, 191, 39.K. HUANG AND G. WYLLIE 21 These may be more neatly expressed in terms of the column matrices {A?} {Aa) and the square matrices {x} {a}. Then we have {E - na}{Aq} = {na>{~), - (44 {E - an){Aa) = {a>{€>, ( 5 4 where {E} is the diagonal unit matrix and { E } is E times the unit column matrix {I}.If the molecule is, as discussed above, too far from the metal surface for tunnel effect to be of importance, E is simply an integral multiple of the reciprocal of the number of atoms sharing the mobile orbitals (e.g. 6 in benzene). If however, the molecule is close to the metal surface but not too much distorted, the above calculation may give a good description of the charge distribution except in those atoms which are directly bound to the surface. In this case, E is to be determined by the consideration that the highest occupied level in the molecule must now coincide in energy with the highest occupied level in the metal. As the energy e0 of the highest filled level in the molecule is a function of the Coulomb integrals a,, Coulson has introduced the derivatives 3e0/3a, which we shall denote by the row matrix where ga = 34,,/3aa.There are two physically interesting possibilities. = (41, 5 2 - - * 6, * - * 5,) Then in first approximation we must have at equilibrium. It follows from (5a) that I - x = {(}{E - a X } - ~ { a } { c ) . - (7) (8) 1 - X and hence E = This in conjunction with (4a) gives the charge distribution in the adsorbed molecule. 11. In the above calculation we have treated the image field in a self-consistent manner ; in particular we have considered the electrons of the molecule as moving in the field of the electrical image of the average electron distribution rather than in the field of the image of the “in- stantaneous ” electron configuration (we are here concerned with the fictitious classical configuration used in setting up the Hamiltonian of the system).It appears, however, from experiments on the emission of electrons from metal surfaces that electrons of energy sufficient to escape from the metal move when near the surface in a field which is at least very closely approximated by the image field. This is the result of the correlation between the movements of the electron considered and those of the other electrons in the metal, which can be quantitatively expressed in terms of the density matrix of the metallic electrons.** 10 The correlation is less important the higher the kinetic energy of the electron. Crudely speaking, the conduction electrons of the metal no longer have time to adapt themselves to its motion.Thus the “in- stantaneous ” rather than the average electrical image will be of importance only for the molecular orbitals of high energy (and so of low average kinetic energy). These are precisely the orbitals which are responsible for chemical binding. However, the difference between this and a self- consistent treatment can only become significant when the molecule is dealt with by a more precise method than that of linear combination of atomic orbitals used in Wigner, ibid., 1934, 46, {&{E - anl-1{4{o* I. 9 Wigner and Seitz, Physic. Rev., 1934, 46, 509. l o Herring and Nichols, Rev. Mod. Physics, 1949, 21, 185. 1002.2 2 MOLECULE NEAR METAL SURFACE Bosworth l1 has attempted to treat the adsorption of a hydrogen atom to a metal surface by a variational method, regarding the image potential as a perturbation.He assumes a perturbed wave junction of the form and chooses the coefficients so as to minimize the energy of the system for a given distance R of the nucleus from the surface. The difficulty of the calculation is that the integral of the Hamiltonian diverges at the surface unless the image field is correctly cut off. Bosworth evades the difficulty by assuming the analytic form, - e2/4x, for the potential energy of the image force for positive and negative x , then integrating straight through the surface and taking the principal value of the resulting improper integral. In any case, a variation calculation which neglects exchange effects can in these circumstances claim little accuracy.A treatment of the exchange interaction between an atom and a metal surface by the Heitler-London method has been given by Pollard who obtains the energy of interaction in terms of a series of integrals involving the density matrix of the metal and atom. He imposes, however, a restriction on the wave function of the system which is only justified by the supposition that the electrons of the metal are in pairs of opposite spin with identical space wave-functions. By doing so, he denies the possibility of covalent bond formation, which is essentially associated with spin exchange, and in consequence his results are only valuable for the repulsive exchange force in physical adsorption, which was the problem in which he was interested.An immediate corollary of Pollard's work l a is that it is not possible by the Heitler-London method to predict important binding by exchange forces between an adsorbed radical and the free conduction electrons. It is necessary in this model that an electron of the metal should have a localized wave-function, more nearly approximating an atomic orbital than a Bloch wave, for formation of a covalent link. On the other hand, it is evident fIom consideration of the usual LCAO molecular-orbital treatment of the addition of an atom to a linear chain of similar atoms, each contributing one binding electron, that in this model it is just the lowering in energy of all the electron waves by the altered boundary con dition that gives rise to the binding of the new atom.A distinction between the two approximations in a given case may be made by magnetic determinations, as one would expect a stronger suppression of para- magnetism i f the Heitler-London picture is in better accord with the physical facts. In order to have some indication of the effects of a covalent link be- tween molecule and metal, we have used the LCAO molecular-orbital method to discuss the simplest model which can be expected to give relevant results. We consider two linear chains of identical atoms, coupled end to end, and examine the electron distribution in one of them when the number of atoms in the other tends to infinity. This constitutes a reduced model of a polyolefine free radical interacting end on with a metal surface.The calculation will merely be outlined here, details being given in Appendix B. For convenience, we consider the number of atoms in each chain to be even, zm in the first, zv in the second, and allow Y to tend to infinity. The secular equation is set up in the usual way, and with some manipula- tion reduces to the form (cos 8 + sin 8 cot zm8)(cos 8 + sin 8 cot zv8) = 0. Evidently this equation has a root 8, in each interval between successive singularities of cot zv8, and two roots in any such interval which also llBosworth, Proc. Roy. SOC., New South Wales, 1941, 74, 538. ?P = a1 $1' + a2 $28 + a3 * 2 m This device is more ingenious than valid. Pollard, Physic. Rev., 1939, 56, 324.K. HUANG AND G. WYLLIE 23 contains a zero of sin (2m + 1)8.The regularity of this distribution is sufficient to ensure that i f f(8) is a function analytic in the interval a < B < b , Examination of the coefficients in the orbitals of the whole system for varying values of 0, shows that we may regard the orbitals of the whole system, which are regularly spaced in 8, as divided into bands centred on the levels for the short chain by itself (corresponding to the zeros of sin (zm + 1)0), the electronic charge in an orbital diminishing sharply with increasing separation in energy from the centre of its band (for the short chain of 2m atoms). The electronic charge on a given atom due t o all the orbitals in the band corresponding to a single level of the short chain may then be evalu- ated by integration in the limiting case.After some approximation, we find for the number of electrons on the sth atom, counting from the free end of the chain, contributed by the Zth band :{I - (1 - P)-+ exp [- ir( - ) '1 SV'I - 8 2 sin2 [~ir/(2m + 111 2m + I 2nz + I $1 2m + I 241 ) I 1 9 2s (I - a2) sin [zZn/(zun + I)] x cos [-(zir - where and 8 is the ratio of the exchange integral between the two atoms at the coupled ends of the chains to the exchange integral between neighbouring atoms in either chain. The approximations used are valid for small 6 ; for sufficiently small 6 the above rather clumsy expiession is quite well approximated by = k2 - 2 cos2 [Z~/(2m + I)] + P cos [2Z~/(2m + I)], irS2 IT 2sIir 2m A{ + I I - exp [ - (2m + 6 4 sin4 (-)I zm + I cos 7-} 2w + I The corresponding expression for the free chain is I (I -cos-).2 S Z n 2.312 + I 'Lm +- I It thus appears that the effect of coupling to a long similar chain is to smooth out the charge variations in each orbital towards the coupled end of the short chain, the effect being most marked for the occupied levels of higher energy ( I approaching m). The importance of geometrical factors for this type of binding is indicated by the high power of 6 appear- ing in the exponential, 6 being itself a very steeply varying function of the atomic separation. A similar calculation carried through for the case that the two chains consist of different atomic species proved the inadequacy of the simple LCAO method. The difficulty is of the same type as arises in the dis- cussion of heterocyclic compounds.8 Unfortunately, it is much easier to obtain a reasonable approximation to the charge distribution, by methods of the sort discussed above, than to obtain a sufficient approximation to the energy of the system to be able to choose reliably between different, a prior2 reasonable, molecular configurations. In order to approach this latter problem, i t will be neces- sary to consider a specific system and use a much more empirical method.However, we may, from the point of view developed here, estimate what might be a profitable approach. The heterogeneous catalytic reactions which have been most ex- tensively studied under well-controlled conditions are the ortho-para- hydrogen conversion, hydrogen-deuterium exchange, and various hydro- genation reactions catalyzed by transition metals, especially of the nickel,24 MOLECULE NEAR METAL SURFACE tungsten, palladium, platinum family.These metals have high work functions which are nevertheless considerably lower than the first ionization potentials of the molecules concerned. It is therefore not possible to account €or their catalytic effectiveness in terms of simple electron transfer in either direction, which we have discussed in 9 I. They have unfilled d levels, which lend themselves, according to the Pauling picture of directed valence l3 to the formation of complex bond- systems. They are strongly paramagnetic, and the paramagnetism of the powdered metals is strongly influenced by the chemisorption of a catalytic pois0n.1~ A preliminary account of experimental work on the relation between catalytic properties and the electronic band structure of the catalyst is given by Couper and Eley.15 It thus appears probable that a representation of electronic conditions at the catalytic metal surface in terms of Pauling's resonating bond theory of the metal structure, with the formation of largely covalent bonds between definite metal atoms and the adsorbed reactants, should give a reasonable physical approximation to the real situation. The authors are indebted to Dr.D. D. Eley, Prof. C. A. Coulson and Prof. N. F. Mott for illuminating discussion of various aspects of the subject- matter of this note. One of us (G. W.) is indebted to the Anglc-Iranian Oil Co. Ltd., for a grant which made this work possible. Appendix A.-Calculation of {a) in a Concrete Case.As an example, we shall consider an ideal model most suited for our treat- ment. It consists of a linear molecule perpendicular to the metal surface. The interatomic distance and the distance of the first atom from the metal surface is assumed to be both equal to d. Metal The atomic orbitals are the usual p function which we assume to be given by the Slater type of function : Since the rigorous integration t o obtain a,, in the manner we have described above is not possible analytically for s i t , we shall suppose that the distri- bution I (b I2 which consists of the two well-known symmetric loops can be re- placed by two points at the charge-centres of the loops. The distance of the charge centre from the symmetry plane is given by * f (13) - I 5 1 _ - - 8 * a,,' This value leads immediately to the following expression for a,, Pauling, Proc.Roy. SOC. A , 1949, 196, 343. Dilke, Eley and Maxted, Nature, 1948, 161, 804. l5 Couper and Eley, ibid., 1949. 164, 578.K. HUANG AND G. WYLLIE 25 For s = t , we have the contribution from the image and the density itself : the former contribution can be obtained with the similar approximation as before For the contribution of the density itself the above approximation obviously breaks down. But we shall find the rigorous integratian can be carried through in this case. In accordance of the procedure we have described above (uJ2 is given by the following integral : The angular parts as they stand are not convenient for integration, but they may be readily converted to the desirable form.The integrand is seen only t o in- volve the relative angles between the fixed p-function axis and the two vectors Y and Y‘, and the integrations over the angles are just uniform integration over all directions of Y. Clearly we may replace them by integrating over all direc- tions of the p-function axis and that of Y‘, whereas regarding Y as fixed in direction. The integral becomes then where the 4 integration of Y is carried out. and the final result is All the successive integrations can be carried out by elementary means, 21 I0 (a8,) = -ape2 ; . (16) (15) and (16) combined give : Appendix B;-Consider a chain of 2m + 2~ similar atoms, of which the first 2m are evenly spaced, while the successive ZY are also evenly spaced with the same interval but the space between the 2mth and ( z n + 1)th atoms is different from the others.Let the wave function for a valence electron in a single atom separated from the rest be t,4 the corresponding energy E,, and the exchange integral between neighbouring atoms a t the normal separation be /3, while that between the 2mth and (2m + 1)th atoms is Sp. Then if the wave function of an electron in the chain be represented by a linear combination of the available wave functions of lowest energy of the different atoms Y, = + a&h2 . . ., and if we neglect all interactions except that of nearest neighbours, the energies E(= E , + e) of the states available for the electrons are given by the secular equation : = o26 MOLECULE NEAR METAL SURFACE where all the elements not on the three middle diagonal lines are zero.we substitute B = 2,3 cos 8, this equation reduces to If now sin ( 2 ~ + 1)s sin (2m + I)8 = 6 2 , sin ZYS sin 2mB which may be written in the form (cot 8 + sin 8 cot 2 m 8 ) ( ~ 0 ~ 8 + sin 8 cot 2r8) = S2. Evidently this equation has a root 8, in each interval between successive singular- ities of cot zr8, and two roots in those of these intervals which also contain a zero of sin (zm + 1)O. The regularity of this distribution is sufficient to ensure that, if f ( 0 ) is a function analytic in the interval a Q 8 < b Again, for a given value oi 0, the coefficients a, are determined by the set of linear equations : - 2 cos ea, + a2 = o a, - 2a2 cos B + a3 = o a,,,-, - 2uZm cos 8 + SU~,,,+~ = o 6a2,,, - 2 ~ ~ , , + ~ cos 8 + u ~ ~ + ~ = o Q2m+2r-1 - zazm+zr cos 6 = 0.Hence S=I J where A , = sin so, where s = I, 2, . . . zm. A,,,, = (6 sin 8)-I[sin (2m+1)8 sin no-82 sin 2m8 sin ( n - I ) B ] n = I , . . . ZY. The denominator in a, reduces to I sin 2m8 cos (2m + 1)s - S2 sin 2m8 sin (zm + 1 ) B If Y is large, this may be approximated by 4 + r/sin2 e p - 2 sin2 (2m + I)e - z cos 8 sin (zm + I ) e sin 2me + S2 sin2 zn~ejtt, where 4 is of the same order of magnitude as m. The factor to be multiplied by r/sin2 8 is a positive definite form, so for very large Y the denominator in a, tends to (r[a2 + sin2 (2m + I ) 8 sin-2 8(6-2 - 2 cos2 8 + P cos 28) + sin (2m + I ) 8 cos (zm + I ) 8 sin-2 8 sin 2 d ( 1 - S Z ) ] ) , . If, then, we suppose 8 to be small, we see that the coefficients of the atomic wave functions in the group I , .. . 2m will be small unless sin ( 2 m + I ) 8 is also small. Thus for the first zm atoms we may regard the almost uniformly spaced energy levels of the system as divided into bands centred on the levels for the 2112 chain by itself (the zeros of sin (2m + I ) 8 ) , with the degree of occupation of the levels in any band falling off with distance from the centre. Within a given band, then, the electronic charge on the sth atom (s < 2 m ) due to a given orbital may be approximated by sin2 s8 r(S2 + a, sin2 (2m + I ) 8 + u2 sin (2m + I ) 8 cos (zm + 1)6'K. HUANG AND G. WYLLIE 27 where a,, a, are constant, since the circular functions of 8, 28 vary only slowly with 8 in comparison with those of (2w + I)@. The total electronic charge on this atom due to orbitals within the band is then the sum of all the similar terms for which 8 lies between (I - 4) w and (I + Q)w, where w = w/(zm + I ) , I being some integer. Then, as observed above, if we make Y tend to infinity, this sum can be replaced by the integral, (2wz '+ 1)n .(::; 62 + a, sin2 8' + u2 sin e' cos 8'1 where we have replaced (2w + 1)8 by 8' in the above expression. If s is so small that sin2 [s8'/(2m + I)] may be taken as constant, the integral can be evaluated at once, giving sin2 sZw/(m + 4) in precise agreement with the expression for the charge on the sth atom due to the corresponding orbital in the isolated 2w chain. For larger s, however, the integral cannot be so simply evaluated. If we replace sin 8' by x and approximate t o the quadratic denominator by A eBa(s-a)* extending the range of integration in x from - io to + 00, and choosing the constants A , B, a to give the correct minimum value of the denominator a t the correct place, and the correct value of the integral for small s. we obtain for the charge on the sth atom due to the Zth band sin2 [s8'/(2m + I)] d8' x cos [-(zT 2 s - I - - sz sin A)]}, z m + I 241 2m + 1 where In 2zn $1 L- 6 - 2 - 2 cos2 - + 62 cos ~ 2113 + I 2m + I' El. H. W i l l s Physical Laboratory, Uqziversity of Bristol.

ISSN:0366-9033    

DOI:10.1039/DF9500800018

出版商:RSC    

年代:1950

数据来源: RSC

摘要:

K. HUANG AND G. WYLLIE 27 ON CONDITIONS FOR THE EXISTENCE OF SURFACE STATES BY C. A. COULSON AND G. R. BALDOCK Received 13th February, 1950 The existence or non-existence of surface states on the boundary of a mono- valent metal is investigated fully for simple cubic models in I, 2 and 3 dimen- sions, using the molecular modification of Bloch wave functions. Limiting values are found for the necessary changes required a t the surface atoms, both for their Coulombic (electronegativity) terms cc and their resonance integrals /I. It is shown that surface states may be induced by the perturbation caused by the approach of a polar, or ionic, group ; and that such surface states are more easily produced close together than separately. In certain non-cubic systems, e.g. graphite, surface states exist even without any necessary changes in cc or /.I on the boundary.Finally, a series of recent theorems on the charge distribu- tion in large molecules is applied to a study of the alternating charge distribution sometimes associated with surface states. From the earliest recognition that there were sometimes surface states associated with a metal, their importance for all types of surface reactions has been appreciated. But very few attempts have been made to see under what conditions such states appear. It is our intention in this note to present some preliminary results which we have just obtained in this field. Since a more complete account of this work will be presented later, we shall be content here merely to summarize our28 EXISTENCE O F SURFACE STATES conclusions, without giving many details of the procedure by which they have been obtained.After we have described the model and our notation, it will be con- venient to report our results first for the simple cubic lattice in one, two or three dimensions, and then for other lattices. We conclude with a short discussion of the validity and relevance of the idea of surface states, using for this purpose some known results in the theory of molecular structure. Notation.-As is usual, we treat a metal by the Bloch method or, more properly, by the “ molecular ” modification of it which recognizes the existence of one or more boundaries of the metal, and therefore replaces the progressive waves of Bloch’s treatment by stationary waves such as (I) below, in which all the coefficients are real.This is simply the familiar molecular-orbital method extended to much larger molecules than those normally found in chemistry, and occupying one, two or three dimensions. This link with molecules will enable us to make use of several quite general theorems recently established in this field (the so- called LCAO approximation) .1 As in the work of Goodwin and others, the metal is supposed to con- sist of a large, but finite, number of positively charged atoms which pro- vide an effective field for the conduction electrons. Each conduction electron is governed by the same Hamiltonian H . Its motion is described by stationary de Broglie waves, which are solutions of the wave equation €I+ = E+. The tight-binding approximation is used to represent the appropriate single-electron wave functions, so that, if the atoms are suitably ordered, any such orbital is where the c, are constants to be determined by a variational calculation and 4, is the atomic orbital which would be used by the conduction electron if it were in the presence of atom I only. We are implicitly neglecting any of the hybridization recently proposed for metals by Pauling, and we concentrate for the moment on systems where all, or nearly all, of the atoms contribute one metallic electron.This model is essentially the same as that used by Goodwin, though we differ from him in the way we deal with the boundary of the array and also in our inclusion of certain overlap integrals. Let us put 16 = Z C r 4 r , - (1) x, = J+:~+,dr, P I S = J4:H+*dr, ‘ (2) sTs = J ~ ? + J T .Then a, may be called, in molecular language, the Coulomb term of atom Y , and p,, and S,, are the resonance and overlap integrals between atoms Y and s. Without loss of generality we may take each 4, to be real : this makes both j3,, and S,, real also, and symmetric in r and s. The coefficients c, and the energy E of the orbital ( I ) are now related by means of the secular equations : . ( 3 ) The summation in (3) is taken over all the atoms of the metal except Y , and there is one equation for each atom r . If we decide to retain prs Coulson and Longuet-Higgins, Proc. Roy. SOC. A , 1947, 191, 39; 1947, Goodwin, Proc. Camb. Phil. SOC., 1939, 35, 205. Mott and Jones, Theory of the Properties of Metals and Alloys (Oxford c,(a, - E ) + z ’ c , ( ~ ~ ~ - ES,,) = 0, r = I, 2, .. . . s 192, I5 ; 1948, 193,4478 456; 1948, 195, 188. Univ. Press, 1936). Pauling, Proc. Roy. SOC. A , 1949, 196, 343.C. A. COULSON AND G. R. BALDOCK 29 between adjacent atoms only, relatively few terms survive in (3). As a rule we shall do this by supposing that interactions between all other pairs of atoms are negligibly small. In at least one of our calculations, however, we consider interactions between next-to-nearest neighbours also. Some explanation is needed regarding the inclusion of the overlap integrals STs. It is true, as Chirgwin and Coulson 6 have recently shown, that there are many cases in which charge distributions and interatomic distances are entirely unaffected by its inclusion.But the energies are always slightly changed and, particularly in the upper half of the con- duction band, as Coulson and Kushbrooke 6 showed for graphitic layers, the shape of the band is strongly dependent on the value of this overlap integral. Now if all the atoms are entirely equivalent, we may put for all Y , a, = a s,, "' = s '}for all neighbouring pairs YS. (4) But it soon follows that for simple cubic crystals, this precludes the possibility of surface states. We shall therefore accept (4) for internal atoms, and be prepared to characterize the surface atoms by a different value of a,, and different values of Brs and S,,. The details of these new values vary from model to model, and are described for each case as it occurs. The questions that we ask are : For what values of the parameters a, 8, S are there solutions of the secular equations that may be interpreted as surface states ? And do the energies of these states lie inside or out- side the band of continuous distribution of enzrgy ? But there are other related questions.Although the existence of surface states is undoubtedly an aid to catalytic action, it is by no means inconceivable that, even if such states do not exist at first, they are never- theless brought into existence by the approach of some other group, particularly polar groups, toward the metal surface. Thxe is a close parallel here to some work by Coulson and Longuet-Higgins,l who studied the perturbations induced in large aromatic molecules by the approach of some charged ion.In our present case, we could approximately de- scribe such activity by a change in the ar of one surface atom. And we ask the question: if one surface atom is changed in this way, will there be a surface state induced in the metal, which was not there before ? A supplementary question, to which we can give only an incomplete answer, is : in such a case, how will two such surface states, associated with two distinct surface atoms, behave towards each other ? Questions of this sort are clearly very important in discussing the variation of cata- lytic activity with fraction of surface occupied. Results.-We must now define a surface state more precisely. If, in one of the single-electron wave functions (I), c, + o as the distance of atom Y from atom m increases, and if this occurs at a rate independent of the total number N of atoms in the crystal (N being assumed large), then $ is said to be a point state associated with atom m.This imFlies that an electron in the orbital t,b is effectively Iestricted to a region close to atom m. The extent of this restriction depends on the rapidity of the convergence of the sequence (c7) to zero. This convergence is not necessarily monotonic, and there may be local increases as well a s de- creases near to atom m. We shall also encounter orbitals for which G, is relatively high in the regions of atoms m, n, 9, . . ., tending to zero away from these atoms. 5 Chirgwin and Coulson, Proc. Roy. soc. A , 1950 (in press). 6 Coulson and Rushbrooke, Proc. Roy. SOC. Edin., A , 1948, 62, 350.30 EXISTENCE O F SURFACE STATES Such states will be termed multiple point states associated with atoms m, n, p , .. . . The definitions of line states and surface states can obviously be formulated in precisely analogous ways. the one- dimensional linear chain, the two-dimensional square lattice, and the simple cubic lattice. For these models we shall outline some of the con- ditions under which these special states may occur. Throughout the following summary, the assumptions (4) are made for all the atoms except for those specifically mentioned. (I) LINEAR CHAIN.-Let there be N atoms in a chain numbered consecutively from I to N , and let We shall first consider three simplified types of crystal: a, = aN = u’ Bla = /3N-l, for the end atoms, = q/3 for the end bonds, where /3 is the resonance integral for all other adjacent pairs and 7 is a multiplier which may be either greater than or less than unity.In most cases q will be greater than I. We have thought it proper to allow for the end resonance integrals having a different value from the internal ones, partly because detailed calculations for the linear case of polyene hydrocarbon chains7 shows that the end links are appreciably shorter than the others, and also because in some unpublished work we have shown that variations may also be anticipated near the surface, and also in the surface, cf three-dimensional aggregates. In this model we include possible next-nearest-neighbour interaction by writing where w will usually be quite small. type we write p 2 4 = 1395 = - * - = BN-3, N-1 = For the end interactions of this p 1 3 = f i N - 2 , N = Wq8* Following the suggestion of Mulliken for molecules, and developed and by de Heer,e we suppose that all overlap by Chirgwin and Coulson integrals S,, are proportional to the corresponding Bra.I t is convenient to define y = p - a s , h = ( a - a’)/y, * ( 5 ) cr = X / ( I + AS), I - p = q 2 / ( I + AS). - (6) and to put These substitutions enable us to express the condition for point states quite simply in terms of cr, p, and W. If u = 0, the end atoms have the same Coulomb term as the internal atoms ; if in addition p = 0, then 9 = I, so that fi12 = /323, etc. (i) u = p = 0. There are no point states, whatever the value of W . (ii) o I. If w2 is neglected we find that the condition for point states depends only on u and p, and not at all on w (second- neighbour interaction). There is a point state whose energy is below the continuous band If (I = o the conditions become T] > 4 2 .If T] = I the conditions become u < - I / ( I + S ) , if CJ + p < - I and one with energy above the band if a - p > I. or a > I / ( I - S ) , Both these states are dcubly degenerate. They are double point and the states correspond to those found by Goodwin. states associated with the end atoms. 7 Coulson, Proc. Roy. SOC. A , 1939, 169, 413. Bde Heer, Phil. Mag., 1950 (in press).C. A. COULSON AND G. R. BALDOCK 31 (iii) u, = cc’. We now consider the possibility of point states occurring when nothing but the Coulomb term of the mth atom is changed.This atom may perfectly well be an internal or boundary atom. In this case the overlap integral S is ignored. The condition for a point state associated with atom m is I A ] > ~ / m . Thus in the interior of the chain, any deviation of a, from cc gives rise to a point state. (11) SQUARE LATTIcE.-(i) In a square lattice the next-to-nearest neighbours are separated by a distance 1 / z times the lattice constant. If we take into account the corresponding resonance integral wfi (without changing any of the other parameters), we find that no point or line state emerges for any value of W . (ii) We now consider the effect of altering the Coulomb term of only one atom (m), on the boundary of the rectangular array, from a to a’. In this case we shall neglect the overlap integral S altogether and write A = ( E - a‘)/fl instead of ( 5 ) .We assume that atom m is not near the corner of the rectangle, and we find that if I A 1 > 2.8 (approx.) there is a state whose energy lies outside the continuous band. This state is a point state associated with atom m. (iii) Suppose now that two atoms, m and n, separated by p atomic distances dong one of the edges, have an altered Coulomb term a’. If p is large, the condition for the existence of double point-states associ- ated with these atoms is I A I > 2.8. As p is reduced, the limiting value of I A I steadily decreases. For example, when p = 2 , so that the altered atoms are separated by only one intervening atom, the condition is I A 1 > 2.3 ; and when p = I , so that they are neighbours, it is I A I > 2 .Since I h I measures the difference in electronegativity of the affected atoms, we infer that induction of surface states is made easier by the presence of a perturbation already existing on the surface ; and that such surface (point) states will tend to be associated together in groups rather than distributed at random over the whole surface. It is possible that we have here a little insight into the nature of the active centres so frequently postulated for catalytic activity. (111) SIMPLE CUBIC LATTICE.-(i) Let us denote any atom in the crystal by Ir, s, t ) , where I < Y < L , I < s < M , ~ < t g N . Evidently there are LMN atoms in the crystal. We shall consider the effect of a change in the parameters for all theatoms on the two opposite faces r = I , Y = L of the crystal.alsl = aJ& = a’ (for all s, t). Also we suppose that the resonance integrals between all neighbouring atoms in these two planes have the value x/3, and that the resonance integrals such as 2g between one atom in the surface and the adjacent one inside the crystal, have the value qfi. All other non-vanishing reson- ance integrals are equal to /3, and we suppose that in every case the overlap integral is proportional to the corresponding resonance integral. We define A, CT, p as in the case of the linear chain (eqn. ( 5 ) , (6)), and we also introduce Y and p defined by For these surface atoms I - Y = K r ) / ( I + AS) p = u + 2v (cos I$ + cos +), where r+ = h / ( M + I) K = I , 2 , . . . M 2 = I, 2 , .. . N. 3 = Zn/(N + I ) The conditions for surface states will now depend on p and p.32 EXISTENCE OF SURFACE STATES There is a band of surface states of low energy if p + p < - I, and one of high energy if p - p > I. These bands consist of levels depending on p and p, and since p may take MN different values for fixed u and v the conditions may be fulfilled for part of one band but not for all of it. Each level is doubly degenerate and all the states are double surface states associated with the faces Y = I, Y = L. There is one such orbital for each of the modified surface atoms. These bands of surface states may ovzrlap the continuous band of energy levels, (ii) If only one atom (m) on the surface has a different Coulomb term u’ and if we neglect overlap, we find the condition for an energy level out- side the continuous band is 1 X ] > 4.5 (approx.).This state is a point state associated with atom m. IV. OTHER CRYSTAL STRucTunEs.--Our previous examples have all been associated with the simple cubic structure, in which the unit cell only contains one atom. But as soon as we go to more complicated structures in which two or more atoms comprise the unit cell, the situation is quite different. For now surface states may appear even without any perturbation of the edge atoms. This is because not all surface atoms are equivalent geometrically (as they were in the earlier cubic crystal), and the differences in environment produce the same effect as a change in a in the simpler model. Fig. I shows a part of a single An example will illustrate this effect.n FIG. I. layer of graphitic carbon, in which the atoms are arranged in regular hexagonal form. The electronic wave functions for such a layer have been discussed fully by Bradburn, Coulson and Rushbrooke,Q who ob- tained the energies in terms of the numbers n and m which determine the size of the layer. These energies are obtained from the secular determinant, which may be factorized, corresponding to nodes of the wave function parallel to the m and n directions. A combination of eqn. (9) and (12) in their paper, together with some rather tedious analy:,is which we shall not reproduce, shows that in a large layer such as Fig. I there are 2nJ3 surface states. Application of the argument developed by Coulson 10 shows that in a layer of this kind all the energies are in the range E , & 38, which is known to be the range covered by the continuum of two-dimensional orbitals.Thus none of the surface states lie outside the continuum. In Fig. I the surface states are associated with the atoms on the extreme left- and right-hand edges, and not those on the top or Bradburn, Coulson and Rushbrooke, Proc. Roy. Soc. Edin. A , 1948, 62, 336. l o Coulson, Proc. Camb. Phil. Soc., 1950, 46, 202.C. A. COULSON AND G. R. BALDOCK 33 bottom. This is linked with the fact that in a graphitic layer the unit cell contains two atoms. Those atoms on the left are all crystallo- graphically equivalent, and so are those on the right, but those a t the top and bottom are not. It may be presumed that similar surface states will appear in other such lattices. We are making further calculations to investigate this in more detail.One conclusion, however, is quite clear from the graphite example: surface states are quite liable to occur even without any changes in Coulomb terms or resonance integrals, but simply on account of the geometrical structure of the boundary. General Molecular Considerations.-It is perhaps worth stressing that certain quite general results may be obtained by treating a crystal as a large molecule and using the general theory developed by Coulson and Longuet-Higgins.1 For example : ( I ) The existence of surface states does not necessarily imply an uneven distribution of charge. Thus, in the graphite example in (117) we are dealing with an " alternant molecule ", and $here will therefore be a Drecisely equal number of electrons associated with each atom.The excess of charge near the edges due to the surface states is compensated by a corresponding excess in the body of the crystal due to the other electrons. (ii) In the same way, as Chirgwin and Coulson have ~ h o w n , ~ if there are no changes in Coulomb terms, but only in resonance integrals, the net charge is uniform. (iii) But if the Coulomb term of one atom is changed in the direction of increasing its electronegativity, it will carry a final net negative charge, and as we proceed away from this atom, other atoms will have an alter- nating positive and negative charge. In the case of a surface layer with increased or-values, the alternation of charge occurs as between one layer and its neighbouis. There are still one or two further molecular considerations that we may. " carry over " to crystal lattices. (iv) There is considerable uncertainty regarding the validity of using the same Hamiltonian operator H for each electron. These operators are not strictly self-consistent, and as Chirgwin and Coulson have shown in some unpublished work, we ought really to use a different operator for each electron, The resulting errors are not likely to be so serious in crystals as in molecules. (v) A more serious difficulty arises from the fact that the so-called " lowest configuration I' is not, by itself, a sufficiently good wave function. As Miss Jacobs l1 has shown for naphthalene, there is often considerable configurational interaction, whi'ch results in a slight unevenness of charge, more particularly a t the edges of the molecule, i.e. at the surface of the crystal. We are investigating this matter more carefully a t the moment, in this Department using a simplified model. Conclusion.-To some extent all the models that we have discussed above are largely formal. And consequently our conclusions are not immediately applicable t o any real problem. But we believe that they do illustrate tendencies and situations likely to be found in actual surfaces, and may serve to " point the way " to further specific calculation. Wheatstone Physics Laboratory, Thus : King's College, London. 11 Jacobs, Proc. Physic. SOC. A , 1g4g,62, 710. B

ISSN:0366-9033    

DOI:10.1039/DF9500800027

出版商:RSC    

年代:1950

数据来源: RSC

摘要:

A CALCULATION OF HEATS OF CHEMISORPTION BY D. D. ELEY Received 3rd April, 1950 Heats of chemisorption are calculated by Pauling’s equation for covalent Quite good agreement is secured for hydrogen on tungsten, copper Calculations for oxygen on tungsten and ethylene on nickel enable bonds. and nickel. us t o rule out certain mechanisms of chemisorption. There are a number of good reasons for believing that in many cases the chemisorptive bond is of a covalent type.l* It is a matter of some interest that this hypothesis allows a calculation of heats of chemisorption. Consider, for example, the chemisorption of hydrogen on tungsten. We write this as The differential heat of chemisorption per mole of hydrogen, Qo, is to be calculated, when the fraction of surface covered 8 --f o and we may neglect effects due to neighbour interactions in the monolayer. The result may be obtained in terms of bond energies E, ZW + H2 -+ zW-H.Qo = 2E(W--H)-E(H-H) . - (1) Considerable success has attended the recent application of electron- pair theory to metal^.^ Therefore I shall assume that the energy of the surface W-H bond may be calculated from Pauling’s equation,4 (2) To evaluate eqn. ( 2 ) we first need to obtain E(W-W). We shall assume that each metal atom has 12 nearest neighbours. This result is true for face-centred cubic lattices, but not strictly for body-centred cubic lattices, where there are 8 nearest and 6 next nearest neighbours. In the latter case, however, no great error is involved in treating the lattice as one with 12 nearest neighbours. Since two atoms are involved in each bond we can write E(W-H) = &(E(W-W) + E(H-H)) + 23-06 (xw - x ~ ) ~ .E(W-W) = 2. s, I 2 where S is the sublimation energy of the metal, listed in Landolt-Born~tein.~ The term involving the difference in electronegativities xw - xH is estimated by Pauling’s approximate rule that it is equal to the dipole moment of the bond in debyes, p. If the measured contact potential of a complete monolayer is V volts, then we may write where C, is the number of sites per cm. of surface, taken here as the mean of the (110) and (100) surfaces, i.e. 1-2 x 1015 for W and 1-38 x 1015 for Ni. This value of p for an atom in a full layer can only be equated to p,, for a dilute layer if we assume depolarization effects to be small. Couper and Eley, this Discussion.Eley, Amer. Chem. SOC. Symposium, June, 1950 (to be published in J . Pauling, The Nature of the Chemical Bond ((New York, 1939). p = v/2ir3ooc,, Physic. Chem.). Pauling, Proc. Roy. Soc. A , 1949, 196, 343. 6 Landolt-Bornstein, Tabellen, Erg. IIIc, 2709. 34D. D. ELEY 35 The calculations have been made for systems where modern experi- mental data are available, and the results presented in the Table. The bond energy values used are due to Pitzer.6 For nitrogen and carbon bonds, two values are possible, " high " and " low " values, depending on the values chosen for the heats of atomization of carbon and nitrogen. The situation is well presented by Coates and Sutton.' Pitzer's values are high values, and for the -N=N- bond, we have also taken the high value given by Coates and Sutton.' The low values give the results which are very little different from those listed.In applying the equation t o multiple bonds, we are making a definite assumption, since the equation was deduced for single bonds. In par- ticular, it is not at all clear that the equation will give a correct estimate of the ionic term. Also, depolarization effects are probably more important for dipoles such as W = 0, 1-76 V contact potential, compared with W-H which has the smaller value of 1-04 V. v, Volts System p9 = x g l - x ~~ zNi+ H, +zNi-H zCu+ H, +zCU-H 2tv-0 +zW=O -- I- -0.34 D -- ? zNi+C,H, -+H,C--CH2 Ni FJi / \ -0.13 ? - 1-76 lo ~ _ _ _ - 1-38 lo ____ +0*83 -0-78 -0.61 -toe32 !?(M - M) kcal. 33.8 164 -- 13.6 2 x 33-8 3 x 33'8 16.4 C(A ~ A) kcal.103.2 103-2 103.2 Experi- mental Specimen Wire Film Powder Film Powder Powder Wire 1 ) ,I Wire Powder Film Discussion The agreement between calculation and experiment is good for W-H and Cu-H. For Ni-H, the calculated result is lower than the value of 31 kcal., which since it was obtained with an evaporated film is more likely to correspond to the true value for a clean surface than the value of 21 kcal. for a powder. The differences in electronegativities are what one might expect from Pauling's thermochemical values for similar bonds. 6 Pitzer, J . Amer. Chem. SOC., 1948, 70, 2140. Coates and Sutton, J . Chem. SOC., 1948, 1187. Bosworth, Proc. Camb. Phil. SOL, 1937, 33, 394. 9 Mignolet, this Discussion. lo Bosworth and Rideal, Physica, 1937, 4, 925.l1 Roberts, Proc. Roy. SOC. A , 1935, 152, 445. l2 Beeck, Rev. Mod. Physics, 1945. 17, 61. l3 Frankenburg, J . Amer. Chem. SOC., 1944, 66, 1827. l4 Eucken and Hunsmann, 2. physih. Chem. B, 1939, 44, 163. l5 Ward, Proc. Roy. SOC. A , 1931~ 133, 506. 16 Johnson and Vick, ibid., 1935, 151, 308. 17 Davies, Jr., J . Amer. Chem. SOC., 1946, 68, 1395.36 A CALCULATION OF HEATS OF CHEMISORPTION Thus for the nearest example, Al, xM = 1.5 and for H, X, = 2.1, so that x, - X, - - 0.6. For W=O and 2W=C,H4, the calculated values are markedly lower than the observed values. However, the calculations re- produce the general features of the observed results quite well, and the discrepancies may be associated with changes in hybridization and loss of resonance energy on adsorption at the surface. The experimental values for ethylene may be too high because of a certain amount of self-hydro- genation.12 The calculated oxygen value may be low because we have under-estimated the ionic term.Thus Pauling’s table 4 would give xAl - x,, = - 2.0 and one should not expect tungsten-oxygen to be very different . The nitrogen value is much higher than the preferred experimental value of 28 kcal. The relatively low stability of nitrogen films as com- pared with ethylene films has been qualitatively demonstrated by other methods,1* adding weight to the low values for Qexpt. This discrepancy may be connected with the relatively large ratio E(N = N) /E(N - K) compared with E(C = C) /E(C-C) .* Another possibility €or chemisorption is hT=h- 2W+N2-+d h but the calculated value is Qcalc.= - 38 kcal. which rules this out. Beeck has suggested that the chemisorbed film of ethylene consists mainly of acetylenic complexes. We have calculated three possible processes of formation, the third one being that favoured by Beeck. C H d H - (1) - ( 2 ) / \ 4Ni + C,H4 -+ Ni Ni + 2NiH Qcalc. = 25-2 kcal. . CH=CH / , \ 2Ni +.C,H4 --f Ni Ni +kHz Qcalc. = 8.0 kcal. CH=CH / 2Ni + 2C2H4 + Ni \ Ni + C2H, Qcalc. = 36-2 kcal.7 (3) The first process is a possible one energetically, although obviously not as likely as the associative adsorption calculated in the Table. How- ever, it is ruled out by the observation that hydrogen deuteride formation is inhibited by ethylene, so that there is no chemisorbed hydrogen in the film.19 The second process is clearly unlikely but the third process is a possible one.Finally, there is the process of dissociative chemisorption suggested by Farkas, 2o Ni + CZH4 + Ni-CH=CH, + &Hz Qcaic. = 4, which gives too small a heat. The associative process given in the Table yields the best value of Qcalc.. All the calculations for ethylene and nitrogen have been repeated using low values of the carbon and nitrogen bond energies concerned with very little difference in the calculated heat values. This is because the changes effect both the bonds disrupted and the bonds formed to metal in the same way. l8 Eley and Rideal, Proc. Roy. SOC. A , 1941, 178, 429. * It has been possible subsequently to solve this problem, cf. the following t 1.e.18.1 kcal. mole of ethylene. 19 Twigg and Rideal, Proc. Roy. SOC. A . , 1939, 171, 55. 2O Farkas, Trans. Faraday SOC., 1939, 35, 906. discussion.D. D. ELEY 37 In one of his later papers, Roberts 21 indicated a new view that possibly The only si mple alternative the oxygen film on tungsten is not atomic, to the process in the Table is 0-0 32 I7 68 36 39'7 Clearly this mechanism is ruled out because of its low heat value. It is hoped to improve this approach to chemisorption in future by a theoretical consideration of the type of bond involved, but even at its present stage, the method offers an approach to the heat of adsorption, which, while it is of great importance in chemical kinetics, is difficult to determine experimentally. The calculations support strongly the notion that the chemisorption bond is an electron pair bond, rather than a completely ionic bond.39 32 51 39 138 I should like gratefully to acknowledge that the two values for nickel contact potentials are taken from the paper by J. Mignolet (Li&ge),a2 and communicated personally to me beforehand. 44 I02 64 43 ADDENDuM.-It is possible to extend the calculations in my paper to all the new data reported by Beeck in his paper on Hydrogenation Catalysts. The Table compares calculated values (kcal./mole gas) with the values observed by Beeck. 15'7 34'7 39 I02 Gas H2 %d C2H4 Metal Jobs. calc. 1 obs. calc. Rh 28 23 50 42 50 Ni 31 I7 58 36 40 Fe 1 Ta The calculated values for C2H4 are for associative chemisorption, i.e. M-CH,-CH,-M. The heats of sublimation of Ta and Rh are not available, but I have found a good linear relation exists between sub- limation energy and melting point for the related metals, from which I have interpolated the values for Ta, S = 184 kcal., and Rh, S = 130 kcal.I have assumed the surface dipoles for H adsorption are the same for Rh, Fe and Ta as for Ni, and for CaH4 adsorption the same for Fe, Ta, W, Rh as for Ni. It seems likely that there will not be any large variations in the ionic term, for one gas with the range of metals, i.e. we should not expect very large variations in surface dipoles. Nevertheless, I would point out that this calculation strictly requires data on contact potentials at low surface coverings of gas, which are not available at present. The fundamental significance of the success of the calculation is this, that the surface M-H bond is closely similar to the M-M bond in the solid, i.e.it may be treated as a covalent bond, but of the metallic type, resonating below the surface of the metal with all the nearest neighbour metal atoms. It assumes that the hybrid orbitals are the same as in the bulk metal, essentially d3sp3 metal orbitals. This, of course, can only be an approximation and for the last two years, Mr. Crowne in my labor- atory has been building up the technique to test this hypothesis, by measuring the change, if any, in the surface paramagnetism of tungsten when hydrogen (and other gases) chemisorb. We know that when dimethyl 21 Roberts, Some Problems on Adsorption (Cambridge University Press, * 1.e. ignoring the possibility of a R bond.19391, PP: 88, 113. z2 This Discussion.38 A CALCULATION O F HEATS OF CHEMISORPTION sulphide is adsorbed on palladium, atomic d orbitals are pressed into service to form surface bonds, but in this case we have a co-ordinate link formed to the metal, rather than the simpler bond we are here considering. Calculations on the nitrogen data of Beeck, Cole and Wheeler enable us to give some quantitative support to views advanced by these authors, and originally by Taylor 23 as to the nature of these films. I give the arithmetic so that the method of calculation is clear. The value for N, on Ta observed is Q,, = 135 kcal. N, + eTa -+ eTa = N Now we calculate Just as for tungsten we calculate Qcalc. = 109 kcal. Qcaic. = 17 kcal. = 25 kcal.H, + 2Ta = N + 2Ta = N - H The steps are :. Ta = N --f Ta = N- The N-H bond is 92-2, the H-H, 103.2. :. Qcaic. = 2(92.2 - 31.9) - 103.2 = 17.4 kcal. The agreement here is such as to convince us that our models are probably right. The observed heats of N, on Fe (10 kcal.) and on W (28 kcal.) must be low because the chemisorption largely gives some species such as M=N-N=M, (for W=N-N=M, Qcalc. =- 3-1) and the pro- duction of the atomic nitrogen films may well be inhibited by an activ- ation energy as suggested by Taylor and Beeck. Finally may I refer to one way in which aromatic resonance energy may lower heats of chemisorption. For benzene Q = -31.9 kcal. To a first approximation where R, - R, is the diflerence in resonance energies between butadiene and benzene, i.e., -39 kcal. Thus Qcslc. = 36 - 39 =- 3 kcal. and benzene should be weakly chemisorbed, compared t o ethylene, in line with the different kinetic behaviour in exchange and hydrogenation ~ e a c t i o n s . ~ ~ Qca~c. = Qcalc.(C&a) + R4 - Re, Note added in proof.-Beeck in Advances in Catalysis, Vol I1 (New York, 1950), p. 183, gives for nitrogen on evaporated tungsten films Qo(expt.)=g5 kcal./mole. This is in good agreement with the calculated value for atomic nitrogen films, and is probably to be preferred to the value based on rates of desorption. The University, Bristol. 23 Joris and Taylor, J . Chem. Physics, 1939, 7, 893. 24 Eley, Quart. Rev., 1949, 3, 221.

ISSN:0366-9033    

DOI:10.1039/DF9500800034

出版商:RSC    

年代:1950

数据来源: RSC

摘要:

THE ACTIVATED COMPLEX IN CHEMISORPTION AND CATALYSIS BY HENRY EYRING, CHARLES B. COLBURN AND BRUNO J. ZWOLINSKI Received 61h February, 1950 The basic assumptions underlying the theory of absolute reaction rates have been analyzed in terms of recent studies. A general treatment of chemi- sorption and catalysis is given in terms of the activated complex theory of chemical kinetics. A mechanism is proposed for the hydrogenation of ethylene which appears to be in agreement with the available data. Through the efforts of investigators such as Rideal, Taylor, Schwab, Langmuir, Hinshelwood and others, the broad outlines of the field of catalysis have been defined and the importance of parameters like extent of surface, nature and condition of surface, coverage, active sites, geometry put in their proper perspectives.However, one is still not in the desir- able position whereby for any one case one may predict and calculate the extent of a surface reaction from first principles. In this regard it may be worth while to Ye-examine the assumptions underlying the theory of absolute rates of reaction and show its applicability in the interpreta- tion of heterogeneous reactions. In formulating the rate of any chemical reaction, consider reaction complexes passing from one region of configuration space to another. Along any one reaction path there will always be a region of phase space corresponding to a maximum free energy separating the initial and final states. The number of reaction complexes passing through this region is given by - dC/dt = XniCnpnt, .(1) n, i where C = total number of complexes in initial state at any time t, X = probability that the reaction complex crosses the barrier in any v = frequency with which the complexes cross the energy barrier. one attempt, The subscripts n and i refer to the quantum numbers associated respectively with the degree of freedom along the reaction co-ordinate and with the remaining internal degrees of freedom of the reaction com- plex. The above equation applies exactly to any rate process under any set of conditions. Assuming a normal distribution of energy among the internal degrees of freedom of the complex or the equivalent idea of an equilibrium existing between the reactants and the activated state at the top of an energy barrier, the well-known expression obtained for the specific rate constant €or a reaction of any order is : Here, X is the average transmission coefficient, F* the partition function of the activated complex, Fg the partition functions for the reactants and c0 the activation energy of the reaction at the absolute zero of tem- perature.Although the strict validity of the equation rests on the establishment of an equilibrium, the interpretation of many varied rate 3940 THE ACTIVATED COMPLEX IN CHEMISORPTION phenomena in terms of the above relation lends support to its applicability to most irreversible processes. The concept for which one could wish more definite proof before proceeding to a study of the mechanics of heterogeneous processes is the equilibrium postulate. For adiabatic reactions involving a rearrangement of matter as em- bodied in the idea of a reaction complex surmounting an energy barrier, it appears to be sufficient to ascribe X, the transmission coefficient, a value of unity.Hirschfelder 1 g and Wigner have considered more closely the shape of the potential energy surfaces in the region of the activated state to find that only in rather exceptional cases can one expect the % to deviate from unity. Born and Weisskopf formulated a mechanism of surface reactions based on the idea of tunnelling through the potential barrier which would be reflected in values of X less than unity. A t the present time there is little evidence to indicate that this may be an important step in catalysis. The Equilibrium Postulate.-Consider a unimolecular decomposi- tion of a molecule on a surface.For a surface to be effective, it is im- perative that a much closer and more specific interaction takes place between the molecule and the surface atoms than can be ascribed to dispersion forces. Regarding this intermediate as the reaction complex assume that reaction consists in the complex passing as a result of molec- ular collisions or vibrations into a set of levels corresponding to the activated state or the final state of the products. The following set of linear equations with constant coefficients is obtained : for the n possible energy levels of the system. The vi5’s are the specific rates of transition from the level i to the level j , which, in principle at least, can be calculated. Solution of the above set of linear differential equations can be carried out readily and takes the following form n C4 = C AkB5, ebkt, .(4) k = l where k f k are the arbitrary constants in the general solution determined by the initial values of the C,’s ; B,, and b, are functions of the transition constants vij, which arise from solution of the secular or characteristic determinant. Each Ci is now a completely determined function of time and an overall rate of reaction can be calculated under any set of equi- librium conditions. To compare the actual rate with the equilibrium rate as determined by a Maxwell-Boltzmann distribution of reacting complexes, a function r is defined whose deviation from unity with the extent of reaction pro- vides a measure of the validity of the equilibrium postulate in chemical rate theory.The actual rate for the forward reaction is given by where k and I refer to the levels of the initial and final states, respectively. Assuming a Maxwell-Boltzmann distribution function, the equilibrium rate for the forward process is then given by the following : €1 E2 v, =- i=l Hirschfelder and Wiper, J . Chem. Physics, 1939, 7, 616. Hulburt and Hirschfelder, ibid., 1943, 1 1 , 276. Born and Weisskopf, Physik. Chem., 1931, 12, 206.EYRING, COLBURN AND Z'CVOLINSKI 41 where C, is the total concentration of complexes in the levels of the initial state a t any time t. Hence, the ratio of the actual rate to the equilibrium rate is 5 i virci i = l j = k + l r = k 1 { h : 1'4 n * . (7) 20-i &i 2 c (Vi,e-s)}; k 2 e-m s = l j = k + l i =1 Calculations of this nature * have been carried out for an extremely simple model of reacting system (with n equals 4) based on chosen values of proper magnitudes for the transition constants.The results are shown graphically in Fig. I. Though the calculations were made on an over- simplified model under rather extreme conditions of non-equilibrium, only an error of 20 yo occurs in the specific rate constant as determined by the theory of absolute rates of reaction for I yo of the material reacted. Essentially similar results were obtained by Kramer who employed classical diffusion theory. Hulburt and Hirschfelder in a recent study regarded the reaction complexes in configuration space as a compressible fluid and employed hydrodynamic theory t o show qualitatively the correctness of the equilibrium postulate.In view of the above studies, a complete rate theory is available which, except for minor refinements, can be applied with confidence to all rate processes. General Treatment of Chemisorption and Catalysis .-The application of the activated complex or transition state theory to surface reactions was carried out by Kimball,' Temkin, 8 Eyring 9~ l1 and more recently by Laidler.ll9 12* 13 A slightly more generalized approach will be developed in the following paragraphs. Zwolinski and Eyring, J . Amer. Chem. SOC., 1947, 69, 2702. 5 Kramer, Physicu, 1940, 7, 284. Hulburt and Hirschfelder, ibid., 1949, 17, 964. Kimball, ibid., 1935, 6, 447. * Tempkin, Actu Physicochim., 1938, 8, 141. Eyring, J.Chem. Physics, 1935, 3, 107. lo Glasstone, Laidler and Eyring, The Theory of Rate Processes (McGraw-Hill l1 Laidler, Glasstone and Eyring, J . Chem. Physics, 1940, 8, 659, 667. l2Laidler, J . Physic. Chem., 1948, 53,712. Book Co., Inc., New York, 1941). Schuler and Laidler, J. Chem. Physacs, 1949, 17, 1212. B"42 THE ACTIVATED COMPLEX IN CHEMISORPTION The following assumptions are made : (I) In every surface process, the activated complex consists of the reactants and the catalyst. In certain specific cases, where-except for the catalyst atoms-the activated state contains the same number and kind of atoms of the reactants as the homogeneous reaction, the differ- ence in energies of activation bet ween the homogeneous and heterogeneous reactions is ascribed to the heat of adsorption of the homogeneous activ- ated complex to the surface of the catalyst.( 2 ) The surface reaction is considered as a homogeneous reaction between the gaseous reactants and the atoms, molecules or ions of the catalyst. In this analysis, we are neglecting volume phenomena, such as solution of reactants, and the effect of reverse reactions. Consider a reacting system consisting of two different gaseous species and a catalyst. The following mechanism can be written based on a model of the two different gaseous reactants interacting w-ith the surface. The kind and number of atoms in the activated complex will determine the kinetics of the overall process, so as to agree with experimental data. Thus one obtains nCi -k mCj + Sk ( c n i c m j s k ) * -% ci+ 1 + cj- 1 + sk, where the C i , C j = gaseous concentration of reactants, Ci+ Ct-r = gaseous concentrations of products, 1 .(8) Sk = kth surface site. J The subscripts n and m in the activated complex are used to denote any fragmentation or dissociation of the original reactants. As is well known, the rate-determining step in catalysis can be one of a number of different processes, e.g. diffusion to the surface, diffusion on the surface (excluding solubility in catalyst), adsorption of reactants, surface dissociation, combination of radicals on the surface and desorption of products. Assuming no alteration in surface characteristics with re- action, it is possible to write, in the most general form, fcr the initial velocity of reaction, the following equation without assuming any one specific activated complex for the mechanism : v = X(Cn,C,,S,)+v .(9) Expressing the concentration of activated complex in terms of the react- ants, one has the result Ff - By proper choice of an activated complex, i.e. specifying the values of n and m the rate equation for any kind of a surface process is obtained. If i t is assumed that all the products and reactants establish equilibrium concentrations on the surface, the effect of pressure and poisons can readily be accounted for by modification of the above equation with the ap- propriate adsorption isotherms. Mechanism of Ethylene Hydrogenation.-To illustrate more fully the application of the above theory the procedure appropriate to the determination of the mechanism of the hydrogenation of ethylene may here be outlined.This reaction was chosen because a successful mechanism for the catalytic hydrogenation has not been proposed, even though the reaction has been studied extensively by a number of workers.EYRING, COLBURN AND ZWOLINSKI 43 (Beeck l4* 16* l6 and co-workers investigated this reaction on numerous catalysts such as chromium, iron, cobalt, nickel, rhodium, palladium, platinum, tantalum and tungsten ; Twigg l7 on nickel ; Taylor and co- workers la, l9 on various oxides ; A. Farkas,,OS 21 L. Farkas 20e 21 and Rideal 22 on nickel ; Toyama 23s 24 on nickel at temperature of oo C and in the temperature range 99-165" ; Pease 25 on copper ; Wheeler and Pease 26 have studied the relative rates of hydrogenation by deuterium and hydrogen on copper.Many other workers have also contributed much to the understanding of the mechanism of hydrogenation. work on the nature of adsorbed layers is fundamental to the knowledge of all surface processes.) From these studies the following facts will have to be explained by or be in agreement with any proposed mechanism : (I) H, and C2H, are rapidly adsorbed by metallic surfaces even a t liquid air temperatures, however, in the case of the hydrogen about 20 yo of the H, can be removed by pumping at room temperature. (2) AHads for H, varies from 30 to 18 kcal. per mole on Ni; AHade for C,H, varies from 60 to 23 kcal. per mole on Ni. The larger value is the heat of adsorption on a clean metal surface and the smaller value is the heat of adsorption on a nearly complete monolayer.( 3 ) The activation energy of the hydrogenation is 10.7 kcal. on Ni, Rh, Co, Fe, Pd, Pt, W, Ta. (4) The value for the average heat of adsorption of ethylene on nickel is 41-5 kcal. (5) The reaction rate may be expressed as V Q : P ~ ~ P & ~ at low tem- peratures. (6) The reaction rate may be expressed as z ~ a ~ ~ ~ P & ~ ~ at high tem- peratures. (7) The overall heat of reaction is 32 kcal. per mole. (8) The hydrogenation appears to be molecular in hydrogen. These observations which must be explained are apparently satisfied only by the following mechanism. Both ethylene and hydrogen are adsorbed on the surface but ethylene being much more tightly held tends to displace hydrogen molecules. The activated complex is an ethane just desorbed from its two positions on the surface.Suppose that for an adsorbed ethylene there are b neighbouring positions which a hydrogen molecule can occupy and still react with the ethylene to form ethane. We let a represent the number of positions per square centimetre accessible to both hydrogen or ethylene and we take u1 and u, as the fraction of these positions covered by ethylene and hydrogen respectively ; k' is the specific rate of reaction of an adsorbed ethylene with an adsorbed hydrogen mole- cule. We shall not take explicit account of the co-operative forces which tend to make adsorbed molecules bunch on the surface. Then the velocity of reaction v in molecules per square centimeter is v = au1u,bk'. - ( 1 4 l4 Beeck, Smith and Wheeler, Proc.Roy. Soc. A , 1940, 177, 62. 1S Beeck, Rev. Mod. Physics, 1945, 17, 61. 16 Beeck, ibid., 1948, 20, 127. l7 Twigg, Trans. Faraday Soc., 1935, 35, 934. l9 Woodman and Taylor, ibid., 1940, 62, 1393. 2O Farkas, Farkas and Rideal, Proc. Roy. Soc. A , 1934. 146, 630. 21 Farkas and Farkas, J . Amer. Chem. Soc., 1938, 60, 22. 22 Rideal, Chem. and Ind., 1943, 62, 335. *3Toyama, Rev. Phys. Chem., Japan, 1937, 1 1 , 152. 24 Toyama, ibid., 1938, 12, 115. 25 Pease, J. Amer. Chem. Soc., 1923, 45, 1196, 2235. 26 Wheeler and Pease, ibid., 1936, 58, 1665. 27 Roberts, Proc. Roy. Soc. A , 1935, 152, 445. Woodman, Taylor and Turkevich, J . Amer. Chem. Soc., 1940, 62, 1397.44 THE ACTIVATED COMPLEX IN CHEMISORPTION To calculate the U'S we define a partition function f, for ethylene such that p1 = - kT In f,, where p1 is the chemical potential of ethylene.Here V is the total gaseous volume which contains n, molecule of C2H4 so that V/n, = kT/P,, where p , is the partial pressure of ethylene. The other quantities in (13) have their usual meaning. f a is defined analogously for hydrogen gas. fs represents the partition function for the surface atoms before they combine with hydrogen or ethylene ; hl and faz repre- sent the partition functions for the compound ethylene-surface and hydro- ge. -surface respectively. Then f S l f 1 =l = fSflf2 + f S l f 2 + f s 2 f i ' and f d l f 2 =2 = f S f l f 2 + f S l f Z + . f , 2 f l ' Thus substituting in (12) gives or Here f38S is the combined partition function for activated ethane with all the surface atoms involved in reaction and f * = f3s8h-2. Since under all experimental conditions v is proportional to the pressure of hydrogen we must suppose the quantity K p = - may always be neglected in comparison with I and with 1% = K,p,.Further, if we write fl = C / p , f s z - f 8 f 2 f S f 1 At low pressures of ethylene ZI ot 9, and at high pressures v Q I @ , in agree- ment with experiment. By setting -(p1(1 + K , p , ) - 2 ) = o we find that for K,pl = I the value of v is independent of pl. Substituting p1 = I / K , gives d dPl Substituting for C and K , gives We now substitute for these quantities. We assume b = 2 corre- sponding to two neighbouring hydrogen molecules being able to com- bine with an adsorbed ethylene. Then ZJ = 170/~ x 1015 x z x 5-6 x rolZ I 8.rr2(8a3ABC*)'~2(kT)512 - 3 e RT h v f 6h3 -- (16) I - e kT r"r i = l I I h v fi h v ( z .r r ~ n ~ ~ k T ) ~ / 2 kT 8dIH2kT -~ h3 P 2 2h2 1 - e-=&i=lI - e - ~ C ~ H 4EYRING, COLBURN AND ZWOLINSKI 45 Here E , is the energy required to pass from gaseous hydrogen and absorbed ethylene to gaseous ethane. This is the heat cf adsorption of ethylene minus the heat of reaction of gaseous hydrogen with gaseous ethylene t o make gaseous ethane and agrees with the experimental activation energy E,, = 10,700 cal. as nearly as we can estimate it. This point is discussed further below. The internal degrees of freedom of ethane plus its rotational degrees have an entropy of 18.46 cal./mole deg. at 300° K. The internal vibrations of ethylene at 300' have the value of 0.57 cal./mole deg.If we use these values and the known values for hydrogen the only things left undetermined in (16) are the two vibrations associated with the motion of ethane tangent to the surface and these same two vibra- tions for ethylene plus its motion normal to the surface. Thus we obtain for the velocity of reaction h v 2 (1 - e-=) 'LI = 1.4 x 10-~p, mole/cm.2 sec. . * (17) I hvi e-kr i = 1 1 - T? This is to be compared with ZI = 1-2 x I O - ~ ~ ~ found by Beeck for un- oriented nickel where the surface roughness was found to have the value 170 which we used in our calculation, Thus, if we assume the vibration frequencies in (17) cancel agreement is too good since many things includ- ing the experimental values may be slightly different. Quite apart from the numerical agreement it does appear that this must be the reaction mechanism.L FIG. 2. If we had an exact value for the heat of adsorption of ethylene our postulated mechanism would enable us to calculate a value for E , to compare with the experimental value E , = 10,700 cal./mole. The situ- ation is as follows. The homogeneous hydrogenation of ethylene requires an activation energy of 43 kcal. together with a AH of reaction of 32-5 kcal. and occurs readily on the surfaces of metals of Group VII such as Rh, Fe, Ni, Pt, Pd as also W, Ta and Cr, with a constant energy of activ- ation at 10.7 kcal. Whereas the AE* remains constant, the temperature- independent factor of the rate constant shows variation by a factor of 10,000 as we progress from W to the much more active Rh.This has been shown by Beeck and co-workers 143 159 who studied this reaction on evaporated films of the above metals. The average heat of adsorption46 THE ACTIVATED COMPLEX IN CHEMISORPTION of ethylene is 41-5 kcal. whereas that of hydrogen is 24 kcal. on prepared Ni evaporated films; thus, the more strongly adsorbed ethylene pre- ferentially covers the surface of the metal catalyst in the place of the hydrogen. The 10.7 kcal. of energy represents the amount of work necessary to form the gaseous ethane from the adsorbed ethylene and the gaseous hydrogen for the condition where the rate of reaction was measured independent of the ethylene pressure. The temperature co- efficient for the reaction will take on different values depending on the magnitudes of the pressure of the two reactants.This is shown in Fig. 2, where the potential energy changes are shown along the reaction co- ordinate. Such specific considerations of the energies of the process are limited to the specially prepared catalytic surfaces as employed by Roberts and by Beeck. One has only to observe the variations in the heats of ad- sorption of ethylene, as summarized in Table I, to realize the importance TABLE I.-HEATS OF ADSORPTION OF ETHYLENE Metal Au Fe . Ni . Cr,O, . CU Pt . ZnO . ZnO-Cr,O, (reduced) ZnO-Cr,O, (oxidized) Pt-Black . Ni . Ni . Heat (kcal./mole) t 8.8- 6.9 16 - 8 10.8 16 9 25 -19 20 -17 9 15 60 -20 I 2 I1 -I0 Reference Beebe-Schwab * 3 3 .I I D I , I , , a , I 9 , Maxted, Moon Toyama 23 Beeck l4 *Schwab, Handbuch der Katnlyse (Springer, 1943). -f Variation of heats of adsorption with extent of surface coverage. Maxted and Moon, Trans. Faraday SOC., 1936, 32, 1375. of catalyst preparation, as is well known. Changes that have been meas- ured in the heat of adsorption indicate the heterogeneity of the catalysts, whose activity is conditioned by the sintering, crystallization and im- purities, e.g. hydrogen and oxygen resulting from the mode of preparation of catalysts from their salts. Such catalysts, however, as pointed out by H. S. Taylor, are of prime importance in industrial application and will remain a constant challenge to the chemist. The authors wish to acknowledge a grant from the United States Naval Research Office which made this investigation possible. Special thanks are due to Dr. R. B. Parlin for reading the paper in manuscript and €or helpful discussions during the course of the study. Department of Chemistry, University of Utah, Salt Lake City, Utah.

ISSN:0366-9033    

DOI:10.1039/DF9500800039

出版商:RSC    

年代:1950

数据来源: RSC

摘要:

THE ACTIVATED COMPLEX IN HETEROGENEOUS CATALYSIS BY KEITH J. LAIDLER Received 16th February, 1950 The evidence that certain surface reactions proceed by interaction between an adsorbed molecule and a gas-phase molecule is reviewed briefly, with special reference to the para-ortho hydrogen conversion and the combination of atoms and free radicals. On the basis of absolute rate theory, general rate expressions are developed for reaction between two molecules A and B, of which A is more strongly adsorbed, assuming the following alternative mechanisms ; (I) inter- action between adsorbed A and adsorbed B, (2) interaction between adsorbed A and gaseous B, (3) interaction between adsorbed B and gaseous A. According to mechanism ( I ) the rate passes through a maximum and later decreases as the concentration of A is increased, but according to (2) and ( 3 ) a limiting rate is reached at high concentrations of A.It is shown that at the maximum accord- ing t o mechanism ( I ) the frequency factor is approximately the same as a t high A concentrations according to (2) and (3). The rate expressions are compared with special reference t o the reaction between ethylene and hydrogen, for which it is shown that the data appear to favour mechanism (I). The low frequency factor for the reaction ( t u 10-6) is explained quantitatively on the basis of the theory, being due to the loss of translational and rotational freedom in forming the activated complex. The close analogy between surface and enzyme reactions is discussed, and it is shown that many enzyme processes can be interpreted on the basis of mechanism ( I ) .The initial step in the dehydrogenation of lactic acid, the urease-catalyzed hydrolysis of urea and other reactions are considered briefly from this point of view. From the standpoint of the theory of absolute reaction rates the central problem in the theoretical treatment of the rates of chemical and physical processes is the determination of the configuration of the activated complex. The manner in which the activated complex is composed of the reactant molecules controls the way in which the rate depends upon the concentrations of the reactants (i.e. the order of the reaction), and the entropy and energy of the complex with respect to the reactants control the rate of the reaction. In principle the structure and energy of the activated complex can be calculated by the methods of quantum mechanics, and hence the rate obtained : in practice this cannot be done satisfactorily, and an empirical method must be used.This has usually consisted of obtaining information as to the configuration of the activated complex from the experimental order of the reaction, and deriving the energy of the complex (corrected to oo K) from the experi- mental activation energy. It is then possible to calculate frequency factors and rates €or postulated mechanisms, and to decide between various possibilities on the basis of the agreement with the experimental data. This type of treatment has been applied successfully to adsorption and desorption processes at surfaces,2 to a variety of chemical processes on surface~,~ and to the para-ortho hydrogen conver~ion.~ In the present Eyring, J .Chem. Physics, 1935, 3, 107. 2 Laidler, Glasstone and Eyring, ibid., 1940, 8, 659. Laidler, Glasstone and Eyring, ibid., 1940, 8, 667. Eley and Rideal, Proc. Roy. Soc. A , 1941, 178, 429. 4748 THE ACTIVATED COMPLEX IN CATALYSIS paper we discuss further examples, and in particular extend the treat- ment to a somewhat different type of surface activated complex, in which only one of two reacting molecules is attached t o the surface. and Hinshelwood * have formulated the theory of bimolecular surface reactions on the assumption that in order for reaction to occur it is necessary for the two reactant molecules to become adsorbed side by side, and the calculations referred to above (except for the ortho-para hydrogen conversion) were a development of this idea.There seems to be little doubt that such mechanisms are applicable to most, if not all, of the reactions to which they have been applied. However, there are a few reactions, which have been the centre of recent interest, in which it appears to be more likely that the activated complex is formed not from two adsorbed molecules but from an adsorbed molecule or atom and a mole- cule or atom in the gas phase or in a van der Waals’ layer. This type of mechanism was first propounded by Rideal,? and was applied by him and Eley to the para-ortho hydrogen conversion, the activated complex for which may be represented as being formed by the process Langmuir H H-H H H H H H H H i H H -s-u-s-s-k- r i l l [ -+ -A&+”- t l ! (activated complex) Such a mechanism seems necessary in this case, since the alternative explanation that the conversion involves an adsorption process followed by rearrangement and desorption, H-H H-H H H -s-s- I t -S-S- i I - 1 1 - -s-s- is excluded by Roberts’ result s that the observed rates of desorption are much too slow.Further support for the Eley-Rideal mechanism is pro- vided by the fact that a quantitative treatment lo gives good agreement between observed and calculated rates. Another class of reactions for which it seems necessary to assume that the activated complex is formed directly from a gas-phase species and a surface species comprises the recombinations of atoms and free radicals on surfacesll These are almost always first-order processes, and one mechanism that would explain this behaviour is surface adsorp- tion of the atoms or radicals followed by recombination on the wall; however, this is again excluded by the facts with regard to the stability of the adsorbed layer.An alternative explanation, and the most probable one, is that the reaction involves interaction between a surface-adsorbed atom or radical and a gaseous one ; thus the recombination of hydrogen atoms on clean glass surfaces may be represented as H H H-€1 H H H H H H i E l H H H H ___f I I I I -LLL -s-s-s-s- lip, - -+ -s-s-./-s (ac:ivated complex) Langmuir, Trans. Faraday Soc., 1921, 17, 621. 6 Hinshelwood, Kinefzcs of Chemzcal CJzangc (Oxford University Press, 1926) p.145 ; (1940)~ p. 187. Rideal, Proc. Camb. Phil. Soc., 1939, 35, 130 ; Chew. and I n d . , 1943, 62,335. Farkas, 2. physik. Chem. B, 1931, 14, 371. Roberts, Trans. Faraday SOC., 1939, 35, 941. l o Eley, Trans. Faraduy SOC., 1948,44,216 ; K. J. Laidler and G. M‘. Castellan, l1 Shuler and Laidler, J . Chem. Physics, 1049, K7, 1212, 1356. (unpublished results).KEITH J. LAIDLEK 49 Detailed calculations on the basis of such a mechanism again give satis- factory agreement with the experimental results. In view of the importance of Rideal mechanisms in processes of this kind it is natural t o inquire whether similar mechanisms are applicable t o reactions which have conventionally been regarded as controlled by interaction between two adsorbed molecules.In the general case of a reaction between two molecules A and B we can formulate the Langmuir- Hinshelwood mechanism as follows : A**.B I I . . A B 1 1 _3 - . -+ . . -s-s- - 3 - S - + products. ( I ) With the Rideal mechanism there are two distinct possibilities : in the first, reaction occurs between a gas phase molecule of A and an adsorbed molecule of B, e.g. I I A + B + - S - S - + -S-S- (activated complex) A B -+ -S- + products; . (2) I B I A+-s- __f -s- (activated complex) in the second, A is adsorbed and B is in the gas phase ; A A B --+ I I B+-S- -S- -c- - + products. . ( 3 ) (activated complex) I n mechanism ( 2 ) it is not necessary that A is not at all adsorbed, but rather that an adsorbed A does not contribute directly t o reaction ; how- ever, it may be noted that if A is adsorbed more than very weakly it will indirectly affect the rate by influencing the concentration of adsorbed B molecules. With a view t o contributing t o the problem of distinguishing between the three mechanisms (I), ( 2 ) and ( 3 ) in any instance we will now formulate the rate laws in each case.It will be assumed throughout that A is much more strongly adsorbed than B, i.e. that there are more adsorbed A mole- cules than B ; however, no other restriction is placed on the degree of adsorption. The equations will then be applied briefly t o the kinetics of the hydrogenation of ethylene, with A = C,H, and B = H,. Beeckl, has suggested that this reaction proceeds by mechanism (z), gaseous ethylene reacting with adsorbed hydrogen ; A (ethylene) is strongly ad- sorbed but the adsorbed ethylene molecules do not interact directly with adsorbed hydrogen molecules.The data certainly exclude mechanism ( 3 ) , but it will be seen that the formulation of the rate laws leads us t o the conclusion that the data are more consistent with mechanism ( I ) than with mechanism (2). Interaction Between Two Adsorbed Molecules (Mechanism (1)) .- The concentration c, of adsorbed -4 is given by where c, is the concentration (in molecular units) of bare surface sites and 12Beeck, Rez. M o d . Physics., 1945, 17, GI. * The derivations given here and in the following two sections employ the same notation and general assumptions as in Glasstone, Laidler and Eyring, The Theory of Rate Processes (McGraw-Hill Book Company, Kew York, 1g41), Chap.VII.5 0 THE ACTIVATED COMPLEX IN CATALYSIS c , that of A in the gas phase ; K is the equilibrium constant, given by K = f,eejkT * (2) Fgfs ' - where the f are the partition functions and the energy of adsorption. Similarly, for the adsorption of B, denoting the quantities by primes, * (3) - _ "' - K'cpl, . C S where K' is now given by In addition, where L is the conzentration of sites when the surface is completely bare. Eqn. (I), ( 3 ) and ( 5 ) give rise to and LKc, I + Kc, + K'c,'' c,= -- ' L K'c ,' I + Kc, + K'c,' c,' = The condition that c , @ c,' implies that Kc, $ k'c,' ; these equations thus reduce to - ( 8 ) LKc, c, = - I + Kc,' ' and The fraction 8' of surface covered by B is clearly c,'/L, i.e. The rate can now be formulated as follows.The average number of adsorbed B's adjacent to any given adsorbed A is so', where s is the maximum possible number of near neighbours; the total number of adsoibed A-B pairs is thus c ~ d ' , which equals sLKK'c,c ,' If these react with an activation energy (at the absolute zero) of E,,, the rate is given by (I + Kc,)a' sLKK'c,~,' kT ff -ro/kT 3 - - (11) - (I + KC,)^ * h ' fTe v = where f* a.nd fa,' are the partition €unctions for the activated complex and for the adsorbed pair of molecules. Expressing the K and K' in the numerator using eqn. ( 2 ) and (4) gives I t is seen that the rate is always proportional to c,' (provided that the condition Kc, ,> K'c,' holds), but that when c , is increased the rate at first increases linearly, later goes through a maximum, and finally decreases.The maximum rate corresponds to c , = I / K , and is equal toKEITH J. LAIDLER 5 1 The activation energy of the reaction increases with increasing con- centration of A owing to the positive heat of adsorption of A, i.e. to the fact that K varies with temperature as eelkT, where E is positive. At low concentrations of A, when I 9 Kc,, it is seen from eqn. (12) that the activation energy at the absolute zero * is - E - E' ; at the maximum eqn. (14) shows it to be e0 - E', while at high concentrations it is eo+ E - E'. Eqn. (12) also predicts that the activation energy will decrease with increasing temperature, owing to the decrease in the importance of Kc, compared with unity in the denominator. In view of these variations the importance of measuring activation energies under well-defined conditions is obvious ; unfortunately this has not always been done.Interaction Between an Adsorbed Molecule A and a Gaseous Molecule B (Mechanism (2)) .-The concentration of adsorbed A is given by eqn. (I), and the rate of reaction with a gaseous B molecule is therefore given by kT f+ e--rAlkT v = cg'ca . - - h . F v Y a The rate now varies with thq concentration of A in a different manner, increasing linearly at first and finally reaching a constant value. The activation energy is ci - E at low concentrations of A and EI, at high ones. Interaction Between an Adsorbed Molecule of B and a Gaseous Molecule of A (Mechanism (3)).-The rate is now given by This mechanism predicts the same type of variation of the rate and activation energy with the concentration of A as does mechanism ( 2 ) .Comparison of the Mechanisms .-An interesting feature of the treatments given above is that a t low concentrations of A all three mechanisms correspond t o approximately the same frequency factor. Moreover, in the region of the maximum rate mechanism ( I ) predicts the same frequency factor as is given by mechanisms ( 2 ) and ( 3 ) at high concentrations of A, when the rate is no longer dependent upon the pressure of A. This conclusion could hardly have been reached without the detailed treatment, and indeed other conclusions have been arrived at on intuitive grounds. Thus Beeck l2 implies that the low experimental frequency factor for the ethylene-hydrogen reaction is in favour of mechanism (3), the argument being that since the surface is sparsely covered with hydrogen only a small fraction of the sufficiently energetic collisions of -ethylene molecules will be effective.The reason that this argument is not valid is that the concentration of adsorbed hydrogen varies with the temperature, so that the effect appears in the activation energy and not in the frequency factor. We shall see later that the low frequency factor is due to the loss of translational and rotational freedom in forming the adsorbed activated complex. The same assumption as * This differs slightly from the value a t experimental temperatures owing t o the temperature dependence of kT/h and the partition functions.5 2 THE ACTIVATED COMPLEX IN CATALYSIS Beeck’s is also implicit in Eley’s discussion l3 of the factors determining whether a reaction will proceed by a Langmuir-Hinshelwood or by a Rideal mechanism.Since the frequency factors are the same the question must be deter- mined by the relative activation energies for the three possible mechanisms. In general this factor will favour mechanism (I), since adsorbed mole- cules are more reactive than gaseous ones. Mechanisms ( 2 ) and ( 3 ) may, however, involve lower activation energies than mechanism (I) if the product of the reaction is strongly adsorbed on the surface, so that a considerable energy of activation is required for its removal. This would seem to be the only factor which will cause a reaction to proceed by mechanism ( 2 ) or ( 3 ) . This situation particularly arises when the product of reaction is a hydrogen molecule.Our general conclusion is therefore that the Langmuir-Hinshelwood mechanism is probably the general rule, and that the Rideal mechanism would seem to apply only when the reaction product is strongly adsorbed on the surface. The Reaction Between Hydrogen and Ethylene .-The hydrogen- ation of ethylene has been very thoroughly investigated, on a variety of surfaces, l4 and will now be discussed briefly in the light of the conclusions derived above. Ethylene is more strongly adsorbed than hydrogen on the surfaces employed, so that A = C,H, and B = H,. The product, ethane, is very weakly adsorbed, so that we should expect the reaction to proceed by the Langmuir-Hinshelwood mechanism (I).Support for this conclusion is provided by the fact that the rate decreases at high ethylene concentrations, a result that is predicted by mechanism (I) but not by mechanisms (2) and (3). That the reaction is frequently stated to be of zero order with respect to ethylene is probably due to the fact that the measurements were made in the neighbourhood of the maximum. ’ We may now consider whether the frequency factor predicted by mechanism ( I ) at the maximum rate is consistent with the experimental data. Beeck l 2 has found on nickel a steric factor of - I O - ~ , - this is the ratio of the rate to the number of ethylene molecules striking the surface with the required energy of activation. According to eqn. (14) the frequency factor at the maximum is where w is the mass of the ethylene molecule and b , is the rotational and vibrational contribution to the partition function.The frequency factor for striking the surface is l5 kT I B - -h (2nrnkT)lle a h The steric iactor for the reaction is therefore l3 Eley, Advamxs in Catalysis (Academic Press, New York, 1948), Vol. I, l4 For full references see Eley.13 l5 Laidler, J . Physic. Chem., 1949, 53, 712. p. 157 : Quart. Rev., 1949, 3, 209.KEITH J. LAIDLER 53 For ethylene at 300' K, (zrmkT)/h2 is 2.6 x 10" and b , is 2.2 x 1 0 3 ; with s = 4 and L = 5 x 1014 the steric factor is found to be BJB, = 0.9 x 10-6, . - (25) in excellent agreement with the experimental value of - 10-6. This low steric factor is seen to be due to the loss of translational and rotational freedom in forming the activated complex, and there is no need to assume that only a fraction of the surface is active.Certain arguments have been invoked by Beeck l 2 in favour of mechan- ism (3). His thermochemical objection to mechanism ( I ) , the main argu- ment, has been answered by Eley,13 while the point with regard to the frequency factor is covered above. Our conclusion is therefore that mechanism (I) is entirely consistent with all the data that have been recorded, and that the evidence favours it strongly in comparison with mechanisms (2) and (3). Reactions Catalyzed by Enzymes.-The above considerations have direct application to the kinetics of enzyme-catalyzed reactions, which may now be considered very briefly. Enzymes are in some ways easier to treat than inorganic surfaces, since the sites at which adsorption can occur are more clearly defined, a fact that can be inferred from the very high specificity. Enzymes can be divided into two classes, according to whether they have one or two different types of surface sites which are concerned in reaction.The former comprises many of the protolytic enzymes, the latter all of the hydrogenases, in which one site interacts with the substrate and the other with the coenzyme. We have else- where l 6 formulated the kinetic laws applicable to the two-site systems, and will here only indicate the analogies between them and the surface reactions considered above. One example is the reaction : lactic acid + coenzyme I --f pyruvic acid + reduced coenzyme I, which is catalyzed by the apoenzyme of lactic dehydrogenase ; we have recently studied this reaction experimentally from the present stand- p0int.l' The rate is found to increase at first linearly with increasing concentrations of lactic acid and of coenzyme. At higher concentrations of lactic acid the rate reaches a constant limiting value, while at higher concentrations of coenzyme the rate passes through a minimum and then diminishes.This may be interpreted by a mechanism which is similar to mechanism ( I ) for the hydrogenation of ethylene. For reaction to occur it is supposed that a lactic acid molecule must be adsorbed on a site of type I, and a coenzyme molecule on a site of type 2 . The in- hibition at high coenzyme concentrations must be due to the fact that a coenzyme molecule can also be attached to a site of type I, replacing a lactic acid molecule. However, lactic acid presumably cannot displace a coenzyme molecule on site 2 , since there is no inhibition at high lactic acid concentrations. A somewhat similar situation appears to exist in the urease-catalyzed hydrolysis of urea, the rate of which passes through a maximum as the urea concentration is increased. Here it is supposed that for reaction to occur a urea molecule must be adsorbed on one type of site and a water molecule on the second type ; urea may, however, exclude the water by becoming adsorbed on a site of type 2 . A similar situation exists in the decomposition of hydrogen peroxide catalyzed by catalase, a reaction that is also inhibited at high substrate concentrations ; presumably two sites are again involved, although a detailed mechanism has not been worked out. When there is no such inhibition, as with the majority of 16 Laidler and Socquet, J . Physic. Chem. (in press). 17 Socquet and Laidler, Arch. Bzochem. 1g50,25, 171. 18 Laidler and Hoare, J . Amer. Chern. Soc., 1949, 71, 2699.54 THE ROLE OF HETEROGENEITY protolytic enzymes, it may be supposed that it is not necessary for the water t o be attached to a site on the enzyme, so that here the situation resembles mechanisms ( 2 ) and (3). Department of Chemistry, The Catholic University of America, Washington, D.C., U.S.A.

ISSN:0366-9033    

DOI:10.1039/DF9500800047

出版商:RSC    

年代:1950

数据来源: RSC

摘要:

54 THE ROLE OF HETEROGENEITY THE ROLE OF HETEROGENEITY IN ADSORPTION AND CATALYSIS BY G. D. HALSEY, Jr. Received 9th January, 1950 Data on adsorption almost always deviate from the Langmuir equation. These deviations often can be formally explained equally well by interaction between absorbed molecules or non-uniformity of the adsorbing surface. The author has emphasized the second of these explanations, and a discussion is given of various proofs or indications that it is a valid one. In some cases, notably physical adsorption near the saturation pressure, interaction plays an important role in determining the isotherm. The author has shown that a refined treatment of a uniform surface does not lead t o the BET equation but leads t o the conclusion that heterogeneity and interaction operate simultaneously.The BET surface area determination using nitrogen as adsorbate, seems completely satisfactory. The reasons that explain this validity in the face of the unreality of the isotherm equation are discussed. The rate of reaction on a non-uniform catalyst surface is formulated, and it is pointed out that the assumption that some one reaction is the rate-deter- mining step is no longer valid. Because a group of sites that are of overwhelming importance catalytically may not contribute appreciably to adsorption, there is no very direct information about catalysis t o be gained from adsorption studies. Also, on a non-uniform surface, the rate of the forward reaction cannot be determined from the equilibrium constant and the rate of the backward reaction, except a t equilibrium.Adsorption on Tungsten.-Frankenburg’s data for the adsorption of hydrogen on tungsten powder have been interpreted on the basis of a non-uniform adsorbing surface by Taylor and Ha1sey.l We showed that a n exponential distribution of adsorption energies over the surface would account for the Freundlich type isotherms discovered by Frankenburg. We maintained t h a t interaction on a uniform surface alone could not account for the strongly varying heat of adsorption, which declined exponentially (excepting for a small amount of constant heat Langmuir adsorption at below 2 yo coverage). Miller a has criticized the conclusion that Frankenburg’s data are explained by the non-uniform surface. He remarks that interaction was rejected by u s because the relation between q and 0 was not the linear one, required by simple theory.Actually we considered a more general case (our eqn. (8)) with higher terms in 8, t o allow the energy of a cluster t o differ from the sum of the isolated pair interactions involved. We thus did not assume a fixed interaction energy. We could confine our attention t o the crude approximation of random distribution because Halsey and Taylor; J . Chem. Physics, 1947, 15, 624. Miller, ibid., 1948, 16. 841.G. D. HALSEY, JR. 5 5 refinements such as the quasi-chemical approximation lessen the effect of repulsive interaction, making the q - 6 curve convex to the axes, while Frankenburg’s heats were strongly concave to the axes. Similarly, Robert~’~ model for the immobile.film leads to curvature in the wrong sense. The rejection of interaction as a sole explanation of the q against 6 curve was based not on the shape of the curve, but its slope at low 6 , where the contributions to the repulsive interaction would come almost entirely from isolated pair interactions. The repulsive energy required would then be many times RT. Therefore the random arrangement of atoms on the surface would be far from the most stable configuration, thus causing the heat curve for a uniform surface to become strongly con- vex to the axes. In short, the chief reason for the rejection of the inter- action theory as a complete explanation is the magnitude of the repulsive energy, coupled with the overall concavity of the q against 6 curve. We do not imply that interactions are not also operating, especially at larger 6 ; it is true, however, that it is not necessary to invoke interactions to explain the data on tungsten.It should be pointed out, nevertheless, that the loophole in our argument is the neglect of other than nearest neighbour interactions. Using an arbitrary function for repulsion against separation, and assuming random distribution over the surface, any desired heat curve can be reproduced. It is apparent, that for large repulsions, and the so-called immobile film randomly distributed, that the configuration is far from equilibrium, and that no equilibrium isotherm, free energy or entropy can be derived. I n view of the complexities of the problem, it seems wise to confine attention to the equilibrium state, experimentally verified by the reversi- bility of the isotherm measurements, and the agreement of isosteric heats with those measured calorimetrically.Physical Adsorption.-An analysis of adsorption on a uniform sur- face,* using the quasi-chemical theory of interaction, has shown that the refined hypotheses of the Brunauer-Emmett-Teller (BET) theory lead to substantially no adsorption beyond the first layer, if the energy of condensation in the second layer equals the energy of liquefaction of the bulk liquid. On a uniform surface even if E , > E , . . . En > EL, a refined treatment predicts an isotherm composed of a series of steps. Non-uniformity of the surface smooths these steps out, explaining the curves observed experimentally.It is apparent that when the monolayer portion of an isotherm in the region of physical adsorption is considered by itself, it may not be easy to choose between repulsion or heterogeneity. This difficulty arises because the required repulsion potentials may not be large compared to kT. Nevertheless the imminence of the attractive interactions that cause multilayer formation, coupled with the necessity of a slightly non-uniform field to smooth out the later part of the isotherm suggest that heterogeneity cannot be neglected. The formidable problem of considering interaction on a heterogeneous surface has recently been attacked by Hill,s but as yet, no experimental case has been quantitatively analvzed. The BET Surface Area.-Although the BET isotherm equation has been shown to be invalid, the surface areas estimated using the equation seem to be remarkably satisfactory.A number of reasons can be given. I . In so far as the isotherms on two similar catalyst preparations are geometrically similar, the ratio of any two corresponding points, for any pressure, will be a constant, giving the relative surface area. 2. The BET plot, although based on a “ theoretical ” equation, can be looked upon as a graphical method of selecting the “ point B ” of the isotherm, having no essential connection with the BET theory. 3 Roberts, Some Problems in Adsorption (Cambridge, 1g3g), 4Halsey, J . Chem. Physics, 1948, 16, 931 ; Hill, ibid., 1949, 17, 106. 2.6, Fig. 14. Hill, ibid., 1949, 17, 762.56 THE ROLE OF HETEROGENEITY 3. The nitrogen isotherms have been found the most " reliable " for estimating surface area ; and, in general, nitrogen gives by far the best- defined point B.4. Point B is located where the affinity of the surface for the gas is changing most rapidly; i t is reasonable to identify this change in ad- sorptive power with the completion of the first layer. 5 . When a well-defined point B is absent (Type I11 isotherm), although a BET plot can be made, no reliable surface area can be assigned. 6. I t is possible to have a completely false point R when a portion of the surface is much more active than the rest, leading to an apparent saturation that does not represent the surface as a whole. based on heats of wetting will give a true surface area for a plane surface, but their relative method is oiily strictly true when the isotherm of the unknown, and the isotherm for the powder used in the absolute method are geometrically similar.Interestingly enough, only an isotherm which certainly will not give a BET plot can be relied on to give a true monolayer volume. For if an apparent point B is followed by an inflexion point, leading to another point B, the second apparent saturation must involve co-operation. In order to involve co-operation, the adsorbate molecules must be close together, almost touching, and one has real proof of a monolayer being formed. Nitrogen isotherms never show this behaviour ; but co-operative adsorption must obtain near p / p , = I ; no inflexion is noted between high p i p , and low p / p , ; so presumably, co-operative adsorption must have started before point B, where the inflexion would be masked by the strongly heterogeneous surface.Thus the nitrogen point B gives a true monolayer volume. has been investigated, and the general conclusions only will be summarized here. The catalyst is presumed to function by strongly adsorbing a reaction product or products, thereby lowering the activation energy for reaction. Then, the reaction product must be desorbed to make way for a second unit reaction to take place. If the adsorption energy is too large, the actual reaction will proceed, but the desorption of products will be so slow that the site will be effectively poisoned. On the other hand, if the energy of adsorption is too small, the reaction will not take place, although the products would be easily desorbed.If the adsorption energy is distributed continuously, it is clear that on the optimum sites these two reactions would be equally difficult. Therefore, the usual assumption that a particular step in a reaction is the rate-determining one is inapplic- able. The rate of reaction on other than optimum sites falls off rapidly with energy, and the location of the optimum site depends on the pressure. Therefore, although a very small proportion of the sites contribute to reaction at a given pressure, no group can be selected and treated as if it were effectively uniform. Data for adsorption and rate of adsorption involve a wide range of sites, and the catalytically active sites may con- tribute negligibly to adsorption. It is clear, then, that there is little direct connection between adsorption and catalysis on a continuously non-uniform surf ace. In addition, away from equilibrium, the backward reaction will pro- ceed on entirely different optimum sites than the forward reaction, and therefore the forward and backward rates cannot in general be determined from one another and the equilibrium constant. 7. The Harkins-Jura absolute method Catalysis.-The rate of reaction on a non-uniform surface Mallinckrodt Chemical Laboratory, Harvard University, Cambridge, Mass., U.S.A. 6 Haxkins and Jura, J . Amer. Chem. Soc., 1944, 66, 1362. 7 Halsey, J r . , J . Chem. Physics, 1949, 17, 758.

ISSN:0366-9033    

DOI:10.1039/DF9500800054

出版商:RSC    

年代:1950

数据来源: RSC

摘要:

STATISTICAL ASPECTS OF CHEMISORPTION BY A. R. MILLER Received 7th March, I950 The basis of the statistical mechanical account of adsorbed monolayers is discussed, and the way in which the properties of the monolayer can be de- duced is indicated. The physical distinction between immobile and mobile monolayers of particles adsorbed on localized or fixed sites is emphasized and important differences in the properties of these two types of films are examined. Tbe way in which the experimental results for adsorption on to clean sur- faces can be interpreted in the light of these ideas is described. For oxygen films adsorbed on tungsten it is shown that these ideas lead to a consistent picture of the way in which successive layeIs of the film can be built up. The application to hydrogen films adsorbed on tungsten is also examined.More recent measurements of the variation of the heat of adsorption of these films suggest that the earlier interpretation of them was oversimplified, although the basic ideas are vindicated. It now appears that hydrogen films adsorbed on tungsten pass through an intermediate region when the surface is about three-quarters covered, and their behaviour changes from that of an immobile film to that of a mobile film adsorbed on localized sites. 1. Introduction.-The classical experiments of Langmuir showed that when a clean surface of a solid or a liquid is exposed to a gas or a vapour, a monomolecular layer of the gas is often formed on the surface. An adsorbed monolayer of this sort is of considerable importance in the study of surface propertics and surface reactions, as well as in the study of the interchange of energy between a solid surface and a gas.The purpose of this paper is to give a review of some statistical aspects of chemisorbed monolayers. Many of these topics are dealt with in my monograph to which the reader is referred for the mathematical details of the argument. Here, I shall restrict myself to considering the basis of the statistical mechanical theory of adsorbed monolayers, and the inter- pretation of the available experimental data in the light of the theoretical deductions. In particular, I want to examine some of the ideas of the statistical theory in the light of experimental results which have become available since my book was written. 2.Physical Model.-Both experimental and theoretical studies have shown that a solid surface provides a periodic Fotential field for an atom or molecule incident on the surface. The potential field near a crystal surface was determined in a number of cases by Lennard-Jones and his collaborator^.^ These calculations provide a potential map of the space as experienced by a gas molecule approaching the surface. The potential field consists of a periodic array of positions of minimum potential energy. The structure of this array is determined by the Langmuir, J . A m e r . Chem. SOC., 1912, 34, 1310; ibid., 1915, 37, 417; Miller, T h e Adsorption of Gases on Solids (Cambridge University Press, Lennard-Jones and Dent, Trans. Faraday SOC., 1928, 24, 92 ; Gen. Elect. Rev., 1926, 29, 153.1949). Lennard Jones, ibid., 1932, 28, 333. 5758 STATISTICAL ASPECTS O F CHEMISORPTION crystal structure of the surface. This work provides a firm basis for the idea of localized sites for adsorption which was advanced by Langmuir. More recently, it has also received direct experimental confirmation. The experiments of Crawford and T~mpkins,~ for instance, on the ad- sorption of a number of gases on barium fluoride crystals have shown that the amount of gas adsorbed in a complete monolayer is independent of the particular gas. Even though ammonia and nitrous oxide mole- cules differ in cross-section by about 50 %, the same amount of each was adsorbed in a complete monolayer. The number of molecules in a mono- layer depends not on their size, for they do not form a close-packed structure on the surface, but on the localized sites for adsorption defined by the potential field provided by the solid surface.This idea of the adsorption of molecules on localized sites is the basis of the examination of adsorbed monolayers using the methods of statistical mechanics. This was initiated by Fowler 6 who derived the adsorption iso- therm statistically on the assumptions that (i) there is a definite number per unit area of localized sites €or (ii) one gas molecule or atom is adsorbed on each site, (iii) the vibrational states of any adsorbed particle are independent (iv) thcre is no interaction between the adsorbed Farticles. adsorption, of the occupation of neighbouring sites, and I t was clearly necessary to extend the theory by taking account of the interactions between the adsorbed particles.6 In this case, assumption (iv) is discarded, but then the regular arrangement of the sites becomes an essential feature of the argument.3. Statistical Theory.-In using the methods of statistical mech- anics to study adsorbed monolayers, the equilibrium between the gas phase and the adsorbed phase is considered. We first consider the case covered by assumptions (i), (ii), (iii) and (iv) of 0 2. If there are N , particles adsorbed on the surface and each is in its lowest state, the energy of the surface layer is - Nux, where x is the difference in energy between the ground state of a particle in the adsorbed phase and the lowest state in the gas phase. If a particle adsorbed on a particular site can occupy a set of states of energy E~ and weight wr, its vibrational partition function is v,(T) = 1 w,.exp (- r,/kT). In the absence of interactions between the adsorbed particles, the energy of the adsorbed phase depends only on the number of adsorbed particles and not on their arrangement on the surface. The partition function of the monolayer can then be written r Let there be N , sites for adsorption on the suriace. where g ( N , , Na) is the number of ways in which N , adsorbed particles can occupy the N, sites available for adsorption. That is g(N,, N J is the weight of the adsorbed state of the whole assembly of energy - hT,x ; for it, we have N , ! g(N3' = N,! ( N , - Na) 1' The contribution of the adsorbed layer to the Helmholtz function of the assembly is Fa = - kT log S.Crawford and Tompkins, Trans. Faraday SOC., 1948, 44, 698. Fowler, Proc. Camb. Phil. SOC., 1935, 31, 260. 6 (a) Fowler, ibid., 1936, 32, 144 ; (b) Peierls, ibid., 1936, 32,471 ; (c) Roberts, Proc. Roy. SOC. A , 1937, 161, 141.A. R. MILLER 59 Consider the gas phase containing N , particles in a volume V in equilibrium with the adsorbed monolayer. The Helmholtz function of the gas phase is where v,(T) is the partition function for the internal degrees of freedom of a particle in the gas phase and the other symbols have their usual meanings. The condition for equilibrium between the gas phase and the mono- layer is This leads immediately to the adsorption isotherm, which can be written in the form 0 h3 exp cxlkl’) u,(T) I - e - ( 2 .r r m ) 3 i z ( ~ ~ ) 5 / 2 * urn * PJ * (4) -- * where 6 = NJN,, has been introduced €or the fraction of the surface covered. So far we have neglected the interactions between the adsorbed mole- cules. Suppose that the interaction between two particles adsorbed on a pair of closest neighbour sites has a fixed value, and neglect the inter- actions between more distant adsorbed particles. Theories of this sort will be referred to as fixed interaction theories. The energy of adsorption of a layer of particles is then where V is the interaction energy between two particles adsorbed on a pair of closest neighbour sites and X is the number of such pairs. The interaction energy now depends on the arrangement of the particles on the adsorbing surface.In other words, the weight of the state having a particular energy depends on the arrangement of the particles on the surface ; and the partition function is - N,x -j- X V , . * ( 5 ) 8 = z g ( N , , No, X ) exp {(N,x - XV)/kT)(v,(T)}Na. * (6) 5 In this expression, g(N,, N,,, X ) has been written for the number of arrangements of No particles on the N, available sites for adsorption so that there are X closest neighbour pairs. An approximate value can be found for S by assuming either (i) that the interacticn energy has its average value@,, for the number of adsorbed particles, or (ii) by using the method of local configurations 6 * ~ 0 in order-disorder theory. Fowler using the forrner approximation, and Peierls using the latter, showed that critical adsorption could occur only when there were strong attractive forces between the particles in the monolayer.I f we use the former approximation, the adsorption energy becomes This expression has not been evaluated exactly. - Na(X + 4ev). The only term in 8 which involves X is then g(N,, N,, X ) and E can be evaluated since The equilibrium states are again determined by eqn. ( 3 ) , and the ad- sorption isotherm is60 STATISTICAL ASPECTS OF CHEMISORPTION Fowler showed that his results were in qualitative agreement with the critical phenomena observed by Cockroft ' in studying the deposition of metallic vapours on to insulating surfaces. However, in systems in which chemisorption occurs, the forces between the adsorbed particles are generally repulsive. Once the equilibrium conditions have been determined in this way, other quantities of interest can be calculated.The heat of adsorption and the way in which it varies as the fraction of the surface covered changes, has been studied widely. The heat of adsorption per molecule is defined as the fall in the energy of the system when one molecule is adsorbed. It is given, as a function of the fraction of the surface covered, by the relation In this case, critical conditions do not arise. in which zt is the energy of a molecule in the gas phase and U(0) is the total energy of the adsorbed film. If 2 is the average number of closest neighbour pairs for a given value of 0 then up) = - N,eX + x(e)v. . - (10) Consideration of the experimental results in relation to simple theor- etical considerations led to an important distinction between the different types of monolayer that can be adsorbed on an array of localized sites.It is necessary to examine these types of adsorbed film, before calculating the variation of the heat of adsorption. 4. Types of Adsorbed Mono1ayers.-The idea of the distinction between immobile and mobile films adsorbed on fixed or localized sites was introduced by Roberts8 In his experiments on the adsorption of hydrogen and oxygen on tungsten wires, Roberts found heats of adsorption of the order of 2 x 105 joule/mole. Taking the vibrational frequency for the adsorbed particles to be of the order of 1olS sec.-l, the frequency of evaporation at room temperature is of the order of I O - ~ ~ sec.-l. These films must therefore be very stable at room temperature.On the other hand, for heats of adsorption of the order of 104 joule/mole. the rate of evaporation would be of the order of 10l0 sec.-l, and quite different behaviour would be expected. In this case, the evaporation of the film, and consequent re-condensation, is so rapid that the particles ad- sorbed on the surface could be expected always to assume an equilibrium (Boltzmann) distribution. For an intermediate value of the heat of adsorption, say, 8 x 104 joule/mole, the rate of evaporation is 0-1 sec.-l. When the heat of adsorption of a system is in this neighbourhood, it is in a transition state between the two extreme cases represented by the other values which have been considered. These orders of magnitude illustrate the two kinds of film adsorbed on localized sites.They can be given formal definitions 8 in the following way. By a mobile film is meant one in which the energy of activation necessary to enable an adsorbed particle to move from a given site to a. neighbouring vacant site is much less than kT, so that the particles move freely from one site to another. This free movement from one localized site to another ensures that the film takes up equilibrium configurations during the occurrence of any process. By an immobile film is meant one in which the energy of activation necessary to enable a particle to move from one site to another is so much greater than kT that, for the times which are concerned in any experimental procedure, the particles may be treated as remaining on the sites on which they are first adsorbed.The particles in such a film will not assume an equilibrium distribution ; Cockroft, Proc. Boy. Soc. A , 1928, 119, 293. Roberts, Proc. Camb. Phil. Soc., 1938, 34, 399 ; see also Miller, ibid., 1947, 43, 232.A. R. MILLER 61 the occupation of sites by the adsorbed particles will be random. It should be noted that not only free mobility on the surface, but also evapor- ation and re-condensation will also set up an equilibrium distribution. The conditions under which evaporation can occur are roughly the same as those under which the adsorbed particles are freely mobile over the surface from one localized site to another. As has already been pointed out there will be intermediate cases. I n these, the particles can be looked upon as being able to move from site to site on the surface but so slowly that there is an appreciable time lag in establishing equilibrium again if it is disturbed in any way. 5.Statistical Theory of the Heat of Adsorption.-The two ex- treme cases which have been specified in $ 4 can be dealt with theor- etically. The methods of statistical mechanics can be used to examine the equilibrium distribution in the mobile film and to examine some properties of the immobile film. Here, we shall determine the equilibrium conditions and show how the variation of the heat of adsorption with the fraction of the surface covered can be determined. For an immobile film in which the particles from the gas phase are adsorbed on single sites, the heat of adsorption varies directly as the fraction of the surface covered.This follows immediately from the fact that in such a film there is a random occupation of single sites. In the adsorption of hydrogen cn tungsten, it is probable that each molecule occupies two sites, one for each atom in the molecule. An immobile film of this sort consists of a random distribution of pairs of sites on the surface. There is not an exactly linear relation between the heat of adsorption and the fraction of the surface covered in this case, but the departure from linearity is not very great. The heat of adsorption of a mobile film is quite different from this. The exact shape of the heat curve depends on the interaction between the adsorbed particles but in all cases it shows a rapid fall in the vicinity of 0 = 0.5.We now show how these results can be obtained by the use of the grand partition function. The grand partition function of the adsorbed layer can be written in the form where Aa is the absolute activity of the particles in the adsorbed phase. It is related to the partial or chemical potential pa by the relation The other symbols in eqn. (11) have the meanings which have been ascribed to them in earlier sections of this paper. Without serious error, as far as finding average values is concerned, the sum in eqn. (11) can be replaced by its maximum term. Denote the values of the parameters in the maximum term by asterisks. Then the grand partition function can be replaced by pa = kT loge Am 3* = g(N,, N,*, X*) exp (- X* V/kT)( A,v,(T) exp (x/kT))Nu* (12) = g(N,, N,*, X " ) exp (- X* V fkT)&va*, where The essence of the method of local configurations is to deal with a small group of sites in detail and to represent the effects of particles adsorbed on sites outside this group by average values.For definiteness, we shall consider a square array of sites, as is provided by the (100) plane of a tungsten crystal, and examine the occupation of a particular site (the central site) and its z closest neighbours (the first shell sites). We introduce average quantities in the following way. Let fav be the geometrical mean contribution per site of the array to the factor has been written for h,v,(T) exp (x/kT).62 STATISTICAL ASPECTS OF CHEMISORPTION let I; be the geometrical mean contribution per pair of occupied sites to the term involving the interaction energy ; and let y be the geometrical mean contribution per site of the array to the combinatory factor.Thus, we define * (13) tF; = IXaVa(T) exp ( x / k ~ ) > ~ a * , y" = g(Nm N,*, X * ) . I;*zNa = qX* = exp (- X*V/kT), Consider a particle adsorbed on a particular first shell site. If the central site is occupied, its interaction with that particle is allowed for by a factor T]. It occupies a site which is a closest neighbour also to z - I other sites ; its possible interactions with particles which may be adsorbed on these sites is represented by a factor P-l, obtained by taking the aver- age value defined in the second of eqn. (13). Each arrangement of par- ticles adsorbed on the group of z + I sites can be considered in detail in this way.Examining the detailed occupation of this group of sites, and using the average values defined in eqn. (13) with regard to the oc- cupation of the N , - z - I sites outside the selected group, the partition function is represented by "(1 + .lgI;"-l)" + (I + 5~Z-l)"]YNIY-Z-1 W - z Z 5 ' (14) where 5 has been written for Aav,(T) exp (x/kT). In considering different modes of occupation of the array, we are concerned only with the ratios of terms in eqn. (14). The last three factors in the right-hand member of this equation can therefore be omitted, without affecting the results which are obtained. Thus, the expression ((1 + s.1)" + (1 + El)", . (15) in which l has been written for @-l, is used for the partition function. This methods is equivalent to that used by Roberts.6c The argument given here is more formal than the physical considerations on which Roberts based his deduction of the essential results.Their equivalence becomes clear on reflecting that successive terms in the right-hand mem- bers of eqn. (II), (14) and (15) give the relative probabilities of different modes of occupation of the sites on the surface. Having constructed an expression for the partition function, the deriva- tion of any quantities of interest can be proceeded with. The equilibrium relations for particles on the surface are obtained by using the fact that each site must be an average site. If a fraction 8 of the sites on the whole array is occupied by adsorbed particles, then the average occupation of both the central and the first shell sites must also be 8.This leads to relations (17) the detailed derivation of which can be found in 0 2.3 of m y monograph. When equilibrium is established with a gas phase in contact with the surface, the absolute activity of an adsorbed particle must be equal to that of a particle in the gas phase. The latter is given by h3 " = (2 mz)% ( kT)610ua (T)' while the former is given by 'a = I exp (- x/kT)/v.(T). 9 Guggenheim, Proc. Roy. Soc. A , 1938, 169, 134.A. R. MILLER 63 When equilibrium between the adscrbed and gas phases is reached, A,, is therefore proportional to the pressure in the gas phase. Eqn. (16) and (17) then give the adsorption isotherm. The value of x is determined by the average occupation of the first shell sites when the central site is occupied.This can be found from the first term of relation (15) to be ~ E J ( I + TCJ. If we use eqn. (9) and (10) with this result, we obtain finally for the heat of adsorption If the adsorbed particles are diatomic molecules which dissociate on adsorption so that a mobile film of adsorbed atoms is formed, the only difference in the expression for the heat of adsorption is that the factor 4 must be omitted from the right-hand member cf eqn. (18). The way in which the heat of adsorption varies with the fraction of the surface covered, according to eqn. (IS), is shown by curve (a) of Fig. I. - R -4.0 FIG. I.-Variation of the heat of adsorption with the fraction of the surface covered, calculated from the statistical theory. Curve ( a ) is for a mobile film on localized sites, and curve ( b ) is for an immobile film.This has been calculated for V = 2-3 x 10-l~ erg per pair of particles and 300OK. This interaction energy corresponds to the difference be- tween the heat of adsorption on a bare surface and on an almost filled surface for hydrogen adsorbed on tungsten. Now let us examine the case in which each particle from the gas phase occupies a pair of closest neighbour sites when it is adsorbed. The grand partition function is again replaced by its maximum term, and we consider the same group of z + I sites as in the other case. Each adsorbed particle can occupy either the central site and one first shell site, or a first shell site and an outer site, or a pair of outer sites. Geometrical mean contributions are introduced by equations which are formally.the same as eqn. (13), but now N: refers to the number of pairs of closest neighbour sites that are occupied by adsorbed particles, and X* refers to the number of closest neighbour interactions between difleerent adsorbed particles. Again, in considering the ratios of terms in the partition function, the last three factors can be omitted without affecting the results which are obtained. Thus, the expression The maximum term is then represented by [((2z-1(1 + q&2i-3)2-1 + (I + 5522-3)z]rNs-Z-lSN~-~-l5)~Ns-22~. AV .%(I + ?)%)*-l 3- (1 + El)., * (19) 10Wang, Proc. Roy. Soc. A , ., 1937, 161, 127. 11 Roberts and Miller, Proc. Camb. Phil. Soc., 1939, 35, 293.64 STATISTICAL ASPECTS OF CHEMISORPTION in which co has been written for t<22-1 and c1 has been written for 552z-3, is used for the partition function.To determine the heat of adsorption it is necessary to determine the probability that if the central site is occupied, a given first shell site is occupied by some other molecule. This is z - I 7)€1 -- I + 7)El' and the expression obtained l2 finally for the heat of adsorption is z - I 7 ) q 4 - 40 -=--- zv z I + 7)EI This formula applies where there is adsorption as molecules to form a mobile film and each molecule occupies a pair of closest neighbour sites on the surface. If an immobile film is formed by the dissociation of molecules, the sites are occupied in pairs, and formula (20) can be applied to this case. An immobile film of this sort corresponds to a random selection of pairs of closest neighbour sites ; a random distribution corresponds to the case 7) = I.The heat of adsorption of an immobile film is therefore given by This is shown by curve (b) of Fig. I, and it is seen that it departs only slightly from a linear relation and is far different from the heat curve for a mobile film. The heat of adsorption of an immobile film in which each particle from the gas phase occupies a pair of closest neighbour sites on the surface was first obtained by a numerical method using a model of the surface l3 and gave a curve in good agreement with eqn. (21). 6 . Structural Discontinuities in the Final Immobile Film.-There is another feature of immobile adsorbed films of the kind which we have been considering which must be examined before we consider the inter- pretation of the experimental results.This is the existence of structural discontinuities or gaps l4 in the immobile film when adsorpticn into the first layer is completed. We have seen that when each particle from the gas phase occupies a pair of closest neighbour sites on the surface to form an immobile film, there is a random distribution of fiairs of sites. As the surface becomes covered, there will be some sites on it which remain bare while all of their closest neighbour sites are occupied. In an immobile film of this sort, such unoccupied sites can never become available for adsorption into the first adsorbed layer, and remain bare when adsorption into the first layer is complete. A surface film of this sort therefore necessarily has structural discontinuities or gaps in it.The extent of these gaps can be determined either numerically using a model of the surface l6 or statistically.'l In the statistical determin- ation it is necessary to determine the probability that the central site is unoccupied while each of its first shell of neighbours is occupied. It is found that the number of single unoccupied sites completely surrounded by occupied sites, in the final film is about 8 yo of the total number of sites. This means that about gz yo of the surface can become covered in the first surface film. l2 Miller, ibid., 1947, 43, 232. l3 Roberts, ibid., 1935, 34, 399. 3 4. J4 Roberts, Nature, 1935, 135, I037 ; P~oc. ROY. SOC. A , 1935, 152, 445 ; ibid., 1937, 161, 141 ; Proc.Camb. Phil. SOC., 1938. 34, 399. Roberts, Proc. Ray. SOC. A , 1935, 152, 464, 5.A. R. MILLER 65 Structural discontinuities of a similar kind occur in any adsorbed film in which each adsorbed particle occupies more than one site on the surface. Another possible case is that in which the occupation of a site precludes the occupation of its shell of closest neighbours by any other particle. In this case,la the coverage in the final film is reduced by about 20 yo. The properties of adsorbed films which have been obtained in this and the preceding section have prcved particularly useful in the inter- pretation of the experimental results. We now consider the data on hydrogen and oxygen films formed on clean tungsten surfaces. 7 . Oxygen Films Adsorbed on Tungsten.-An oxygen film adsorbed on tungsten has a very high heat of adsorption.That on a bare surface is about 500,000 joule/mole of oxygen; and it would be expected from the considerations advanced in 0 2, that here we have to deal with an immobile film. We have seen that the final film will then have gaps in it. These might be expected to provide preferential sites for adsorption into a second film. There would be no such preferential sites if the film adsorbed immediately on the metal surface were a mobile film adsorbed on localized sites. The detailed structure of the adsorbate built up of successive layers can then provide information about the nature of the film. The structure of the oxygen film adsorbed on tungsten was deter- mined by the measurements of Morrison and R0berts.l' The basis of their method is the sensitiveness of the accommodation coefficients of neon and helium against tungsten to traces of adsorbable impurity.Changes in the accommodation coefficient thus provide a sensitive test of the presence of adsorbed films on the surface and also of any changes in them. The results which were obtained for oxygen adsorbed on tungsten can be indicated briefly. The accommodation coefficient of neon for a bare tungsten surface is 0.057. When oxygen is admitted, it rises to a final steady value which depends on the partial pressure of oxygen in contact with the surface. This can be plotted as a function of pressure and extra- polated to low pressures of oxygen ; this gives a value 0.226, which apparently corresponds to a layer of oxygen adsorbed on the tungsten.The higher steady values of the accommodation coefficient, which depend on the partial pressure of oxygen, are apparently due to the adsorption of a second layer of oxygen. The rise in the final value of the accommoda- tion coefficient with the partial pressure of oxygen, indicates that when adsorption into the second layer is completed, the accommodation co- efficient has reached a value 0.36. It is also found that the accommodation coefficient varies with the pressure in much the same way as the fraction of the surface covered does ; it can therefore be used as a measure of the fraction of the surface covered in the second adsorbed layer. The adsorption isotherm deter- mined from the experimental results in this way agrees well with that calculated statistically.16 This agreement justifies the determination of the coverage in the second layer from the accommodation coefficient by the formula which Morrison and Roberts used.There is one other point to be noted. When the wire carrying the adsorbed layer corresponding to an accommodation coefficient of 0.226 is heated to IIOO' K, the accommodation coefficient falls to 0.177, but no further evaporation occurs until it is heated to 1700OK. This in- dicates that the first layer is itself composite and consists of two distinct films. Furthermore, comparison of the changes in the accommodation coefficient suggests that the fall in it from 0.226 to 0-177 corresponds to the evaporation of much less than a complete monolayer. This would not be possible if we were dealing with mobile monolayers on an array Roberts, Proc.Camb. Phil. Soc., 1938, 34, 577, 5 7 ; see also Miller, ref. 2, eqn. (6.4). Roberts, ibid., 1930, 129, 146 ; 1932, 135, 192 ; 1933, 142, 518. C l7 Morrison and Roberts, Proc. Roy. Soc. A , 1939, 173, I.66 STATISTICAL ASPECTS OF CHEMISORPTION of localized sites; but it is possible if the more stable film in the first layer is immobile. Its intense stability to heating up to 1700~ K lends weighty support to this view, as also do the very high heats of adsorption which are observed. The first adsorbed layer of oxygen on tungsten consists of a very stable immobile film. This film is probably atomic and formed by the dissociation of an oxygen molecule and the adsorption of its two atoms on a pair of closest neighbour sites.It therefore has 8 yo vacant sites ; and these provide preferential sites for further adsorption. The first layer is completed by the ad- sorption of molecules in these gaps; corresponding to this, the ac- commodation coefficient rises from 0.177 to 0.226. On top of this composite layer a second layer is then adsorbed. It probably consists of molecular oxygen adsorbed on the array of localized sites determined by the tungsten substrate, and its coverage depends on the partial pressure of oxygen. These experiments about oxygen films on tungsten provide conclusive evidence for the existence of mobile and immobile films adsorbed on localized sites. The differences in the behaviour of these two kinds of film and of their structure indicate the importance of the distinction.The application of these ideas in the present instance, as it was developed largely by the late Dr. J. K. Roberts, indicates also their power and utility in the interpretation of otherwise complex data. 8. Hydrogen Films Adsorbed on Tungsten.-The heat of adsorp- tion of hydrogen on tungsten wires which were cleaned by flashing at about zoooo C before each experiment, has been measured by Roberts.140 The heat of adsorption varied from about 180,000 joule/mole of hydrogen for a bare surface to 80,000 joule/mole of hydrogen for a filled surface. The relative values of the heat of adsorption for successive admissions of hydrogen to the surface could be determined much more accurately than the absolute values which would be needed to compare the results obtained in different experiments.This uncertainty can, however, be overcome by plotting relative values of the heat of adsorption Q/Qo. where Q o is the heat of adsorption for a bare surface. Accordingly, I have re-plotted Roberts' results for the adsorption of hydrogen on tungsten and they are shown by the points in Fig. 2. The values ob- tained in each separate run are shown by a different symbol. The full line shown in Fig. 2 is the curve obtained theoretically for the variation of the heat of adsorption of the immobile film which is obtained when a diatomic molecule dissociates on adsorption, and its two atoms occupy a pair of closest neighbour sites on the surface, given by eqn. (21). The agreement between the experimental points and the theoretical curve is good.The important point is that these experimental results could not be fitted to a curve such as (u) of Fig. I, which is the other possible theoretical curve. These experiments appear to establish that the hydrogen film adsorbed on tungsten is an immobile film on localized sites, as we have defined it in 0 4. Similar results have been obtained by Beeck and Wheeler lS who have examined the adsorption of various gases on evaporated metal films at liquid air and room temperatures. Their results for hydrogen adsorbed on nickel show a variation of the heat of adsorption from 130,000 joule/mole of hydrogen for a bare surface to 60,000 joule/mole of hydrogen for the filled surface. The experimental points (Fig.3) show an almost linear variation over this range, and this suggests that the hydrogen film adsorbed on nickel is also an immobile film, formed by the adsorption of the two atoms of a hydrogen molecule on a pair of closest neighbour sites. We are led to the following consistent picture. 19 Beeck and Wheeler, J . Chem. Physics, 1939, 7, 631 ; Beeck, Rev. Mod. Physics, 1945, 17, 61.A. R. MILLER 67 The question is not, however, quite so clear cut as these results suggested at first. So far, we have considered what I have called a fixed interaction theory. However, the interactions between the adsorbed I 200,OOL la.4 m FIG. 2.-Experimental values of the relative heats of adsorption of hydrogen on tungsten (Roberts) as a function of the fraction of the surface covered compared with the theoretical curve for an immobile film.particles ensure that for a surface which is only partly covered, the ad- sorbed particles will be dimlaced from the Dotential minima Drovided by the surface. When thiLfactor between two particles with their distance apart are taken into ac- count, it can be expected that the heat curves will bz changed. These effects have been con- sidered only for a linear chain.20 The calculations are tedious and there is no immediate extension to the two-dimensional case. As far as they go, they indicate that there is a less marked difference between the heat curves for mobile and immobile films than is ob- tained with the fixed interaction theory. However, the heat curve for the immobile film is still much more nearly linear than that for a mobile film.The theoretical curve for the immobile film represents the experimental results for hy- drogen films adsorbed on tungsten and nickel better than does the curve for a mobile film. More recently, Trapnell *1 has obtained experimental results for the adsorption of hydrogen on tungsten which differ from those obtained bv Roberts. As he is and the ;ariation of the interaction I %I Fruchn of Surfice Covered B lorno ,0*2 10.4 ,O-6 ,0081 FIG. 3.-Experimental values of the heat of adsorption of hydrogen on nickel (Beeck and Wheeler) as a function of the fraction of the surface covered, compared with the theoretical curve for an immobile film. to Dresent his results later in this Discussion, I shall say merely that A they suggest that in Roberts' Miller and Roberts, PYOC.Camb. Phil. SOC., 1941, 37, 82. 21 Trapnell, this Discussion.68 STATISTICAL ASPECTS OF CHEMISORPTION experiments the surface of the wire was never more than about seven- tenths covered. If this be so, it would require a reconsideration of the data. This is reinforced by the fact that at his highest coverages, Trapnell obtains a flattening of the heat curve, which is more typical of a mobile film adsorbed on localized sites than it is of an immobile film. It should also be noted that at these highest values of 8, the heat of adsorption has fallen to a value at which one would expect appreciable evaporation and re-condensation in the time required to make a measure- ment. It may be that in this region, the behaviour of the film is changing from that typical of an immobile film to that typical of a mobile film ; this is, in fact, the intermediate region spoken of in 0 4.The point is that the two types ~f adsorbed film which we have described are charac- teiized by heats of adsorption which differ by a factor of four or five. But the change in the heat of adsorption of hydrogen on a tungsten sur- face as it becomes fully covered is sufficiently great, and it is in such a range of values, that it overlaps regions typical of each kind of film. The nature of the hydrogen films on tungsten must at present be re- garded as obscure, and the original view that it forms an immobile film needs some qualification. While it has not been refuted, it is perhaps an over-simplification. FIG.4.-Drop in the heat of adsorption in the neighbourhood of a region in which a film adsorbed on localized sites changes from immobile to mobile in character. The full line represents the likely shape of the heat curve if this change takes place at about 8 = 0.75. It is possible that the new results which appear to cast some doubt on the original interpretation of Roberts’ measurements, strongly vindic- ate the essential ideas-which have been developed in the statistical theory given in earlier sections-on which it was based. Consider what happens if both the factcrs which have just been mentioned are operative. That is, we assume that the lowest heats of adsorption of hydrogen on tungsten measured by Roberts referred, for some reason not at present known, to a film covering seven-tenths of the surface.At this stage, the heat of adsorption is about 80,000 joule/mole, and evaporation and re-condensation are approaching the rate at which a mobile film would be set up. If it be assumed that there is a sudden change at this point from an immobile to a mobile film, there would be a sudden drop in the heat of adsorption as is shown by the dotted vertical line in Fig. 4. Allowing for the fact that the change in behaviour could not be ab- solutely sudden, and that the film would pass through a region of inter- mediate behaviour, the complete heat curve would show a drop of this sort but rounded off a bit. A curve such as that shown by the full line in Fig. 4 would then result. This is very like the results obtained by Trapnell.A. R. MILLER 69 This is why these latter results which at first sight appear to cast doubt on the detailed interpretation of Roberts’ results for hydrogen films on tungsten, also appear to vindicate the basic ideas on which it was based. For only a view of adsorption phenomena which contains the possibility of two kinds of behaviour would appear to have much hope of explaining these results. On this view, even the later measure- ments provide support for the basic ideas which have been developed in the statistical theory. 9. Conclusion.-The conclusion to be drawn from all these experi- mental results is, I think, as follows. For adsorption on an array of localized sites, the distinction between mobile and immobile films is important. These two kinds of film show markedly different behaviour as far as the variation of the heat of adsorption is concerned, and the statistical theory leads to ideas about the structure of immobile films which can play a major role in the interpretation of the experimental data about oxygen films adsorbed on tungsten, and which make it possible to give a consistent picture of the way in which successive layers are built up on the surface. While the original interpretation of the be- haviour of hydrogen films adsorbed on tungsten appears now to be only partly correct, the essential validity of the ideas on which it was based appears to be vindicated. Cawendisk Laboratory, Cam bridge.

ISSN:0366-9033    

DOI:10.1039/DF9500800057

出版商:RSC    

年代:1950

数据来源: RSC