SURFACE CHEMISTRY ADSORPTION ENERGY AND ADSORPTION EQUILIBRIA By A. V. KISELEV (ADSORPTION LABORATORY CHEMISTRY DEPARTMENT M. V. LOMONOSOV STATE UNIVERSITY OF Moscow U.S.S.R. SURFACE CHEMISTRY GROUP OF THE INSTITUTE OF PHYSICAL CHEMISTRY The Theory of Adsorption Equilibria and Adsorption Energy FOR a long time adsorption was interpreted mainly by empirical and semi- empirical methods. Thus Polanyi’s theory by its very nature does not permit derivation of adsorption potentials or even of the shapes of adsorption isotherms. The adsorption potential is determined by purely empirical means from the experimental isotherm. From the Langmuir and the B.E.T. theory for localised adsorption on homogeneous surfaces the shape of the adsorption isotherm can be found theoretically but the equili- brium constants of adsorbate-adsorbent interactions are again determined from the experimental adsorption isotherm.These theories are therefore semi-empirical. The same is true of the modifications to the Langmuir and the B.E.T. theory which take into account adsorbate-adsorbate interactions. The simplest equations of this type are the approximate relationships suggested for unimolecular localised adsorption by the present author :l OF THE U.S.S.R. ACADEMY OF SCIENCES) 8 or ~ = Kl + KlK,8 8 K,(1 - 8) (1 + Kn8) h - h(l - 8) and for multi-molecular adsorption by the author and D. P. Poshkus:l where 8 is the surface coverage h = p/ps is the relative vapour pressure and Kl and K are the respective equilibrium constants of adsorbate- adsorbent and adsorbate-adsorbate interactions. As in the Langmuir and B.E.T.equations which are particular cases of equations (1) and (2) when K = 0 only the shape of the 8-h plot is found theoretically while the constants Kl and K are determined from the experimental adsorption isotherms.2 Similarly Hill’s and deBoer’s e q ~ a t i o n ~ ~ ~ for non-localised unimolecular adsorption,* exp [q(i - e) - ~ ~ e ] (3) 8 Kl(1 - 8) h = * Also the appropriate Hill’s equation for multimolecular adsorption. A. V. Kiselev Doklady Akad. Nauk S.S.S.R. 1957 117 1023; Kolloid Zhur. 1958 20 338; A. V. Kiselev and D. P. Poshkus Izvest. Akad. Nauk S.S.S.R. Otdel. khim. Nauk 1958 1520. a A. V. Kiselev N. V. Kovaleva V. A. Sinitsyn and E. V. Khrapova Koffoid. Zhur. 1958,20,444. * J. H. de Boer “The Dynamical Character of Adsorption,” Oxford 1953. T. L. Hill.J. Chem. Phys. 1946. 14 441. 4. 99 100 QUARTERLY REVIEWS gives only the shape of the adsorption isotherm eqn. 3 is found by means of the Gibbs equation from the empirical two-dimensional equation of state while the constants Kl and K are found from the experimental i s o t h e r m ~ . ~ ~ ~ Thus equation (3) is also semi-empirical. The same is true of many attempts to obtain an adsorption-isotherm equation by statistical thermodynamics in these cases only the general shape of the 0-p curves is usually found while the equilibrium constants containing the partition function of a given adsorbate on a given adsorbent are not calculated theoretically but are found from the experimental isotherms. All this renders it impossible to surmount the limits of purely experi- mental investigation each time a new adsorbent-adsorbate system has to be studied new experiments have to be made and the adsorption equilibria found experimentally.This state of affairs is further complicated by the very scanty information on the structure of adsorbents so that to take their irregularities into account one must again proceed from the experimental adsorption isotherms and adsorption heats All this makes a rather dismal picture showing how the theory of adsorption equilibria lags behind the present-day theory of chemical and many bulk-phase equilibria. However considerable progress has been made recently; this gives grounds for greater optimism. First adsorbents have been obtained with surfaces sufficiently homogeneous to enable verification of the simplest theories and sufficiently large to make possible accurate measurement of adsorption isotherms as well as adsorption heats and specific heats of adsorption systems.We are referring primarily to graphitised carbon bla~ks,~-l~ especially thermal carbon blacks heated to -3000" whose surface consists mainly of basal faces of graphite crystals.5* 9*13-15 Secondly a method has been devised for calculating the potential energy of adsorption @ of molecules on homogeneous crystal faces starting from S. Ross and W. Winkler J. Colloid Sci. 1955 10 319 330. R. A. Beebe J. Biscoe W. R. Smith and C. B. Wendell J. Amer. Chem. Sac. 1947,69,95; R. A. Beebe M. H. Polley W. R. Smith and C. B. Wendell ibid. p. 2294; R. A. Beebe and D. M. Young J. Phys. Chem. 1954,58 93. ' N. N. Avgul G. I. Beresin A. V. Kiselev and I.A. Lygina Zhur. fiz. Khim. 1956 30,2106; Izvest. Akad. Nauk S.S.S.R. Otdel. Khim. Nauk 1956,1304; 1957,1021 ; 1959 787; A. V. Kiselev N. N. Avgul G. T. Beresin T. A. Lygina and G. G. Muttik J. Chim. phys. 1958 197. * A. V. Kiselev Proc. 2nd Tnternat. Congress on Surface Activity Vol. 11 London 1957 p. 168. M. H. Polley W. D. Schaeffer and W. R. Smith J. Phys. Chem. 1953 57 469; C. H. Amberg W. B. Spencer and R. A. Beebe Canad. J. Chem. 1955,33,305; R. A . Beebe and R. M. Dell J. Phys. Chem. 1955,59,746,754; W. B. Spencer C. H. Amberg and R. A. Beebe ibid. 1958,62,719. lo J. W. Ross and R. J. Good J. Phys. Chem. 1956,60 1167. l1 E. L. Pace J. Chem. Phys. 1957,27 1341. l2 N. N. Avgul G. I. Beresin A. V. Kiselev and A. Ya. Korolev Kolloid. Zhur. 1958 l3 A. V. Kiselev and E. V. Khrapova Kolloid.Zhur. in the press. l4 N. N. Avgul A. V. Kiselev and I. A. Lygina Kolloid. Zhur. in the press; Izvest. l5 A. A. Isirikyan and A V. Kiselev Kolloid. Zhur. in the press. 20 298. Akad. Nauk S.S.S.R. Otdel. Khim. Nauk in the press. KISELEV SURFACE CHEMISTRY 10 1 information on only the structure and physical properties of the adsorbent and adsorbate. It is true that this method encounters two difficulties even in the simplest cases when adsorption occurs under the influence of only electrokinetic (dispersion) attractive forces. It is based on using the Kirkwood-Miiller formula16 to calculate the energy constant C1 of electrokinetic attraction in the term Clr6 (r is the distance between inter- acting centres) and similar f o r m u l ~ e ~ ~ - ~ ~ for the subsequent terms C2r8 and C3r-l0.However these quantum-mechanical formulze are not strictly accurate. Moreover the exponential repulsion constant p in the 6 exp (r/p) type potential is usually found empirically from compressibility experiments while the constant b is excluded when the condition of equilibrium (minimum @ at a certain selected distance from the surface) is introduced. The constant b is then replaced by a different constant related to the equilibrium distance between the closest interacting centres which is calculated from the constants of the respective lattices taken separately i.e. under potential-field conditions which differ somewhat from such conditions for the adsorbate-adsorbent system. However with due regard for these difficulties which have not as yet been overcome by present-day quantum mechanics we can obtain the value of the adsorp- tion potential from the physical properties of the adsorbate and the adsor- bent.The numerous calculations carried out so far by this method have resulted in -@ values satisfactorily close to the most reliable measured heats of a d ~ o r p t i o n . ~ J ~ J ~ - ~ ~ Thirdly definite progress is noticeable also in the statistical-ther- modynamic treatment of adsorption equilibria. The simplest cases were examined by Hill,27 Pace,ll and Fisher and McMillan.21~28 Hill made a direct attempt to calculate the equilibrium constant of the B.E.T. equation for certain of the simplest cases confining himself to an “ideal” adsor- bent. In this connection mention should also be made of Kemball’s paper29 which contains attempts to calculate the adsorption entropy by an examination of various models of adsorbate-molecule movement at the adsorbent surface.Proceeding from a theoretical calculation of @ and l6 J. G. Kirkwood Phys.Z. 1932,33,57; A. Muller,Proc. Roy. Soc. 1937 A 161,476. A. V. Kiselev Vestnik Akad. Nauk S.S.S.R. 1957 No. 10 p. 43. 18N. N. Avgul A. A. Isirikyan A. V. Kiselev I. A. Lygina and D. P. Poshkus lo A. V. Kiselev and D. P. Poshkus 2hur.fi.z. Khim. 1958,32,2824. 2o R. M. Barrer Proc. Roy. SOC. 1937 A 161 476. 21 B. B. Fisher and W. G. McMillan J. Chem. Phys. 1958,28,562. 32 W. J. C. Orr Proc. Roy. SOC. 1939 A 173 349. 23 A. D. Crowell and D. M. Young Trans. Faraday Soc. 1953 49 1080; A. D. Crowell J. Chem. Phys. 1954,22 1397; 1957,26 1407. 24 T. Hayakawa Bull. Chem. SOC. Japan 1957,30 236.25 R. A. Pierotti and D. Halsey J. Phys. Chem. 1959 63 680. 26 E. L. Pace and A. R. Siebert J. Phys. Chem. 1959,63 1398. 27 T. L. Hill J. Chem. Phys. 1948,16 181 ; J. W. Drenan and T. L. Hill ibid. 1949 B. B. Fisher and W. G. McMillan J. Chem. Phys. 1958,28 555. 29 C. Kemball Proc. Roy. SOC. 1946 A 187 73 ; 1947 A 190 1 17. Izvest. Akad. Nauk S.S.S.R. Otdel. khim. Nauk 1957 1314. 17 775. 102 QUARTERLY REVIEWS the entropy values obtained by Kemball the present author and D. P. Poshkus30 attempted to calculate the equilibrium constant of the B.E.T. equation for the adsorption of benzene on graphite and on magnesium oxide. However the entropy values used in these calculations were ob- tained by Kembal129 for models which were selected rather arbitrarily. Therefore selection of the models of adsorption-complex movement based on independent facts is a very important problem.These facts must be obtained by spectral and magnetic investigations. Only preliminary attempts have been made in this direction as yet.31s32 Such in general terms is the state of the problem of theoretical calcula- tion of adsorption energies and adsorption equilibria. It shows that at present this question should be posed in all its aspects to draw it to the attention of both experimentalks and theoreticians. There are grounds for hope that despite inevitable disappointments the properties of adsorp- tion systems will with increasing frequency become theoretically predic- table from their nature. This Review deals with several examples of the effect of the nature of adsorption systems (Le.the surface chemistry and molecular structure of the adsorbate) on adsorption properties mainly the adsorption energy but partly the adsorption equilibria. Adsorption Heats Heats of Adsorption of Vapours of Non-polar Substances on Graphitised Carbon Blacks. The heats of adsorption of the simple gases and a number of hydrocarbons on graphitised carbon blacks have been dete~mined.~-~~@ Preliminary calculations of the adsorption potential of non-polar molecules on graphite reported by the present authorS at the Second International Congress of Surface Activity in London in 1957 were soon afterwards refined in the works of N. N. Avgul I. A. Lygina D. P. Poshkus and the present a ~ t h o r . ’ ~ ~ ~ These refinements involved account- ing for the later terms in the equation for dispersion energy introduction of more accurate values for the exponential repulsion constant p and summation over a large number of graphite carbon atoms.The adsorp- tion energy was computed by the formula @ = -Cil L’r,j-s - Ci2Crij-s f - Ci3Pij-l0 + B ‘ P p ( - rij/p) where i is the force centre of the adsorbate molecule; the constant Cil of electrokinetic interaction of this centre with the carbon atom j of the graphite was calculated by the Kirkwood-Miiller formula and the con- stants Ciz and Ci3 by similar f o r r n ~ l a e . ~ ~ ~ ~ ~ The contribution of the term - Ci2pij-8 was about 10% of @ and of the term Ci3Pij-l0 about 1 % 30 A. V. Kiselev and D. P. Poshkus Proc. 2nd Internat. Congress on Surface Activity Vol. TI London 1957 p. 202. 31 G. L. Kington “The Structure and Properties of Porous Materials,” p.247 ed. D. H. Everett F. Stone London 1958. 35 N. N. Avgul A. V. Kiselev I. A. Lygina and D. P. Poshkus Zzvest. Akud. Nauk S.S.S.R. Otdel. khim. Nauk 1959 1196. (4) A. V. Kiselev and V. I. Lygin Kolloid. Zhur. in the press. KISELEV SURFACE CHEMISTRY 103 (therefore owing to the approximate nature of the calculation the latter term may be neglected). The constant B' was found from the condition of minimum energy of interaction with the entire lattice @ at an equilibrium distance from the outer phase. The value p = 0.28 A resulted in @ values close to those obtained in c a l ~ u l a t i n g ~ ~ ~ ~ ~ ~ ~ ~ the contribution of the repulsion potential by the Lennard-Jones exponential formula B" Crij-12. i / / X / I 1 I I I I - - r - - - i h 3 4 5 6 7 8 9 Values of n - I4 7r n -12 a -.3 -10 ; - 8 -6 1 FIG. 1. Experimental values of standard diyerenrid heats of adsorption Quo (points) and theoretical energies - @O calculated by equation (4) (lines) for normal alkanes (jhll line) and olejins (broken line) with n carbon atoms on graphitised carbon black. References are 0 7 8; D 10; 0 6; A 6; 8 34; x 34; V 15 39. Fig. 1 is a cornparism of the refined calculation of @ according to equation (4) (with approximate allowance for the adsorbate-adsorbate interaction energy for standard surface coverage 6 = 0.5 ) with the experi- mental values of standard differential adsorption heats of a number of n-alkanes and olefins on graphitised carbon black.* Table 1 lists the results * Measurements of the differential adsorption heats Q of n-hexane vapour on T-1 thermal carbon black graphitised at 3000" showed15 that the region of initial Q.drop due to residual heterogeneity of the specimen had greatly narrowed. But the region of increase of Q. on filling of the monolayer by adsarbate-adsorbate interaction had become wider and the height of the maximum had increased in comparison with Spheron-6 1700" carbon b l a ~ k . ~ ~ ~ For adsorption of benzene complete monolayer coverage of the surface involves hardly any increase in the heat of adsorption. This is perhaps due to partial compensation of the weaker electrokinetic adsorbate-adsorbate attraction by electrostatic repulsion of the H-C dipoles in the ring plane and of the quadrupoles formed by the system of n-electrons and residual charges on the carbon a toms of benzene.35 4- 104 QUARTERLY REVIEWS for several other adsorbates particularly isoalkanes for which the different distances of the separate links of the molecule from the graphite surface were taken into account.' These results show that calculation by equation (4) gives first the correct sequence of the adsorption energy values (for example - @O as Qao for benzene are smaller than for hexane) and secondly satisfactory quantitative agreement,l* The calculations and experiments of Crowell and Young23 and of Pacell for argon and those of Pace and Siebert26 for hydrogen and deuterium suggest the same conclu- sion.TABLE 1. Graphite adsorption energies - Qi0 calculated by us,18*34 and experimental diflerential adsorption heats Q ao on the surface of graphitised carbon blacks at standard coverage 8 = 0.5 (kcal./mole).Adsorbate Hydrogen Deuterium Neon Argon Krypton Nitrogen Propane n-Butane n-Pentane n-Hexane n-Heptane n-Octane 2,ZDimethylbutane 3-Methylhexane 2,2,4-Trimethylpentane Cyclopentane Met hylc yclopen t ane Propene Benzene Toluene - @O 0.90* 0.95" 1.0 2-6 3.7 2-6 6.8 8.5 10.4 12.4 14.2 16.1 10-2 13.2 12.6 9.6 10.4 6.2 10.3 12.0 Q ao 0.9 1 0.95 1.0 2-7; 2.6; 2.3 3.5; 4.5 2-8; 2.3 6.5 8.7; 8.3 10.2 12.1; 12.5 14-0 16.0 10.0 12.7 12.7 8.9 10.2 6-2 10.0; 10-3 12.1 Ref. 26 26 34 6 11 37 5 9 6 37 34 6 10 7 8 7 8 15 778 7 8 7 8 7 8 7 8 7 8 7 8 34 7 8 38 7 8 Heats of Adsorption of Alcohols and Water on Graphitised Carbon Black. The adsorption energy of alcohols differs from that of the cor- responding hydrocarbons in that the dispersion interaction of the hydro- * After Pace and Siebert,26 with a 10 % correction introduced by us for the contribu- tion of the term - Ci2 L'rijm8.34 A. G. Bezus V. P. Dreving and A. V. Kisclev Kolloid. Zhur. in the press. 35 A. V. Kiselev and D. P. Poshkus Doklady Akad. Nauk S.S.S.R. 1958,120,834. 36 J. G. Aston and J. Greyson Proc. 2nd Intcrnat. Congress on Surface Activity 37 S . Ross and W. W. Pultz J. Colloid Sci. 1958 13 397. 38 A. A. Isirikyan and A. V. Kiselev J. Phys. Chem. in the press. j Vol. 11 London 1957 p. 39. KISELEV SURFACE CHEMISTRY 105 carbon part of the molecule is supplemented by hydroxyl interaction namely the weak electrokinetic interaction of the hydroxyl oxygen atom with graphite and electrostatic polarisation of the graphite carbon atoms by the OH dipole. Besides in this case a strong adsorbate-adsorbate interac- tion comes into play involving formation of a hydrogen bond between the hydroxyl groups of the alcohol molecules.14 \V I 2 4 6 8 10 O( mole / m.*) FIG.2. Dependence of diferential heat of adsorption Q. of butan-1-01 vapour on the amount adsorbed per unit area a by graphitised thermal carbon blacks. The horizonta broken line here and in other fisirres represents the heat of condensation. Fig. 2 shows the dependence of the differential heat of adsorption Qo of butan-1-01 on thermal carbon black graphitised at 3000" on a (the amount adsorbed per unit area of surface) as obtained by N. N. Avgul and I. A. Lygina. Residual surface heterogeneity hinders determination of the initial heat of adsorption of isolated alcohol molecules in the region of coverage of the more homogeneous part of the surface (where the curve begins to rise) the heat of adsorption of butan-1-01 is already considerably higher than that of n-butane.Thus at 8 = 0-5 Quo for butan-1-01 is 14.4 and for butane is 8.4 kcal./mole; the difference between these values 6-0 kcal./mole is close to the energy of the hydrogen bond in alcohols. In the region of predominant second-layer adsorption Qu again passes through a weak maximum. Fig. 3 presents the Qa-a curves for adsorption of a number of alcohols on a carbon black with a less homogeneous surface (Spheron-6 calcined at 2800°).14 The increment per CH group in the Qao values of the lower alcohols (1 -5 kcal./mole) is smaller than the corresponding increment for 106 QUARTERLY REVIEWS FIG. 3. Dependence of the differential heat of adsorption Qa on the amount adsorbed per unit area a of normal alcohol vapours on Spheron-6 2800" carbon black.L's are the corresponding heats of condensation. Here and below solid points indicate desorp- tion. 1 Methanol; 2 ethanol; 3 propan-1-01; 4 butan-1-01. -2' 10 \ E O 1 & O O . 10 2 0 3 0 40 5 0 o( (166 rnole/g.j FIG. 4. Dependence of differential heat of adsorption Qa of water vapour on the amount adsorbedper unit area a and a by Spheren-6,2800' carbon black. KISELEV SURFACE CHEMISTRY 107 n-alkanes (1 -90 kcal./mole) ; this is because in hydrogen-bonded alcohols the hydrocarbon part of the alcohol molecule closest to the hydroxyl group cannot assume the most favourable orientation. Fig. 4 shows the &-a relation for adsorption of water on the same carbon black.14 Measurement of the heat of adsorption at low p/ps is greatly complicated in this case owing to the exceedingly small adsorption values.Nevertheless it can be confidently concluded that the heat of adsorption Qa of water vapour on the surface of the graphitised carbon black is smaller than its heat of condensation L. 0 0 E - 0 . 0 5 0.1 5 10 15 Plps P (mm.) FIG. 5 . Adsorption isotherm of ( 1 ) butan-1-01 and (2) n-butane on Spheron-6 2800° carbon black. Fig. 5 shows the adsorption isotherms of butane and butan-1-01 in relation to p and p / p s . At identical values ofp the adsorption of butan-1-01 is greater than of butane and at equal p/p8 the reverse. This agrees with the fact that the full heat of adsorption Qa of butanol is larger than that of butane while the net heat of adsorption Qa-L of butanol is less than that of butane.14 Fig.6 shows the adsorption isotherms of water and of alcohols. These isotherms are described satisfactorily by equations (1) and (2) for localised adsorption in conformity with the fact that in this case the adsorbate-adsorbate interaction cannot be neglected in com- parison with the adsorbate-adsorbent interactions.* Heats of Adsorption of Hydrocarbons on Magnesium Oxide. The dependence of the heats of adsorption of n-hexane and benzene on the surface coverage of magnesium oxide calcined at 1000" is illustrated in * At the transition to graphitised thermal carbon blacks with more homogeneous scrfaces the imtherms of adsorption of lower alcohols are represented better by the isotherm equations for non-localised adsorption.14 This is probably connected with the increase in the regions of free migration for these molecules.108 d Q I QUARTERLY REVIEWS 0. I 0.2 0.3 0.4 0.5 P h FIG. 6 . Adsorption isotherms of (1) water vapour (2) nzethanol ( 3 ) ethanol (4)proparz-I - 01 and ( 5 ) butan-1-01 on Spheron-6 2800" carbon black. The curves are calculated bv means of equation (2). Fig. 7.39 At medium monolayer coverage the heat of adsorption depends little on 6 and therefore the Qao values at 6 = 0.5 can be accepted as the standard values of the differential heat of adsorption. Table 2 lists these values in comparison with the values of - @O calculated from equation (4) after allowance for polarisation of the adsorbate molecules and correction for the energy of adsorbate-adsorbate interaction at 8 = 0-5,1s~19 The energy of induction attraction is very small here because ions of opposite signs alternate on the (100) face of the magnesium oxide.It can be seen from the Table that the calculated energies of adsorption agree satis- factorily in this case with the measured heats of adsorption. The agreement between the calculated and the measured energies of adsorption of nitrogen krypton and methane on sodium bromide has been pointed out by Fisher and McMillan.21 A. A. Isirikyan and A. V. Kiselev Zhur. fiz. Khim. 1960 34 2817. KISELEV SURFACE CHEMISTRY 109 TABLE 2. Calculated energies of adsorption - @jO on the (100) face of magnesium oxide and experimental diferential heats of adsorption Q a0 on magnesium oxide at 8 = 0.5 (kcaLlmole.) Absorbat e - @O Q a' Ref.n-Hexane 9.7 9.4 39 n-Heptane 11.1 11.3 39 n-Octane 12.6 12.4 39 Benzene 8.6 9.1; 9.2 39,40 Toluene 10.1 10-3 40 h I - I I I I 0-4 0 - 8 2 I I I I I I I 0.2 0-4 0.6 o( (IO-~ mole /g> FIG. 7. Dependence of diferential heat of adsorption Q. of (1) benzene (2) n-hexane and ( 3 ) n-octane vapours on surface coverage of magnesium oxide. *O S. D. L. Shreiner and C. Kemball Trans. Faraday Soc. 1953 49 1080. 110 QUARTERLY REVIEWS Heats of Adsorption of Hydrocarbons on Magnesium Hydroxide. Investigation of the energy of adsorption on hydroxides is of major interest as identical and identically oriented hydroxyl dipoles project from the surface in this case. They create a more homogeneous though weaker electrostatic field than does the (100) face of magnesium oxide and similar ionic lattices.41 This causes an increase in the energy of adsorption of molecules that have markedly non-uniform electron-density distribution.Such distribution occurs when a molecule has either a dipole or a large quadrupole moment formation of a strong or weak hydrogen bond then being possible if the orientation is favourable. Interaction arises (supple- mentary to the dispersion energy) more for benzene than for hexane. In the benzene molecule the 7-electron clouds increase the electron density on both sides of the hexagon of carbon atoms,35 causing a weak hydrogen bond with the hydroxyl groups on the outer surface of the magnesium hydroxide. The energy contribution of the electrokinetic interaction with this lattice as in the case of graphite is higher for hexane than for benzene.41 In conformity with this are the experimental Qao values:42 for n-hexane 9-0 and for benzene 9.6 kcal./mole.Complete calculation of the energy of interaction of the benzene molecule with magnesium hydroxide is difficult owing to the absence of reliable data on the charge distribution in the hydroxyl of Mg(OH),. Therefore the problem has been solved so far only as functions of the degree of covalency of the bond and of the value of the OH dipole moment .43 Heats of Adsorption on Silicas with Hydrated and Dehydrated Surfaces. Adsorption on amorphous hydroxides with large surfaces-silica gels and aerosols-is of great practical importance. By drying silica gels after their formation at not more than 150° or by hydrothermal treatment of de- hydrated silicas completely hydrated silica surfaces can easily be ~ b t a i n e d .~ ~ ~ ~ Sufficiently prolonged evacuation at ordinary temperatures (not above 150”) makes it possible to free these surfaces almost completely from adsorbed water retaining a dense coating of hydroxyl groups of the silica proper. This is demonstrated by the reversibility of the isotherms and by the heats of adsorption of the water vapour as well as by a study of the infrared spectrum in the region of valency vibrations of the hydroxyl in Si-OH or %-OD and in the region of deformation of the water mole- c u l e ~ . ~ ~ Fig. 8 shows first the infrared spectrum of an evacuated silica gel with a hydrated surface. There is a major absorption by silica-hydroxyl in the region of valency vibrations with an indication of a weak hydrogen 41 D.P. Poshkus and A. V. Kiselev Zhur. $2. Khim. 1960 34 2640. 42 A. V. Kiselev and D P. Poshkus Kolloid. Zhur. 1960 22,403. 43 D. P. Pcshkus and A. V. Kiselev Zliur. 3 2 . Khim. 1960 34 2646. 44 A. V. Kiselev Kolloid Zhur. 1936 2 17. 45 A. V. Kiselev “The Structure and Properties of Porous Materials,” ed. D. H. 46 A. V. Kiselev and V. I. Lygin Kolloid. Zhur. 1959,21 581 ; 1960,22,403. Everett F. Stone London 1958 p. 195. KISELEV SURFACE CHEMISTRY 10- , 3 .'as..._ .:. I [ . . . . . . . . I '00 1600 Id 111 lo W a v e n u m b e r s (cm?) FIG. 8. Infrared absorption spectra in the system silica gel-water. Left Region of va1enc.y vibrations of silica gel hydroxyl groups. Right Region of' deformation vibrations of water hydroxylgroups. (1 1 After evacuation at 200"; (2) afer adsorption of monolayer of water ( 3 ) after capillary condensation.bond between them.*' In the region of deformation vibrations of the water molecules there is no absorption and therefore there is practically no water on the surface in the form of adsorbed molecules. Secondly Fig. 8 shows the corresponding spectrum after adsorption of approximately a monolayer of water. It now displays a hydrogen bond between the water molecules and the silica gel hydroxyls and considerable absorption in the region of deformation vibrations in the water molecules. Finally after capillary condensation of water both these effects became stronger almost reaching the normal effects in ordinary liquid water.46 The presence of a hydroxyl coating on the surface of hydrated silica results not only in strong adsorption of molecules capable of forming hydrogen bonds with the silicic acid hydroxyl groups (water alcohol *' A.V. Kiselev and V. I. Lygin Proc. 2nd Internat. Congress on Surface Activity Vol. 2 London 1957 p. 204; V. I. Lygin Vestnik Moskovskovo Universiteta 1958 No. 1 223. I12 QUARTERLY REVIEWS e t ~ . ~ ~ ~ ~ * ) but also as in the case of magnesium hydroxide in a sharp in- crease in the adsorption of molecules non-polar on the whole but with a very non-uniform electron-density distribution. With favourable orienta- tion of the quadrupole moment (parallel to the hydroxyl axis) these molecules are adsorbed much more strongly than are molecules of similar dimensions having the same or even higher polarisability but a smaller quadrupole moment. D. P. Poshkus and the author demon~trated~~ that calculation of the Coulomb contribution to the energy of electrostatic interaction of the benzene molecule with the surface hydroxyl groups (quadrupole-dipole electrostatic interaction) results in energy values which make it possible to account for the f a ~ t ~ ~ 9 ~ ~ that the heat of adsorp- tion of benzene on a hydrated silica gel surface is greater than that of hexane (Fig.9).* This conforms with the shifts of stretching frequency in the infrared absorption spectra of the surface hydroxyl groups observed by A. N. Terenin and V. N. phi limo no^^^ in the overtone region during the adsorption of benzene ( d v = 236 cm.-l) and n-hexane ( d Y = 70 cm.-l>.t This also accounts for the sharp lowering of the heat of adsorption of benzene (in contrast to hexane) on dehydration of the silica ~ u r f a c e ~ ~ - ~ (see Fig.9) and the corresponding decrease in the adsorption of whose molecules possess a rather large quadrupole moment. The higher adsorption of nitrogen on the hydrated surface is in conformity with the relatively high values of the shift in vibration frequency of the silica hydroxyls. 55 9 56 Fig. 10 shows plots of (Qa - L) against a for n-hexane and benzene,4g and Table 3 gives the values of their differential adsorption heats at 8 = 0.5 on a series of adsorbents (both with and without hydroxyl groups) coated on their surface. It can be seen from the Figure and the Table that in passing from the non-polar adsorbent-graphitised carbon black to silica gel which has a highly hydrated surface the difference of the heats of adsorption of these hydrocarbons changes its sign.* For the same reasons the standard heat of adsorption on a hydrated silica gel surface is higher for propene than for propane60 (7.4 and 5.0 kca.l./mole) and higher for but-1-ene than for butane.51 7 For the main spectral region V. I. Lygin et recently obtained the values 90 and 26 cm.-l for the stretching frequency shifts of groups OD in a silica gel surface coated by adsorption of benzene and hexane. 48 A. V. Kiselev Proc. 2nd Internat. Congress on Surface Activity Vol. 2 London 1957 p. 179. 49 L. D. Belyakova and A. V. Kiselev in the collection “Obtaining the Structure and Properties of Sorbents,” Leningrad 1959 p. 180 (in Russian). 5 0 A. G. Bezus V. P. Dreving and A. L. Klyachko-Gurvich Kolloid. Zhur. in the press. 51 W. R. Smith and R.A. Beebe Ind. Eng. Chem. 1949,41,1431. 62 A. N. Terenin in the collection “Surface Properties of Chemical Compounds and their Role in Adsorption Phenomena.” ed. A. V. Kiselev Moscow State Univ. Press 1957 p. 206 (in Russian); V. N. Philimonov Optika i Spekroskopiya 1956,1,490. 63 A. V. Kiselev and V. I. Lygin Kolloid. Zhur. in the press. 64 A. V. Kiselev and E. V. Khrapova Kolloid. Zhur. 1957 19 572. 56 R. McDonald J. Amer. Chem. SOC. 1958 79 850. 66 G. J. C. Frohnsdorff and G. L. Kington Trans. Faraday Soc. 1959,55 1173. KISELEV SURFACE CHEMISTRY 4 I I I I I I I I I I 1 I I I I I I I I I I I I I I I I I I I I I m a 114 QUARTERLY REVIEWS I l l 1 2 3 4 5 3 FIG. 10. Dependence of differential net heat of adsorption Pa-L on adsorption a for benzene (solid curves) and n-hexane (broken curves) on surfaces of silica with mean surface concentration of hydroxyl groups aOH = 12.5 p-moleslm.2; 2-ditto with = 10.8; 3-ditto with aOH = 3.5; 4-ditto with aOH as.follows (1) 12.5 (2) 10.8 (3) 3.5 and (4) 1.0 x mole/m.2; and ( 5 ) on magnesium oxide amd (6) on Spheron-6 1700" carbon black.Standard heats of adsorption Qao of n-hexane and benzene Adsorbent Hexane Benzene Hexane - Benzene TABLE 3. vapours on various adsorbents (kcal./mole). Graphitised carbon black 12.5 10.3 +2.2 Magnesium oxide 9.4 9.2 +0*2 dehydrated surface 8.6 8.5 +0.1 Silica gel with strongly Magnesium hydroxide 9.0 9-6 -0.6 Silica gel with strongly hydrated surface 8.8 10.4 -1.6 Heats of Adsorption on Silica with its Surface Chemically Modified by Trimethylsilyl Grours. In this case trimethylsilyl groups are chemically bonded to tke silica s ~ r f a c e .~ ' ? ~ ~ Fig. 11 shows the scheme of this bonding 57 H. W. Kohlschiitter P. Best and G. Wirzing 2. anorg. Chem. 1950 285 236. 58 A. V. Kiselev N. V. Kovaleva A. Ya. Korolev and K. D. Shcherbakova Doklady. Akad. Nauk S.S.S.R. 1959 124 617; 1. Yu. Babkin V. S. Vasilyeva J. V. Drogalyeva A. Ya. Korolev and K. D. Shcherbakova ibid. 1959,129,131. KISELEV SURFACE CHEMISTRY 115 FIG. 1 1. (a) Possible combinatio:i (6) Model of close-packed nierhj (c) Tridinzite structiire. 0 4 m (v 0 - ~~ 0 I 0 u of triinethylsilyl group with silicon-oxygen tetrahedroti . GI group layer with (above) adsorbed n-hexane molecule. and a simplified model of the modifying layer.5g After sufficient modifica- tion of the surface the adsorbate moves away from it causing the adsorp- tion potential to drop sharply especially in the case of molecules adsorbed b g I.Yu. Babkin and A. V. Kiselev Dokludy. Akad. Nauk S.S.S.R. 1959 129 357. .- cn I Q 116 QUARTERLY REVIEWS not only by electrokinetic but also by electrostatic interactions (polar quadrupole) with the hydrated silica surface. A calculation of the energy of adsorption on such a modified surface made by I. Yu. Babkin and the resulted in values for n-hexane and benzene of about 4. and 4. kcal./mole. i.e. much smaller than the heats of condensation. Measurements of differential heats of adsorption carried out by us with aerosol specimens modified in A. Ya. Korolev’s FIG. 12. amount SiMe, I 2 3 O( mote /m2) Dependence of diferential heat of adsorption Qa of benzene vapour on the adsorbed per unit area a by modified aerosols.Surface concentration of o,O; n-60%; A-80%; v-90%; 0 100%. l a b ~ r a t o r y ~ ~ showed that despite the residual surface heterogeneity the net heats of adsorption of hydrocarbons on sufficiently modified specimens were actually negative (Fig. 1 2).60 Incipient capillary condensation at the contact points between the aerosol particles results in excessive Qa values 6o 1. Yu. Babkin A. V. Kiselev and A. Ya. Korolev 1961 136 373. Doklady Akad. Nauk S.S.S.R. KISELEV SURFACE CHEMISTRY 117 and therefore the true values for the pure adsorption interaction are still smaller i.e. still closer to those calculated in ref. 59. Fig. 13 presents the corresponding adsorption isotherms. Increasing the degree of modification often lowers the adsorption value by dozens of times.58~so~61 4 n hl € \ W 0 - 2 I .% Is 0.2 0.4 0.6 0.8 PIPS FIG.13. Adsorption isotherms of benzene vapour on modified aerosols. Surface concen- tration of SiMe, 0 0; 0 - 60q/ ; A - 80% ; v w 90% ; 0 N 100%. The lowest isotherm is on a larger scale. The sharp drop in the energy of universal electrokinetic interactions and the possibility of obtaining very homogeneous surfaces and of bonding a modifying layer (which screens the adsorbent) of new active functional groups to the surface make chemical modification a good method of controlling the properties of fillers for various media pigments and adsorbents for chromatography particularly for the application of gas chromatography to mixtures of heavy hydrocarbons and their derivatives and associated compounds.62 For instance by hydrothermal treatment of silica gel and chemical modification of its surface by trimethylsilyl groups it was possible to separate benzene and hexane vapours even at room temperat~re.~~ O1 A.V. Kiselev A. Ya. Korolev R. S. Petrova and K. D. Shcherbakova Kolloid. Zhur. 1960 22 671. O2 A. V. Kiselev and K. D. Shcherbakova “Gas-Chromatographie. Material zum 2. Symposium iiber Gas-Chromatographie in Bohlen,” Oktober 1959 ed. R. E. Kaiser A. G. Struppe p. 198. O3 V. S. Vasilyeva I. V. Drogaleva A. V. Kiselev A. Ya. Korolev and K. D. Shcher- bakova Doklady Akad. Nauk S.S.S. R. in the press. I18 QUARTERLY REVIEWS Adsorption Equilibria An Attempt at Complete Statistical-thermodynamic Calculation of Adsorption Equilibria. As was pointed out in the first section the chief problem in this field is to calculate isotherms for adsorption on a homo- geneous surface proceeding only from the structure and physical properties of the adsorbent and the adsorbate.Several papers dealing with this trend were mentioned above. D. P. Poshkus and the present author6* carried out a statistical-thermodynamic calculation of the change in chemical potential when argon is adsorbed on a graphite basal face for low 8 according to the formula derived on the basis of the expression given by Hill2' for the equilibrium constant. Here h and k are the Planck and Boltzmann constants m is the mass of the adsorbate molecule o, is the area it occupies in a dense monolayer j is the partition function for internal degrees of freedom of the adsorbate molecule in the gas; 8 = Naw,,/s and fa' = fa/s (fa is the partition function of the adsorbate molecule over the entire surface s and Nu is the number of adsorbed molecules).As Hill2' did when calculating fa we used the appro~imation~~ f =fclassv** Here we have the fully classical partition function (n = number of degrees of freedom of the molecule H = Hamiltonian for the adsorbate molecule and Y** = f (harm. oscill. quant.)/f (harm. oscill. class.) (8) where f (harm. oscill. quant.) andf(harm. oscill. class.) are the partition functions of harmonic oscillators in the quantum-mechanical and classical form respectively calculated from the shape of the potential-energy surface of the adsorbed molecule in the vicinity of the minimum). The potential energy in the Namiltonian was calculated for the adsorbed atom by means of equation (4) as a function of the co-ordinates x y and z (xu is the plane passing through the carbon atom of the graphite basal 64 A.V. Kiselev and D. P. Poshkus Doklndy Akad. Nauk S.S.S.R. 1960 132. 872; K. S. Pitzer and W. D. Gwinn J . Chem. Phys. 1942 10 428. KISELEV SURFACE CHEMISTRY 119 face and z is the direction normal to this plane). Substitution into equation (7) and integration with respect to the impulse components p gives:27 where (3a22/3)/2 is the area of the hexagon formed by the carbon atoms of the basal face (a = 1.418A is the graphite lattice constant) erf - - ( :y2 is the probability integral. Integration with respect to x and y in equation (9) is carried out within the limits of a single hexagon. The value of the integral was calculated graphically.Integration was carried out for those values of z for which the potential energy of the adsorbed atom @(x y z ) The value of exp [(- @ (x y z)/kT] for argon on graphite with z/z deviating from unity (2 being the equilibrium distance depending on x y ) falls rapidly. Since in the limits of z/zo within which integration was carried out the value of the factor erf (- @/kT)1/2 is substantially equal to unity we neglected it. For an argon atom located above a graphite surface the quantum- mechanical factor v** = hv - - x [ l -exp (- hvx E)] hv E[1 -exp (- hv zf)] -l kT kT exp (-%)I-' where v, vv and v are the frequencies of vibration of the adsorbed argon atom parallel to the corresponding axes near the potential minimum (above the centre of the hexagon for z = z,).Calculating the frequencies of oscillation 1 K 1 % 1 Fa v = 2~ -4- m v y = 2.rr J v z = 2n -J- m we estimated the constants K, Ky and K analytically according to the formula K = (&:)3 x = o y = o z = zo K = (g)7 x = o y = o z = zo x = o y = o z = zo In this case v = 3.35 x loll v y = 5.8 x lo1' and v z = 1-5 x 10l2 set.-' whence v** = 2.00. 1 20 QUARTERLY REVIEWS The value om depends on the packing of the argon atoms over the surface. The partition functions j,. for the internal degrees of freedom of the argon atom were assumed to be the same in the adsorbed as in the gaseous phase. Substituting the corresponding expressions and value into expression ( 5 ) we obtained the relation between d p and 8 during the transition of argon from a gas atpo = 760 mm.H g on to the surface of the graphite basal face at T = 7 7 . 8 " ~ (this relation being almost independent of corn) d p = - 1.25 + 0.35 log, 8 (kcal./mole) (13) Fig. 14 compares the initial regions of the experimental and the calculated plots of - d p against 8. The experimental curve was calculated from the adsorption isotherm measured in expression ( 5 ) by the thermodynamic 2 " i O F 0.05 ,g 0-10 FIG. 14. Dependence of change in chemical potential - A p of argon on coverage 8 of graphite surface. (1) Calculated. ( 2 ) Experimental. formula d p = RT log, [p(8)/760]. The calculated curve lies fairly close to the experimental one.* Thus on the basis of theoretical calculations of the adsorption energy the change in chemical potential of argon on passing from the gaseous phase to the adsorbed state can be calculated at low graphite surface coverages by a statistical method.An Attempt to Base the Model of the Adsorbate Molecule Movement on Spectral Data. A proper choice of the model for adsorption complexes is very important because the model affects the calculation of the partition * Analysis shows that the difference between the calculated and the experimental curve lies within the limits of error of the calculation.66 At higher values of 8 interaction between the adsorbed molecules has an effect on the experimental curve. We have not taken this into account in the calculated curve (the energy of this interaction was calculated in ref. 11). E6 D. P. Poshkus and A. V. Kiselev Zhur. fiz. Khim. in the press. KISELEV SURFACE CHEMISTRY 121 functions and entropies of the complexes.Very important in this connec- tion are the spectral investigations of chemical compounds and adsorption complexes formed on a surface. To solve these problems systematic and detailed investigations of infrared spectra must be available. V. I. Lygin and the present tried to estimate the entropy of water adsorbed on a hydrated silica surface with allowance for the frequencies of the valency and deformation vibrations of the hydroxyl groups of the silica and the adsorbed water molecules. The calculation was carried out for two localised models a water molecule bonded (i) to one surface hydroxyl group by a single hydrogen bond (which allows free rotation around this bond) and (ii) to two surface hydroxyl groups by two hydrogen bonds (retarded rotation libration).Estimates were made of the values of rotational vibrational and configurational entropies. Their sum amounted to about 7.5 e.u. for the first model and 4-5 e.u. for the second. The experimental result6' indicates higher values. Possibly this is related to the necessity of taking into account the oscillations parallel to the surface and to non-uniformity of distribution of the hydroxyl cover over the surface. This estimate of the entropy of water-hydroxyl adsorption complexes on silica is very approximate because so far the models have been selected on the basis of only average adsorption characteristicsg5 and frequencies-on the basis of spectral data obtained only in the main region of the spectrum where they give information chiefly on the internal vibrations of the atoms in the molecules.In the future a study must be made of the vibrational and rotational spectrum in the far infrared region for the molecule as a whole with respect to its surface. It is essential also that the frequencies of the retarded rotation should make it possible to estimate the height of the potential barriers. Semiempirical Calculation of Adsorption Equilibrium on a Homogeneous Surface. Formula 1-3 ~how,l-~ as was pointed out in the first section the type of functional relation between 8 and p orp/ps the constants Kl and Kn in (I) (2) or Kl and K2 in (3) being found from the experimental isotherm. Since 8 = &/am where 01 is the absolute adsorption at 8 = I to calculate 8 from experimental data we must know the value of the area w occupied by an adsorbate molecule in a dense monolayer (01,)~ = l/owL).This value of can be found independently of adsorption from the van der Waals dimensions of the adsorbate molecule and their probable orientation and packing.39 At high K and low Kn i.e. when the adsorbate-adsorbate interaction can be neglected with respect to the adsorbate-adsorbent interaction this equation describes an isotherm with a convex* beginning and one inflexion i.e. approaches the B.E.T. isotherm. When these interactions are commensurate equation Equation (2) describes three types of * In this context convex means dvldx is increasing. A. G. Foster J. 1945 360. 1 22 QUARTERLY REVIEWS (2) describes an isotherm with a concave beginning and two inflexions (for example alcohols on graphitised carbon blacks see Fig. 6). Finally when the adsorbate-adsorbent interaction is very weak the isotherm is concave throughout (water on graphitised carbon14).The values of the constants Kl and K, though of but relative importance are nevertheless interesting because they make it possible to compare conveniently the adsorption isotherms of various substances on the same adsorbenP or of the same vapour on different adsorbent~.~~ Table 4 lists the rounded values of the ratios of these constants for adsorption of a number of vapours on graphitised carbon blacks at temperatures close to room temperature. TABLE 4. Ratio of equilibrium constants of adsorbate-adsorbent K1 and adsorbate-adsorbate K interactions for adsorption of various vapours on graphitised carbon black. Adsorbate KVtIKl Shape of isotherm* Benzene 0.003 Convex with one inflexion C yclopentane 0.12 Concave at first with two inflexions Sulphur dioxide 7.0 Concave at first with two inflexions Methylamine 13 Concave at first with two inflexions Methanol 350 Concave at first with two inflexions Water (50,000) Concave throughout Of major interest are the wave-shaped isotherms of unimolecular and multimolecular adsorption of vapours.For example for nitrogen vapour at -195” on graphitised thermal carbon black the isotherm is at first concave and then passes through several inflexion points. Each wave of this isotherm can be describedI3 by an equation of the same type namely equation (2) with the corresponding (different for different waves) pairs of values of the constants K and K,. Fig. 15 gives the experimental points and curves calculated with the aid of three pairs of Kl and K constants found by the three successive waves in co-ordinates of equations (1) and (2).A complete theoretical calculation of the equilibrium constants in this case requires statistical-thermodynamic treatment of multimolecular adsorption with allowance for adsorbate-adsorbate interactions. Several steps in this direction have been made by Pace.ll Empirical Accounting for Geometrical and Chemical Surface Hetero- geneity. Discussion of these methods is not the object of this Review and therefore we shall only indicate their possibility. In studies of the dependence of experimental adsorption on the pore size and degree of * In this context convex means dyldx is increasing. 68 A. V. Kiselev “Adsorption Brief Description of Exhibits on the Stand at Soviet Science Technology and Culture Exhibition in New York 1959,” U.S.S.R.Academy of Sciences Moscow 1959. KISELEV SURFACE CHEMISTRY 123 lo4 p/ps (Lower curve) FIG. 15. Adsorption isotherm of nitrogen vapour on thermal carbon black graphitised at 3000". The curves are calculated by means of equations (1) and (2). chemical modification of the surface (for example the degree of hydration of a silica gel surface) adsorption can be expressed as a function of these factors. Comparing the corresponding graphs for a given adsorbate- adsorbent system at various p/ps the adsorption isotherms can be found from them by knowledge of the pore size and the degree of chemical modification of the surface. Examples of the application of this method to the adsorption of benzene vapour on silica gels are given in ref.45. This group of empirical methods of isotherm calculation includes also the 124 QUARTERLY REVIEWS Polanyi theory as developed by M. M. Dubinin and his co-worker~.~~ The equations of the adsorption isotherms are derived in these works the type and constants being found experimentally. This method is convenient for finding the adsorption isotherms of various substances at different temperatures from a single isotherm for one substance. Conclusion The examples discussed above illustrate the value of different methods for describing and interpreting adsorption equilibria and heats of adsorp- tion; these methods should be developed in parallel. However as methods of calculating adsorption energies and partition functions im- prove as the models of the movement of adsorption complexes introduced into the calculations become better founded on spectral and other physical methods and finally as more accurate information on the structure of adsorbents accumulates so the absolute calculation of heats of adsorption and adsorption equilibria purely from the structure and physical proper- ties of the adsorbent and the adsorbate should acquire greater importance.And though this method will long remain inferior in accuracy to direct measurement it has already the notable advantage that it makes it possible to determine not so much what the adsorption properties of the system in question are as why they are what they are. 69 M. M. Dubinin and E. D. Zaverina Zhur. fit. Khim. 1949 23 1129; K. M. Nikolayev and M. M. Dubinin Izvest. Akad. Nauk S.S.S.R. Otdel. Khim. Nauk 1958 1 165 ; M. M. Dubinin “Industrial Carbon & Graphite,” Pergamon Press London 1958 p. 219.