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is formulated, and it is pointed out that the assumption that some one reaction is the rate-deter- mining step is no longer valid.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.