Adsorption Isotherms on Homogenous Surfaces

Adsorption Isotherms on Homogeneous Surfaces.—The integral equation describing adsorption on a patchwise heterogeneous surface requires the choice of a local or model isotherm to describe the adsorption on individual patches 

Widdler, An Introduction to Transform Theory , Academic Press, New York and London, 1971, p. 128. 

In spite of the earlier work of Adam and Jessop showing clear and reproducible evidence of two-dimensional condensation of fatty acids on the water surface, reliable data demonstrating two-dimensional condensation on solid surfaces was not forthcoming until later. This was partially due to the 

de Boer, The Dynamical Character of Adsorption , The Clarendon Press, Oxford, 1953. T. L. Hill, J. Chem. Phys., 1946, 14, 441. 

Ross and G. E. Boyd, New Observations on Two-Dimensional Condensation Phenomena , MDDC Rep. 864, USAEC, 1947. 

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Of these shapes, long linear isotherms are uncommon for adsorption on solids (Just like type c in fig. 2.8) and occur only if penetration into the solid takes place, leading to a Nemst-type distribution law as in liquid-liquid partitioning, see (1.2.20.1]. Linearity is also found for the (relatively short) initial parts of all isotherms on homogeneous surfaces. We shall call them, as before, Henry isotherms or the Henry parts of curved Isotherms. 

Probably the reason why the (1 — 0) concept has received such widespread credence is that Langmuir was able to derive his famous adsorption isotherm on the basis of this concept. Since the Langmuir isotherm equation has been experimentally verified in many cases, it was felt that the (1 — 0) concept must be essentially correct. This again is fallacious reasoning, since in the derivation two other assumptions are necessarily made which are not in accord with recent experiments. These are ( ) the rate of evaporation is proportional to 0 and (2) one can treat the experimental data as if the surface were homogeneous. Because of this situation, it is desirable that someone derive the Langmuir isotherm equation on more realistic assumptions. (See ref. 10a.)... 

For the adsorption isotherm on a well determined homogeneous part of the surface 0H(Q, P) the Langmuir equation is often used. 

Two-dimensional condensation—on homogeneous surfaces—leads to sudden jumps in the adsorption isotherm. These jumps may already be found at very low pressures of the gas which is in equilibrium with the adsorbed layer (242). Heterogeneous surfaces do not give rise to sudden jumps but to gradual slopes (Sec. V,12). There is sometimes a tendency to consider such jumps as indications of multimoleeular adsorption this is not correct. It is of course true that stepwise adsorption can also occur together with multimoleeular adsorption. (See also Sec. V,12.)... 

Regarding the application of the Langmuir equation to physical gas adsorption on homogeneous surfaces, good examples are difficult to find. Those systems that do obey the Langmuir equation appear to be microporous. Of course, the Initial parts of multilayer isotherms fulfil the Langmuir equation, and these will be dealt with in the appropriate section. The various ways of plotting and the Information obtainable from such plots have been discussed in sec. 1.4. 

The isotherm that is most easily understood theoretically and widely applicable to experimental data is, known as the Langmuir isotherm. This is also the simplest model of a nonlinear isotherm. It accounts well for the adsorption of single components on homogenous surfaces at low to moderate concentrations, or for the adsorption to isolated type-I or type-II sites [103, 110, 111]. The Langmuir adsorption isotherm equation is written ... 

Isotherm Models for Ideal Adsorption on Homogeneous Surfaces. 81... 

The latter problem is usually ignored. The local adsorption isotherms can be represented by one of the many existing equations derived for adsorption on homogeneous surfaces and there are good reasons for choosing a correct adsorption model. 

Many isotherm equations for submonolayer loealized adsorption on homogeneous surfaces may be rewritten as follows [32] ... 

For materials with an assumed single-pore geometry and an energetically homogeneous surface, the measured experimental adsorption isotherm on a mieroporous solid can be considered to be... 

The derivation of surface areas from water-vapor adsorption isotherms on the same samples, however, does not lead to constant or nearly constant results for the areas of the two suites of kaolinite in different ion forms. The large variation that is observed is adequately expressed in the data in the last column of Table 1 for the apparent cross-sectional areas of a water molecule at monolayer coverage. This apparent area is derived from the monolayer coverage for water and the nitrogen area. The apparent areas deviate considerably from the accepted value for a monolayer of water on a homogeneous surface, about 10.8 A. Both... 

FIG. 5 Schematic representation of adsorption isotherms in the region of the first-order phase transition on a homogeneous (solid line) and heterogeneous (filled circles) surface. 

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