Adsorption energy surface thermodynamic meaning

When the main purpose of the gas adsorption measurements is to characterize the adsorbent surface or its pore structure, the preferred approach must be to follow the change in the thermodynamic quantity (e.g. the adsorption energy) with the highest available resolution. This immediately leads to a preference for the differential option, simply because the integral molar quantity is equivalent to the mean value of the corresponding differential quantity taken up to a recorded amount adsorbed. Their relationship is indicated by the mathematical form of Equation (2.64), which is explained in the following section. 

Of course, most surfeces are not exposed large single crystal faces. However the variations in gas-solid energy with changes in the lateral position t over the surface will reflect the atomic structure of the surface even if it is amorphous or if it is a defective crystal plane or planes. Many of the simulations of physical adsorption have been devoted to investigations of the effects of these variations upon the structural and thermodynamic properties of the adsorbed films [13]. Often, the reference system for the simulations is the adsorption produced by the structureless surface that means a surface for which the term in equation (13) with g=0 is the only one. In the case of an inverse 12-6 power site-site energy [14],... 

The analytical forms of the adsorption isotherms and energy distribution functions given by Eqs.(3-6) were presented in our review [1]. By means of these equations there can be obtained the energy distribution function and parameter n which are important characterizations for the experimental adsorption systems. Consequently, by means of the functions F(Ei2) and the parameters n one can obtain quantitative characterization of the adsorbent heterogeneity, sorption properties of the solid, possibility to calculate the surface phase composition and potentiality for calculating the thermodynamic functions which characterize adsorption at the solid - liquid interface. 

Using Eqs. (75) [or Eq. (76)] and (74), we can easily obtain the adsorption isotherm assumed for the adsorption energy distribution. In the framework of the mean field approximation expressions for any thermodynamic quantity (e.g. internal energy, heat capacity) can be readily derived [234]. Adsorption on randomly heterogeneous surfaces has been studied in terms of the above-described approach. It has been demonstrated that this mean-field-type theory was valid only at very high temperatures. Below the critical two-dimensional temperature, the predictions of theory seriously underestimate the heterogeneity effects on phase transitions in adsorbed monolayers [12,234],... 

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