Statistical mechanical aspects of adsorption systems obeying the Temkin isotherm

Abstract

A model was set up for adsorption systems obeying the Temkin isotherm, in which both the lateral interaction between the adsorbed molecules and the energetic surface heterogeneity in adsorption were quantitatively described and then characterized by parameters, respectively. On the basis of this model, by using the ensemble theory in statistical mechanics as a theoretical tool, was derived the Temkin isotherm, in the form of 6 = ( R T / a ) ln(AP), its validity being examined both theoretically and experimentally. The derived statistical mechanical expression for the Temkin isotherm established the relation between the constants A and (Y and the microscopic properties of the adsorbed molecules, including the parameter of lateral interaction and the parameter of surface heterogeneity in adsorption, as proposed in the model. It was with this relation that these parameters were evaluated from the experimental data of the chemisorption of hydrogen on iron films. From the evaluated parameter of lateral interaction was further evaluated the molar lateral interaction energy between the adsorbed hydrogen molecules on iron films, the value of which was compared with that estimated from a Lennard-Jones (12, 6 ) potential.

Statistical Mechanical Study on Variation in Energy of the Lowest Energy State of Molecules during Adsorption

“…[7] that, for a given adsorption system at constant temperature, q decreases linearly with increasing coverage, which is the form implied by the Temkin isotherm equation, thus leading to the verification of Eq. [7]. To evaluate the heat of adsorption from the value of −( S o − G o ) using Eq.…”

“…, [7] where dzw/dT is the derivative of zw with respect to T , and da/dT is the derivative of a with respect to T , both being constant for a given adsorption system at a given temperature. Physically, in Eq.…”

“…Physically, in Eq. [7], the terms Lzwθ and −LT (dzw/dT )θ can be regarded as contributions to the decrease in the heat of adsorption (q) by the lateral interaction between the adsorbed molecules, and the term 2RT 2 (da/dT )θ can be regarded as that by the surface heterogeneity in adsorption. It is shown in Eq.…”

“…To evaluate the heat of adsorption from the value of −( S o − G o ) using Eq. [7], some simplifying assumptions are made below. Assuming that dzw/dT and da/dT are small, and noting that the value of zw is 25.4 × 10 3 k (as evaluated in Ref.…”

“…Theoretically at least, this correlation can be obtained with statistical mechanics as a theoretical tool (6). Actually, for an adsorption system obeying a certain adsorption isotherm equation (in its empirical form or derived theoretically), this correlation is implicitly given by the statistical mechanical expression for this adsorption isotherm equation (7). Therefore, the present study is confined to those adsorption systems which obey a certain adsorption isotherm equation, with its statistical mechanical expression being worked out.…”