Analysis of application of Langmuir isotherm to heterogeneous systems: high-pressure conditions

In this paper, an adsorption model that is based on the statistical mechanics approach was applied to study the saturation phenomena in adsorption to calculate the minimum pressure needed to attain the complete surface coverage on a physical adsorption. The fundamental integral equation, Theta(T)(Q)=integral N(Q)Theta(Q)dQ, for the calculation of the coverage degree of the surface was developed for an exponential distribution function, N(Q)=(m/RT)exp(-mQ/RT), and the representation of local adsorption sites is given by the Langmuir expression, Theta(Q)=b(0)C exp(Q/RT)/(1+b(0)C exp(Q/RT)). At high values of the pressure C, a solution of the fundamental integral equation was obtained by imposing the condition b(0)C>1. The expression for the saturation condition, b(0)C>m/(m+1), was obtained; that is, the saturation phenomenon is dependent on two parameters, correlated with the energetic heterogeneity and adsorption energy of the system. The pressure in the analysis of the cited expression shows that, for low m values (more heterogeneous systems), saturation is attained for b(0)C>>m, while for m congruent with 1 (more homogeneous systems), the saturation is attained for b(0)C>>0.5.