Derivation of an Adsorption Isotherm, Chemical Potential, and Entropy for 2D Gas Adsorbates with Packing Exclusions and Attractive Interactions

Weakly bound adsorbates on surfaces may display 2D gasproperties.In this work, we consider connections between chemical potential,partition functions, and equations of state and utilize these equationsto derive isotherms for 2D gas adsorbates. After starting with equationsfor an ideal 2D gas, we extend the equations to the case of moleculesapproximated as hard discs (including the possibility of interadsorbateattractions) and show how the chemical potential and adsorption isothermcan be derived from either the equation of state or the partitionfunction. An equation of state and adsorption isotherm are derivedbased on a generalized form of the van der Waals equation, accountingfor both packing exclusion and the possibility of attractions betweenhard discs (gvdw-PEHD). We compare the derived isotherms to alternatives,including the Volmer equation. The gvdw-PEHD isotherm derived in thiswork uses a more realistic treatment of molecular properties and predictsa slower functional-form approach to saturation coverage for 2D gasadsorbates, when compared to the & sigma;-Volmer equation. We alsonote that the absolute coverage form (the & sigma; form) of equationsis most convenient for use in thermodynamic analyses of 2D gas isotherms,as use of & theta; isotherms (such as the & theta;-Volmer equation)for 2D gas thermodynamic analyses can result in interpretation errors.