Uniqueness of Gibbsian Surface Excess

Abstract

The Gibbsian surface excess (GSE) can unequivocally measure the extent of adsorption of a gas on a solid adsorbent. A differential iso-excess heat of adsorption based on the GSE thermodynamic framework provides a physically and thermodynamically consistent description of the adsorbent heterogeneity or homogeneity. The actual amount adsorbed (AAA) cannot be experimentally measured. It must be estimated from the experimental GSE by making extraordinary assumptions regarding the nature of the adsorbed phase. Thus, the AAA is a model dependent variable. A differential iso-steric heat of adsorption based on the AAA thermodynamic framework can be misleading and artificial. The NET amount adsorbed (NAA) is an experimental variable. It is also directly related to GSE. Thus, it provides no further insight into the adsorption system vis a vis the GSE. A differential iso-NET heat of adsorption based on the NAA thermodynamic framework can be misleading and fictitious.

Perspectives of Gas Adsorption and Storage in Kerogens and Shales

“…The Gibbs surface excess (GSE) is the experimental parameter measured in gas adsorption studies. The amount adsorbed cannot be determined directly and must be estimated from the experimental measurements of GSE using assumptions about the nature of the adsorbed phase. − The relationship of GSE ( n ex ) for the adsorption of gas and the absolute or actual amount adsorbed is defined by the equations below n ex = V ads ( ρ ads − ρ g ) = n ads − V ads ρ normalg n ads = V ads ρ ads = n ex + ρ normalg V ads n ads = n ex / ( 1 − ρ g ρ ads ) where V ads is the specific volume of the adsorbed phase, ρ ads is the specific density of the adsorbed phase, and n ads is the absolute amount adsorbed in equilibrium with gas at specific conditions of the temperature ( T ), pressure ( P ), and density (ρ g ). The surface excess is the amount adsorbed that is present more than ρ g V ads (the amount corresponding to the adsorbed phase volume with the gas phase density).…”

“…In the adsorbed layer model, the part described as “allocated to gas phase” (yellow in Figure ) is assigned to the absolute adsorption isotherm. At high pressures, the surface excess isotherm is determined experimentally in gas adsorption studies, and various extraordinary assumptions have to be made about the nature of the adsorbed phase, to calculate the amount adsorbed and absolute isotherm from the surface excess measurement . Therefore, the amount adsorbed depends upon the model used in the calculation.…”

“…The Gibbs surface excess is the only measurable experimental quantity for the adsorption of pure gases and mixtures . It can be used unambiguously to describe all practical aspects of adsorption . Absolute isotherms can be calculated from the surface excess isotherm using eqs and .…”

“…23 It can be used unambiguously to describe all practical aspects of adsorption. 22 Absolute isotherms can be calculated from the surface excess isotherm using eqs 2 and 3. The absolute adsorption isotherms depend upon the assumptions made for the nature of the adsorbed phase; for example, constant adsorbed phase density and V ads are equal to the entire volume under all conditions.…”