differential molar energy of adsorption

When the addition of a differential amount $d n i σ$ or $d n i s$ is effected at constant gas volume, the differential molar energy of adsorption of component $i$ , $Δ a U i σ$ or $Δ a U i s$ , is defined as:

$Δ a U i σ = U i σ − U i g$

$Δ a U i s = U i s − U i g$

where the differential molar surface excess energy, $U i σ$ , is given by

$U i σ = ( ∂ U σ ∂ n i s ) T , m , n j σ = ( ∂ U ∂ n i σ ) T , m , V g , p i , n j σ$

and the differential molar interfacial energy, $U i s$ , by

$U i s = ( ∂ U ∂ n i s ) T , m , V g , p i , n j σ = ( ∂ U ∂ n i s ) T , m , V g , V s , p i , n j s$

$U i g$ is the differential molar energy of component $i$ in the gas phase, i.e.

$( ∂ U ∂ n i g ) T , V , n i g$

Source:

PAC, 1972, 31, 577 (Manual of Symbols and Terminology for Physicochemical Quantities and Units, Appendix II: Definitions, Terminology and Symbols in Colloid and Surface Chemistry) on page 603

differential molar energy of adsorption

Also contains definitions of: differential molar interfacial energy, differential molar surface excess energy