differential molar energy of adsorption

Also contains definitions of: differential molar interfacial energy, differential molar surface excess energy
When the addition of a differential amount dniσ or dnis is effected at constant gas volume, the differential molar energy of adsorption of component i, Δa.Uiσ or Δa.Uis, is defined as: \[\Delta _{a}U_{i}^{\sigma }=U_{i}^{\sigma }- U_{i}^{\text{g}}\] or \[\Delta _{a}U_{i}^{\text{s}} = U_{i}^{\text{s}}- U_{i}^{\text{g}}\] where the differential molar surface excess energy, Uiσ, is given by \[U_{i}^{\sigma }=(\frac{\partial U^{\sigma }}{\partial n_{i}^{\text{s}}})_{T,m,n_{j}^{\sigma }}=(\frac{\partial U}{\partial n_{i}^{\sigma }})_{T,m,V^{\text{g}},p_{i},n_{j}^{\sigma }}\] and the differential molar interfacial energy, Uis, by \[U_{i}^{\text{s}}=(\frac{\partial U}{\partial n_{i}^{\text{s}}})_{T,m,V^{\text{g}},p_{i},n_{j}^{\sigma }}=(\frac{\partial U}{\partial n_{i}^{\text{s}}})_{T,m,V^{\text{g}},V^{\text{s}},p_{i},n_{j}^{\text{s}}}\] Uig is the differential molar energy of component i in the gas phase, i.e. \[(\frac{\partial U}{\partial n_{i}^{\text{g}}})_{T,V,n_{i}^{\text{g}}}\]
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 (https://doi.org/10.1351/pac197231040577)