surface excess, \(n^{\sigma}\)

https://doi.org/10.1351/goldbook.S06171
For an interface, the adsorption or surface excess of a given component is defined as the difference between the amount of component actually present in the system, and that which would be present (in a reference system) if the bulk concentration in the adjoining phases were maintained up to a chosen geometrical dividing surface (Gibbs dividing surface). For a solid/liquid interface in which no component of the liquid phase penetrates into the solid, the surface excess (or adsorption) of component i is defined as: \[n_{i}^{\sigma }=n_{i}- V^{\text{l}}\ c_{i}^{\text{l}}\] where n i is the total amount of i in the system, V l is the volume of an arbitrarily chosen amount of bulk liquid (in the framework of the so-called algebraic method) and cil is its bulk concentration in the liquid.
See: Gibbs adsorption
Sources:
Green Book, 2nd ed., p. 63 (https://dev.goldbook.iupac.org/files/pdf/green_book_2ed.pdf)
PAC, 1986, 58, 967. 'Reporting data on adsorption from solution at the solid/solution interface (Recommendations 1986)' on page 969 (https://doi.org/10.1351/pac198658070967)