Simple theory for the critical adsorption of a fluid

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Abstract
Isotherms for the adsorption of a fluid can be obtained from standard theories of fluids by regarding the surface as a single giant sphere dissolved in the fluid. The amount adsorbed is then an integral over the giant-sphere–fluid-molecule correlation function. Simple considerations show that the critical exponent for the adsorption isotherm is related to γ, the critical exponent for the compressibility. Using the mean-spherical approximation, it is argued that the adsorption-isotherm critical exponent is γ/2 if the surface-fluid interaction is sufficiently short-ranged. This result is in reasonable agreement with the recent experimental findings of Blümel and Findenegg.