Thermodynamics of fluids in quenched disordered matrices

Using the replica method, we derive the thermodynamic relations for a fluid in equilibrium with a quenched porous matrix. In particular, the appropriate Gibbs–Duhem equation is obtained as well as the equivalence between grand canonical and canonical ensembles. The exact compressiblity and virial equations are derived. Whereas the compressibility equation remains a direct and practical way to obtain the adsorption isotherm, the virial equation involves terms which do not relate easily to the properties of the fluid/matrix system. This explains the inconsistency between previous theoretical predictions and computer simulation results.

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