Structure and thermodynamic properties of a polydisperse fluid in contact with a polydisperse matrix

We present expressions that allow the determination of the structural and thermodynamic properties of a polydisperse liquid mixture in contact with a polydisperse matrix; polydispersity of the fluid and of the matrix are described by distribution functions ff ( ) and fm ( ), where and characterize the size of the fluid and of the matrix particles. The formalism is based on the replica trick (to describe the properties of a fluid in contact with a matrix) and on the expansion of size-dependent functions in terms of orthogonal polynomials associated with the distribution functions ff ( ) and fm ( ). In our expressions structural and thermodynamic properties are calculated from coefficient functions (of these expansions) which are obtained from a numerical solution of the generalized replica Ornstein–Zernike equations, solved along with a suitable closure relation.