Density profiles of a hard sphere chain fluid near a hard wall: applications to adsorption onto a crystalline surface

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Abstract
Density profiles and adsorption coefficient of a hard sphere chain fluid near a hard wall are investigated using the Percus-Yevick approximation for the associative Henderson-Abraham-Barker equation. The chain molecule is represented as a hard sphere with two independent attractive sites. The wall-particle correlation functions are given both numerically and analytically (as the Laplace transform) as functions of the bulk number density η and mean chain length m. An analytical expression for the adsorption coefficient is obtained. The density profile prediction for the Wertheim totally dimerized hard sphere case and the case under consideration (with m = 2) are compared. The results for the density profiles (m = 3, m = 4, m = 20) are compared with Monte Carlo data and with the results of density functional theory. The contact values of the correlation functions are used to calculate the adsorption isotherm of polymer chains onto a crystalline wall. It is shown that the intramolecular correlations lead to a new kind of critical behaviour at low densities, which could be interpreted as the adsorption of distinct chains.