Microscopic approach for the site distribution and thermodynamic properties of a single-component polymer subjected...

A microscopic statistical mechanics approach is proposed for a nonuniform single-component freely jointed tangential hard-sphere polymer in the framework of density-functional theory. The present approach avoids the use of single-chain simulation in the theory by treating bonding interaction on the basis of the properties of the Dirac delta function. The present excess free energy includes all terms of functional perturbative expansion around the uniform bulk fluid in the form of the Verlet-modified bridge function. The second-order direct correlation function of a uniform polymer melt as the input parameter is obtained by solving numerically the polymer-reference-interaction-site-model integral equation with the Percus-Yevick closure. Predictions of the present approach for such microscopic structural and thermodynamics properties as the site density distribution, the partition coefficient, and the adsorption isotherm near a hard wall or between two hard walls are compared with computer-simulation results and with those of previous theories. The comparison indicates that the present approach is more accurate than the previous integral equation theory and the most accurate Monte Carlo density-functional theories. The predicted oscillations of the medium-induced force between two hard walls immersed in polymer melts are consistent with the experimental results available in the literature. The relation of the present approach with self-consistent-field theory, as well as the differences between the two, are discussed.