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Mean End-to-End Distance of a Polymer Confined between Two Interacting Plates

The mean end-to-end distance of a polymer confined between two plates, and interaction with the plates, were studied in the presence of excluded volume interaction. The polymer surface interaction is included exactly in the unperturbed distribution function of the confined polymer as the boundary condition. The excluded volume interaction is introduced perturbatively using the homotopy parameter expansion method. The component of the mean square end to end distance parallel to the plates is calculated as the function of DW and D/〈Rz2〉∞1/2, where D is the interplate distance, W is the the polymer-plate interaction parameter and 〈Rz2〉∞ is the component of the mean square end to end distance perpendicular to the plates in an unconfined state. It was found that the attractive interaction between the polymer and the plates has a larger effect on chain dimensions than the repellent interaction between them. The parallel components of the mean end-to-end distance of the chain where one end is fixed at an assigned position is also calculated.