An infinitely long flexible polymer chain in between two parallel plates

TL;DR

This paper models an infinitely long flexible polymer confined between two parallel plates using a directed self-avoiding walk on a cubic lattice, deriving its thermodynamic properties analytically.

Contribution

It introduces an analytical method to study the equilibrium statistics of a confined polymer of any length and plate separation.

Findings

Derived the force of confinement and surface tension.

Obtained monomer density profiles.

Proposed a general calculation method for confined polymers.

Abstract

We consider a fully directed self-avoiding walk model on a cubic lattice to mimic the conformations of an infinitely long confined flexible polymer chain; and the confinement condition is achieved by two parallel athermal plates. The confined polymer system is under good solvent condition and we revisit this problem to solve the real polymer's model for any length of chain and also for any separation in between the plates. The equilibrium statistics of the confined polymer chain is derived using an analytical calculations based on the generating function technique. The force of the confinement, the surface tension and the monomer density profile of confined chain is obtained. We propose that a method of calculations is suitable to understand thermodynamics of an arbitrary length confined polymer chain.