Forces and pressures in adsorbing partially directed walks

Abstract

Polymers in confined spaces lose conformational entropy. This induces a net repulsive entropic force on the walls of the confining space. A model for this phenomenon is a lattice walk between confining walls, and in this paper a model of an adsorbing partially directed walk is used. The walk is placed in a half square lattice with boundary , and confined between two vertical parallel walls, which are vertical lines in the lattice, a distance w apart. The free energy of the walk is determined, as a function of w, for walks with endpoints in the confining walls and adsorbing in . This gives the entropic force on the confining walls as a function of w. It is shown that there are zero force points in this model and the locations of these points are determined, in some cases exactly, and in other cases asymptotically.