Forces and pressures in adsorbing partially directed walks
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A polymer in a confined space loses entropy and exerts an entropic force on the walls of the confining space. In this paper a partially directed walk model of the entropic forces in a confined polymer is introduced and analysed. The walk is a model of a 2-dimensional adsorbing polymer placed between confining plates (which are lines in the lattice). The walk spans the space between the confining plates, and adsorbs into the x-axis. We determine the free energy of the walk by using the kernel method to solve for its generating function, and determine the entropic forces and pressures exerted by the walk on the confining plates. We show that there are zero force points (where the forces vanish). The locations of the zero force point are determined; in some cases exactly, and in other cases by an asymptotic expression. Since the walk loses entropy in a confining space (due to the loss of conformational entropy), there are entropic forces acting on the confining plates. These forces push the plates apart if they are too close together, and pull them together if they are too far apart. In several cases asymptotic expressions for the forces are derived and shown to be repulsive if the plates are too close together and attractive if the plates are too far apart.
AuthorsRensburg, EJJV; Prellberg, T
- Applied Mathematics