Confining multiple polymers between sticky walls: a directed walk model of two polymers
Abstract
We study a model of two polymers confined to a slit with sticky walls. More precisely, we find and analyse the exact solution of two directed friendly walks in such a geometry on the square lattice. We compare the infinite slit limit, in which the length of the polymer (thermodynamic limit) is taken to infinity before the width of the slit is considered to become large, to the opposite situation where the order of the limits are swapped, known as the halfplane limit when one polymer is modelled. In contrast with the single polymer system we find that the halfplane and infinite slit limits coincide. We understand this result in part due to the tethering of polymers on both walls of the slit. We also analyse the entropic force exerted by the polymers on the walls of the slit. Again the results differ significantly from single polymer models. In a single polymer system both attractive and repulsive regimes were seen, whereas in our two walk model only repulsive forces are observed. We do, however, see that the range of the repulsive force is dependent on the parameter values. This variation can be explained by the adsorption of the walks on opposite walls of the slit.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 October 2014
 DOI:
 10.1088/17518113/47/41/415002
 arXiv:
 arXiv:1406.0020
 Bibcode:
 2014JPhA...47O5002W
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Mathematics  Combinatorics
 EPrint:
 doi:10.1088/17518113/47/41/415002