Semiflexible directed polymers in a strip with attractive walls
Abstract
We study a model of a semiflexible long chain polymer confined to a twodimensional slit of width $w$, and interacting with the walls of the slit. The interactions with the walls are controlled by Boltzmann weights $a$ and $b$, and the flexibility of the polymer is controlled by another Boltzmann weight $c$. This is a simple model of the steric stabilisation of colloidal dispersions by polymers in solution. We solve the model exactly and compute various quantities in $(a,b,c)$space, including the free energy and the force exerted by the polymer on the walls of the slit. In some cases these quantities can be computed exactly for all $w$, while for others only asymptotic expressions can be found. Of particular interest is the zeroforce surface  the manifold in $(a,b,c)$space where the free energy is independent of $w$, and the loss of entropy due to confinement in the slit is exactly balanced by the energy gained from interactions with the walls.
 Publication:

arXiv eprints
 Pub Date:
 November 2019
 arXiv:
 arXiv:1912.00151
 Bibcode:
 2019arXiv191200151B
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Mathematical Physics;
 Mathematics  Combinatorics;
 05A15;
 05A16;
 82B23;
 82B27 82B41
 EPrint:
 25 pages, 10 figures