E J Janse van Rensburg

arXiv2019

Force-induced desorption of 3-star polymers in two dimensions

We investigate the phase diagram of a self-avoiding walk model of a 3-star polymer in two dimensions, adsorbing at a surface and being desorbed by the action of a force. We show rigorously that there are four phases: a free phase, a ballistic phase, an adsorbed phase and a mixed phase where part of the 3-star is adsorbed and part is ballistic. We use both rigorous arguments and Monte Carlo methods to map out the phase diagram, and investigate the location and nature of the phase transition boundaries. In two dimensions, only two of the arms can be fully adsorbed in the surface and this alters the phase diagram when compared to 3-stars in three dimensions.

cond-mat.stat-mech↗

arXiv2007

Directed Paths in a Wedge

Directed paths have been used extensively in the scientific literature as a model of a linear polymer. Such paths models in particular the conformational entropy of a linear polymer and the effects it has on the free energy. These directed models are simplified versions of the self-avoiding walk, but they do nevertheless give insight into the phase behaviour of a polymer, and also serve as a tool to study the effects of conformational degrees of freedom in the behaviour of a linear polymer. In this paper we examine a directed path model of a linear polymer in a confining geometry (a wedge). The main focus of our attention is $c_n$, the number of directed lattice paths of length $n$ steps which takes steps in the North-East and South-East directions and which is confined to the wedge $Y=\pm X/p$, where $p$ is an integer. In this paper we examine the case $p=2$ in detail, and we determine the generating function using the iterated kernel method. We also examine the asymtotics of $c_n$. In particular, we show that $$ c_n = [0.67874...]\times 2^{n-1}(1+(-1)^n) + O((4/3^{3/4})^{n+o(n)}) + o((4/3^{3/4})^n) $$ where we can determine the constant $0.67874...$ to arbitrary accuracy with little effort.

cond-mat.soft↗