Two-dimensional polymer networks at a mixed boundary: Surface and wedge exponents

TL;DR

This paper derives general formulas for the configurational exponents of 2D polymer networks near mixed boundary wedges and validates them through exact enumeration of linear chains with various boundary conditions.

Contribution

It introduces new general formulae for surface and wedge exponents of polymer networks with mixed boundary conditions in two dimensions.

Findings

Derived explicit formulas for surface and wedge exponents.

Validated formulas through exact enumeration of linear chains.

Analyzed effects of boundary conditions on polymer configurations.

Abstract

We provide general formulae for the configurational exponents of an arbitrary polymer network connected to the surface of an arbitrary wedge of the two-dimensional plane, where the surface is allowed to assume a general mixture of boundary conditions on either side of the wedge. We report on a comprehensive study of a linear chain by exact enumeration, with various attachments of the walk's ends to the surface, in wedges of angles $\pi/2$ and $\pi$, with general mixed boundary conditions.