A simple and exactly solvable model for a semiflexible polymer chain interacting with a surface

TL;DR

This paper presents an exactly solvable lattice model for semiflexible polymers interacting with surfaces, analyzing conformational and adsorption properties in 2D and 3D with exact solutions and enumeration methods.

Contribution

It introduces a simple, exactly solvable lattice model incorporating chain stiffness and surface interactions, providing analytical and numerical insights into polymer adsorption.

Findings

Exact critical surface attraction values for adsorption in 2D and 3D.

Persistent length as a function of chain stiffness.

Excellent agreement between enumeration and analytical results.

Abstract

We use the lattice model of directed walks to investigate the conformational as well as the adsorption properties of a semiflexible homopolymer chain immersed in a good solvent in two and three dimensions. To account for the stiffness in the chain we have introduced energy barrier for each bend in the walk and have calculated the persistent length as a function of this energy. For the adsorption on an impenetrable surface perpendicular to the preferred direction of the walk we have solved the model exactly and have found the critical value of the surface attractions for the adsorption in both two and three dimensions. We have also enumerated all the possible walks on square and cubic lattices for the number of steps N <= 30 for two-dimensions and N <= 20 for three dimensions and have used ratio method for extrapolation. The transition located using this method is in excellent agreement with the results found from the analytical method.