Effect of geometrical constraint on conformational properties and adsorption transition of a semiflexible polymer chain

TL;DR

This paper investigates how geometrical constraints affect the conformational properties and adsorption transition of a semiflexible copolymer chain on a square lattice, providing exact partition functions and comparing constrained and unconstrained cases.

Contribution

It introduces exact analytical expressions for the partition function of a constrained semiflexible copolymer, analyzing the impact of geometrical constraints on its phase transition behavior.

Findings

Geometrical constraints alter the adsorption transition point.

Exact partition functions for various interaction scenarios are derived.

Constrained chains show different conformational properties compared to unconstrained chains.

Abstract

We analyze equilibrium properties and adsorption desorption phase transition behaviour of a linear semiflexible copolymer chain under constrained geometrical situation on square lattice in a good solvent. One dimensional stair shaped line imposes geometrical constrain on the chain. Lattice model of fully directed self avoiding walk is used to model the chain, semiflexibility of the chain is accounted by introducing energy barrier for each bend of the chain. Exact expression of the partition function of the chain is obtained using generating function technique for the cases, viz. (i) constrained copolymer chain is in the bulk, (ii) constrained copolymer chain interacting with an impenetrable flat surface, (iii) constrained copolymer chain interacting with constraint itself and (iv) general expression of the partition function of the copolymer chain, interacting with a flat surface and geometrical constraint (stair shaped line). We have compared bulk properties and adsorption desorption transition behaviour of a linear semiflexible homopolymer chain without constraint to the case when the chain is constrained.