A theoretical estimate on the probability of the formation of a self-avoiding copolymer macromolecule

TL;DR

This paper provides an analytical estimate of the probability of forming an infinitely long self-avoiding semi-flexible copolymer chain using a lattice model, revealing independence from chain stiffness and differences from Gaussian chain models.

Contribution

It introduces a recursive analytical method to estimate copolymer formation probability, highlighting independence from stiffness and contrasting with Gaussian chain behavior.

Findings

Probability of chain formation is independent of stiffness.

Self-avoiding copolymer behavior differs from Gaussian chains.

Average bonding types vary with chain properties.

Abstract

A lattice model of the directed self-avoiding walk is used to estimate the possibility on the formation of an infinitely long linear semi-flexible copolymer chain. The copolymer chain is assumed to composed of four different types of the monomers. A method of the recursion relations is used to solve the proposed model analytically to show that the probability of the formation of a self-avoiding semi-flexible copolymer chain is independent of the stiffness of the chain. It is a distinct result from our earlier study on the formation of a Gaussian semi-flexible copolymer chain and the Gaussian chain is made up of these four monomers, [P. K. Mishra, J. of Adv. Appl. Sci. Res. 2(4) 1-8 (2020)]. We have also calculated the average number of different types of the bonding in the copolymer chain to show the distinctions in the behaviour of the self-avoiding copolymer chain from the Gaussian polymer chain.