Universal features of complex $n$-block copolymers

TL;DR

This paper investigates the universal conformational properties of complex $n$-block copolymers, deriving analytical expressions for their scaling behavior and validating findings with numerical simulations.

Contribution

It introduces a renormalization group approach to analytically determine the scaling exponent and size measures of $n$-block copolymers, highlighting their universal conformational features.

Findings

Derived analytical expression for the scaling exponent $\gamma(n)$.

Quantified the extension degree of blocks based on $n$ and position.

Performed numerical simulations for $n=2$ to illustrate conformational behavior.

Abstract

We study the conformational properties of complex polymer macromolecules, consisting in general of $n$ subsequently connected chains (blocks) of different lengths and distinct chemical structure. Depending on the solvent conditions, the inter- or intrachain interactions of some blocks may vanish, causing the rich conformational behavior. Our main attention is focused on the universal conformational properties of such molecules. Applying the direct polymer renormalization group approach, we derive the analytical expressions for the scaling exponent $\gamma(n)$, governing the number of possible conformations of $n$-block copolymer, and analyze the effective linear size measures of individual blocks. In particular, it is quantitatively estimated the degree of extension of the block sizes as functions of $n$ and position of blocks in sequence. The numerical simulations of the simplest $n=2$-block copolymer chain are performed as well for better illustration of the conformational behavior of such molecules.