Crosslinked polymer chains with excluded volume: A new class of branched polymers?

TL;DR

This paper introduces a new class of branched polymers called microgels with excluded volume interactions, revealing two distinct types with different size scaling laws based on their crosslinking and swelling behavior.

Contribution

It provides a theoretical analysis of microgels with excluded volume, identifying two types with unique size scaling laws, expanding understanding of branched polymer structures.

Findings

Two types of microgels with distinct size scaling laws.

A special branched polymer scales as R ∝ N^{2/5} M^{-1/5}.

c* microgels have mesh sizes scaling as r = a (N/M)^{3/5}.

Abstract

In this note microgels with and without excluded volume interactions are considered. Based on earlier exact computations on Gaussian mircogels, which are formed by self-crosslinking (with $M$ crosslinks) of polymer chains with chain length $N$ Flory type approximations are used to get first insight to their behavior in solution. It is shown that two different types of microgels exist: A special type of branched polymer whose size scales as $R \propto N^{2/5} M^{-1/5}$, instead of $R \propto N^{1/2}$. The second type are $c^*$ - microgels whose average mesh sizes $r$ are swollen and form self avoiding walks with a scaling law of the form $r = a (N/M)^{3/5}$.