Behavior of a polymer chain in a critical binary solvent

TL;DR

This paper uses field-theoretic renormalization group methods to analyze how a polymer chain behaves in a binary solvent near its critical demixing point, revealing new critical exponents and scaling behavior.

Contribution

It introduces a mapping of the polymer in a critical binary solvent to a bicritical field theory, deriving new critical exponents related to the chain's end-to-end distance.

Findings

Derived the critical exponent  for the polymer's end-to-end distance.

Calculated the mean end-to-end length near the critical point.

Mapped the problem to a -model with mass anisotropy.

Abstract

We present a field-theoretic renormalization group analysis of a polymer chain immersed in a binary good solvent close to its critical demixing point. We first show that this problem can be mapped on a bicritical field theory, i.e. a $(\Phi^{2})^{2}$-model with a mass anisotropy. This implies that the end-to-end distance of the polymer is now controlled by a new critical exponent $\nu_{B}$ related to the quadratic mass anisotropy operator $B$. To show this we solve the RG equation and calculate explicitly the exponents and the mean end-to-end length of the chain.