Behavior of a polymer chain in a critical binary solvent

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.