Randomly Charged Polymers: An Exact Enumeration Study

TL;DR

This study uses exact enumeration to analyze how random charged polymers, or polyampholytes, transition between compact and extended states depending on charge and temperature, revealing phase transitions and critical behavior.

Contribution

It provides the first exact enumeration analysis of polyampholytes, identifying phase transitions and estimating critical parameters for small polymer chains.

Findings

Phase transition from compact to extended at charge Q_c ≈ q_0 √N.

Indications of a transition between two compact states at small Q.

Estimates of condensation energy, surface tension, and critical exponent ν.

Abstract

We perform an exact enumeration study of polymers formed from a (quenched) random sequence of charged monomers $\pm q_0$. Such polymers, known as polyampholytes, are compact when completely neutral and expanded when highly charged. Our exhaustive search included all spatial conformations and quenched sequences for up to 12--step (13--site) walks. We investigate the behavior of the polymer as a function of its overall excess charge $Q$, and temperature $T$. At low temperatures there is a phase transition from compact to extended configurations when the charge exceeds $Q_c\approx q_0 \sqrt{N}$. There are also indications of a transition for small $Q$ between two compact states on varying temperature. Numerical estimates are provided for the condensation energy, surface tension, and the critical exponent $\nu$.