Buckling, Fluctuations and Collapse in Semiflexible Polyelectrolytes

TL;DR

This paper analyzes how stiff polyelectrolyte chains with intrachain attractions undergo buckling and collapse, revealing the role of fluctuations and constructing a phase diagram of transitions.

Contribution

It introduces a systematic statistical mechanical framework to study buckling and collapse in semiflexible polyelectrolytes, incorporating fluctuation effects beyond mean-field theory.

Findings

Fluctuations renormalize the persistence length but do not alter buckling behavior in the semiclassical approximation.

Thermal fluctuations induce a transition from buckling to polymer collapse.

A phase diagram of collapse transitions terminating at a buckling instability is constructed.

Abstract

We present a systematic statistical mechanical analysis of the conformational properties of a stiff polyelectrolyte chain with intrachain attractions that are due to counterion correlations. We show that the mean-field solution corresponds to an Euler-like buckling instability. The effect of the conformational fluctuations on the buckling instability is investigated, first, qualitatively, within the harmonic (``semiclassical'') theory, then, systematically, within a 1/d-expansion, where d denotes the dimension of embedding space. Within the ``semiclassical'' approximation, we predict that the effect of fluctuations is to renormalize the effective persistence length to smaller values, but not to change the nature of the mean-field (i.e., buckling) behavior. Based on the 1/d-expansion we are, however, led to conclude that thermal fluctuations are responsible for a change of the buckling behavior which is turned into a polymer collapse. A phase diagram is constructed in which a sequence of collapse transitions terminates at a buckling instability that occurs at a place that varies with the magnitude of the bare persistence length of the polymer chain, as well as with the strength and range of the attractive potential.