Dynamic charge density correlation function in weakly charged polyampholyte globules

TL;DR

This study calculates the dynamic charge density correlation function within weakly charged polyampholyte globules, revealing how charge fluctuations relax over different length and time scales in semi-dilute globular interiors.

Contribution

It provides a theoretical calculation of the charge density correlation function in weakly charged polyampholyte globules using the quadratic approximation, focusing on the interior dynamics.

Findings

Charge fluctuations relax as g(q,s) = q^2(1-s^(1/2)) at short times.

At intermediate times, g(q,s) = q^2 s^(-1/2).

Results are valid for wave vectors q > 0.1, where entanglements are negligible.

Abstract

We study solutions of statistically neutral polyampholyte chains containing a large fraction of neutral monomers. It is known that, even if the quality of the solvent with respect to the neutral monomers is good, a long chain will collapse into a globule. For weakly charged chains, the interior of this globule is semi-dilute. This paper considers mainly theta-solvents, and we calculate the dynamic charge density correlation function g(k,t) in the interior of the globules, using the quadratic approximation to the Martin-Siggia-Rose generating functional. It is convenient to express the results in terms of dimensionless space and time variables. Let R be the blob size, and let T be the characteristic time scale at the blob level. Define the dimensionless wave vector q = R k, and the dimensionless time s = t/T. We find that for q<1, corresponding to length scales larger than the blob size, the charge density fluctuations relax according to g(q,s) = q^2(1-s^(1/2)) at short times s < 1, and according to g(q,s) = q^2 s^(-1/2) at intermediate times 1 < s < q^(-4). We expect these results to be valid for wave vectors q > 0.1, where entanglements are unimportant.