Variation of Weak Polyelectrolyte Persistence Length through an Electrostatic Contour Length

Abstract

There is currently no consensus that the classical perspective of electrostatic persistence length (the so-called Odijk–Skolnick–Fixman, or OSF, formulation), derived by equating changes in electrostatic energy with bending rigidity, is applicable to weak polyelectrolytes. Here, with a focus on polyelectrolyte chains of finite length at a single scale, we formulate a simple and general theoretical model featuring the electrostatic persistence length, Pe, through the introduction of an electrostatic contour length, Le, such that the electrostatic energy balance is applicable to highly flexible charged polyelectrolytes (where the intrinsic stiffness, P0 is on the order of Pe). To isolate the effect of ionization, only the salt-free regime is considered. At the upper limit (relatively rigid molecules), the new formulation converges to the classical OSF form, while the lower bound (highly flexible molecules) approaches proportionality to the Debye screening length, κ–1. In general, the electrostatic persistence can be described retroactively by the Debye screening, κ–1, and the ratio of electrostatic to intrinsic contour lengths, A/a, complementary to predictive theoretical formulations. The theory is validated via full atomistic molecular dynamics simulations of single, isolated model weak polyelectrolyte chains in explicit solvent—specifically poly(acrylic acid), PAA, and poly(allylamine hydrochloride), PAH, both of which undergo significant increases in persistence length under ionization. An ensemble of equilibrated polymer states is obtained via temperature assisted sampling, implementing molecular dynamics to drive the polymers into physically accessible conformations via cyclical temperature fluctuations and equilibration.