Electrostatic Persistence Length Revisited. II. Simulations and Comparison to Experiment

Abstract

For decades, debate has surrounded the electrostatic persistence length (EPL) controlling local polyelectrolyte stiffening, centered on two competing power laws: the linear BJ prediction, ${\text{l}}_{\mathrm{e}}\sim r_{\mathrm{D}}$, and the quadratic OSF/KK scaling, ${\text{l}}_{\mathrm{e}}\sim r_{\mathrm{D}}^2$, where $r_{\mathrm{D}}$ is the Debye screening length. Building on the asymptotic scaling theory developed in the accompanying paper, we validate a complete diagram of limiting regimes using large-scale coarse-grained Monte Carlo simulations of ideal chains with charged monomers interacting through a screened Coulomb potential. By simulating long chains of up to $N\simeq 10^4-10^5$ Kuhn segments, we demonstrate that the electrostatic stiffening of both semiflexible and flexible polyelectrolytes obeys the same quadratic OSF/KK law. We track the exponent $\alpha$ which measures how the chain size $R$ grows with the Debye radius, $R\sim r_{\mathrm{D}}^{\alpha }$. For both cases, in agreement with the OSF/KK theory, $\alpha$ rises past 3/5 and slowly approaches 1 as the chain length increases, whereas within the BJ theory it can never exceed 2/5. We further find that three common size measures, the end-to-end distance $R_{\mathrm{ee}}$, radius of gyration $R_{\mathrm{g}}$, and hydrodynamic radius $R_{\mathrm{h}}$, reach this asymptotic behavior at progressively increasing chain lengths. Consequently, for any real polyelectrolyte, the apparent exponents obey ${\alpha }_{\mathrm{ee}}\ge {\alpha }_{\mathrm{g}}\ge {\alpha }_{\mathrm{h}}$, making $R_{\mathrm{g}}$ a sharper experimental probe than $R_{\mathrm{h}}$. Finally, we re-analyze the available experimental data and show that they rule out the linear BJ law and support the quadratic KK scaling, thereby resolving contradictions that stem from mistaking the apparent slopes measured for short chains for the true asymptotic exponent.