再探静电持久长度. II. 模拟及与实验的对比
Electrostatic Persistence Length Revisited. II. Simulations and Comparison to Experiment
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中文总结 AI 辅助
该研究通过大规模粗粒化蒙特卡洛模拟验证聚电解质静电刚化遵循二次OSF/KK定律，分析尺寸指数特性，重新分析实验数据并排除线性BJ定律，解决了相关矛盾。
中文摘要 AI 辅助
数十年来，围绕控制聚电解质局部刚化的静电持久长度（EPL）的争论一直存在，核心是两种相互竞争的幂律：线性BJ预测$\textbf{l}_\text{e} \backsim r_\text{D}$，以及二次OSF/KK标度$\textbf{l}_\text{e} \backsim r_\text{D}^{2}$，其中$r_\text{D}$为德拜屏蔽长度。基于配套论文中建立的渐近标度理论，我们通过对带有带电单体、通过屏蔽库仑势相互作用的理想链进行大规模粗粒化蒙特卡洛模拟，验证了完整的极限区域相图。通过模拟长度达$N \backsimeq 10^{4} - 10^{5}$个库恩段的长链，我们证明半柔性和柔性聚电解质的静电刚化均遵循相同的二次OSF/KK定律。我们追踪指数$\boldsymbol{\textit{\text{α}}}$，其表征链尺寸$\textit{\text{R}}$随德拜半径的增长关系$\textit{\text{R}} \backsim r_\text{D}^{\textit{\text{α}}}$。对于两种情况，与OSF/KK理论一致，$\boldsymbol{\textit{\text{α}}}$会超过3/5，并随链长增加缓慢趋近于1；而在BJ理论中，它永远无法超过2/5。我们进一步发现，三种常见的尺寸度量——末端距$R_\text{ee}$、回转半径$R_\text{g}$和流体力学半径$R_\text{h}$——会在逐渐增加的链长下达到这种渐近行为。因此，对于任何真实聚电解质，表观指数满足$\boldsymbol{\textit{\text{α}}_\text{ee} \backsimeq \textit{\text{α}}_\text{g} \backsimeq \textit{\text{α}}_\text{h}}$，这使得$R_\text{g}$比$R_\text{h}$更适合作为实验探针。最后，我们重新分析了现有实验数据，表明这些数据排除了线性BJ定律，支持二次KK标度，从而解决了因将短链表观斜率误认为真实渐近指数而产生的矛盾。
英文摘要
For decades, debate has surrounded the electrostatic persistence length (EPL) controlling local polyelectrolyte stiffening, centered on two competing power laws: the linear BJ prediction, $\textbf{l}_\mathrm{e} \sim r_\mathrm{D}$, and the quadratic OSF/KK scaling, $\textbf{l}_\mathrm{e} \sim r_\mathrm{D}^{2}$, 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 $α$ which measures how the chain size $R$ grows with the Debye radius, $R \sim r_\mathrm{D}^α$. For both cases, in agreement with the OSF/KK theory, $α$ 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 $α_\mathrm{ee} \geq α_\mathrm{g} \geq α_\mathrm{h}$, 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.
