再探静电持久长度 I. 理论
Electrostatic Persistence Length Revisited. I. Theory
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中文总结 AI 辅助
本研究构建涵盖柔性与半刚性/刚性聚电解质的统一标度理论，识别9种构象标度区，推广静电团与排斥体积概念，揭示盐浓度调控的构象演化规律，验证了静电持久长度的平方标度关系。
中文摘要 AI 辅助
加盐稀溶液中聚电解质的单链构象问题，以及相关的静电持久长度$\textbf{l}_\text{e}$概念，数十年来一直未得到解决。为应对这一挑战，我们构建了一套全面的标度理论，并通过模拟对其进行验证。我们构建了统一的标度图，涵盖柔性聚电解质和本征半刚性/刚性聚电解质，识别出9种不同的标度区域，每个区域具有不同的构象统计特征。用于描述柔性聚电解质的高斯静电团（Gaussian electrostatic blob）$ξ_\text{e}$的概念被推广到半刚性体系，并引入了被称为棒状静电团（rodlike electrostatic blob）的新特征长度$ξ_\text{e}^{|}$。这一拓展得以界定重要的转变区域，同时展现出半刚性链与柔性链之间的相似性。我们还重新审视并推广了静电排斥体积的概念。随着盐浓度升高（即德拜长度$r_\text{D}$减小），链构象依次演变：(i) 棒状伸展态，(ii) 高斯链态，(iii) 以$\textbf{l}_\text{e}$为特征的带局部静电刚性的溶胀线团态，(iv) 无刚性增强但存在静电排斥体积的溶胀线团态，最终变为(v) 准中性高斯线团态。在(ii)类和(iii)类区域中，静电持久长度与$r_\text{D}$的平方成正比，分别与针对半刚性链的OSF预测和针对柔性链的KK预测一致：$\textbf{l}_\text{OSF} \backsimeq r_\text{D}^{2}/ξ_\text{e}^{|}$，$\textbf{l}_\text{KK} \backsimeq r_\text{D}^{2}/ξ_\text{e}$。这些渐近标度关系已在配套论文的粗粒化模拟中得到证实。
英文摘要
The problem of single-chain conformations of polyelectrolytes in salt-added dilute solutions, and the associated concept of the electrostatic persistence length $\textbf{l}_\mathrm{e}$, has remained unresolved for decades. To address this challenge, we develop a comprehensive scaling theory and corroborate it with simulations. A unified scaling diagram is constructed that encompasses both flexible and intrinsically semiflexible/stiff polyelectrolytes. Nine distinct scaling regimes are identified, each characterized by different conformational statistics. The concept of the Gaussian electrostatic blob $ξ_\mathrm{e}$ used in the description of flexible polyelectrolytes is extended to the semiflexible case, and the new characteristic length $ξ_\mathrm{e}^{|}$ referred to as the rodlike electrostatic blob is introduced. This enables delineating the important crossovers and showcasing an analogy between semiflexible and flexible chains. The concept of electrostatic excluded volume is also reconsidered and generalized. Upon increasing the salt concentration, i.e., decreasing the Debye length $r_\mathrm{D}$, chain conformations evolve from (i) rodlike stretches to (ii) Gaussian and then (iii) swollen coils with local electrostatic stiffening characterized by $\textbf{l}_\mathrm{e}$, followed by (iv) swollen coils without stiffening but with electrostatic exclude volume, and finally to (v) quasi-neutral Gaussian coils. In regimes of type (ii) and (iii), the electrostatic persistence length scales quadratically with $r_\mathrm{D}$, in agreement with the OSF and KK predictions for semiflexible and flexible chains, respectively: $\textbf{l}_\mathrm{\mathrm{OSF}} \simeq r_\mathrm{D}^{2}/ξ_\mathrm{e}^{|}$ and $\textbf{l}_\mathrm{\mathrm{KK}} \simeq r_\mathrm{D}^{2}/ξ_\mathrm{e}$. These asymptotic scalings are confirmed by coarse-grained simulations presented in the accompanying article.
