Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA 91125.
Proc Natl Acad Sci U S A. 2022 Sep 6;119(36):e2209975119. doi: 10.1073/pnas.2209975119. Epub 2022 Aug 29.
There is notable discrepancy between experiments and coarse-grained model studies regarding the thermodynamic driving force in polyelectrolyte complex coacervation: experiments find the free energy change to be dominated by entropy, while simulations using coarse-grained models with implicit solvent usually report a large, even dominant energetic contribution in systems with weak to intermediate electrostatic strength. Here, using coarse-grained, implicit-solvent molecular dynamics simulation combined with thermodynamic analysis, we study the potential of mean force (PMF) in the two key stages on the coacervation pathway for symmetric polyelectrolyte mixtures: polycation-polyanion complexation and polyion pair-pair condensation. We show that the temperature dependence in the dielectric constant of water gives rise to a substantial entropic contribution in the electrostatic interaction. By accounting for this electrostatic entropy, which is due to solvent reorganization, we find that under common conditions (monovalent ions, room temperature) for aqueous systems, both stages are strongly entropy-driven with negligible or even unfavorable energetic contributions, consistent with experimental results. Furthermore, for weak to intermediate electrostatic strengths, this electrostatic entropy, rather than the counterion-release entropy, is the primary entropy contribution. From the calculated PMF, we find that the supernatant phase consists predominantly of polyion pairs with vanishingly small concentration of bare polyelectrolytes, and we provide an estimate of the spinodal of the supernatant phase. Finally, we show that prior to contact, two neutral polyion pairs weakly attract each other by mutually induced polarization, providing the initial driving force for the fusion of the pairs.
在聚电解质复合凝聚中，实验和粗粒模型研究之间存在显著的热力学驱动力差异：实验发现自由能变化主要由熵主导，而使用具有隐溶剂的粗粒模型进行模拟通常报告在静电强度较弱到中等的系统中存在大的、甚至主导的能量贡献。在这里，我们使用粗粒、隐溶剂分子动力学模拟结合热力学分析，研究了对称聚电解质混合物凝聚途径上两个关键阶段的平均力势（PMF）：聚阳离子-聚阴离子络合和聚离子对-对凝聚。我们表明，水中介电常数的温度依赖性导致静电相互作用中存在大量的熵贡献。通过考虑这种由于溶剂重排而产生的静电熵，我们发现，在常见的（单价离子，室温）水相条件下，这两个阶段都是强烈的熵驱动，能量贡献可以忽略不计，甚至不利，这与实验结果一致。此外，对于较弱到中等的静电强度，这种静电熵而不是抗衡离子释放熵是主要的熵贡献。从计算的 PMF 中，我们发现上清相主要由聚离子对组成，几乎没有裸露的聚电解质，并且我们提供了上清相的旋节线的估计。最后，我们表明，在接触之前，两个中性聚离子对通过相互诱导极化而微弱地相互吸引，为对的融合提供初始驱动力。
