Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003, USA.
J Chem Phys. 2012 Apr 7;136(13):134901. doi: 10.1063/1.3698168.
We present a theory for polyelectrolyte gels that allow the effective charge of the polymer backbone to self-regulate. Using a variational approach, we obtain an expression for the free energy of gels that accounts for the gel elasticity, free energy of mixing, counterion adsorption, local dielectric constant, electrostatic interaction among polymer segments, electrolyte ion correlations, and self-consistent charge regularization on the polymer strands. This free energy is then minimized to predict the behavior of the system as characterized by the gel volume fraction as a function of external variables such as temperature and salt concentration. We present results for the volume transition of polyelectrolyte gels in salt-free solvents, solvents with monovalent salts, and solvents with divalent salts. The results of our theoretical analysis capture the essential features of existing experimental results and also provide predictions for further experimentation. Our analysis highlights the importance of the self-regularization of the effective charge for the volume transition of gels in particular, and for charged polymer systems in general. Our analysis also enables us to identify the dominant free energy contributions for charged polymer networks and provides a framework for further investigation of specific experimental systems.
我们提出了一种聚合物凝胶的理论，该理论允许聚合物主链的有效电荷进行自我调节。我们使用变分法得到了凝胶的自由能表达式，该表达式考虑了凝胶弹性、混合自由能、抗衡离子吸附、局部介电常数、聚合物链段之间的静电相互作用、电解质离子相关以及聚合物链上的自洽电荷调节。然后，我们通过最小化这个自由能来预测系统的行为，其特征是凝胶体积分数作为外部变量（如温度和盐浓度）的函数。我们提出了无盐溶剂、单价盐溶剂和二价盐溶剂中聚电解质凝胶的体积转变的结果。我们的理论分析捕捉到了现有实验结果的基本特征，同时也为进一步的实验提供了预测。我们的分析强调了有效电荷的自调节对于凝胶体积转变的重要性，特别是对于带电荷的聚合物体系。我们的分析还使我们能够确定带电聚合物网络的主要自由能贡献，并为进一步研究特定实验系统提供了框架。
