Budkov Yu A, Kolesnikov A L, Georgi N, Kiselev M G
Institute of Solution Chemistry of the Russian Academy of Sciences, Ivanovo, Russia.
Ivanovo State University, Ivanovo, Russia.
J Chem Phys. 2014 Jul 7;141(1):014902. doi: 10.1063/1.4884958.
We present a statistical model of a dilute polymer solution in good solvent in the presence of low-molecular weight cosolvent. We investigate the conformational changes of the polymer induced by a change of the cosolvent concentration and the type of interaction between the cosolvent and the polymer. We describe the polymer in solution by the Edwards model, where the partition function of the polymer chain with a fixed radius of gyration is described in the framework of the mean-field approximation. The contributions of polymer-cosolvent and the cosolvent-cosolvent interactions in the total free energy are treated also within the mean-field approximation. For convenience we separate the system volume on two parts: the volume occupied by the polymer chain expressed through its gyration volume and the bulk solution. Considering the equilibrium between the two subvolumes we obtain the total free energy of the solution as a function of radius of gyration and the cosolvent concentration within gyration volume. After minimization of the total free energy with respect to its arguments we obtain a system of coupled equations with respect to the radius of gyration of the polymer chain and the cosolvent concentration within the gyration volume. Varying the interaction strength between polymer and cosolvent we show that the polymer collapse occurs in two cases--either when the interaction between polymer and cosolvent is repulsive or when the interaction is attractive. The reported effects could be relevant for different disciplines where conformational transitions of macromolecules in the presence of a cosolvent are of interest, in particular in biology, chemistry, and material science.
我们提出了一种在低分子量共溶剂存在下，处于良溶剂中的稀聚合物溶液的统计模型。我们研究了共溶剂浓度变化以及共溶剂与聚合物之间相互作用类型所引发的聚合物构象变化。我们用爱德华兹模型描述溶液中的聚合物，其中在平均场近似框架下描述了具有固定回转半径的聚合物链的配分函数。聚合物 - 共溶剂和共溶剂 - 共溶剂相互作用对总自由能的贡献也在平均场近似内进行处理。为方便起见，我们将系统体积分为两部分：通过聚合物回转体积表示的聚合物链所占体积和本体溶液。考虑这两个子体积之间的平衡，我们得到溶液的总自由能作为回转半径和回转体积内共溶剂浓度的函数。在总自由能关于其变量取最小值后，我们得到了关于聚合物链回转半径和回转体积内共溶剂浓度的耦合方程组。改变聚合物与共溶剂之间的相互作用强度，我们发现聚合物塌缩发生在两种情况下——要么是聚合物与共溶剂之间的相互作用为排斥力时，要么是相互作用为吸引力时。所报道的这些效应可能与不同学科相关，在这些学科中，共溶剂存在下大分子的构象转变是人们感兴趣的，特别是在生物学、化学和材料科学领域。
