A theoretical formalism based on mode-coupling theory( MCT) was established to study the long-time diffusion coefficient of nanoparticles in polyelectrolyte solutions. By introducing an approximate summa-tion form forΓpp( k,t) , Dmicro can be calculated straightforwardly and it is necessary to investigate explicitly how D depends on the concentration c of the polymer solution and the nanoparticle size R . For illustration, the theoretical approach is taken to analyze the diffusion of polystyrene nanoparticles in semidilute polyacrylamide solutions which has been studied in detail experimentally. As a result, our theoretical results show very good quantitative agreements with the experimental data in many aspects, such as the strong dependence on c , the large deviation from Stokes-Einstein relation particularly for small particles. Such good agreements clearly demonstrate the validity of our MCT framework, which may serve as a good starting point to study many more complex dynamical behavior associated with polymer solutions.%采用模耦合理论( MCT)建立了研究纳米粒子在聚电解质溶液中长时扩散系数D的介观统计方法,提出了有效的聚合物溶液动态散射函数Γpp( k,t)的约化形式。定量计算了溶液微观密度涨落对扩散系数的贡献,考察了扩散系数 D对溶液浓度 c及纳米粒子半径 R的依赖关系,并定量分析了 MCT 与经典 Stokes-Einstein( S-E)关系的偏离。结果表明, MCT方法的研究结果与实验数据吻合。当纳米粒子尺寸小于聚电解质特征尺寸时,其扩散系数对S-E关系明显偏离。本文建立的基于微观描述的MCT方法为进一步研究纳米粒子在聚合物溶液中的含时扩散动力学行为奠定了理论基础。
展开▼
