Diffusion Coefficient of Nanoparticles in Semidilute Polyelectrolyte Solutions Based on Mode Coupling Theory

A theoretical formalism based on mode-coupling theory (MCT) was established to study the longtime diffusion coefficient of nanoparticles in polyelectrolyte solutions. By introducing an approximate summation form for Gamma(pp)(k,t), D-micro 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.