Diffusion of nanoparticles in semidilute polymer solutions: A mode-coupling theory study.

We have proposed a theoretical formalism to study the long-time diffusion behavior of nanoparticles in polymer solutions by using mode-coupling theory (MCT). The non-hydrodynamic part Dmicro of the total diffusion coefficient D is calculated in the MCT framework where the polymer dynamic scattering function Γpp(k, t) in the solution plays an important role. By introducing an approximate summation form for Γpp(k, t), where both limits of short and long length scales are properly accounted for, we can compute Dmicro straightforwardly and investigate explicitly how D depends on the volume fraction ϕ of the polymer solution, the nanoparticle size R, the degree of polymerization N, as well as the entanglement effects. For illustration, we adopt our theoretical approach to analyze the diffusion of gold nanoparticles in semidilute poly(ethylene glycol) (PEG)-water solutions which has been studied in detail experimentally. We find that our theoretical results show very good quantitative agreements with the experimental data in many aspects, such as the strong dependence on ϕ, the large deviation from Stokes-Einstein relation particularly for small particles, as well as the effects of the PEG molecular weight. 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 behaviors associated with polymer solutions.