Nanoparticle Diffusion within Dilute and Semidilute Xanthan Solutions

We measured the translation diffusion coefficient ( D) of nanoparticles within dilute and semidilute solutions of a semiflexible polymer, xanthan. Our results showed that for particle diameters ( d) of 5 and 10 nm, the obstruction theory can explain the concentration ( c) dependence of D in the dilute regime. Diffusion in semidilute solutions is better explained by additionally considering the modified Darcy flow with the hydrodynamic screening length varying according to κ ≈ c^-0.76_. The depletion effect is operative for larger particles ( d = 30 nm) within semidilute solutions. We used a scaling relation for the depletion layer thickness δ ≈ ξ^ν, where ξ is the static correlation length and the exponent ν ≈ 0.42 that can explain our data. This is in contrast with a flat surface, where the exponent is expected to be 1. Our results showed that in the situation, when the polymer network relaxation is much slower compared to the diffusive time-scale of particles, no single theory is capable to describe the concentration and size dependence of particle mobility.