Diffusion of Small Charged Nanoparticles within a Semidilute Polyelectrolyte Solution

We studied the diffusion of charged gold nanoparticles within a semidilute solution of weakly charged polyelectrolyte, polyacrylic acid (PAA) of high molecular weight (M_w=10⁶ g/mol) by using fluctuation correlation spectroscopy (FCS). Nanoparticle size (2R) was varied between 5 nm to 40 nm and PAA volume fraction (Φ) in water ranged from about Φ* to 5Φ*, where Φ* is the overlap volume fraction. The measured diffusion coefficients (D) showed a scaling relation, D~(R/ξ)^-1 in the range of 2R/ξ between 0.05 and 0.85. Additionally, rheology measurements showed a zero shear rate viscosity and shear thinning, which are typical of high molecular weight polyelectrolytes. The local viscosity experienced by the particles is slightly (a factor of 3-4) more compared to solvent viscosity and significantly smaller compared to zero shear rate viscosity.