(255h) Translational and Rotational Diffusion of Polymer Grafted Nanoparticles in Synovial Fluid and Hyaluronan Solutions
HA solutions with molecular weight 1,100 kDa at concentrations spanning from the dilute to the semi-dilute regime (with C/C* between 0.4 and 8) were used in the study. Cobalt ferrite particles coated with polyethylene glycol of 5kDa and with PEG5kDa_PDLLA6kDa used in the study had hydrodynamic diameters of 44 nm and 220 nm, respectively. Translational diffusion measurements of the nanoparticles suspended in the moderately flexible biopolymer solutions were performed using x-ray photon correlation spectroscopy measurements. The characteristic time obtained from exponential fits to the autocorrelation function was used to extract the diffusion coefficients. The rotational diffusivity of the nanoparticles in polymer solutions was characterized through dynamic magnetic susceptibility measurements by measuring the rotational response of the polymer coated particles to an oscillating magnetic field as a function of frequency.
Experiments using viscosity-matched glycerol solutions showed excellent agreement between measured rotational and translational viscosities and Stokes-Einstein (SE) predictions using macroscopic viscosity measurements. However, measurements in HA solutions indicated translational and rotational diffusivities of the nanoparticles were higher than SE predictions based on the low shear viscosity measured in a rheometer. The ratio of the translational and rotational diffusivities was found to be proportional to the hydrodynamic diameter of the nanoparticles and independent of the concentration of HA in solution. Nanoscale viscosities determined from the measured diffusivities and SE relation using the measured hydrodynamic diameters were similar between nanoparticles and techniques, and corresponded to the high shear viscosity and the concentration dependent equation of viscosity for all HA concentrations. In case of synovial fluid, the translational and rotational diffusivities of the 44 nm particles were found to be in the same order as predicted from the high shear rate viscosity of synovial fluid. The translational and rotational diffusion coefficient of 220 nm were found to be lower than that predicted from the SE relation using the high shear viscosity, but was still about 50 times higher than expected based on the low shear rate viscosity of the synovial fluid. We believe these observations can be extended to the diffusion of nanoparticles in solutions of higher molecular weight and moderately flexible polymers which can have important implications to understanding the transport of nanoparticles in biological fluids.