Particle Diffusivity and Free-Energy Profiles in Inhomogeneous Hydrogel Systems from Time-Resolved Penetration Profiles

A combined experimental/theoretical method to simultaneously determine diffusivity and free-energy profiles of particles that penetrate into inhomogeneous hydrogel systems is presented. As the only input, arbitrarily normalized concentration profiles from fluorescence intensity data of labeled tracer particles for different penetration times are needed. The method is applied to dextran molecules of varying size that penetrate into hydrogels of polyethylene-glycol (PEG) chains with different lengths that are covalently cross-linked by hyperbranched polyglycerol (hPG) hubs. Extracted dextran bulk diffusivities agree well with fluorescence correlation spectroscopy data obtained separately. Scaling laws for dextran diffusivities and free energies inside the hydrogel are identified as a function of the dextran mass. An elastic free-volume model that includes dextran as well as PEG linker flexibility describes the repulsive dextran-hydrogel interaction free energy, which is of steric origin, quantitatively and furthermore suggests that the hydrogel mesh-size distribution is rather broad and particle penetration is dominated by large hydrogel pores. Particle penetration into hydrogels is for steric particle-hydrogel interactions thus governed by an elasticity-enhanced size-filtering mechanism that involves the tail of the hydrogel pore-size distribution.