Shear Modulus Dependence of the Diffusion Coefficient of a Polymer Network

Dynamics of a polymer gel network is described by the theory proposed by Tanaka, Hocker, and Benedek (THB) that gives the diffusion coefficient of a polymer network (D=K+43Gf). Here, K is the osmotic bulk modulus, G is the shear modulus, and f is the friction coefficient between the polymer network and the solvent. Although several experimental studies investigated the dynamics of a polymer gel network, the THB theory has yet to be quantitatively validated. In this study, we quantitatively validate the THB theory by comparing D and G of Tetra-poly(ethylene glycol) gels measured by dynamic light scattering and dynamic viscoelastic measurement. The THB theory well described the linear increase in D with increasing G and gave K and f from the slope and the intercept. The gel network structural parameter dependences of the given K and f were well explained by the scaling laws. These results suggest that the THB theory is almost valid.