Viscoelasticity near the sol-gel transition

Abstract

Measurements of viscoelastic properties near the sol-gel transition demonstrate that viscoelastic phenomena are described by power laws. To describe these phenomena, we derive the distribution of relaxation times for branched polymers, both in the reaction bath and in the dilute solution. From this spectrum we can compute viscoelastic properties such as the shear relaxation modulus G(t) and the complex shear modulus G(ω). Near the gel point we find G(t)∼$t^{\mathrm{-}\Delta }$, with Δ a universal exponent, for times that are small compared to a divergent time ${\tau }_z$: For longer times the decay is a stretched exponential. The exponent Δ is found to be sensitive to dilution. Likewise, the storage and loss parts of the complex shear modulus are found to scale as ${\omega }^{\Delta }$. These results for the dynamics lead to a theory for the critical growth of the equilibrium shear modulus E above the gel point, and the divergence of the steady-state creep compliance $J_e^0$ above the gel point. Finally, we discuss the concentration dependence of the viscosity of a solution of branched polymers.