Gel-sol transition of thermoresponsive poly(vinyl alcohol) solution: Validation of the universal critical scaling relations

While undergoing gelation transition, a material passes through a distinctive state called the critical gel state. In the neighborhood of this critical gel state, how viscosity, equilibrium modulus, and relaxation times evolve are correlated by scaling relations, and their universality has been validated for materials undergoing the sol-gel transition. In this work, we extend this approach for the gel-sol transition of a thermoresponsive polymeric system of aqueous poly(vinyl alcohol) (PVOH) gel that passes through the critical state upon increasing temperature. We observe that, in the neighborhood of the critical gel state, the equilibrium modulus and viscosity demonstrate a power law dependence on the relative distance from the critical state in terms of normalized temperature. Furthermore, the relaxation times in the gel and the sol state shows symmetric power law divergence near the critical state. The corresponding critical power law exponents and the dynamic critical exponents computed at the critical gel-sol transition state validate the scaling and hyperscaling relations originally proposed for the critical sol-gel transition very well. Remarkably, the dependence of complex viscosity on frequency at different temperatures shows a comprehensive master curve irrespective of the temperature ramp rate independently in the gel and the sol state. This observation demonstrates how the shape of relaxation time spectrum is independent of both the temperature as well as the ramp rate. Since sol-gel and the gel-sol transitions are opposite to each other, the applicability of the scaling relations validated in this work suggests broader symmetry associated with how the structure evolves around the critical state irrespective of the direction.