The Superposition Principle Observed over the Dynamic Viscosity and the Longest Relaxation Time During Physical Gelation of Polyacrylonitrile Solution Induced by Freezing and Thawing Cycles

The viscoelastic evolution through the sol-gel transition, during the repeated cycles of freezing and thawing (FT cycles), was measured for the polymer solution of poly(acrylonitrile-co-vinyl acetate) and dimethyl sulfoxide (PAN solution) as a function of the cycle number (L) which is considered a parameter to control the extent of gelation. The obtained data were manipulated to plot the dynamic viscosity (|η*|) as a function of the frequency (ω) and L, where pre-gel, critical, and post-gel states appeared differently according to both the L value and the solution concentration. The power law relation was observed between |η*| and ω at the critical gel state, thus implying a statistically self-similar structure with respect to the network induced by the FT cycles. Then, the viscoelastic variables of η0, Ge, τmax-S and τmax-G were determined using the protocols applied with the extrapolation lines provided in the double-logarithmic plot, from which the plot of normalized |η*| was constructed. Concerning the unique superposition of |η*|, several advantages were highlighted in developing a comprehensive linear viscoelastic model to describe the sol-gel transition from a particular extent of gelation to arbitrary extents of gelation.