Rheological Images of Poly(vinyl chloride) Gels. 2. Divergence of Viscosity and the Scaling Law before the Sol−Gel Transition

The zero shear viscosity η 0 of poly(vinyl chloride) (PVC)/bis(2-ethylhexyl) phthalate (DOP) pregels has been measured as a function of polymer concentration c as well as molecular weight. It was observed that the zero shear viscosity diverged as the gelling system approached the gel point. The establishment of the scaling law, η 0 ∝ ε -γ, was examined where γ is the scaling exponent and ε the relative distance defined as ( c g − c )/ c g . Here c g is the critical concentration for the sol−gel transition. Two methods were used to determine the scaling exponent γ. One is the direct determination of γ using the c g obtained by means of the frequency independence of loss tengent. The other is called the Takigawa method that determines simultaneously γ and c g by mathematically transforming the scaling law into −η 0 -1 (dη 0 -1 /d c ) -1 = ( c g − c )/γ. Good agreement was obtained between the two methods. The scaling law, η 0 ∝ ε -γ, was found to hold well for the PVC pregels, and the scaling exponent γ was a constant (=1.5 ± 0.1) and was independent of the PVC molecular weight. The results suggest that the gelation rate defined as −dη 0 /dε (=γη 0 /ε) is related to PVC molecular weight, and at the same ε increases with decreasing molecular weight. The errors in determining the scaling exponent γ were also discussed.