Rheological Images of Poly(vinyl chloride) Gels. 3. Elasticity Evolution and the Scaling Law beyond the Sol−Gel Transition

The elasticity evolution of poly(vinyl chloride) (PVC)/bis(2-ethylhexyl) phthalate (DOP) gels beyond the gel point c g has been studied as a function of polymer concentration c and molecular weight. The gel elasticity G e, which was defined as the frequency-independent dynamic storage modulus G ‘ at low frequencies, developed as a function of polymer concentration. The scaling law for the elasticity evolution, G e = k ε z, was found to hold well for all the PVC gels with different molecular weights. Here, ε [=( c − c g )/ c g ] is defined as the relative distance, z the scaling exponent, and k the front constant. The z obtained was constant ( z = 2.6 ± 0.1), independent of the PVC molecular weight, being excellently consistent with the theoretical prediction ( z = 8 / 3 ) using the percolation model. Furthermore, the analysis of the front constant k provided information about the dependence of the gel elasticity on molecular weight. As a result, the gel elasticity could be described as G e = 10 14 M w -2.4 ε 8/3, allowing one to discuss separately the molecular weight contribution and the relative distance contribution. The ability of this relation to predict the elasticity evolution has also been examined.