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

Abstract

The zero shear viscosity η0 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, η0 ∝ 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 −η0 -1 (dη0 -1/dc)-1 = (c g − c)/γ. Good agreement was obtained between the two methods. The scaling law, η0 ∝ 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 −dη0/dε (=γη0/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.

Oil absorbents based on styrene-butadiene rubber

“…The material at gel point, termed the critical gel (CG), is in an intermediate state between liquid and solid. In dynamic mechanical experiments9–24 the CG has been shown to have a power law behavior in frequency. The storage modulus, G ′, and the loss modulus, G ″, at gel point are where the gel strength, S , and relaxation exponent, n , are the only material parameters; Γ(1 − n ) is the gamma function, and ω is the frequency.…”

Dielectric Behavior of PVC Gels and Sols in Dioctyl Phthalate.

“…[1][2][3][4][5][6][7] The PVC chains formed the gel and sol at low and high temperatures (T), and the sol-gel transition was characterized with divergence of the zero-shear viscosity and growth of the equilibrium modulus, both being described by scaling relationships. [1][2][3]5,6) The critical PVC gel at the gelation point exhibited the powerlaw dependence 8,9) of its dynamic modulus on frequency 1) and surprisingly weak nonlinearities. 4) These features are well related to the gel network structure physically crosslinked at the PVC crystal domains, including the fractal network structure 10) in the critical gel.…”

Electrolyte effect on gelation behavior of oppositely charged nanocrystalline cellulose and polyelectrolyte

“…The results suggested the sol-gel transition of complex solution composed of QHEC, NCC and NaCl could be well described by Winter and Chambon theory. The approximate value of the zero-shear viscosity (Á 0 ) could be obtained from the complex viscosity Á * at ω → 0, therefore, the value of Á * at the lowest tested frequency was defined as Á 0 (Li, Uchida, & Aoki, 1997). Fig.…”