The molecular weight dependence of critical gel properties was determined for poly(c-caprolactone) diol end-linked with a three-functional isocyanate. The critical gels exhibit the typical scaling behavior with a power law relaxation spectrum H(X) = Go/r(n)(t/Ap, X > b, where GO = G, was found to be the modulus of the fully cross-linked polymer and XO = vo/G, was found to depend on the viscosity of the difunctional prepolymer, 70. The relaxation exponent, n, decreases with increasing cross-linker concentration (increasing stoichiometric ratio, r = [NCOI/[OHl) and increasing molecular weight of the prepolymer. This suggests that the fractal dimension of the critical gel increases with increasing molecular weight and stoichiometric ratio.
Novel polymer properties can be achieved by blending high molecular weight linear chains into a cross-linking system of short linear chains. This study is concerned with the rheological properties that are dominated at first by the highly entangled linear chains. However, with increasing extent of cross-linking, the short chains connect into a network structure and begin to dominate the rheology. The material here consists of cross-linking poly(ε-caprolactone) diol (PCL) and up to 40% of linear poly(styrene-co-acrylonitrile) (SAN) of high molecular weight. The blend was molecularly mixed before cross-linking. Three competing processes determine the structure of the system, (1) chemical cross-linking of the low molecular weight species into a sample spanning network of interpenetrating chains, (2) fluctuations in composition due to phase separation at increasing extents of reaction, and (3) crystallization of the PCL, which we tried to suppress as much as possible. At the gel point, systems with low SAN content show the typical scaling behavior of the critical gel with a self-similar relaxation spectrum, H(λ) = G o/Γ(n) (λ/λo)- n , λ > λo, at low probing frequencies, ω < 1/λo. However, for the systems with high concentrations of the inert component, the self-similar region did not develop, possibly due to the phase separation induced by the cross-linking. The relaxation exponent, n, decreased with increasing concentration of the highly entangled linear component. The results suggest that dynamic mechanical methods are applicable for determination of the gel point for homogeneous semi-IPN systems.
A systematic procedure was developed for determining the temperature dependence of critical gel properties. The polymer system was a poly(ccapro1actone) diol (PCL) end-linked with a three-functional isocyanate. Samples varied in prepolymer molecular weight and stoichiometric ratio. Time-temperature superposition was found to apply to the self-similar relaxation modulus G(t) = S P . A prerequisite of timetemperature superposition is that the relaxation exponent n is independent of temperature. As a consequence, criticalgels have theunique property that their loss tangent is independent of temperature. This was confirmed experimentally. The gel stiffness S(T) = S(To)a?/bTshifta with an Arrhenius type temperature dependence. The temperature shift factors for the PCL critical gels seem to be identical with those for the viscosity of the difunctional prepolymer ( t o ) and the modulus of the fully cross-linked polymer (G& This suggests that an experimental relationship of S = G,(T)[qo(T)/G,(T)ln is valid for our polymers at the experimental temperatures between 90 and 130 "C. IntroductionTemperature affects chemical gelation experiments in two major ways. High temperature accelerates the crosslinking reaction and thus speeds up the gelation process. It also accelerates relaxation processes so that the characteristic time scales of rheology become reduced. For analyzing the temperature dependence of gelation, we will use the rheology at the gel point as reference.Cross-linking polymers undergo a transition from liquid (sol) to solid (gel) when the extent of cross-linking @) reaches a critical value at the gel point (GP). The leading molecular cluster and the corresponding longest relaxation time diverge to infinity for the ideal material exactly at
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