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Dynamic mechanical measurements allow direct determination of the instant at which a network polymer gels. In such a n experiment, the evolution of G ' ( t , w o ) and G"( t,wo) is measured in small amplitude oscillatory shear as a function of cross-linking time t. The frequency wo is kept constant throughout. At the beginning of the experiment, G " is orders of magnitude larger than G', and at completion of reaction, this order is reversed. It recently has been suggested by Tung and Dynes that the gel point (GP) might occur at the time at which G' and G " cross each other. However, there is much dispute whether GP occurs exactly at the crossover or just somewhere in its vicinity. This study resolves the dispute by modeling the rheological behavior at GP: There is only one class of network polymers for which GP coincides with the crossover. This class of polymers exhibits, when reaching GP, power law relaxation G ( t )t-" with a specific exponent value n = Y2. Examples are stoichiometrically balanced network polymers and networks with excess cross-linker, however, only at temperatures much above the glass transition. Otherwise, the power law behavior would be masked by vitrification. Power law relaxation seems to be property of polymers at GP in general. However, some polymers have a different exponent value, n # 1/2, in which case the crossover occurs before GP (for n < 1/21 or after GP (for n > V2): i.e., the crossover cannot be used for detecting GP. While there are no networks known to us with n < %, recent experiments showed that network polymers that are lean on cross-linker exhibit power law relaxation with n > %. A new method is suggested for measuring GP of these imbalanced networks.

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A powerful but still easy to use technique is proposed for the processing and analysis of dynamic mechanical data. The experimentally determined dynamic moduli, G'(co) and G"(co), are converted into a discrete relaxation modulus G (t) and a discrete creep compliance J(t). The discrete spectra are valid in a time window which corresponds to the frequency window of the input data.A nonlinear regression simultaneously adjust the parameters gi, 2i, i= 1,2,•.. N, of the discrete spectrum to obtain a best fit of G', G", and it was found to be essential that both gi and 2i are freely adjustable. The number of relaxa-

Early stages of crystallization of polymers may be viewed as physical gelation. This is shown with four commercial isotactic polypropylenes, which have been studied by dynamic mechanical experiments at low degrees of undercooling, ∆T ) 10-26 K, below their nominal melting temperature. The physical gel point is manifested by slow power law dynamics, which expresses itself in a shear relaxation modulus G(t) ) St -n at long times, λ0 < t < λpg, where S is the gel stiffness, n is the relaxation exponent, λ0 is the crossover to short time dynamics (entanglements, glass modes), and λpg is the longest relaxation time, which can be considered to be infinite for our experiments due to the long lifetime of the physical bonds. The time to reach the gel point (gel time tc) decreases exponentially with ∆T, and the critical gel becomes stiffer (smaller n, larger S) with increasing ∆T. The absolute critical crystallinity at the gel point, Xc, was found to be only about 2% or less. This value was determined from published DSC data which, however, needed to be extrapolated to tc, as measured by mechanical spectroscopy. This very low crystallinity suggests that only a few junctions are necessary to form a sample spanning network. The network in this case is "loosely" connected, and the critical gel is soft.

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.