RELAXATION PATTERNS OF NEARLY CRITICAL GELS

We measure the complex rheological behavior of nearly critical gels an d analyze the data by searching for characteristic patterns and abstra cting those patterns into a self-consistent model. The sample is a lin ear, flexible, nearly monodisperse polybutadiene which gets cross-link ed on its vinyl side groups. The dynamic mechanical storage and loss m oduli of cross-linking polymers change smoothly during the liquid-soli d transition, while equilibrium rheological properties (e.g., zero-she ar viscosity and equilibrium compliance) diverge. During gelation, the relaxation occurs in a distinct pattern which can be described in a q uantitative way with a minimum number of parameters. The pattern can b e understood as a combination of the BSW spectrum (representing the pr ecursor relaxation behavior) and the selfsimilar Chambon-Winter gel sp ectrum (modeling the terminal relaxation due to growing clusters). The spectrum is cut off at the material's longest relaxation time, lambda (max). Our model parameters, lambda(max) and G(e) (equilibrium modulus ), exhibit characteristic scaling behavior with respect to the distanc e from the gel point, \p - p(c)\. The relaxation exponent, n, in the t erminal zone is a function of the extent of reaction. Hence, dynamic s caling (requires constant n values) is not valid for our system. The p roposed model passes the self-consistency test by predicting the mecha nical behavior (at different frequencies) as a function of the extent of reaction and other rheological observations during the sol-gel tran sition.