Relaxation Patterns of Nearly Critical Gels

Abstract

We measure the complex rheological behavior of nearly critical gels and analyze the data by searching for characteristic patterns and abstracting those patterns into a self-consistent model. The sample is a linear, flexible, nearly monodisperse polybutadiene which gets cross-linked on its vinyl side groups. The dynamic mechanical storage and loss moduli of cross-linking polymers change smoothly during the liquid-solid transition, while equilibrium rheological properties (e.g., zero-shear viscosity and equilibrium compliance) diverge. During gelation, the relaxation occurs in a distinct pattern which can be described in a quantitative way with a minimum number of parameters. The pattern can be understood as a combination of the BSW spectrum (representing the precursor relaxation behavior) and the selfsimilar Chambon-Winter gel spectrum (modeling the terminal relaxation due to growing clusters). The spectrum is cut off at the material's longest relaxation time, λmax. Our model parameters, λmax and Ge (equilibrium modulus), exhibit characteristic scaling behavior with respect to the distance from the gel point, |p -pc|. The relaxation exponent, n, in the terminal zone is a function of the extent of reaction. Hence, dynamic scaling (requires constant n values) is not valid for our system. The proposed model passes the self-consistency test by predicting the mechanical behavior (at different frequencies) as a function of the extent of reaction and other rheological observations during the sol-gel transition.

Tube theory of entangled polymer dynamics

“…This prediction is in accord with experimental results on crosslinked systems with Z x < 1 [303]. Crosslinking linear chains that are already entangled, however, does indeed lead to a much more striking enhancement of viscosity, consistent with the exponentially slow retraction mode of dangling arms [304,305]. Recent experiments on reacting monodisperse precursor polymers have shown that careful crosslinking of linear segments using a urethane condensation technique does indeed create a much more slowly relaxing melt when Z x > 1, and that, for the systems so far explored up to Z xˆ1 3:6, the dynamic exponent u ' 1=Z x with a prefactor close to unity [306,307].…”

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“…This argument was confirmed experimentally by Mours and Winters in. 16,17 Another study by Emri 18 also agrees with the observation by Mours and Winters, arguing that high molecular weight (9) T g − T g0…”

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“…The stiffness of the critical gels increases with ∆T and the relaxation exponent adopts values of about 0.5 (which is very similar to the relaxation exponent of chemical critical gels from high molecular weight precursors 37 ).…”