Reversible Gelation of Entangled Ionomers

Dynamics of entangled associative polymers near the sol-to-gel transition is examined both theoretically and experimentally. Explicit expressions are provided for the elastic modulus and the relaxation time at varying degrees of gelation ε. Linear viscoelasticity data are presented for samples derived from polystyrene containing about 5 entanglements per chain, which are sulfonated to different levels and neutralized with sodium hydroxide. The characteristic features of the sol-to-gel transition are observed, which can be categorized into three regimes according to the value of ε: sol (−1 < ε ≤ 0), mixture of sol and gel (0 < ε ≤ 1), and gel (1 ≤ ε). The sol samples exhibit a steep relaxation with no well-defined power-law scaling, suggesting a strong dynamic dilution effect. The mixtures of sol and gel fail to obey the time–temperature superposition at high T where the ionic association is activated, and thus, the relaxation dynamics of the sol chains and the gel network vary with temperature differently. Detailed analysis of the thermorheological behavior suggests that the ionic association energy is about 70 kJ/mol, consistent with the value for the nonentangled sulfonate polystyrene. The gel samples exhibit relaxation behavior that lends support to the sticky-reptation theory.