Linear viscoelasticity of sulfonated styrene oligomers near the Sol-Gel transition

Linear viscoelastic complex modulus (reported by Weiss and Zhao, 2009) of three ionomers, obtained through random sulfonation of oligomeric styrene at low ionic contents, p = 2.5, 4.8, and 6.5mol%, were analyzed using mean-field gelation theory with the fraction of repeat units that are sulfonated the effective extent of reaction p. Oligomeric styrene with low M = 4000 g/mol, having N = 38 repeat units, ensures absence of entanglement effects. The dynamics change in a complicated way with ion content p because the gel point pc = 1/(N-1) = 2.7 mol%. For ionomers having p = 2.5 mol%, the system is below but quite close to the gel point. The terminal relaxation is governed by the effective breakup of large clusters into subclusters of comparable sizes, as anticipated by Rubinstein and Semenov. The samples with p = 4.8 mol% and 6.5 mol%, are beyond the gel point and exhibit properties of reversible gels.