Viscoelasticity of reversible gelation for ionomers

Linear viscoelasticity (LVE) of low-ion-content and low-molecular-weight (nonentangled) randomly sulfonated polystyrene shows a sol-gel transition when the average number of ionic groups per chain approaches unity. This transition can be well understood by regarding the number of ionizable sites over a chain as the relevant functionality for cross-linking. For ionomers below but very close to the gel point, the LVE shows power law relaxation similar to gelation of chemical cross-linking. Nevertheless, ionomers near and beyond the gel point also show terminal relaxation not seen in chemically cross-linking systems, which is controlled by ionic dissociation. Careful analysis of the power law region of the frequency dependence of complex modulus close to the gel point shows a change in exponent from ∼1 at high frequency to ∼0.67 at low frequency, which strongly suggests a transition from mean-field to critical percolation known as the Ginzburg point. A mean-field percolation theory by Rubinstein and Semenov for gelation with effective breakup has been modified to include critical percolation close to the gel point and predicts well the observed LVE of lightly sulfonated polystyrene oligomers.