Necessary conditions for shear thickening in associating polymer networks

We study shear-thickening phenomena observed in thermoreversible gels of telechelic associating polymers on the basis of the transient network theory. We introduce nonlinear models for the elongational properties of the middle chain; the tension along middle chains contains a nonlinear term with an amplitude A that diverges if the chain is fully stretched. Models for the dissociation rate of end chains from network junctions are also introduced; the dissociation rate is coupled to the middle-chain tension by a coupling constant g. The balance between the nonlinearity strength and coupling intensity determines the necessary condition for thickening. A strong nonlinearity in the tension caused by a large A leads to thickening if the dissociation rate of the end chains is weakly coupled to the middle-chain tension. In contrast, if it is strongly coupled, the end chains easily dissociate upon a small nonlinear elongation of the middle chains, thus leading to thinning. We present theoretical phase diagrams showing the boundary of the thickening/thinning transition in the A–g plane, and we show the existence of a critical point for thickening in these diagrams.