Cross-Linking in Shear-Thickening Ionomers

Ionic groups attached at wide intervals along nonpolar polymer chains produce strong associating interactions in solution. In certain cases, such solutions exhibit shear thickening; the viscosity increases with the flow rate. We sketch a mechanism for shear thickening in which the flow produces increased association between chains at the expense of associations within a chain. We calculate in a mean-field approximation how chain elongation produced by flow alters the balance between intra- and interchain associations. The effect is sufficiently large to account qualitatively for the observed dependence of viscosity on shear rate and on concentration. Surprisingly, the effect is maximized when the number of associating groups per chain is kept small.