On the relationship between plateau modulus and shear relaxation time in transient networks

The linear rheology of unentangled Maxwellian transient networks formed from reversibly associating telechelic polymers can be characterized by a plateau modulus and a shear relaxation time. The concentration dependences of both these properties have been modeled using a variety of theories. An expression is introduced here that allows the concentration dependence of shear relaxation time to be determined (to within a constant, the microscopic chain lifetime) directly from the concentration dependence of the plateau modulus, subject to some approximations. This prediction is tested against experimental results for hydrophobic ethoxylated urethane (HEUR) and against results of simple-model simulations. The nature of the approximations needed to derive this relationship and the scope of its applicability are discussed. A simple equation relating the microscopic lifetime of associating chains in a transient network to the shear stress relaxation time, in terms of the concentration dependence of the plateau modulus, is proposed and tested against published experimental data on associating polymers near the gelation transition and against simulated networks well above the gelation transition.