Normal stresses at the gelation transition

A simple Rouse-type model, generalized to incorporate the effects of chemical cross-links, is used to obtain a theoretical prediction for the critical behavior of the normal-stress coefficients Psi(1) and Psi(2) in polymeric liquids when approaching the gelation transition from the sol side. While the exact calculation shows Psi(2)=0, a typical result for these types of models, an additional scaling ansatz is used to demonstrate that Psi(1) diverges with a critical exponent l=k+z. Here, k denotes the critical exponent of the shear viscosity and z the exponent governing the divergence of the time scale in the Kohlrausch decay of the shear-stress relaxation function. For cross-links distributed according to mean-field percolation, this scaling relation yields l=3, in accordance with an exact expression for the first normal-stress coefficient based on a replica calculation. Alternatively, using three-dimensional percolation for the cross-link ensemble we find the value lapproximate to4.9. Results on time-dependent normal-stress response are also presented.