Normal stresses at the gelation transition

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A simple Rouse-type model, generalised to incorporate the effects of chemical crosslinks, is used to obtain a theoretical prediction for the critical behaviour of the normal-stress coefficients Ψ₁ and Ψ₂ at the gelation transition. While the exact calculation shows Ψ₂≡ 0, a typical result for these types of models, an additional scaling ansatz is used to demonstrate that Ψ₁ 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 crosslinks distributed according to mean-field percolation, this scaling relation yields ℓ =3, in a accordance with an exact expression for the first normal-stress coefficient based on a replica calculation. Alternatively, using three-dimensional percolation for the crosslink ensemble we find the value ℓ ≈ 4.9. Results on time-dependent normal-stress response are also presented.