# Correlations for Relaxation-Times for Monodisperse Polystyrene Solutions

## Abstract

Relaxation tests after cessation of steady flow at constant shear rate ί, were performed in a broad range of ί (10^{-3} to 10^{2} sec^{-1}) with monodisperse polystyrene solutions in dibutyl-phthalate (Molecular weight, M, ranging from 140000 to 1300000 and concentration, c, from 5% to 40%). The apparent relaxation time of shear-stress curves in the range 2x10^{-2} to 10^{2} sec. Modification of our Weissenberg Rheogoniometer allow us to determine these shear stress without mechanical coupling. For all ί the bracking time is less than 16 m sec.

From these experimental curves one can deduce the transient viscosity n (t; ί) for t > τ_{m.} τ_{m.} depends on the bracking time but also on the time dependence of the velocity field near the rigid boundary.

Then, using a corotational Maxwell model, two relaxation times are inferred from η (t; ί). The largest one, Ϗ_{2} (ί, M, c) is characteristic of the behaviour near the rest state. The shortest one Ϗ_{1}(ί, M, c) is characteristic of the behavior of entanglements subjected to large shear rates.

The well-known correlations as η × M_{w} ^{3.4}; J° × c^{-2} are verified. As usual, the elastic compliance J_{c} = N_{1}(ί) /2 ί^{2} η^{2} (ί) is found to be dependent of ί. We show that the another measure of elasticity: [d η (t; ί)/dt ]_{t = 0} is independent of ί.

(Note that in the linear theory for ί → 0, [d η (t; ί) /dt]_{t=0} ^{=G}/ (o)).

We present then the variation of the two relaxation times with shear rate, molecular weight and concentration. For instance, τ_{2} is found to be independent of ί as expected for a parameter characteristic of the behavior near the rest state.