Correlations for Relaxation-Times for Monodisperse Polystyrene Solutions
Relaxation tests after cessation of steady flow at constant shear rate ί, were performed in a broad range of ί (10-3 to 102 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 102 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 > τm. τm. 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, Ϗ2 (ί, M, c) is characteristic of the behaviour near the rest state. The shortest one Ϗ1(ί, M, c) is characteristic of the behavior of entanglements subjected to large shear rates.
The well-known correlations as η × Mw 3.4; J° × c-2 are verified. As usual, the elastic compliance Jc = N1(ί) /2 ί2 η2 (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, τ2 is found to be independent of ί as expected for a parameter characteristic of the behavior near the rest state.