Elongational flow opto-rheometry for polymer melts

Abstract

Polymer melt elongation is one of the most important procedures in polymer processing. To understand its molecular mechanisms, we constructed an elongational flow opto-rheometer (EFOR) in which a high precision birefringence apparatus of reflection-double path type was installed into a Meissner's new elongational rheometer of a gas cushion type (commercialized as RME from Rheometric Scientific) just by mounting a small reflecting mirror at the center of the RME's sample supporting table. The EFOR enabled us to achieve simultaneous measurements of tensile stress σ(t) and birefringence Δn(t) as a function of time t under a given constant strain rate $$\dot \varepsilon _0$$ within the range of 0.001 to 1.0s−1. σ(t) can be monitored upto the maximum Hencky strain ɛ(t) of 7 as attained, in principle, with RME, while the measurable range of the phase difference in the birefringence was 0 to 250 π (0 to 79 100 nm for He-Ne laser light) within the accuracy of ±0.1 π (±31.6 nm) up to ɛ(t) ∼ 4. The performance was tested on an anionically polymerized polystyrene (PS) and a low density polyethylene (LDPE). For both polymers σ(t) first followed the linear viscoelasticity rule in that the elongational viscosity, $$\eta _E (t) \equiv \sigma (t)/\dot \varepsilon _0$$ , is three times the steady shear viscosity, 3η o(t), at low shear rate $$\dot \gamma$$ , but the η E (t) tended to deviate upward after a certain Hencky strain $$\varepsilon (t) = \dot \varepsilon _0 t$$ was attained. The birefringence Δn(t) was a function of both Hencky strain $$\varepsilon (t) = \dot \varepsilon _0 t$$ and strain rate $$\dot \varepsilon _0$$ in such a way that the stress-optical law holds with the stress-optical coefficient C(t) = Δn(t)/δ(t) being equal to the ones reported from shear flow experiments. Interestingly, however, for PS elongated at low strain rates the C(t) vs σ(t) relation exhibited a strong nonlinearity as soon as σ(t) reached steady state. This implies that the tensile stress reaches the steady state but the birefringence continues to increase in the low strain-rate elongation. For the PS melt elongated at high strain rates, on the other hand, C(t) was nearly a constant in the entire range observed. For LDPE with long-chain branchings, σ(t) exhibited tendency of strain-induced hardening after certain critical strain, but C(t) was nearly a constant in the entire range of σ(t) observed.