Elongational flow opto-rheometry for polymer melts1. Construction of an elongational flow opto-rheometer and some preliminary results

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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\dot \varepsilon _0$$ \end{document} 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, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\eta _E (t) \equiv \sigma (t)/\dot \varepsilon _0$$ \end{document}, is three times the steady shear viscosity, 3ηo(t), at low shear rate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\dot \gamma$$ \end{document}, but the ηE(t) tended to deviate upward after a certain Hencky strain \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\varepsilon (t) = \dot \varepsilon _0 t$$ \end{document} was attained. The birefringence Δn(t) was a function of both Hencky strain \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\varepsilon (t) = \dot \varepsilon _0 t$$ \end{document} and strain rate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\dot \varepsilon _0$$ \end{document} 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.