Abstract
Shear step strain experiments with various strain amplitudes have been performed on poly(vinylidene fluoride) (PVDF) and poly(methyl methacrylate) (PMMA) melts using both stress-controlled and strain-controlled rheometers. Firstly, the onset of the rheological nonlinearity, i.e., nonlinear stress damping behavior, occurring after a large step strain is found to be a phenomenological consequence of an abrupt stress decline within the transient period of strain actuation. Such a feature, analogous to the stress overshoot in a fast startup shear with sufficiently high rates, is interpreted based on theoretical frameworks concerning chain disentanglement/re-entanglement arising from chain retraction. Furthermore, this work infers that full technical considerations in step strain experiments are indispensable for acquisition of accurate stress relaxation data, as some common but easily overlooked technical problems are influential, probably introducing errors. For instance, a too long finite rise time and a stress overload enable to hinder the nonlinearity onset in the transient period, resulting in inaccurate experimental data. In this sense, the stress-controlled rheometer is advantageous relative to the strain-controlled one, although the inertia in the stress-controlled mode incurs a strain overshoot effect. Nevertheless, the amplitude-dependent strain overshoot offers a very subtle effect on the stress damping behavior. Moreover, transducer compliance problems need to be taken into account, especially for high stiffness polymers. Overall, the effects of such technical factors are dictated by their ability to influence the chain stretching/retraction and the disentanglement. A well-considered experimental methodology is necessary to achieve confidence windows in step strain experiments for analysis accuracy.
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Alcoutlabi M, Baek SG, Magda JJ, Shi X, Hutcheson SA, McKenna GB (2009) A comparison of three different methods for measuring both normal stress differences of viscoelastic liquids in torsional rheometers. Rheol Acta 48:191–200
Archer LA, Sanchez-Reyes J, Juliani (2002) Relaxation dynamics of polymer liquids in nonlinear step shear. Macromolecules 35:10216–10224
Boukany PE, Wang SQ (2009) Exploring origins of interfacial yielding and wall slip in entangled linear melts during shear or after shear cessation. Macromolecules 42:2222–2228
Boukany PE, Wang SQ, Wang X (2009) Step shear of entangled linear polymer melts: new experimental evidence for elastic yielding. Macromolecules 42(16):6261–6269
de Gennes PG (1971) Reptation of a polymer chain in the presence of fixed obstacles. J Chem Phys 55(2):572
Dealy JM, Larson RG (2006) Structure and rheology of molten polymers: from structure to flow behavior and back again. Hanser, Munich
Doi M, Edwards SF (1986) The theory of polymer dynamics. Clarendon, Oxford, pp 189–234
Dutcher CS, Venerus DC (2008) Compliance effects on the torsional flow of a viscoelastic fluid. J Non-Newtonian Fluid Mech 150:154–161
Ferri D, Greco F (2006) Nonlinear stress relaxation of molten polymers: experimental verification of a new theoretical approach. Macromolecules 39(17):5931–5938
Filipe S, Cidade MT, Wilhelm M, Maia JM (2006) Evolution of the morphological and rheological properties along the extruder length for compatibilized blends of a commercial liquid-crystalline polymer and polypropylene. J Appl Polym Sci 99:347–359
Flory A, McKenna GB (2004) Finite step rate corrections in stress relaxation experiments, a comparison of two methods. Mech Time-Dep Mater 8:17–37
Gevgilili H, Kalyon DM (2001) Step strain flow: wall slip effects and other error sources. J Rheol 45(2):467–475
Graham RS, Likhtman AE, McLeish TCB, Milner ST (2003) Microscopic theory of linear, entangled polymer chains under rapid deformation including chain stretch and convective constraint release. J Rheol 47:1171–1200
Ianniruberto G, Marrucci G (2014) Convective constraint release (CCR) revisited. J Rheol 58:89
Islam MT, Sanchez-Reyes J, Archer LA (2001) Nonlinear rheology of highly entangled polymer liquids: step shear damping function. J Rheol 45(1):61–82
Juliani, Archer LA (2001) Linear and nonlinear rheology of bidisperse polymer blends. J Rheol 45:691
Kolkka RW, Malkus DS, Rose TR (1991) Finite rise time step strain modeling of nearly monodisperse polymer melts and solutions. Rheol Acta 30:430–446
Läuger J, Stettin H (2010) Differences between stress and strain control in the non-linear behavior of complex fluids. Rheol Acta 49:909–930
Laun HM (1978) Description of the non-linear shear behavior of a low density polyethylene melt by means of an experimentally determined strain dependent memory function. Rheol Acta 17(1):1–15
Lee PC, Park HE, Morse DC, Macosko CW (2009) Polymer-polymer interfacial slip in multilayered films. J Rheol 53:893–915
Marrucci G (1996) Dynamics of entanglements: a nonlinear model consistent with the Cox-Merz rule. J Non-Newtonian Fluid Mech 62:279–289
Ravindranath S, Wang SQ (2007) What are the origins of stress relaxation behaviors in step shear of entangled polymer solutions? Macromolecules 40(22):8031–8039
Rolon-Garrido VH, Wagner MH (2009) The damping function in rheology. Rheol Acta 48:245–284
Roy D, Roland CM (2013) Reentanglement kinetics in polyisobutylene. Macromolecules 46(23):9403–9408
Schweizer T, Bardow A (2006) The role of instrument compliance in normal force measurements of polymer melts. Rheol Acta 45:393–402
Silva J, Machado AV, Maia JM (2007) Rheological behavior of compatibilized and non-compatibilized PA6/EPM blends. Rheol Acta 46(8):1091–1097
Soskey PR, Winter HH (1984) Large step shear strain experiments with parallel-disk rotational rheometers. J Rheol 28(5):625–645
Stadler FJ, Auhl D, Münstedt H (2008) Influence of the molecular structure of polyolefins on the damping function in shear. Macromolecules 41(10):3720–3726
Sussman DM, Schweizer KS (2012) Microscopic theory of quiescent and deformed topologically entangled rod solutions: general formulation and relaxation after nonlinear step strain. Macromolecules 45:3270–3284
Venerus DC (2005) A critical evaluation of step strain flows of entangled linear polymer liquids. J Rheol 49:277–295
Venerus DC, Vrentas CM, Vrentas JS (1990) Step strain deformations for viscoelastic fluids: experiment. J Rheol 34:657
Vrentas CM, Graessley WW (1981) Relaxation of shear and normal stress components in step strain experiments. J Non-Newtonian Fluid Mech 9:339–355
Vrentas CM, Graessley WW (1982) Study of shear stress relaxation in well-characterized polymer liquids. J Rheol 26:359
Wagner MH, Ehrecke P (1998) Dynamics of polymer melts in reversing shear flows. J Non-Newtonian Fluid Mech 76:183–197
Wagner MH, Meissner J (1980) Network disentanglement and time-dependent flow behaviour of polymer melts. Dienst Makromol Chem 181:1533–1550
Wang SQ, Ravindranath S, Boukany P, Olechnowicz M, Quirk RP, Halasa A, Mays J (2006) Nonquiescent relaxation in entangled polymer liquids after step shear. Phys Rev Lett 97:187801
Wang SQ, Ravindranath S, Wang YY, Boukany PY (2007) New theoretical considerations in polymer rheology: elastic breakdown of chain entanglement network. J Chem Phys 127:064903
Wang SQ, Wang YY, Cheng SW, Li X, Zhu XY, Sun H (2013) New experiments for improved theoretical description of nonlinear rheology of entangled polymers. Macromolecules 46:3147–3159
Yaoita T, Isaki T, Masubuchi Y, Watanabe H, Ianniruberto G, Marrucci G (2012) Primitive chain network simulation of elongational flows of entangled linear chains: stretch/orientation-induced reduction of monomeric friction. Macromolecules 45:2773–2782
Yoshimura A, Prud’homme RK (1988) Wall slip corrections for couette and parallel disk viscometers. J Rheol 32:53
Zhang H, Lamnawar K, Maazouz A (2012) Rheological modeling of the diffusion process and the interphase of symmetrical bilayers based on PVDF and PMMA with varying molecular weights. Rheol Acta 51:691–711
Zhang H, Lamnawar K, Maazouz A (2013) Rheological modeling of the mutual diffusion and the interphase development for an asymmetrical bilayer based on PMMA and PVDF model compatible polymers. Macromolecules 46:276–299
Zhang H, Lamnawar K, Maazouz A, Maia JM (2014) A nonlinear shear and elongation rheological study of interfacial failure in compatible bilayer systems. Submitted to J. Rheol. (under review)
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The authors express their appreciation to the reviewers for their constructive and meticulous assessment of this work. They thank ARKEMA for providing the PMMA and PVDF samples.
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Zhang, H., Lamnawar, K., Maazouz, A. et al. Experimental considerations on the step shear strain in polymer melts: sources of error and windows of confidence. Rheol Acta 54, 121–138 (2015). https://doi.org/10.1007/s00397-014-0814-y
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DOI: https://doi.org/10.1007/s00397-014-0814-y