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The scaling relations established for the relaxation modulus of concentrated solutions of polystyrene (PS) in oligomeric styrene [Wagner, Rheol. Acta 53, 765-777 (2014); Wagner, J Non-Newtonian Fluid Mech. (2015)] are applied to the solutions of PS in diethyl phthalate (DEP) investigated by Bhattacharjee et al. [Macromolecules 35, 10131-10148 (2002)] and Acharya et al. [AIP Conf. Proc. 1027, 391-393 (2008)]. The scaling relies on the difference μTg between the glass-transition temperatures of the melt and the glass-transition temperatures of the solutions. μTg can be inferred from the reported zero-shear viscosities, and the Baumgaertel, Schausberger, and Winter (BSW) spectra of the solutions are obtained from the BSW spectrum of the reference melt with good accuracy. Predictions of the extended interchain pressure (EIP) model, which is based on the assumption that the relative interchain pressure in the melt and in the solutions is identical, are compared to the steady-state elongational viscosity data of PS/DEP solutions. The Rouse stretch relaxation times as calculated from the respective scaling relation are a factor of 2-3 higher than the Rouse time defined by the experimentally observed upturn of the elongational viscosity at WiR = ***τR → 1. This may be caused by DEP being a good solvent at room temperature and/or polymer degradation. Using the experimentally determined Rouse times, quantitative agreement is obtained between experimental data and model. Except for a possible influence of solvent quality, linear and nonlinear viscoelasticity of entangled PS solutions can thus be obtained from the linearviscoelastic characteristics of a reference polymer melt and the shift of the glass-transition temperature between melt and solution. [ABSTRACT FROM AUTHOR]

Characterizing elongational behavior of polymer melts in constant elongation rate or constant tensile stress experiments is hampered by the onset of 'necking' instabilities according to the Considère criterion: For an elastic filament, homogeneous uniaxial extension is not guaranteed for strains larger than the strain at which a maximum occurs in the force versus extension curve. Although simulations and experiments seem to indicate that in viscoelastic fluids viscosity effects delay the onset of necking to higher strains, integral measurements of elongational viscosities in Meissner- or Münstedt-type elongational rheometers are often affected by inhomogeneous deformations. A simple means of avoiding the consequences of the Considère criterion consists in operating at constant tensile force, but little attention has been paid so far to constant force elongational rheometry since the pioneering work of Raible et al. [J. Non-Newtonian Fluid Mech. 11, 239 (1982)]. Constant force elongation is also of great industrial relevance, since it is the correct analog of steady fiber spinning, as, e.g., exemplified by the so-called Rheotens test. We present experimental data for two long-chain branched polyethylene melts obtained in constant elongation rate and constant tensile force modes by use of a Sentmanat extensional rheometer in combination with an Anton Paar MCR301 rotational rheometer. The accessible experimental window and experimental limitations are discussed. Constant force elongation can be subdivided into three distinct deformation regimes: At small deformations (regime 1), constant force elongation is equivalent to creep at constant tensile stress. This is followed by regime 2, which is characterized by a steep increase in tensile stress at roughly constant strain rate, while regime 3 corresponds to elongation of a viscous power-law fluid. All three regimes can be modelled quantitatively by a single integral constitutive equation, and a constitutive analysis reveals substantial underestimation of the effective strain-hardening effect observed in constant strain-rate elongation in comparison to constant tensile force extension, which may be indicative of the effect of necking under constant elongation-rate conditions. [ABSTRACT FROM AUTHOR]

Studying the mechanical response of nearly monodisperse linear and comb polystyrene (PS) melts to medium amplitude oscillatory shear (MAOS), Hyun and Wilhelm [Macromolecules 42, 411 (2009)] identified two important scaling relations: (1) The relative intensity I3/1 of the third harmonic compared to the first harmonic scales with the strain amplitude according to γ02. Consequently, a new nonlinear coefficient Q≡I3/1/γ02 as well as the so-called intrinsic nonlinearity Q0≡limγ0→0 Q was introduced. (2) In the terminal relaxation regime, the intrinsic nonlinearity Q0(ω) scales with ω2 and was found to be a very sensitive measure regarding molecular topology by identifying and separating relaxation processes in model branched polymers. A constitutive analysis based on a general single integral constitutive equation, which includes the Doi-Edwards model without (DE) and with (DE IA) independent alignment assumption as well as the molecular stress function (MSF) model, confirms both scaling relations. We show that the nonlinear viscoelastic moduli can be expressed as sums of their linear-viscolelastic counterparts at frequencies of ω, 2ω, and 3ω. The absolute value of Q0(ω) depends on the difference (α-β) between the third order orientational effect (parameter α) according to the DE or DE IA model and the second order isotropic stretching effect (parameter β) according to the MSF model. When comparing MAOS data to constitutive models, the apparent values of Q0(ω) measured in parallel-plate geometry have to be rescaled in order to take the non-uniform shear deformation into account. Both the DE and DE IA models fail to describe the experimental data. The data of four linear PS melts are quantitatively described by the MSF model with nonlinear parameters α=5/21 (corresponding to the DE IA model) and β=0.12 in the terminal relaxation regime. For the comb polymers, with the same orientational parameter of α=5/21, stretch parameters of β=0.14 for a polymer with unentangled branches and of β=0.18 for two polymers with entangled branches are found. However, the model predicts a plateau at the level of the maximum of the experimental data, while the experimental values of Q0 decrease with increasing frequency. For the comb polymers with entangled branches, a minimum in Q0 is observed, and a second increase of Q0 at higher frequencies, which correspond to the terminal relaxation times of the branches. Surprisingly, these features can be modeled quantitatively if only the terminal relaxation modes of the backbone and, if present, the branches are assumed to deforming non-affinely and responding to the nonlinearity. The shorter modes seem to be deforming affinely and are excited only in the regime of finite linear viscoelasticity. We are presently not aware of any molecular mechanism that could explain this behavior. [ABSTRACT FROM AUTHOR]