Radek Pivokonsky

The role of the Gordon–Schowalter derivative term in the constitutive models—improved flexibility of the modified XPP model

Constitutive models that complete the set of equations describing the flow of polymer melts should respect objective thermodynamics and stability conditions ensuring their validity in the whole range of possible deformation flow. However, in practice, a very good description of flow situations can be achieved with the models not complying with the physical assumptions in all respects. Analogously to the term characterizing yield stress in empirical viscoplastic models, the term represented by the Gordon–Schowalter (GS) derivative in the differential constitutive models contributes to better fitting the experimental data, especially shear thinning. Efficiency of the recently presented modified eXtended Pom-Pom model (just one non-linear parameter per mode) implementing the GS derivative term (one additional non-affine motion parameter per mode) is improved (documented on LDPE, HDPE, and polyvinyl butyral (PVB) materials), and a comparison with the exponential Phan-Tien–Tanner (PTT) and PTT-XPP models (a priori containing the GS derivative term) are presented.

Two Ways to Examine Differential Constitutive Equations: Initiated on Steady or Initiated on Unsteady (LAOS) Shear Characteristics

The exponential Phan–Tien and Tanner (PTT), Giesekus, Leonov, and modified extended Pom–Pom (mXPP) differential constitutive models are evaluated in two ways: with regard to steady shear characteristics and with regard to large amplitude oscillatory shear characteristics of a solution of poly(ethylene oxide) in dimethyl sulfoxide. Efficiency of the models with nonlinear parameters optimized with respect to steady shear measurements is evaluated by their ability to describe large amplitude oscillatory shear (LAOS) characteristics. The reciprocal problem is also analyzed: The nonlinear parameters are optimized with respect to the LAOS measurements, and the models are confronted with the steady shear characteristics. In this case, optimization is based on the LAOS measurements and equal emphasis is placed on both real and imaginary parts of the stress amplitude. The results show that the chosen models are not adequately able to fit the LAOS characteristics if the optimization of nonlinear parameters is based on steady shear measurements. It follows that the optimization of nonlinear parameters is much more responsible if it is carried out with respect to the LAOS data. In this case, when the optimized parameters are used for a description of steady shear characteristics, efficiency of the individual models as documented differs.

An examination of the differential constitutive models under large amplitude oscillatory shear flow

The exponential Phan-Tien and Tanner, Giesekus, Leonov, and modified eXtended Pom-Pom models are examined under large amplitude oscillatory shear flows using poly(ethylene oxide) solution. Optimization of the nonlinear adjustable parameters of the individual models is based on Fourier transform coefficients of the largest amplitude oscillatory shear characteristics where both magnitude and phase are taken into account. An efficiency of the individual models is shown for large amplitude oscillatory shear characteristics as well as for steady shear characteristics.

Applicability of the modified XPP model to a description of flow behaviour of polymeric materials

A 3N-parameter (3 parameters per mode) phenomenological modification of the XPP model for a description of the rheological properties of polymer melts is proposed. The predictive/fitting capabilities of the modified XPP model are compared with the Giesekus, XPP, and modified Leonov models using various polymeric materials in steady shear and uniaxial elongational flows. Its predictability of the rheological properties of the studied materials seems to be very good, including strain hardening in uniaxial elongational flow. Consequently, the GS derivative term was implemented into this modified XPP model. Then the model contains two linear parameters per mode (relaxation time and shear modulus) and two non-linear ones (the fitting parameter simultaneously controlling both strain hardening in elongation flow and shear thinning, and the slip parameter influencing almost solely shear thinning). The efficiency of this model is tested using LDPE and HDPE materials and compared with the modified Leonov model and ...

On the (ir)reproducibility of measurements of elongational viscosity using an SER universal testing platform

An SER Universal Testing Platform represents a widely used instrument determined for the measurement of elongational viscosity of various materials. Apart from an initial pre-selection of materials and an a priori range of extension strain for which this method can be applied, there is a series of other factors substantially influencing quality and reproducibility of the obtained results. They are prevailingly connected with the preparation of the samples and their fixing to the elongation rheometer. Among them it is possible to name an unevenness of sample thickness, appearance of air bubbles within the material studied, slant of fixed sample with respect to the rheometer drums axes. The aim of this contribution is to show the reasons of possible bad reproducibility of elongation measurements and visually determine the ranges of selected parameters within which the measurements are acceptable.

Rheological Characterization and Constitutive Modeling of Two LDPE Melts

Experimental data of two low‐density polyethylene (LDPE) melts at 200° C for both shear flow (transient and steady shear viscosity as well as steady first normal stress coefficient) and elongational flow (transient and steady‐state elongational viscosity) as published by Pivokonsky et al. [1] were analyzed by use of the Molecular Stress Function (MSF) model for broadly distributed, randomly branched molecular structures. For quantitative modeling of melt rheology in both types of flow and in a very wide range of deformation rates, only three nonlinear viscoelastic material parameters are needed: While the rotational parameter, a2, and the structural parameter, β, are found to be equal for the two melts considered, the melts differ in the parameter fmax2 describing maximum stretch of the polymer chains.