A. Schausberger

The relaxation of polymers with linear flexible chains of uniform length

The analysis of dynamic mechanical data indicates that linear flexible polymer chains of uniform length follow a scaling relation during their relaxation, having a linear viscoelastic relaxation spectrum of the formH(λ) = n1GN0 × (λ/λmax)n1 forλ≤λmax. Data are well represented with a scaling exponent of about 0.22 for polystyrene and 0.42 for polybutadiene. The plateau modulusGN0 is a material-specific constant and the longest relaxation time depends on the molecular weight in the expected way. At high frequencies, the scaling behavior is masked by the transition to the glassy response. Surprisingly, this transition seems to follow a Chambon-Winter spectrumH(λ) = Cλ−n2, which was previously adopted for describing other liquid/solid transitions. The analysis shows that the Rouse spectrum is most suitable for low molecular-weight polymersM ≈ Mc, and that the de Gennes-Doi-Edwards spectrum clearly predicts terminal relaxation, but deviates from the observed behavior in the plateau region.

Linear elastico-viscous properties of molten standard polystyrenes

This paper contains an extensive presentation of dynamic mechanical data (complex moduli), as obtained on the melts of a series of standard polystyrenes of narrow molar mass distributions. It also shows the way of obtaining structural parameters (plateau modulus and friction factor) which are needed for an interpretation of these data in terms of simple theoretical models (Maxwell elements, Doi-Edwards model). A linear mixing rule is used for taking into account the finite width of the molar mass distributions.

A simple method of evaluating the complex moduli of polystyrene blends

AbstractIn the search for a workable mixing rule, use was made of experimental data for complex moduli of melts of narrow molar mass distribution polystyrenes and their homogeneous blends. In the course of this work two basic observations were made as to the nature of the relaxation time spectra of these blends:a)The relaxation strength (a product of the weight fraction and the plateau modulus) of a component of large molecules is reduced by the presence of shorter molecules, the latter molecules acting like ordinary diluent molecules even if their molar masses are larger thenMc.b)The relaxation time of a molecule (known from measurements on the respective monodisperse component) is considerably changed by the blending. The width of the distribution of relaxation times, as expected from the known composition of the blend, is significantly reduced. For both processes approximate empirical equations could be found. It turned out that, after the application of the required modifications, the complex moduli of the components could successfully be added in order to obtain the complex moduli of the blend at circular frequencies characteristic for the flow and rubber transition regions. On the basis of these results one may expect that for the melt of any linear polymer the linear viscoelastic properties can be evaluated with reasonable accuracy from the knowledge of the molar mass distribution.

An improved algorithm for calculating relaxation time spectra from material functions of polymers with monodisperse and bimodal molar mass distributions

Using the basic concept of Emri and Tschoegl, the algorithm for calculating relaxation time spectra has been improved such that excellent results are provided in the difficult case of polymers with narrow molar mass distributions. These spectra can be compared with those calculated by nonlinear regularization (Weese 1992), which we regard as a very exact method, and show equally good results with even less mathematical effort. Examples of dense relaxation time spectra (up to eight points per decade) are given for nearly monodisperse polystyrene melts and for mixtures of these up to four components. The relaxation time spectra describe the dynamic mechanical experimental data in each case with an overall error of less than 3%. The filtering method used to avoid physically senseless oscillations has been proven to resolve the characteristic peaks contributed by monodisperse polymers accurately.

Reptation model in polymer melt rheology: On the validity of a useful basic assumption

A mixing rule as suggested by the Doi-Edwards theory is checked experimentally. For this purpose, the dynamic shear moduli as functions of circular frequency are measured first for the melts of a series of polystyrenes of narrow molecular mass distributions. After the careful preparation of mixtures the same moduli are also determined for these mixtures. A discussion is given of the remarkable but limited validity of the additivity of contributions by the single macromolecules to the mentioned moduli.

Investigation of relaxation properties of polymer melts by comparison of relaxation time spectra calculated with different algorithms

In this paper a recently introduced algorithm (Brabec and Schausberger, 1995) for the calculation of relaxation time spectra is compared with two standard methods, i.e., Weeses regularization, and Baumgaertels and Winters regression algorithm. A reasonable agreement between those three algorithms is found for the relaxation properties of mono-, polydisperse, bi-, and multimodal polystyrene samples. All three numerical methods reproduce the relaxation properties for long and medium times correctly, but they show some disagreement at short times because of sparse experimental data. The high numerical accuracy opens the possibility to test and improve the physical models which underlie the calculations. The good agreement of the different algorithms suggests that small inconsistencies to physical models are not due to a failure of the numerical methods, but due to an insufficiency of the generalized Maxwell model.

A description of the linear viscoelasticity of molten linear monodisperse polystyrenes with the aid of a generalized discrete relaxation time spectrum

For an investigation into the relationship between the molar mass distribution of a polymer and the viscoelastic properties of its melt a good description of the rubberlike liquid behavior of nearly monodisperse polymers is needed as a prerequisite. Such a knowledge would also be very helpful for further studies of the motion of flexible chains. As, in general, available data on nearly monodisperse polymers are affected by the glassy behavior, an attempt was made to figure out the purely rubberlike liquid behavior by simply subtracting the contribution of the glassy behavior from these data. First, a discussion of experimental dynamic moduli is given. In consequence, a generalized discrete relaxation time spectrum is proposed. This spectrum is the sum of two spectra. One describes the rubberlike liquid behavior and has a strongly molar-mass-dependent leading relaxation time but a molar-mass-independent leading relaxation strength. Its shape is molar mass independent as well. The other describes the influence of the glassy behavior and is molar mass independent in its entirety. The application of the proposed model to the above-mentioned investigation is discussed.

The role of short chain molecules for the rheology of polystyrene melts.

Atactic polystyrenes of narrow molar mass distribution with average molar masses larger than the critical molar massMc were mixed with similar polystyrenes of molecular masses lower thanMc. Linear viscoelastic melt properties of these binary blends were measured with a dynamic viscometer of the concentric cylinder type. One of the experimental findings is that the time-temperature shift factorsaT are dependent on the composition of the samples. This can be understood, if free volume due to chain-ends is taken into account. A computer-fitted WLF-equation being modified in a proper way leads to the following results: At the glass-transition-temperature the fraction of free volume in polystyrene of infinite molar mass is only 0.015. At a temperature of 180 °C the mean value of the free volume at a chain end is 0.029 nm3 for the polystyrene investigated.

Polypropylene—Polyethylene Melts: Phase Structure Determination by Rheology

Using dynamic moduli and transmission electron microscopy images the phase structure of polypropylene‐polyethylene melts was studied. Blends consisting of 80% base material (polypropylene‐homopolymer or ethylene‐propylene copolymer) and of 20% modifier polymer (a C2/C8‐elastomer, a linear low density polyethylene or a high density polyethylene) forming a two‐phase structure in the melt were investigated. The influence of the viscosity ratio and the interfacial tension on the particle size of the inclusions was investigated. Both factors can be determined from dynamic moduli by using the emulsion model of Palierne [1] to calculate the interfacial tension.

The Influence of Shear Thinning on Elongation Hardening of Long‐Chain Branched Polypropylene

Long‐chain branched polypropylenes show pronounced strain hardening in elongation. This property, important for various applications is strongly reduced by shear applied to the melt before elongation. In this work the influence of shear history on the rheological properties of blends from a linear (L‐PP) and a long‐chain branched (LCB‐PP) polypropylene was studied in detail. Shear thinning is produced in a cone‐plate device and the annealing of it is recorded by the storage modulus, G′(ω), immediately after applying the shear deformation. In the case of L‐PP this recovery function is simple exponential, whereas additional relaxation processes are found with the presence of LCB‐PP in the blend. In order to investigate the elongational behaviour after various shear histories the sheared sample is removed from the cone‐plate system, compressed into a flat sheet and quenched very fast to ensure residual shear thinning. Constant elongation rate experiments have been performed using a uniaxial extensional rheom...