Christian Carrot

From dynamic moduli to molecular weight distribution: A study of various polydisperse linear polymers

The linear viscoelastic behavior of various polydisperse linear polymers in the melt is used to predict their average molecular weights and polydispersity index. The method is based on simplified molecular dynamics and has been previously shown to enable a correct description of the dynamic moduli of polypropylenes from the knowledge of their molecular weight distribution (MWD). This so-called forward calculation only requires a few parameters, namely the scaling law for the zero-shear viscosity of narrow fractions η0=f(M), the plateau modulus GN0, and the value of the molecular weight between entanglements Me. The main goal of the present work is to find a solution to the “inverse” problem. To avoid the problem of becoming ill-posed, the shape of the MWD has to be prescribed. Using the assumption of a typical logarithmic bell-shaped Wesslau MWD, the method has been proven to be successful for the recovery of the weight average molecular weight and of the polydispersity index of many linear polymers in a ...

Rheological characterization of ethylene vinyl acetate copolymers

A series of ethylene vinyl acetate (EVA) copolymers was studied by dynamic mechanical spectroscopy to understand the relative influence of composition, structure, and molecular weight distribution on their rheological behavior in the melt. The examination of their viscoelastic properties in a large temperature range showed that the glass transition temperature is nearly independent on their composition because of the statistical nature of the copolymers, though some long sequence of polyethylene homopolymer may exist at low vinyl acetate (VA) content. The successful use of the time temperature superposition for oscillatory experiments in the melt confirmed the previous remarks, because the application of the Williams Landel Ferry (WLF) equation leads to a unique set of WLF coefficient, whatever the composition of the EVA. This enables the comparison of the rheological behavior in the melt at the same temperature, in the same free volume condition, and at last it was shown that in the terminal zone, the molecular weight distribution is more influent on the behavior of EVA copolymers than their composition.

Rheological behavior of degraded polypropylene melts: From MWD to dynamic moduli

The linear viscoelastic behavior of polydisperse polypropylenes in the melt is predicted using the molecular weight distribution (MWD) as determined from gel permeation chromatography, on the basis of simplified molecular dynamics: single exponential form of the relaxation modulus of narrow fractions, double reptation, tube renewal, and constraint release. Owing to a few approximations, the calculation only requires a few parameters, namely the scaling law for the zero shear viscosity of narrow fractions η0 = f(M), the plateau modulus G, and the value of the molecular weight between entanglements Me. Using this method a relaxation spectrum of Maxwellian contributions with a large number of modes is obtained. This spectrum well predicts the rheological behavior in the terminal zone of samples obtained by controlled peroxydic degradation of polypropylene with polydispersity ranging from 4 to 10. Attention is focused on the zero shear rate viscosity, frequency, and modulus of the crossover of the storage and loss moduli from experiments and calculations, because these parameters are generally thought to be sensitive to both average molecular weight and polydispersity and are relatively easy to get from dynamic experiments. How the initial spectrum can be conveniently reduced to a more simple spectrum with only a few modes, without significant loss of information, is shown. This spectrum may be useful and time saving in calculations, for example, to describe the memory function in nonlinear constitutive equations while keeping its physical meaning in relation to the MWD.

Rheological behavior of a semi-crystalline polymer during isothermal crystallization

The theological behavior of a molten semi-crystalline polymer, namely, a high density polyethylene (HDPE), was investigated during isothermal crystallization from the melt, using dynamic oscillatory experiments at 1 tad/s in a parallel plates rheometer. The theological results were compared with those obtained from differential scanning calorimetry in the same conditions. During the crystallization, the molten and crystallizing polymer provides a useful model for filled polymers, the crystalline phase being the filler and the liquid phase being the matrix. In most cases, the filler can be considered to be spherical shaped (spherulites). Owing to the amorphous phase linking liquid and crystallites, the adhesion between matrix and filler in this system is perfect. The filler content increases continuously during the crystallization. This model might be used to test laws relating the theological parameters to the volume fraction of filler. Problems related to the rheometry for such systems are discussed and the key parameters insuring reproducibility and accuracy in the measurements are pointed out. The relative sensitivity of the various theological parameters (storage and loss moduli, loss angle) to structural changes of the liquid has been out forward. Some preliminary equations relating the variation of these parameters to the volume fraction of filler, through the use of simple fractal exponents have been derived and discussed in comparison with laws provided by various authors.

Extrudate swell and isothermal melt spinning analysis of linear low density polyethylene using the Wagner constitutive equation

Abstract The rheological behaviour of a linear low density polyethylene melt is studied using a wide range of techniques: shear and elongational stress growth at constant strain rate, steady shear flow, extrudate swell and isothermal melt spinning. The analysis of the behaviour is based on the Wagner constitutive equation which appears to be suitable. Moreover, the extrudate swell and the isothermal spinning are simulated by taking into account the past shear and elongation deformation in the reservoir, the contraction and the die of a capillary rheometer. For this purpose, the Finger deformation tensor is evaluated using a Protean coordinate system. This approach is shown to be very useful to test the validity of the constitutive equation and to determine its characteristic parameters.

Determination of Primary Relaxation Temperatures and Melting Points of Ethylene Vinyl Acetate Copolymers

The relationship between copolymer composition and transition temperatures was studied by means of differential scanning calorimetric analysis and dynamic mechanical spectroscopy. Six samples of ethylene vinyl acetate (EVA) copolymers containing from 5 to 40 mass per cent of vinyl acetate (VA) were studied. The differential scanning calorimetric analysis revealed that each EVA copolymer displays two endothermic peaks (Tm1 and Tm2 ) in the melting zone. Dynamic mechanical spectroscopy was used to determine the primary relaxation temperature (Tα ) for EVA copolymers. This latter characteristic is relatively insensitive to the level of vinyl acetate contained in the copolymer and is influenced by the pulsation frequency ω, also named the angular frequency.

Elongational flow of polyethylenes in isothermal melt spinning

The elongational behavior of two polyethylenes with different structures, namely, a low‐density polyethylene and a linear low‐density polyethylene, has been investigated by isothermal melt spinning. The length along the spinline has been rescaled according to time. The evolution of the calculated elongational viscosity versus time has been compared to the transient elongational viscosities measured after imposition of a constant extension rate. The data demonstrate that these two situations, which are in many ways similar, give nearly the same results. Consequently, the viscosity which can be obtained from a fiber spinning experiment is a transient elongational viscosity. Differences in the elongational behavior between the long branched and the linear polyethylene are presented such as displayed in the spinning experiment. The strong influence on practical parameters such as melt strength or breaking stretch ratio is demonstrated.

Polypropylene during crystallization from the melt as a model for the rheology of molten‐filled polymers

Polarized light microscopy shows that polypropylene crystallizes from the melt into a well-distinguished spherulitic structure. Therefore, it provides a useful model for molten-filled polymers, where the growing spherulites are considered to be filler particles dispersed in a matrix fluid. Although spherulites are randomly dispersed in the space, two dispersion models (simple cubic and centered cubic) are discussed to correlate the transformed fraction α(t) with the volume fraction of filler ϕ(t). The combination of these results with those of differential scanning calorimetry (DSC) shows that the transformed fraction α(t) is a direct indication of the volume fraction of filler ϕ(t). The rheological study, using oscillatory experiments coupled with DSC results, shows the relative sensitivity of the rheological functions to structural changes of the liquid during crystallization. Furthermore, they reveal the existence of a yield effect above a certain criticl value of the filler content (ϕc = 0.4). In the absence of this yield effect, a model is proposed to predict the variation of the rheological functions with the filler content. This model shows not only a variation of the plateau modulus, but also the modification of the characteristic times of relaxation of the polymer matrix, whereas the shape of the relaxation spectrum remains unchanged.

Crosslinking in the melt of EVA using tetrafunctional silane: gel time from capillary rheometry

Crosslinking of ethylene vinyl acetate (EVA) copolymers can be performed in the melt by use of a transesterification reaction using tetrapropoxysilane as a crosslinking agent and dibutyl tin oxide as a catalyst [Polymer 43 (2002) 6085]. Whether the kinetics of the reaction can be suitably controlled is an important point that must be answered before any processing method such as extrusion or injection molding is considered. This investigation was carried out in a capillary rheometer. Various stoichiometric ratio and processing temperatures were studied. Viscosity was measured during the reaction and the evolution of the flow curves with reaction time was calculated. Gel point under shear conditions was considered to be achieved at the appearance of a yield stress on the flow curves. It was shown that an excess of propoxy groups slows down the reaction kinetics but until 120 °C, the gelling time is longer than 8 minutes which is long enough for processing with conventional techniques.

Validation of cogswell's convergent flow analysis

The behavior of two polymers, namely, low-density and linear low-density polyethylenes, was studied in transient and steady-state shear and elongational flows. The predictions of Wagners model with a damping function using a generalized invariant were calculated. The model appears to be suitable for predictions of the shear and elongational transient flows on the range of strains experimentally tested. The shear flow curves can also be recovered by the model on a very broad range of shear rates. The model is then used to assess extensional data obtained with the convergent flow analysis proposed by Cogswell.