Selection of ethylene-vinyl-acetate properties for modified bitumen with enhanced end-performance

Bitumen modification with ethylene-vinyl acetate (EVA), in a wide range temperatures (between ??30 and 100 °C), has been studied as a function of polymer concentration and EVA characteristics (vinyl acetate (VA) content and melt flow index (MFI)). Viscous flow, dynamic shear (DSR) temperature sweep, and technological tests were conducted to assess binder performance at medium-to-high in-service temperatures. Evaluation of binder low-temperature viscoelastic behavior has been performed using a solid rectangular fixture (SRF) in torsional mode, either in the linear viscoelastic region or under non-linear conditions (by strain breakage tests between ??30 and 0 °C). Further microstructural analysis based on modulated differential scanning calorimetry (MDSC) and optical microscopy was conducted to support rheological and technological results. Hence, total crystalline fraction (related to the VA content and polymer concentration) turned out to be a key parameter to achieve a suitable binder modification at medium-high temperatures. In addition, MFI appears to be an important EVA parameter at low temperatures, as it was found that lower MFI values enhanced resistance to low-temperature cracking.     

A numerical study of various rheological polydispersity measures

Model calculations were performed in order to investigate the sensitivity of various rheological polydispersity parameters for variations in the moments of the molar mass distribution (MMD) of linear polymers. Molar mass distributions were generated with the Gaussian and the Generalised exponential distribution functions, using a fixed weight average molar mass M _w and variable M _w /M _n and M _z /M _n . Assuming linear entangled polymeric chains, the linear viscoelastic properties were predicted by calculating the stress relaxation modulus of the consecutive monodisperse fractions with the BSW relaxation time spectrum and blending these curves with the double reptation blending rule. BSW relaxation parameters appropriate for polypropylene were used.  It was found that both the zero-shear viscosity and the so-called cross-over frequency, at which and are equal, depend mostly on M _w but also significantly on both M _w /M _n and M _z /M _w . By contrast, the steady-state compliance depends mainly on M _z /M _w , its functional dependence on moments of the MMD being best described by the Ferry equation.  None of the polydispersity parameters PI (from the modulus cross-over), MODSEP (the modulus separation) or PDR (from the shape of the flow curve), as introduced in literature depends solely on the polydispersity M _w /M _n . PI is the most sensitive indicator for this purpose. Finally, the parameters ER ( at a fixed low value of , MODSEP en DRI (from the shape of the flow curve) are shown to be good indicators for the weight (M _z /M _w ) of the high molar mass tail of the molar mass distribution. Received: 5 May 1998 Accepted: 30 July 1998     

Process rheokinetics and microstructure of recycled EVA/LDPE-modified bitumen

Knowledge of the kinetics of the manufacturing process of polymer–bitumen blends is of great interest because it provides information on the behaviour of the binder at different stages of the mixing operation, which is useful for the establishment of the optimum processing conditions, involving temperature and operation time. The purpose of this research was to study the evolution of the rheological properties and microstructure of a polymer-modified bitumen during its processing. A 60/70-penetration grade bitumen and recycled EVA/LDPE were mixed under different processing conditions. Measurements of the evolution of viscosity with time, at different temperatures and agitation speeds, were carried out with an experimental device known as ‘rheomixer’, that is, a helical ribbon impeller inside a mixing vessel coupled with the transducer and motor of a conventional rheometer. Under the experimental conditions selected (within the laminar region, Re<10), temperature is the most important processing variable. Hence, low agitation speeds and a processing temperature of around 180°C should be chosen for bitumen modification with the polymer used.     

Effect of vinyl acetate content and silicate loading on EVA nanocomposites under shear and extensional flow

In this study, three EVAs (ethylene-vinyl acetate co-polymers) with different vinyl contents (VA) ranging from 9 wt% to 28 wt% (EVA9, EVA18 and EVA28) were melt blended with organo-clay to obtain polymer layered silicate nanocomposites. Filler intercalation and exfoliation were evidenced by X-ray diffraction. The melt state viscoelastic properties of EVA nanocomposites were studied to examine the influence of clay in altering the flow properties of these polymeric nanocomposites. The EVA18 and EVA28 nanocomposites exhibited remarkable difference in dynamic and steady shear properties compared to neat polymers. On the other hand, EVA9-5% nanocomposite did not exfoliate and exhibited rheological behaviour very similar to that of the neat polymer. Furthermore, the first normal stress difference was found to be dependent on the silicate loadings when measured at low shear stresses. The uniaxial extensional viscosity measurement indicated that the strain hardening was weaker in EVA nanocomposites compared to neat polymers. Environmental scanning electron (ESE)-microscopy elucidated a possible reason for reduced strain hardening in these systems.     

Influence of long-chain branching on time-pressure and time-temperature shift factors for polystyrene and polyethylene

Rheological characterizations were carried out for two polystyrenes. One was a linear polymer with M _w =222,000 g/mol and M _w /M _n =2, while the other was a randomly branched polystyrene with M _w =678,000 g/mol and a broad molecular weight distribution. Experiments performed included oscillatory shear to determine the storage and loss moduli as functions of frequency and temperature, viscosity as a function of shear rate and pressure, and multi-angle light scattering to determine the radius of gyration as a function of molecular weight. The presence of branching in one sample was clearly revealed by the radius of gyration and the low-frequency portion of the complex viscosity curve. Data are also shown for three polyethylene copolymers, one (LLDPE) made using a Ziegler catalyst and two made using metallocene catalysts, one (BmPE) with and one (LmPE) without long-chain branching (LCB). While the distribution of comonomer is known to be much more uniform in LmPE than in LLDPE, the pressure shift factors were the same for these two polymers. The pressure and temperature shift factors of the two polystyrenes were identical, but, in the case of polyethylene, the presence of a small amount of LCB in the BmPE had a definite effect on the shift factors. These observations are discussed in terms of the relative roles of free volume and thermal activation in the effects of temperature and pressure.     

Mesophase formation in high molecular-weight xanthan solutions

After a short review of theoretical background on mesophase formation in polymer solutions, this paper describes the liquid crystal phase transition and the corresponding rheological properties for aqueous solutions of a high-molecularweight xanthan sample (M _w 1.8 10⁶). The formation of mesophases has been studied using polarizing microscopy and viscometry. The effects of the presence of salts, bacteria cells and proteins have been investigated. The variations in the viscosity, due to mesophase formation, are in qualitative agreement with the predictions of Matheson's theory, but the onset of the ordered phase occurs at very low polymer concentrations and the diphasic domain is much broader than predicted by thermodynamic models. These characteristics of the phase transition are related to the very high molecular weight of the sample studied and can be explained mainly by the effects of cooperative interactions between xanthan chains and of chain flexibility reducing translational entropy.     

Viscosity and compliance from molar mass distributions using double reptation models

Various empirical correlations between linear viscoelastic properties and molar mass distribution of linear polymers have been proposed. Many of these summarize the distribution in terms of the first few moments. This is sufficient when studying samples of limited variability. In parallel, various fundamental models that enable calculation of these rheological characteristics from the full distribution have been proposed. The advantage of the modeling approach is the ease of creating distributions, thus enabling independent control of moments up to any desired order. It is the goal of this contribution to explore this advantage and compare the findings of the single exponential (DRSE) and modified time-dependent diffusion (DRmTDD) double reptation models with the empirical relations. The models predict that η ₀ is primarily a function of the weight-average molar mass M _w, with subtle dependence on polydispersity. Furthermore, the model depends mainly on a combination of the second (M _z/M _w) and third (M _z+1/M _z) polydispersity index. The DRmTDD model shows that conventional moment-based fit equations are only valid for limited distribution parameter ranges. General fit equations are proposed based on genetic programming. The details of the predictions are sensitive to the precise physical model formulation and need to be validated from experiments.     

Determination of critical molecular weight for entangled macromolecules using the tensile strength data

The multivariable power dependence of polymer properties on molecular characteristics (Dobkowski, 1981) has been applied to molecular weight dependence of tensile strength, and the known equation of Flory (1945) has been extended taking polydispersity of polymers into account. Constant parameters of the relevant regression equations have been calculated using experimental data on tensile strength and molecular weight averagesM _n andM _w of polystyrene (PS) and polycarbonate (PC). Then, the critical molecular weight for entanglementsM _c has been obtained from the following relationship:A=K M _cwhereA and are parameters of the extended Flory equation for the tensile strength, and the constantK = 2 is assumed for linear polymers. It has been found thatM _c of injection and compression moulded PS is equal to 34000 and 37350g/mole, respectively, whileM _c of injection moulded PC equals to 5000 g/mole. The values ofM _c calculated from the polymer tensile strength are consistent with published data obtained by other methods and with the computer modeling calculations. Branched polymers have only qualitatively been discussed. Dimensionless equations have been proposed for tensile strength characteristics for polymer materials.The described procedure can be suggested as applicable to various polymers for the determination of theirM _c values. However, more experimental data on another polymer materials will be necessary to support hitherto obtained results.The essential part of a lecture presented during the NATO Advanced Study Institute Rheological Fundamentals of Polymer Processing, Alvor, Portugal, 26 September–7 October 1994     

Evaluation of molecular weight distribution from dynamic moduli

A method to evaluate molecular weight distribution (MWD) from dynamic moduli is presented here. It relies on the least-square fitting of the dynamic data to a model whose parameters depend on the MWD. In particular, the analytical solution for the relaxation modulus previously obtained from the double reptation model, with the Tuminello step relaxation function and the Generalized Exponential Function (GEX) describing the MWD (Nobile and Cocchini 2000), has been used. A Finite Element Approximation (FEA) has been applied to calculate dynamic moduli from the relaxation modulus as a function of MWD. The sensitiveness of the GEX-double reptation dynamic moduli on the model parameters has also been investigated and the results show that large changes of the M_w/M_n ratio weakly affect the dynamic moduli, while small changes of the M_z/M_w ratio significantly deform the dynamic moduli curves. The use of rheological data to obtain MWD, by the model used in this paper, will, therefore, be able to give rather well defined M_z/M_w ratios, while more uncertainty will be presented in the M_w/M_n results. The so-called GEX-rheological model for the dynamic moduli was applied to fit the experimental data of different polymers in order to obtain the best-fit parameters of the MWD of these polymers, without the need for the inversion of the double reptation integral equation. The stability of the results has been confirmed through the evaluation of the 90% confidence intervals for the first molecular weight averages. Finally, concerning the M_w and M_z values, the predictions obtained from the dynamic moduli measurements differ by less than 10% from those obtained from GPC measurements while, as expected, more uncertainty is present in the M_n predictions. Received: 6 February 2000 Accepted: 22 August 2000     

Rheologische Messungen an Polypropylenschmelzen

Zusammenfassung Es wurden Fließkurven von Polypropylenschmelzen bei 190 °C in einem Schergefällebereich von etwa 10^–1 bis 10² sec^–1 aufgenommen, wobei drei Serien von Polymerproben herangezogen wurden: eine Serie PP 1–7 von isotaktischen Propylenpolymerisaten mit einer Molekulargewichtsverteilung, die durch¯M _w /¯M _n 4–6 gekennzeichnet war; eine zweite Serie PP 1d–5d von abgebauten Polymerproben mit¯M _w /¯M _n 2–3; eine dritte Serie PP 1m–3m, die aus Mischungen von Polypropylenen bestand und die durch¯M _w /¯M _n >10 gekennzeichnet war. Es wurde der Einfluß des Molekulargewichts und der Molekulargewichtsverteilung auf die Fließkurven untersucht, insbesondere der Einfluß auf den Exponentenn in derOstwald-de Waele-Gleichung=KD ⁿ . Es wurde versucht, die Ergebnisse durch die universaleVinogradov-Viskositätsfunktion darzustellen, wobei sich aber sehr wesentliche Abweichungen infolge Variation des Molekulargewichts und der Molekulargewichtsverteilung ergaben.

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Summary Flow curves of molten polypropylene were determined at 190 °C over a shear gradient range of about l0^–1 to 10² sec^–1. Three series of polymer samples have been used: one series PP 1–7 of isotactic propylene polymerization products with a molecular weight distribution characterized by¯M _w /¯M _n 4–6, another series of degraded polymer samples PP 1d–5d with¯M _w /¯M _n 2–3, and still another series of polymer mixtures PP 1m–3m with¯M _w /¯M _n >10. The influence of molecular weight and molecular weight distribution on the flow curves was investigated, particularly on the exponentn in theOstwald-de Waele-power law=KD ⁿ . An attempt to plot the results by the universalVinogradov-viscosity function produced marked deviations due to variation of molecular weight and molecular weight distribution.

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Vorgetragen auf der Arbeitstagung der Sektion Rheologie des Vereins Österreichischer Chemiker am 17. November 1967 in Graz. Mitteilung I, II: Rheol. Acta5, 89 (1966); ibid. im Druck [Messung und Interpretation von Filmkurven].     

Linear and non-linear rheology of linear polydisperse polyethylene

Rheological techniques, size-exclusion chromatography, and molecular spectroscopy are the most widely used tools for describing polymer molecular structure in polyolefins. The detection of long-chain branching, and to some extent, its quantification, have been based on quantifying the deviation of polyethylene??s (PE) rheological behavior from that of a linear reference. Although metallocene-based PE has been extensively studied, linear polydisperse originating from Ziegler or Chromium-based catalysts are not often thoroughly considered, despite their high industrial importance. Within this work, we study the linear and non-linear rheology of a set of polydisperse PEs, for which the topological linearity is confirmed by GPC-MALLS measurements. Thus, we can safely quantify the effect of broad molecular weight distribution, high and ultra-high molecular weight fractions on rheological quantities and model parameters. Specifically, the zero-shear viscosity, ?? ₀ vs. M _w, relaxation spectra, phase lag vs. the complex modulus plot (van Gurp?CPalmen method) were applied and significant deviations from the ??rheologically linear?? behavior were observed, attributed only to M _w, M _z and polydispersity. Since the elongational viscosity was typical of linear PE, large-amplitude oscillatory shear and FT-Rheology were applied to quantify the non-linear rheological behavior. The latter was described by a single parameter, $Q=I_{3/1}/\gamma_0^2$ , which for linear polydisperse PE was correlated to the high molecular weight fraction and was constant over a broad range of applied Deborah numbers for the respective excitation frequencies. Since we need to correlate structural features such as broad MWD and HMW to polymer performance under processing conditions, we have to extend the analysis of linear rheological parameters, such as zero-shear viscosity, to non-linear parameters, e.g., the Q parameter quantified and used here.     

Extensional flow of polymer solutions through porous media

The flow behaviour of various polymer solutions of non-hydrolyzed polyacrylamide, hydrolyzed polyacrylamide, polyox and Xanthan was investigated in a plexiglass column having a succession of enlargements and constrictions, and compared with the flow behaviour and mechanical degradation of a solution of non-hydrolyzed polyacrylamide in a packed column of non-consolidated sand. The flow behaviour of this solution was found to be very similar in both the sand pack and plexiglass pore.Apart from the Xanthan solution, all other polymer solutions showed a viscoelastic behaviour in the plexiglass pore. The onset of viscoelastic behaviour, which has previously been defined using the shear rate ( ), stretch rate ( _s ) and Ellis number (E ₁), could be more precisely evaluated using a modified stretch rate (S _G). The pressure losses across the plexiglass pore for different polymer solutions of the same type were found to follow a unique curve provided the suggested group (S _G) was used, a situation which was not achieved with the other rheological parameters.The multipass mechanical degradation of the non-hydrolized polyacrylamide was tested through the sand pack against the suggested group (S _G) and Maerker's group (M _a). It was found that the loss of the solution viscoelasticity due to multipass mechanical degradation was better represented usingS _G thanM _a. A cross-sectional area (cm²) - C ^* critical concentration of polymer (ppm) - d plexiglass pore enlargement diameter - D average sand grain diameter (cm) - e equivalent width for the plexiglass pore - E ₁ Ellis number (a Deborah number) - F _R resistance factor - F _Ri resistance factor at the first pass - h height of the flow path of the plexiglass pore - K power-law constant - K _h,K _w effective permeability to hydrocarbon and water, respectively (10^–8 cm²) - M _a Maerker's group for a given porosity (s^–1) - M _ai value ofM _a at the first pass - N _D Deborah number - n power-law index - Q flow rate (cm³/s) - R capillary radius (cm) - R _g radius of gyration - S _G suggested group of rheological parameters representing a modified maximum stretch rate (s^–1) - S _Gi value ofS _G at the first pass - T _R,t characteristic time for the fluid (s) - t _s residence time (s) - V ₀ superficial velocity (cm/s) - V mean velocity of flow through a porous medium (cm/s) - average axial velocity in the enlargement section of the plexiglass pore (cm/s) - V ₁,V ₂ maximum velocity at a plexiglass enlargement neck and centre - [] intrincis viscosity - viscosity (mPa s) - _r relative viscosity (ratio of the viscosity of the polymer solution to that of the solvent) - shear rate (s^–1) - _s stretch rate (s^–1) - characteristic time for the polymer solution (s)     

Uniaxial elongational behavior of poly(vinyl chloride) physical gel

A poly(vinyl chloride) (PVC,  M_w = 102×10³)(\mbox{PVC,}\;{\rm M}_{\rm w} =102\times 10^3) di-octyl phthalate (DOP) gel with PVC content of 20 wt.% was prepared by a solvent evaporation method. The dynamic viscoelsticity and elongational viscosity of the PVC/DOP gel were measured at various temperatures. The gel exhibited a typical sol–gel transition behavior with elevating temperature. The critical gel temperature (T_gel) characterized with a power–law relationship between the storage and loss moduli, G^′ and G^″, and frequency ω, G￠=G^￠￠/tan  ( np/2 ) μ wⁿ{G}^\prime={G}^{\prime\prime}{\rm /tan}\;\left( {{n}\pi {\rm /2}} \right)\propto \omega ^{n}, was observed to be 152°C. The elongational viscosity of the gel was measured below the T_gel. The gel exhibited strong strain hardening. Elongational viscosity against strain plot was independent of strain rate. This finding is different from the elongational viscosity behavior of linear polymer solutions and melts. The stress–strain relations were expressed by the neo-Hookean model at high temperature (135°C) near the T_gel. However, the stress–strain curves were deviated from the neo-Hookean model at smaller strain with decreasing temperature. These results indicated that this physical gel behaves as the neo-Hookean model at low cross-linking point, and is deviated from the neo-Hookean model with increasing of the PVC crystallites worked as the cross-linking junctions.     

Predictions of linear viscoelastic properties for polydisperse entangled polymers

Different blending laws have been proposed in the literature to describe the polydispersity effect on the rheological behavior of polymer melts. In this paper predictions of linear viscoelastic properties of entangled polydisperse polymers have been derived from the double reptation mixing rule. The results in terms of the relaxation modulus, the zero shear-rate viscosity, η₀, and the steady-state compliance, J _e ⁰, have been obtained using three different relaxation functions for the monodisperse fractions, namely the Tuminello step function, the single exponential function and the BSW function. Both discrete and continuous molecular weight distributions (MWDs) have been investigated. The Generalized Exponential Function (GEX) has been considered in the continuous case. The results showed that, in systems with a large number of components, the predictions of linear viscoelastic properties mainly depend on the double reptation mixing rule assumption, while the choice of the relaxation function is not crucial. In particular, the mathematical simplicity of the Tuminello step relaxation function has allowed analytical computation of the linear viscoelastic properties in closed form. Indeed, the analytical results indicated a dependence of η₀ on the MWD that could be expressed in terms of (M _z/M _w)^0.8, in agreement with experimental results reported in the literature. In the case of J _e ⁰, the analytical model defines a dependence on (M _z/M _w)^5.5, i.e. as expected a strong dependence on the MWD is predicted for the steady-state compliance. Finally, dynamic moduli have been computed from the relaxation modulus and their predictions have been favorably compared with experimental results from the literature. Received: 19 July 1999/Accepted: 24 November 1999     

Creep recovery behavior of metallocene linear low-density polyethylenes

The rheological behavior of two metallocene linear low-density polyethylenes (mLLDPE) is investigated in shear creep recovery measurements using a magnetic bearing torsional creep apparatus of high accuracy. The two mLLDPE used are homogeneous with respect to the comonomer distribution. The most interesting feature of the two mLLDPE is that their molecular mass distributions are alike. Therefore, as one of the mLLDPE contains long-chain branches, the influence of long-chain branching on the elastic properties of polyethylene melts could be investigated. It was found that long-chain branches increase the elasticity of the melt characterized by the steady-state recoverable compliance. The long-chain branched mLLDPE has a flow activation energy of 45 kJ/mol which is distinctly higher than that of the other mLLDPE. The shear thinning behavior is much more pronounced for the long-chain branched mLLDPE. A discrepancy between the weight average molecular mass M _w calculated from size exclusion chromatography measurements by the universal calibration method and the zero shear viscosities of the two mLLDPE was observed. These observations are discussed with reference to the molecular architecture of the long-chain branched mLLDPE. The rheological properties of the long-chain branched mLLDPE are compared with those of a classical long-chain branched LDPE. It is surprisingly found that the rheological behavior is very much the same for these two products although their molecular mass distributions and presumedly the branching structures differ largely. Received: 15 February 1999 Accepted: 10 June 1999     

Rheological and electrical properties of EVA copolymer filled with bamboo charcoal

The electrical and rheological properties of an ethylene vinyl acetate (EVA) copolymer filled with bamboo charcoal were investigated. The composites were prepared by melt process in an internal batch mixer. Size distribution analysis showed that d₍₅₀₎ and d₍₉₀₎ values of the bamboo charcoal particles are 12.7 and 40 μm, respectively, with a mean diameter of 22 μm. Scanning electron microscopy proved that the particles of bamboo charcoal present a rectangular shape. The electrical percolation threshold was observed at 0.18 volume fraction (35 wt%) of bamboo. Beyond the percolation threshold, a considerable increase in electrical properties was observed up to a limit value of 10^-2 S/m. The rheological percolation was studied from different rheological models. As a result, the rheological percolation threshold was observed at 0.3 volume fraction (50 wt%) of bamboo charcoal contents. So, the electrical percolation occurs before the rheological percolation. This is principally due to the filler’s characteristics such as the specific surface area, the aspect ratio, and the surface properties. Finally, the bamboo charcoal confers high electrical properties to the EVA composite without inducing strong changes in its viscoelastic properties.     

Dependence of the zero shear-rate viscosity and the viscosity function of linear high-density polyethylenes on the mass-average molar mass and polydispersity

Linear high-density polyethylenes with molar masses M _w between 240 and 1,000,000 g/mol, obtained by metallocene catalysts, were characterized in shear using oscillatory and creep tests. The polydispersities of the molar mass distributions (MMDs) lay between 1 and 16. The resulting zero shear-rate viscosities η₀ covered a range from 2.5×10⁻³ to around 10⁸ Pas. Above a critical molar mass of M _c≈2,900 g/mol, the experimental results can be described by the relation η₀ ∼ M _w^3.6, independently of the MMD. The oscillatory data were fitted with a Carreau–Yasuda equation. The resulting parameters were correlated to molecular structure. The parameter a, being a quantity for the width of the transition between the Newtonian and the non-Newtonian regime, showed a dependence on the molar mass M _w but not on M _w/M _n. The parameter λ of the Carreau-Yasuda equation was found to be the reciprocal crossover frequency for all samples with a log-Gaussian MMD. λ depends on the molar mass M _w and also on M _w/M _n.

Rheological properties of branched polystyrenes: linear viscoelastic behavior

Oscillatory shear measurements on a series of branched graft polystyrenes (PS) synthesized by the macromonomer technique are presented. The graft PS have similar molar masses (M _w between 1.3×10⁵ g/mol and 2.4×10⁵ g/mol) and a polydispersity M _w /M _n around 2. The molar masses of the grafted side chains M _w,br range from 6.8×10³ g/mol to 5.8×10⁴ g/mol, which are well below and above the critical entanglement molar mass M _c of linear polystyrene. The average number of side chains per molecule ranges from 0.6 to 6.7. The oscillatory measurements follow the time–temperature superposition principle. The shift factors do not depend on the number of branches. The zero-shear viscosities of all graft PS are lower than those of linear PS with the same molar mass, which can be attributed to the smaller coil size of the branched molecules. It is shown that the influence of branching on the frequency dependence of the dynamic moduli is weak for all graft PS that were investigated, which can be explained by the low entanglement density.Electronic Supplementary Material Supplementary material is available for this article at This article has already been published online first (DOI: ). Due to an oversight at the publisher's, this version contained several mistakes. The article is herewith republished in its entirety as a "publisher's erratum".     

Modification of Whitham's ray shock theory for analyzing the reflection of weak shock waves over small wedge angles

The weak Mach reflection phenomenon has been analyzed by applying both the shock dynamics approach and the disturbance propagation concept. The analysis which is based on modified Whitham's ray shock theory results in analytical expressions for the triple point trajectory angle,, and the shape of the curved Mach stem, which are functions of the incident shock wave Mach number,M _i, and the reflecting wedge angle, _w. The analytical results were found to be in good agreement with experimental results.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Determination of the weight-average molecular weight of polyamide-6 on the basis of melt viscosity

A theory of a two-point rheometrical method of determination of the weight-average molecular weightM _w of polyamide-6 is presented. The method is based on the measurement of the instantaneous values of zero-shear-rate viscosity of the degrading polymer melt, and a formula is derived which enables the calculation of the initial value ofM _w (i.e. at zero-residence-time in molten state) of the investigated sample. The experimental verification of the method proves its applicability. The considerations carried out may be regarded as a first step towards developing a theory of an in-line rheometer for a continuous determination ofM _w .