Numerical simulation of large amplitude oscillatory shear of a high-density polyethylene melt using the MSF model

We study the flow response in large amplitude oscillatory shear of the molecular stress function (MSF) model that has recently been proposed by Wagner et al. [M.H. Wagner, P. Rubio, H. Bastian, The molecular stress function model for polydisperse polymer melts with dissipative convective constraint release, J. Rheol. 45 (2001) 1387–1412]. The MSF model is derived from molecular theory and has only two parameters to describe the non-linear material response. The model predictions are analysed in both the frequency and time domain. It shows good agreement with experimental data for a linear high-density polyethylene melt. At low and medium strains, MSF model predictions are in excellent agreement with experimental data and predictions of a six-mode Giesekus model which has six parameters to describe the non-linear material response. At medium strains, the basic Doi–Edwards model, which has no non-linear parameters, already underpredicts the data. At high strains, the MSF model predictions agree slightly better with the experimental data than the Giesekus model. Surprisingly, however, it is the Doi–Edwards model that shows excellent agreement with experimental data at high strains. For the linear melt we consider, it outperforms the models that have non-linear parameters, both in the time and frequency domain.     

Theoretical analysis of non-uniform extensional flows in relation to processing rheology and predictions of some constitutive equations

In this paper, a characteristic equation involving the stream function, already given by one of the authors in a previous work for classifying axisymmetric incompressible flows, is re-considered. Non-uniform nearly extensional flows are derived as particular solutions from this equation. Using experimental data in the literature for polymer solutions and melts, it is proved that particular solutions of the characteristic equation lead to kinematics very close to those encountered in the fiber-spinning process. The kinematic equations satisfactorily correlating the fiber-spinning data are used in order to determine the ability of constitutive equations to predict realistic stresses in the flow domain. The rheological parameters of the fluids, obtained from experiments, are used for computation of differential and integral constitutive equations in the spinning conditions. Comparisons with the stress response of adequate constitutive equations are given and discussed.Also affiliated to: Université Joseph Fourier Grenoble I and Institut National Polytechnique de Grenoble, Associé au CNRS (URA 1510)     

A network model with free-strand dynamics for polymer melts

 A network model for polymer melts is presented in which disentangled strands relax under flow conditions and may rejoin the network before complete relaxation. For simplicity, we study Gaussian strands that move affinely when incorporated in the network. Network strands are created and lost according to a time constant λ. Free strands have their dynamics given by the Bird-DeAguiar model as a crude representation of reptation and the hindered rotation experienced by polymer strands in melts. The model yields a shear-thinning viscosity with overshoot in the start-up viscosity η⁺ (t). The double-step strain results compare well with available experimental data. Received: 10 July 2000 Accepted: 10 July 2001     

The “decaying springs” model for irreversibility in polymer melts

In this work, entanglements in a polymer melt are modeled as a system of parallel springs which form and decay spontaneously. The springs are assumed to be nonlinear, and a certain fraction of them is torn apart by a certain strain.Based on these assumptions, a model of behavior in simple shear is developed. This model is shown to predict a behavior comprising that of a Wagner fluid, and is generalized to a tensorial model of single integral type. The integrand depends on a product of a material function, modeling reversible behavior, and a material functional which takes irreversible processes into account.Irreversibility of network disentanglement, which may occur when deformation changes or reverses direction, can be modeled in this way. It is shown that the two well-known Wagner constitutive equations with and without irreversibility assumptions are special cases of the model developed. In case of a deformation which does not change directions, the new material function and the material functional are multiplied to yield Wagner's damping function.When the rate of spring formation is a function of temperature, the developed model is shown to predict thermorheologically simple behavior. A constitutive equation for non-isothermal flow of polymers is developed with this assumption.     

On the viscosity-temperature behavior of polymer melts

Based on the free volume concept and the equation by Doolittle, an empirical equation is offered for the flow activation energy, E ^*, for polymer melts for the range of over 150°C above glass transition temperature, T _g. This E ^* represents the temperature coefficient of viscosity for the Newtonian region which is also equal to the value measured at constant shear stress for non-Newtonian flow. Data show that the E ^* of linear polymers approaches a constant value for a temperature range above T _g+150°C. Data on 17 polymers are correlated. The proposed equation for this region predicts the E ^* of polymer melts from the volume expansion coefficient, _l, above T _g and also from the T _g.Correlations have also been developed between E ^* and _l and between E ^* and T _g by simplifying the equation by use of the Simha-Boyer expression. A polymer having a lower _l or higher T _g generally has a higher E ^*. However, more satisfactory results are obtained by calculating E ^* from both _l and T _g. The E ^* calculated is found to agree with measurements within the experimental precision of about ±1 Kcal/mole.The effects of polymer composition, molecular weight, branching and microstructure on E ^* are also discussed. These factors influence E ^* in the way in which they effect _l and T _g.     

A differential constitutive equation for polymer melts

A modification of the Giesekus constitutive equation is derived by incorporating (approximately, via the Peterlin approximation) the finite extensibility of polymer molecules into dumbbell kinetic theory along with the anisotropic hydrodynamic drag suggested by Giesekus. The constitutive equation that is obtained retains much of the simplicity of Giesekus' constitutive equation, but it involves terms that are cubic in the stress as well as those that are quadratic. It is shown that the constitutive equation quantitatively describes the steady elongational viscosity of the IUPAC polymer melt A (including the strain softening of the melt), but it cannot describe the elongational and shear viscosities simultaneously. It is also shown that the constitutive equation satisfies the Lodge-Meissner relation for shear strains less than unity.     

The Intrusion of the Meissen Pluton (Elbe Valley-Zone): Evidence from Geochemical and Isotopic Data

Abstract

Geochemical and mineralogical investigations of plutonic rocks from the Meiβen massif indicate different magmatic evolution trends of the Freital sequence as well as for the central part of the complex Constant ε-Nd_T-345 values of ?1.5 of the Freital sequence and major/trace element data point to a fractional crystallization process. Based on ε-Nd values, ¹⁴⁷Sm/¹⁴⁴Nd ratios as well as on geochemical data affinities to alkali basalts cannot be excluded.

Analogous conclusions have been drawn regarding mineral chemical data [10] and cathodoluminescence spectra of apatite [13]. Assimilation of old continental crust, reflected by relics of apatite and zircon, may be the reason that the ε-Nd values plot at the lower end of the “mantle array”. The pyroxene-monzodiorite from Gröba belongs to the same source environment as the Freital sequence (Nd-characteristics).

The geological evolution of the central part of the studied plutonic complex is completely different to the Freital sequence: most of the intrusions show signatures of open system fractionation processes. The ε-Nd_T-345 value of ?1.46 of the Leuben monzonite indicates a narrow relation to the Freital sequence, whereas the ε-Nd_T-345 value of +2.27 of the Spitzgrund monzonite either reflects the derivation of another basic material then the Freital-type or the participation of other mixing component(s) from geologically young crust.

Fabric and mineral chemical investigations of the porphyry-like granite GII point to a mixing process of basic xenocrysts, resembling the corresponding minerals of the Freital sequence, and granite melts [10]. Large amounts of old zircon cores [11] indicate the inheritance of continental crust components by the Hauptgranit. Isotopic investigations on various granitic samples (GII, Hauptgranit and Riesensteingranit) reflect an increasing trend towards the crustal source(s) of their parental melts. The ε-Nd_T-345 values are ?3.75, ?4.16 and ?6.13, respectively.

Chemical parameters and the ε-Nd_T value of the Riesensteingranit agree with data of granites from the Saxonian Granulite Massif (see e.g. Wand et al. [8]; von Quadt, 1992). Thus, it may be possible that both granite types derived from similar sources.     

分子动力学模拟纯镁熔体凝固过程中结构演化

采用分子动力学模拟方法模拟了在周期性边界条件下由500个原子构成的液态Mg模型系统的凝固过程,分别考察了在5×10^14 K/s、5×10^13 K/s、1×10^13 K/s 、1×10^12 K/s的冷却速率下液态Mg熔体的凝固行为。模拟结果很好地重现了实验值。模拟中原子间作用势采用FS势,结构分析采用径向分布函数、均方位移、系统总能量分析、H-A键对分析技术等方法。结果表明,当冷却速率为5×10^14 K/s时,系统形成以1541键对为主的非晶态结构;当冷却速率分别为5×10^13 K/s、1×10^13 K/s、1×10^12 K/s时,系统形成以1421、1422键对为主的hcp晶态结构;另外,在快速冷却形成非晶的过程中,大部分bcc结构被保留下来,而在慢冷形成晶态的过程中,大部分bcc结构最终演化形成了hcp结构。     

Thermodynamic analysis of LiF-BeF2 and KF-BeF2 melts by a structural model

An earlier structural model for binary silicate melts and glasses is extended to MF-BeF₂ (M = Li, K) systems. The evaluation of the thermodynamic properties as well as the phase diagrams for the binary LiF-BeF₂ system and the integral enthalpy of mixing of the KF-BeF₂ system are carried out with this model. This thermodynamic model is based on the assumption that each alkali fluoride produces the depolymerization of BeF₂ network with a characteristic free energy change. A least squares optimization program permits all available thermodynamic and phase diagram data to be optimized simultaneously. In this manner, data for these binary systems have been analysed and represented with a small number of parameters. The model predicts the chain-length distribution of polymeric ions, even though these are not explicitly treated as structural units of the model. The calculated fluoride polyanion chain-length distribution for the LiF-BeF₂ system is in quantitative agreement with the predictions reported in the literature.