聚乙烯熔体的离散松弛时间谱与熔融指数的关系

该文通过动态线性小振幅剪切震荡实验所得的聚乙烯熔体储能模量Ｇ′（ω）和耗能模量Ｇ″（ω）数据,采用最小二乘法线性回归、正则法和非线性回归法分别计算得到离散松弛时间谱,比较三种方法得到结果的差别,讨论计算参数、温度和材料对离散松驰时间谱影响．     

Rheological properties of polymer melts

A new method of treating experimental data on the viscous and viscoelastic properties of various polymer melts is suggested. The dependence of the apparent viscosity on the molecular weight, temperature and shear stress can be represented as the product of three independent functions, each of them having a single argument. All three functions are universal, at least in first approximation, and the dependence of the apparent viscosity on the variables indicated is determined by two parameters (glass transition temperature and critical molecular weight), characteristic of each homologous polymer series. The viscoelastic characteristics (dynamic, relaxation, creep, as well as relaxation and retardation spectra) of polymer melts are universal in shape in the linear region and contain only one individual polymer parameter, viz., maximum Newtonian viscosity. It is shown that upon normalization of certain nonlinear characteristics with respect to the maximum Newtonian viscosity, they can also be represented in the universal form.     

On continuous relaxation spectrum. Method of calculation

A method of continuous relaxation spectrum calculations based on the Mellin integral transform has been proposed. It was demonstrated that the equivalent results were obtained regardless an experimental viscoelastic function used a base for calculations. It proves the correctness of the proposed method. The obtained relaxation spectrum provides right predictions in calculation of different viscoelastic functions for various polymeric materials regardless their relaxation state.     

Apparent relaxation‐time spectrum cutoff in dilute polymer solutions: An effect of solvent dynamics

The apparent short time cutoff of the relaxation‐time spectrum at surprisingly long times for polymers in solution is a well known but not yet understood observation. To elucidate its origins we revisit viscoelastic and oscillatory flow birefringence data for solutions and melts of two linear polymers (polystyrene and polyisoprene) and present new measurements of oscillatory flow birefringence of the latter. Previous measurements have suggested that the “flexibility” of both polymers in solution is smaller than in the melt on the basis of the breadth of the relaxation‐time spectrum of the solution as compared with that of the melt. Our new measurements have explored a higher effective frequency range than was previously possible. This has allowed us to observe the effect of the rotational relaxation time of the solvent on the dynamics of the solution at high frequencies. To obtain the polymer global motion contribution, one now needs to subtract from the solution properties a frequency‐dependent complex solvating environment contribution. We show that the decrease in apparent “flexibility” for solutions arises from the presence of a solvent that exhibits a rotational relaxation time and thus simple viscoelastic behavior somewhat near the frequency window of the experiment. Although recent predictions of a model for a chain in a solvent with a single relaxation time are in qualitative agreement with our results, our data suggest that the solution results may reflect the influence of solvent on the development of the “entropic spring” forces at short times. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2860–2873, 2001     

Experimental problems and recent results in polymer melt rheometry

Recent developments helped to solve some experimental problems in polymer melt rheometry: By a stability test one can find out whether under test conditions the individual polymer melt is sufficiently long stable. For melts with long relaxation times, an incomplete creep-test followed by recovery is proposed to determine the linear viscoelastic material functions. In a cone-and-plate rheometer, a very constant heating system and the separation of the plate into a central disk and an outer ring allow us to measure the two normal stress differences in viscometric flows also at higher temperatures. For a commercial LCP, a special sample preparation technique is reported. Melt elongation followed by recovery in combination with morphological studies are presented for a polymer blend (PMMA/PS). From the combination of recovery after melt extension and morphology the interface tension between the melts of PS and PMMA can be determined.     

Length-scale dependent relaxation shear modulus and viscoelastic hydrodynamic interactions in polymer liquids

A quantitative theory of hydrodynamic interactions in unentangled polymer melts and concentrated solutions is presented. The study is focussed on the pre-Rouse transient time regimes (t < τ(R), the Rouse relaxation time) where the hydrodynamic response is governed mainly by the viscoelastic effects. It is shown that transient viscoelastic hydrodynamic interactions are not suppressed (screened) at large distances and are virtually independent of polymer molecular mass. A number of transient regimes of unusual and qualitatively different behavior of isotropic and anisotropic hydrodynamic response functions are elucidated. The regimes are characterized in terms of two main length-scale dependent characteristic times: momentum spreading time τ(i) ∝ r(4∕3) and viscoelastic time τ(?) ∝ r(4). It is shown that for t > τ(i) the viscoelastic hydrodynamic interactions can be described in terms of the time or length scale dependent effective viscosity which, for t < τ(R) and/or for r < R(coil), turns out to be much lower than the macroscopic "polymer" viscosity η(m). The theory also involves a quantitative analysis of the length-scale dependent stress relaxation in polymer melts. The general predictions for hydrodynamic interactions in thermostated systems with Langevin friction are obtained as well.     

Flow induced crystallization of long chain branched polypropylenes under weak shear flow

In the present work long chain branched polypropylene (LCB PP) polymers were prepared by linear polypropylene and multi-functional monomer through melt grafting reaction. A quantitative rheological method was adopted to analysis the structure parameters of LCB PP. The effects of chain branched level on the crystallization kinetics of PP were investigated by rheology, differential scanning calorimetry, polarized optical microscope and wide-angle X-ray diffraction. The dynamic viscoelastic properties of LCB PP showed that the increase in the chain branched level caused a typical deviation from the terminal behavior and a different distribution of the melt relaxation spectrum in the long relaxation time regime. It was found that the chain branched level had a significant effect on the flow induced crystallization (FIC) process of PP melts. The crystallization of LCB PP was more sensitive to shear flow than that of linear PP during induced period at low shear rates. This result also indicated that the longer relaxation time of the polymer chains played an important role in the nucleation of PP under shear flow fields. LCB PP with high chain branched level showed accelerated crystallization kinetics in comparison with that with low chain branched level.     

Measurements of relaxation time of a polyethylene melt

A device for measuring the elasticity of polymer melts has been designed by one of us (B. Maxwell). The device was used to obtain the relaxation modulus in shear of a linear polyethylene melt. From these data a discrete relaxation spectrum was derived. The range of the obtained spectrum was confirmed to correspond to the terminal zone of the “entanglement plateau” of the spectrum. The limiting dynamic viscosity (as frequency approaches zero) was obtained by integrating the relaxation modulus with respect to time. The viscosity and its activation energy were found to agree closely with the flow viscosity and the flow activation energy, respectively, involved in capillary flow.     

分数Maxwell模型应用于PTFE松弛模量的研究

用分数Maxwell模型对聚合物PTFE(Polytetrafluoethylene)的应力松弛过程进行了研究. 分数Maxwell模型的渐近行为是确定其参数的基本依据, 但根据实验数据确定的松弛时间与渐近解成立的条件并不自恰. 通过适当选定松弛时间, 利用起始时段的实验数据确定初始松弛指数和松弛模量, 并适当优化末端松弛指数, 分数Maxwell模型可以对粘弹性应力松弛过程给出非常好的描述.     

Nonlinear stress relaxation of a styrene–butadiene random copolymer

The isothermal uniaxial stress relaxation response in the vicinity of the glass-to-rubber transition has been measured for a lightly crosslinked poly(styrene–butadiene) random copolymer, 85% styrene by weight. The volume change during stress relaxation was determined by measuring the time-dependent lateral contraction of the specimen with a Hall-effect proximity detector. The specimen exhibited an instantaneous dilation upon application of the strain and a subsequent time-dependent volume decrease. The stress relaxation behavior and the associated volume relaxation were determined for a variety of strains and temperatures in both the linear and nonlinear viscoelastic regime. As the applied strain was increased the isothermal tensile modulus decreased and the shape of the log(modulus) vs. log(time) curve was altered. At equal levels of strain the tensile modulus exhibited increasing deviations from the linear viscoelastic response as the temperature was decreased. The maximum difference between the nonlinear tensile modulus and the linear viscoelastic response was observed at short times. Subsequently, the nonlinear tensile modulus began to approach the linear viscoelastic modulus with increasing time. Both the instantaneous dilation and the magnitude of the time-dependent part of the volume change increased as the level of applied strain was increased and/or as the temperature was decreased. The observed nonlinearity in the tensile stress relaxation response has been quantitively related to the experimentally measured volume relaxation with a free-volume model.     

Model Theory of Visco-Elastic Properties and Relaxation Spectra of Two Different Interpenetrating Polymer Networks

Dynamic viscoelastic models of the system of two different interpenetrating polymer networks with different topology and type of interactions were used for calculating spectra of relaxation times of the system under consideration. It was shown, that two branches of the relaxation spectrum appear for two models of interpenetrating networks with different components. One of the branches is the branch of the collective motion of double network consisting of two initial interacting networks. Parameters of this branch of relaxation spectrum are defined by both own elastic constants of each of interacting networks and by effective quasi-elastic interactions between two networks. This branch is the low frequency one and is described by broad relaxation time spectrum. The second branch is the high frequency one and characterizes mutual local motions of two interacting networks. The relaxation spectrum of this branch is comparatively narrow and depends on the quasi-elastic constants and mutual friction which is defined by the entanglements of the networks and by its effective rigidity. The second branch does not contain extremely large relaxation times for infinitely large networks.     

Shear rheology of lyotropic liquid crystals: a case study

We have investigated the rheological properties of lyotropic liquid crystals (LCs) formed by self-assembled neutral lipids and water, their relationship with the topology of the structure, and their dependence on temperature and water content. The phase diagram of a representative monoglyceride-water system, determined by combining cross-polarized optical microscopy and small-angle X-ray scattering (SAXS), included four structures: lamellar, hexagonal, gyroid bicontinuous cubic (Ia3d), and double diamond bicontinuous cubic (Pn3m), as well as several regions of two-phase coexistence of some of the above structures. Rheology in the linear viscoelastic regime revealed a specific signature that was characteristic of the topology of each structure considered. The order-order transitions lamellar-to-cubic and cubic-to-hexagonal, as well as the order-disorder transitions from each LC to an isotropic fluid, were easily identified by following the development of the storage and loss moduli, G' and G', respectively. The viscoelastic properties of both bicontinuous cubic phases were shown to be strongly frequency-dependent, following a pseudo-Maxwell behavior, with multiple relaxation times. Cubic-to-cubic transitions were nicely captured by scaling the longest relaxation time, tau, with either temperature or water volume fraction. Therefore, the set of the three main parameters used to establish the rheological behavior of the structure, that is, G', G', and relaxation time, tau, constitutes a consistent ensemble to identify the structures of the liquid crystal. Finally, relaxation spectra, extracted for all liquid crystalline phases, allowed an additional possible identification criterion of the various structures considered.     

Simultaneous monitoring of viscoelastic and dielectric properties of curing epoxy resins using a vibrating electrode

Both dielectric and mechanical dynamic analysis can characterize the curing of epoxy resins. As the reproducibility of this process is poor, data from separate measurements cannot be compared. To allow for a simultaneous measurement of frequency-dependent viscoelastic (0.5–8 kHz) and dielectric (50–800kHz) properties, a vibrating electrode is used. The curing measurements of four different epoxy-amine systems show a frequency-dependent drop in both the dielectric and compliance real parts. Higher frequencies are sensitive to the relaxation of smaller molecules, hence, the step due to vitrification occurs first at higher frequencies. Accompanied by a loss maximum the dielectric step shifts down over four decades to a lower frequency region and appears eventually in the mechanical spectrum. The simultaneous investigation reveals that the dielectric and the longitudinal compliance function have almost the same frequency dependent reaction kinetic behavior. The mechanical time behavior can be extrapolated in the frequency domain by a power law to obtain the dielectric time parameters and vice versa.     

Discrete version of Wiener-Khinchin theorem for Chebyshev’s spectrum of electrochemical noise

A discrete version of Wiener-Khinchin theorem for Chebyshev’s spectrum of electrochemical noise is developed. Based on the discrete version of Wiener-Khinchin theorem, the theoretical discrete Chebyshev spectrum for the Markov random process is calculated. It is characterized by two parameters: the dispersion and the relaxation frequency (or relaxation time). The noise of corrosion process and the noise of recording equipment are measured. Using the theoretical Chebyshev spectrum, the Markov parameters were found both for the noise of the corrosion process and for the noise of the measuring equipment.     

The state of the art in the rheology of polymers: Achievements and challenges

The state of the art in the rheology of polymer fluids (polymer solutions and melts) and filled composites is reviewed. This review includes two parts: analysis of the basic principles for the construction of rheological constitutive equations in terms of the continuum mechanics and finding correlations between the rheological characteristics and molecular structure of polymers on the basis of molecular models. Possible approaches to the formulation of constitutive equations are discussed. Special attention is focused on the correct selection of the form of the elastic potential for rubbery deformations induced under the flow of polymer fluids. The use of a power-law potential leads to the best results. To gain unequivocal results and minimize the number of free constants, viscoelastic characteristics of polymer fluids should be described in terms of a continuous relaxation spectrum as a power-law function limited by the maximum relaxation time. To solve the boundary problems by the selected constitutive equation, analysis of the dynamic stability is required, because the combination of viscosity and elasticity controls the limits of flow upon shear and tensile. Deformation can also lead to changes in the phase state of a polymer system. Furthermore, correct formulation of the boundary conditions is necessary because, in many cases, polymer fluids and, in particular, filled materials tend to efficient slip along walls. The existing molecular models adequately describe the characteristics of monodisperse polymers; however, on passing to polydisperse polymers, the additional use of semiempirical approaches is required. The modern level of experimental studies allows test measurements over a wide range of deformation rates, frequencies, and temperatures. However, in this field, the mainstream tendency in experimental studies is concerned with hybrid methods, which combine direct rheological measurements with optical observations of local structure and its evolution in the material. In this case, various physical principles of measurements are applied. In recent years, much interest has been focused on studying polymer compositions containing nanosized fillers, which are able to produce their structures in melt.     

Relaxation spectra of the electrode impedance

A new analytical form is proposed enabling one to calculate the impedance of systems that contain no inductances. The method is based on breaking the overall impedance into a sum of isolated contours corresponding to a set of intrinsic frequencies of the system. Intrinsic frequencies, which exist in any real system, can be uniquely determined from the frequency characteristics. In this, they advantageously differ from speculative elements of equivalent circuits. For inductionless circuits, sets of intrinsic frequencies are replaced by intrinsic sets of reciprocal relaxation times. This allows one to construct a relaxation spectrum for the system, which describes quantitative contributions made by each relaxation contour to the overall impedance. As a result, one can estimate quantitatively conditions under which the system’s individual parameters may be observed, evaluate the resolving power of the experimental setup, and determine the full information capacity of an experiment (the maximum number of system’s parameters that can be determined).     

Quasielastic light scattering,mutual diffusion and viscoelasticity of polymer solutions

Quasielastic light (QEL) scattering studies of semidilute solutions of polystyrene in benzene and benzene plus diethyl phthalate mixed solvents have been carried out. Comparisons are made between experiment and theoretical results. It is found that the relative amplitude of the viscoelastic modes depends on the coupling parameter β (defined in the text). For the solutions with β=0, no viscoelastic component is observed in the QEL scattering spectrum, consistent with the theoretical prediction. The amplitude and a relaxation time distribution of the viscoelastic component of the QEL scattering spectrum of PS in the mixed solvent are found to depend on time. Steady state values are obtained only after the solution is equilibrated for more than a month. Time evolution of the QEL spectrum has been investigated.     

A RHEOLOGICAL MODEL FOR POLYMER MELTS WITH INTERNAL STRUCTURE IN FLOW FIELDS*

Conceptually, an imagined conformation ellipsoid is supposed to represent the shape of a polymerchain for polymer melts in flow fields and to be equivalent to the volume element in a mathematical sense incontinuum mechanics. A power law dependence of shear modulus of polymer melts on detC, referred to asenvelope volume, is proposed. Based on those assumptions and the non-linear relation of shear modulus, aphenomenological viscoelastic model is derived. The model is tested in simple shear flow, simpleelongational flow, oscillatory shear flow, and relaxation process after flow suddenly stopped. The resultsshow that the model works well to predict the change of internal structure and viscoelastic performance ofpolymer melts in flow fields.