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.     

Relaxation behaviour of stretched polymer melts

The relaxation behaviour of stretched polymer melts is described with the aid of the Lodge-model, in which a finite deformation time is incorporated. The theoretical predictions, based on this model, are in fair agreement with experimental results, at least for relatively small deformations. A simple shift factor is introduced to fit the theoretical and experimental curves in the case of larger deformations.     

Rheological effects of structure formation in polymer melts

The viscosity of a number of molten polystyrenes and polypropylenes obtained in various ways from solutions is found to be very strongly dependent on the history of dissolution of the polymer (the concentration of the solution and the “goodness” of the solvent), and on the presence of certain organic oligomeric compounds in very small amounts. The viscosity of the melt may be orders of magnitude less than that of the original samples. The present discussion of these effects is based on the concept of structure formation in amorphous polymers. The structure formed on the solution appears to be very stable with respect to heating and prolonged standing at elevated temperature, although it (and hence the viscosity) strongly depends on the initial concentration of the solution and the nature of the solvent. The role played by additives, present in amounts of small fractions of a percent, is accounted for by the fact that the melt retains the microheterogeneity of the medium. The material moves without its micromosaic structure being disturbed, and the role of the additives is reduced to surface (with respect to structural elements) phenomena.     

Atomic level picture of stress relaxation in polymer melts

We have been developing a physical picture on the atomic level of stress relaxation in polymer melts by means of computer simulation of the process in model systems. In this article we treat a melt of freely jointed chains, each with N = 200 bonds and with excluded-volume interactions between all nonbonded atoms, that has been subjected to an initial constant-volume uniaxial extension. We consider both the stress relaxation history σ(t) based on atomic interactions, and the stress history σ_e(t; N_R) based on subdividing the chain into segments with N_R bonds each, with each segment regarded as an entropic spring. It is found that at early times σ(t) > σ_e(t; N_R) for all N_R, and that, for the remainder of the simulation, there is no value of N_R for which σ(t) = σ_e(t; N_R) for an extended period; by the end of the simulation σ(t) has fallen just below the value σ_e(t; 50). The decay of segment orientation, 〈P₂(t; N_R)〉, and of bond orientation 〈P₂(t; 1)〉, is computed during the simulation. It is found that the decay of the atom-based stress σ(t) is closely related to that of 〈P₂(t; 1)〉. This result may be understood through the concept of steric shielding. The change in local structure of the polymer melt during relaxation is also studied. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36 : 143–154, 1998     

Models for the dynamics of monodisperse polymer melts based on lateral chain motions

A recently developed model for the dynamics of monodisperse polymer melts of linear chains is briefly reviewed. Within the simplifications inherent in the model, it is found that the obstacles to the motion of a given chain, which are imposed by neighboring chains, do not suppress the lateral chain motion. The model associates a length scale with each obstacle, and compares it with the length scale for chain motion. If the obstacle length is greater than the length scale for chain motion, the obstacle is deemed impassable. The cooperative motion of the mutually impassable obstacles is considered, and this gives rise to predictions that are in excellent agreement with experimental observations. If the model were modified to include the additional complexities of real polymer systems, various features of the model might change. The implications of a number of possible modifications in the model are explored. Specifically, the impact of varying the behavior of the function which determines the fraction of obstacles that are impassable is examined in detail. In addition, in the original model it is assumed that chain memory is relaxed due to the slowing of lateral chain motion by the obstacles imposed by neighboring chains. The effect of the opposite assumption of essentially no memory relaxation is also studied. Finally, the influence of limiting the extent of the correlations between the motions of various chain segments because of finite chain length is also considered. It is found that these features have effects that can largely cancel each other. As a result, a range of lateral motion models, which are consistent with the known phenomenology of these systems, are possible.     

Frequency and molecular-mass-dependent nonexponential proton NMR relaxation in polymer melts

A theoretical treatment of the nonexponential relaxation behavior of the different proton nuclear magnetic resonance (NMR) relaxation processes in polymer melts is presented. Formulas are derived for a three-component model given by two versions and a homogeneous distribution of correlation times. The theoretical results were tested with measurements of T₁, T_2e, and T₂ as functions of frequency and molecular mass in linear fractionated polyethylene samples. While the T₁ relaxation always yields exponential magnetization decays, the T_2e and T₂ measurements show biexponential relaxation behavior. From the calculations it was found that the correlation time of the local motion is independent of the molecular mass, whereas the correlation time of the slowest motional process increases with M^2.8_w for the three-component model and with M^2.2_w for the distribution of correlation times, respectively. © 1992 John Wiley & Sons, Inc.     

Significance of cross correlations in the stress relaxation of polymer melts

According to linear response theory, all relaxation functions in the linear regime can be obtained using time correlation functions calculated under equilibrium. In this paper, we demonstrate that the cross correlations make a significant contribution to the partial stress relaxation functions in polymer melts. We present two illustrations in the context of polymer rheology using (1) Brownian dynamics simulations of a single chain model for entangled polymers, the slip-spring model, and (2) molecular dynamics simulations of a multichain model. Using the single chain model, we analyze the contribution of the confining potential to the stress relaxation and the plateau modulus. Although the idea is illustrated with a particular model, it applies to any single chain model that uses a potential to confine the motion of the chains. This leads us to question some of the assumptions behind the tube theory, especially the meaning of the entanglement molecular weight obtained from the plateau modulus. To shed some light on this issue, we study the contribution of the nonbonded excluded-volume interactions to the stress relaxation using the multichain model. The proportionality of the bonded/nonbonded contributions to the total stress relaxation (after a density dependent "colloidal" relaxation time) provides some insight into the success of the tube theory in spite of using questionable assumptions. The proportionality indicates that the shape of the relaxation spectrum can indeed be reproduced using the tube theory and the problem is reduced to that of finding the correct prefactor.     

Structure transformation behaviour of polymer melts investigated by Brillouin spectroscopy

Colloid and Polymer Science -     

Relaxation spectra of polymer melts from relaxation and steady-state flow data

Accurate measurements of stress relaxation after steady-state flow have been carried out, in the Newtonian flow region, for a polystyrene and a poly(methyl methacrylate) melt, with a cone-and-plate rotational rheometer. From the stress relaxation σ(t) versus t curves the relaxation spectra H were calculated by means of the first approximation equation: \documentclass{article}\pagestyle{empty}\begin{document}$ H = - ({1 \mathord{\left/ {\vphantom {1 {\dot \gamma t)d\sigma {{(t)} \mathord{\left/ {\vphantom {{(t)} d}} \right. \kern-\nulldelimiterspace} d}}}} \right. \kern-\nulldelimiterspace} {\dot \gamma t)d\sigma {{(t)} \mathord{\left/ {\vphantom {{(t)} d}} \right. \kern-\nulldelimiterspace} d}}}\ln t $\end{document}. The shear stress–shear rate curves, σ versus \documentclass{article}\pagestyle{empty}\begin{document}$ {\dot \gamma } $\end{document} were also measured, in large ranges of shear rates, for the same melts, and from these data the relaxation spectra H were obtained by means of equations given by Faucher and Ferry. The Faucher equation, \documentclass{article}\pagestyle{empty}\begin{document}$ H = - \dot \gamma ^2 d{\sigma \mathord{\left/ {\vphantom {\sigma d}} \right. \kern-\nulldelimiterspace} d}\dot \gamma ^2 $\end{document}, has been found to give results which compare satisfactorily with those obtained from the first approximation equation. It has been found that the Ferry equation has to be modified for comparable agreement.     

Transient rheological behaviour of melts of liquid-crystalline polymers compared with that of flexible polymer melts

Transient rheological behaviour of melts of flexible polymers can be described qualitatively by factorable constitutive equations, the functions of which can be obtained by oscillatory and step strain experiments. In start-up experiments thermotropic LCP melts can exhibit very large overshoots of the stresses, followed by minima, after which steady states are reached through damped oscillations of the signals. It is also possible that the normal stress remains periodic for long times, with large amplitudes, as is shown for a nematic copolyester melt that has been squeezed during the gap setting process. These periodicities scale with the number of revolutions of the rotating plate. After cessation of flow the stresses relax quickly to values that may be unequal to zero and dependent on the position in the period of the stresses where flow is stopped. Dynamic experiments reveal that the melts are very elastic in that state.     

Rheological behaviour of polymer systems in the vicinity of critical regions

Flow induced phase separation in polymer solutions can be considered taking into account that mechanical motion proceeds in Minkowski space‐time. The spinodal temperature shift increasing with increase of the shear rate is interpreted as a result of relativistic effects. Relativistic phenomena can play the important role in processes of flow, especially when velocity of kinetic units on microscopic or mesoscopic level approaches some limiting velocity. The role of the value of limiting velocity in manifestation of relativistic effects was considered and changes of properties of polymers were discussed.     

Network theory of the nonlinear behaviour of polymer melts. Simple shear flow

Summary The network model developed in a previous paper is applied to the simple shear flow of polymer melts. The constitutive equation obtained consists of two terms. One of them describes the stress due to the network strands which exist at the onset of the deformation, dissociate during the deformation and result in a single integral constitutive equation with a strain dependent damping function. The formulation of the damping function in invariant form seems to be almost impossible.The second normal stress differenceN ₂ of the model is not zero,but has negative values. According to our model this is a consequence of the deformation dependence of the disentanglement process. The theory is compared with experimental data for a LDPE melt. It is found that the model explains the main features of the shear flow behaviour of the LDPE melt investigated preciously.

---

Zusammenfassung Das Netzwerk-Modell, das in einer vorangegangenen Arbeit entwickelt wurde, wird für die einfache Scherströmung von Polymerschelzen angewendet. Die abgeleitete rheologische Zustandsgleichung besteht aus zwei Gliedern. Das erste beschreibt die Spannung-Dehnung-Beziehung der Kettensegmente, die zu Beginn der Deformation existieren und während der Deformation aufgelöst werden. Es hat die Form der einfachen Integralbeziehung mit einer Gedächtnisfunktion. Es ist kaum möglich, die dabei erhaltene Gedächtnisfunktion als Funktion der Invarianten der der Tensoren darzustellen. Die zweite Normal-SpannungsdifferenzN ₂ des Modells ist nicht Null und hat einen negativen Wert. Dies ist nach unserem Modell eine Folge der Deformationsabhängigkeit des Entschlaufungsprozesses. Die Theorie wird mit dem experimentellen Daten für eine LDPE-Schmelze verglichen, wobei sich zeigt, daß das Modell die wesentlichen Merkmale des Scherverhaltens der LDPE-Schmelze gut erklärt.

     

Deuteron and proton spin-lattice relaxation dispersion of polymer melts: intrasegment, intrachain, and interchain contributions

Proton and deuteron field-cycling NMR relaxometry was applied to deuterated and undeuterated bulk polyethyleneoxide and polybutadiene melts and mixtures thereof with molecular weights above the critical value. Spin-lattice relaxation data due to intrasegment (quadrupolar) couplings and intra- and interchain (dipolar) interactions were evaluated. Diverse dynamic limits are identified both with the proton and deuteron frequency dispersion data. The comparison between the intrachain and the interchain contributions leads to the conclusion that only model theories based on largely isotropic chain dynamics can account for the experimental findings. The extremely anisotropic character of the well-known tube/reptation model is too restrictive in this respect.     

Universal scaling, dynamic fragility, segmental relaxation, and vitrification in polymer melts

Our theory of dynamic barriers, slow relaxation, and the glass transition of polymers melts is numerically applied using parameters relevant to real materials. The numerical results are found to be in qualitative agreement with all the approximate analytic expressions previously derived with quantitative differences on the order of approximately 20-30% or much less. The analytic prediction of a universal temperature dependence of the alpha relaxation time, and its intimate connection with the idea of a nearly universal crossover time, is established. Inter-relations between the breadth of the deeply supercooled regime, two definitions of the dynamic fragility, and the magnitude of the fast local Arrhenius process at the glass transition temperature are demonstrated and system-specific limitations identified. A quantitative application to segmental relaxation over 16 orders of magnitude in a polyvinylacetate melt yields encouraging results regarding the accuracy of the theory. The theoretical relaxation time results are well fit by multiple empirical forms (generally containing an assumed singular aspect) using parameters consistent with experimental studies. No physical significance is ascribed to this finding, but it does provide additional support for the temperature dependence of the alpha relaxation process predicted by the theory.     

A model for the plateau in the relaxation modulus for linear chain polymer melts

A simple model is considered for the free energy associated with the relaxation of a linear chain polymer melt. The relaxation of the chain configurations results in an adjustment of the locations of the interchain contacts. The change in the distribution of the positions of the contacts between a pair of relaxing chains is hindered by the presence of other nearby chains in the melt. There is less configuration space available to the relaxing chains, due to the noncrossability of the chain backbones, than would be the case for phantom chains. This results in an increase in the free energy of the relaxing system. The analysis presented indicates that, given the free energy models considered, the extent of relaxation decreases as the length scale for relaxation increases. This results in a plateau in the relaxation modulus. This qualitative prediction of a plateau does not rely on the assumption of a specific mechanism for the chain dynamics, and is relatively insensitive to the form chosen for the terms in the free energy. If reasonable assumptions are made concerning the form of the free energy, then it is shown that the plateau which results depends on monomer length, Kuhn length, the monomer density for the melt, and, for solutions, the polymer concentration in a manner consistent with experimental data.     

Non-Newtonian behavior of polydisperse polymer melts as a consequence of the evolution of their relaxation spectra

The non-Newtonian flow of polydisperse polymer melts is shown to be described by a model according to which an increase in the shear rate leads to the suppression of the dissipative losses of the relaxation modes of each fraction. The higher the shear rate, the greater the suppression. The relaxation spectrum of each monodisperse fraction is represented by the Rouse distribution, and only this form of spectrum leads to a ??spurt?? effect at the critical shear stress. Hence, the physical content of the model that relates the non-Newtonian behavior of polymer melts to their molecular-mass distributions consists in the fact that the relaxation modes responsible for energy dissipation are gradually truncated from the side of high relaxation times. The higher the M of a given fraction, the greater the contribution of this part of the spectrum to the total viscous losses. In this case, the truncation of the spectrum from the side of high relaxation times is equivalent to the gradual ??elimination?? of high-molecular-mass fractions of the polydisperse polymer from the contribution to dissipation. The shear-rate-dependent evolution of the relaxation spectrum of the medium is the structural mechanism that causes the non-Newtonian flow of polymer melts. The efficiency of the proposed model is shown through calculation of the flow curves for polymers with known molecular-mass distributions. The calculation results are in agreement with the experimental data. The theoretical ideas developed with the use of the ?? function to describe molecular-mass distributions have made it possible to solve the inverse problem, i.e., to establish a quantitative relationship between the shape of the flow curve and the molecular-mass distribution and, thus, to calculate the molecular-mass distributions according to the shearrate dependence of the apparent viscosity.