Molecular Theory Of Viscoelasticity Research Articles

A Study on the Relationships between Network Structure and Mechanical Properties of Interpenetrating Polymer Networks-Part I: A New Molecular Theory of Viscoelasticity for Thermoplastic Polyurethane Elastomers

A new molecular theory of nonlinear viscoelasticity for crystallizable thermoplastic polyurethane elastomers (CTPUE) possessing the capability of characterizing the mechanical properties both at small and at large deformations is presented and verified by experimental data. Based on the proposed structure for CTPUE and the mechanism of large deformation, the probability distribution functions of the end-to-end vectors for five kinds of constituent chains were calculated. Also, the free energy of deformation for the microstructures including three kinds of networks and induced crystallites was calculated. The theory successfully related the viscoelastic behaviors to molecular constitution by three important network parameters (C,100, C020 and C200). The constitutive equations for various types of deformation were obtained and the relation of modulus to relaxation time was derived. It provides a theoretical foundation for studying the relations between the structure of networks and the mechanical properties of CTPUE at large deformations.

Mobility anisotropy and nonlinear effects in molecular viscoelasticity theory of linear polymers

Various methods of taking the mobility anisotropy into account in modeling of the behavior of polymer fluids in a simple shear flow are compared. Both the qualitative coincidence of the results of the analysis and the difficulties of quantitatively estimating the anisotropy microparameters on the basis of the available data concerning steady shear are noted. For axial tension the dependence of steady viscosity on tensile stress is considered. This dependence is determined by two independent scalar functions: the slip coefficient and the flow anisotropy coefficient.

Rheology of miscible blends of poly(methyl methacrylate) with poly(styrene- co-acrylonitrile) and with poly(vinylidene fluoride)

The rheological behaviour of miscible blends of poly(methyl methacrylate) (PMMA) with poly(styrene- co-acrylonitrile) (PSAN) and with poly(vinylidene fluoride) (PVDF), in the molten state, was investigated. For this study, both steady and oscillatory shear flow measurements were made for PMMA/PVDF and PMMA/PSAN blends, which were prepared by melt blending in a twin-screw compounding machine. The following observations were made from the experimental results obtained: (1) plots of the logarithm of the zero-shear viscosity (log η ob) versus blend composition show positive deviations from linearity for the PMMA/PSAN blend system, but negative deviations from linearity for the corresponding PMMA/PVDF system, under isothermal conditions; (2) plots of log η ob versus blend composition for the PMMA/PVDF blend system show minimum values at certain blend compositions as the viscosity ratio of the constituent components becomes smaller than a certain critical value and; (3) logarithmic plots of the dynamic storage modulus ( G′) versus the dynamic loss modulus ( G″) for all of the blend compositions lie between those obtained for the constituent components in both of the PMMA/PSAN and PMMA/PVDF blend systems. The experimental results are interpreted by using a molecular viscoelasticity theory recently developed by Han and Kim.

On the use of time-temperature superposition in multicomponent/multiphase polymer systems

Abstract In view of the fact that log G′ versus log G″ plots for homogeneous polymer systems are virtually independent of temperature, we have suggested that before attempting to apply time-temperature superposition to multicomponent and/or multiphase polymer systems, one must first observe whether or not plots of log G′versus log G″ show temperature independence. We have demonstrated that log G′ versus log G″ plots are very sensitive to a variation in the morphological state of multicomponent/multiphase polymer systems (e.g. immiscible polymer blends, microphase-separated block copolymers, liquid crystalline polymers). We have pointed out that whereas the so-called Cole-Cole plot is strictly an empirical correlation, plots of log G′ versus log G″ have a basis of molecular viscoelasticity theory and thus the two are not related to each other.

Rheology and phase behaviour of blends of poly(ethylene oxide) with poly(vinyl acetate) and with poly(vinyl acetate- ran-ethylene)

The dynamic viscoelastic properties of blends of poly(ethylene oxide) (PEO) with poly(vinyl acetate) (PVAc) and with poly(vinyl acetate- ran-ethylene) (PVAE) were measured, using a cone-and-plate rheometer in the oscillatory shear mode. For the study, two grades of PEO, one with weight-average molecular weight M W = 20 000 (PEO20) and the other with M W = 100 000 (PEO100), were used. The PVAE used was found to be amorphous, as determined by differential scanning calorimetry, and it had M W = 12 600, as determined by gel permeation chromatography, and 73.4 wt% vinyl acetate, as determined by elemental analysis. It was found that the amorphous phase of the PEO20/PVAc blend system has one glass transition temperature T g over the entire range of blend compositions, whereas the amorphous phase of the PEO100/PVAc blend system has one T g for blend compositions up to 50 wt% PVAc, but two T g values for blends with greater amounts of PVAc. Melting-point depression measurements were conducted to determine the Flory interaction parameter χ to be: (a) −0.211 for PEO20/PVAc pair; (b) −0.069 for PEO100/PVAc pair; (c) −0.027 for PEO20/PVAE pair; and (d) −0.024 for PEO100/PVAE pair. Our experimental results show that plots of the logarithm of zero-shear viscosity versus blend composition at constant temperature exhibit negative deviations from linearity for the PEO20/PVAc blend system, but positive deviations from linearity for both PEO20/PVAE and PEO100/PVAE blend systems. These experimental observations are interpreted using a molecular viscoelasticity theory recently developed by Han and Kim.

Rheological behavior of homogeneous poly(α-methylstyrene)-block-polystyrene copolymers

Oscillatory shear flow properties of α-methylstyrene)/styrene block copolymers having molecular weights ranging from 120000 to 250000 and different block length ratios prepared by anionic polymerization were measured using a Rheometrics mechanical spectrometer at temperatures ranging from 116 to 251°C. It is concluded that these polymers are homogeneous as determined by DSC and by logarithmic plots of dynamic storage modulus versus dynamic loss modulus. The Stockmayer-Kennedy molecular viscoelasticity theory which was developed on the basis of the Rouse theory was modified using the concept of the tube model

Simple forms of determining equation of concentrated polymer solutions and melts as a consequence of molecular viscoelasticity theory

Simple forms of determining equation of concentrated polymer solutions and melts as a consequence of molecular viscoelasticity theory

The molecular theory of viscoelasticity for thermoplastic elastomer SBS (SIS) at large deformations

A microstructure model for SBS and SIS triblock copolymers with hard domains as multifunctional reinforcing fillers is proposed. Based on this model and proposed mechanism of large deformations, the probability distribution function of the end-to-end vector for each constituent chain and the free energy of deformation for the total networks was calculated by the combination of statistical thermodynamics and kinetics. A new molecular theory of non-linear visco-elasticity for SBS and SIS at large deformations is presented. It is successful in relating the viscoelastic state to molecular constitution by three important parameters (C100,C020, andC200) of the networks. The relations of stress to strain for four types of deformation, the elastic modulus and the constitutive equation for the stress relaxation were derived from this theory. It provides a theoretical foundation for studying the relationships of multiphase network structures and mechanical properties at large deformations. An excellent agreement between the theoretical relationships and experimental data from the experiments and the reference was obtained.

Molecular theory of viscoelasticity for homogeneous block and graft copolymers

Abstract The Rouse-Bueche-Zimm molecular theory of viscoelasticity has been extended to compute the relaxation time spectra of radial block and graft copolymers of various configurations and compositions. The basic assumption of the model is that the effect of foreign blocks and grafts on the relaxation spectrum is attributable to differences in the friction coefficients and submolecular chain dimensions from those of the host chain. In addition, the nearest-neighbor matrix must also be appropriately modified to take into account the nonlinear nature of the chain structure. Relaxation spectra can then be obtained by solving the equation of motion numerically on a computer. The resulting viscoelastic relaxation times of those copolymers are given as a function of copolymer composition, number of side chains, their lengths and the spacings between them. The model is restricted to bulk homogeneous copolymers or those copolymers dissolved in appropriate solvents to preclude microphase separation.

Viscoelastic properties of entangled polymers: Ternary blends of monodisperse homopolymers

In a previous publication from this laboratory, the Rouse-Bueche-Zimm molecular theory of viscoelasticity has been extended by using a transient network model to apply to binary blends of monodisperse polymers with chain entanglements. The dynamics of the entanglements were modeled both by the enhanced frictional coefficients and by the additional elastic couplings. It was recognized that entanglements not only may form between chains of the same lengths (intracomponent entanglements) but also between those of different lengths (intercomponent entanglements). At a given intercomponent entanglement, the longer chain was assumed to have the frictional coefficient of the shorter chain. Similarly, for blends consisting of several monodisperse components with different molecular weights, such modifications are also required to predict their linear viscoelastic behavior. The frequency of these interactions is assumed to be proportional to the weight ratio of the respective component chains in the blend. Equations of motion are formulated for each component and solved numerically for the relaxation time spectra. Linear viscoelastic properties such as the dynamic mechanical moduli, stress relaxation moduli, and zero-shear viscosity can then be computed for these systems by linear summation of those of the components. The reduced steady-state shear compliance of the blends can also be computed from the component relaxation times. Results are found to be in good agreement with experimental data on polystyrene ternary blends.

Viscoelastic Properties of Entangled Polymer. IV. Binary Blends of Monodisperse Homopolymers

In a previous publication from this laboratory, the Rouse‐Bueche‐Zimm molecular theory of viscoelasticity has been extended by using a transient network model to apply to monodisperse polymers with chain entanglements. Effects of the entanglements were modeled both by the enhanced frictional coefficients and by the additional elastic couplings resulting from the transient entanglement network. For binary blends consisting of two monodisperse polymers with different molecular weights, additional modifications are now required to predict their linear viscoelastic behavior. It is recognized that entanglements not only may form between chains of the same length, but also between those of different lengths. For the latter case, the longer chain will in fact have the frictional coefficient of the shorter chain at the point of entanglement. The frequency of such interactions is assumed to be proportional to the weight ratio of the respective component chains in the blend. Equations of motion are formulated for each component and solved numerically for the relaxation spectra. Linear viscoelastic parameters such as the dynamic mechanical moduli, stress relaxation moduli, and zero shear viscosity can then be computed for the blends by linear summation of those of the components. The reduced steady state shear compliance of the blends can also be computed from knowledge of the component relaxation times. Results are found to be in excellent agreement with literature data on polystyrene, poly(dimethyl siloxane), and poly(methyl methacrylate).

Viscoelastic Retardation Time Computations for Homogeneous Block Copolymers

Abstract : The Rouse-Bueche-Zimm molecular theory of viscoelasticity has been extended to compute the retardation time spectra of block copolymers of various configurations and compositions. The basic assumption of the block copolymer model is that the effect of the presence of foreign blocks on the retardation spectrum is due exclusively to the difference in the friction coefficients. Mathematically this modification is accomplished by introducing into the equations of motion a frictional coefficient matrix. Retardation spectra can then be obtained by numerically solving for the eigenvalue spectrum on a computer. Results show that the viscoelastic retardation spectra and maximum retardation times of the block copolymers vary as a function of the block configurations, block composition and the friction coefficient ratio of the blocks.

Viscoelastic relaxation times of a homogeneous block copolymer

AbstractThe molecular theory of viscoelasticity has been modified in a previous publication for homogeneous block copolymers; the theory predicts that the maximum relaxation time of the block copolymer can be computed with the knowledge of submolecular sizes and monomeric friction coefficients. Stress‐relaxation experiments were carried out for two samples of styrene‐(α‐methyl styrene)‐styrene triblock copolymers. Maximum relaxation times were determined from the viscoelastic master curve through the use of procedure X developed by Tobolksy and Murakami. Experimental results were found to be in reasonable agreement with theoretical predictions. The theory also predicts the existence of a singularity in the distribution of relaxation times at very short relaxation times, but as is discussed, this prediction cannot be verified by existing experimental techniques.

A treatment of static and dynamic birefringence in linear amorphous polymers by an extension of the molecular theory of viscoelasticity

Calculations are made of the time and frequency dependence of the bire-fringence of a linear amorphous polymer held at constant extension and subjected to an oscillating extension (or compression) respectively. The method involves an extension of Mooney's version of the molecular theory of viscoelasticity. The birefringence is expressed in terms of a discrete number of relaxation times each of which is related to a normal mode of molecular motion. At constant strain the stress-optical coefficient is predicted to be independent of time. For a sinusoidally imposed strain the birefringence and stress should be in phase and the ratio of birefringence amplitude to stress amplitude should be independent of frequency and equal to the stress-optical coefficient. The frequency and temperature limits of applicability of the analysis are briefly discussed.

A note on the molecular theory of viscoelasticity of polymers

A note on the molecular theory of viscoelasticity of polymers