Nonlinear viscoelastic behavior of styrene‐[ethylene‐(ethylene‐propylene)]‐styrene block copolymer

Studies on the nonlinear viscoelastic behavior of styrene‐[ethylene‐(ethylene‐propylene)]‐styrene block copolymer (SEEPS) were carried out. The nonlinear viscoelastic region was determined through dynamic strain sweep test, and the critical shear strain (γ_c) of transition from linear viscoelastic region to nonlinear viscoealstic region was obtained. The relaxation time and modulus corresponding to the characteristic relaxation modes were also acquired through simulating the linear relaxation modulus curves using Maxwell model, and the damping functions were evaluated. Meanwhile, it is found that the nonlinear relaxation modulus obtained at relatively low shear strains follows the strain–time separation principle, and the damping function of SEEPS can be fit to Laun double exponential model well. Moreover, the successive start‐up of shear behavior, the steady shear behavior, and the relaxation behavior after steady shear were investigated, respectively. The results showed that Wagner model, derived from the K‐BKZ (Kearsley‐Bernstein, Kearsley, Zapas) constitutive equation, could simulate the experiment data well, and in addition, experiment data under the lower shear rates are almost identical with the fitting data, but there exists some deviation for data under considerable high shear rates. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1309–1319, 2006     

Nonlinearity and slip behavior of n-hexadecane in large amplitude oscillatory shear flow via nonequilibrium molecular dynamic simulation

Molecular dynamic simulation is used to investigate the viscoelastic properties of n-hexadecane under oscillatory shear flow. Rheometric simulations of an ultra-thin molecular film are studied and compared with the results of a bulk simulation. Strain amplitude sweep tests at a fixed frequency show that strain thinning (the dynamic modulus monotonically decreases with increasing strain amplitude) exists at extreme strain for both bulk and thin film systems. Fourier analysis is performed to characterize the nonlinear behavior of the viscoelasticity. No even harmonic was found in our study even though wall slip occurs. Furthermore, we show that a Fourier series with odd harmonics can be used to perfectly describe the simulation results by plotting Lissajous loops. Shear wave propagation appears when the frequency is larger than a certain value. Moreover, the molecular orientation and molecular potential energies, including those for bonding potential, intra- and intermolecular van der Waals interactions are plotted against the strain amplitude to examine the changes in the microscopic structures with respect to the macroscopic thermodynamic states.     

Phase behavior actuating morphology and rheological response of polybutadiene/polyisoprene blends under small amplitude oscillatory shear

The morphology evolution and the corresponding linear viscoelastic behavior of the phase-separating polybutadiene （PB）/low vinyl content polyisoprene （LPI） blend have been investigated by phase contrast optical microscopy （PCOM）, small-angle light scattering （SALS） and rheometxy. Two kinds of structure evolutions and rheological responses have been observed. It is found that the co-continuous structure generally gives a power law behavior of the dynamic storage modulus versus frequency and the coarsening of co-continuous structure leads to a decrease of the storage modulus. For the droplet-matrix structure, a platform modulus is observed at the mediate frequencies, followed by the typical terminal relaxation behavior of storage modulus at the extremely low frequencies. The decreasing platform modulus and increasing terminal modulus with the growth of droplets are observed and can be well interpreted by the simplified Palieme model. The platform modulus and terminal modulus at a given frequency are found to be scalable with the phase separation time. Besides, the characteristic relaxation time and domain size of the droplets have been obtained by theology. And it seems that the theologically determined droplet dimensions are consistent with the ones determined by PCOM and SALS.     

Linear shear viscoelasticity of confined,end-attached polymers in a near-theta solvent

Diblock copolymers of polystyrene and polyvinylpyridine, end-attached to mica by the traditional method of selecting one block to be insoluble and the other block to be soluble in the solvent, were studied with surface-force experiments while immersed in trans-decalin, a near-theta solvent for the polystyrene block, with special attention given to the small-amplitude shear viscoelastic response. The relaxation time, defined as the inverse frequency at which the effective loss modulus equaled the effective storage modulus, was studied not only as a function of the film thickness but also as a function of the grafting density. The relaxation times started to slow in direct proportion to diminishing surface separation when the surface separation took the value D ≈ L_o/3 (where L_o is the thickness of the uncompressed end-attached layer). Attempts to make comparisons with available theories met with limited success. To test experimentally the origin of this shear viscoelastic slowdown, similar measurements were made with adsorbed polystyrene with a molecular weight similar to that of the polystyrene moiety of the diblock copolymer, and it was found that high magnitudes of the effective viscoelastic shear moduli appeared only when the compression was much larger. In a control experiment in which interpenetration between opposed end-attached chains was precluded, we also studied the case of adsorbed polystyrene–polyvinylpyridine on one side and a bare mica surface on the other side, and the effective viscoelastic shear forces were reduced by nearly 1 order of magnitude. By inference, in the opposed diblock copolymer systems, we attributed the slowdown of the relaxation times with decreasing film thickness to the interpenetration of end-attached chains. Additional comments are made regarding the ratio of shear forces to compressive forces, which is called the small-strain friction coefficient. This is believed to be the first quantification of the linear-response relaxation time of end-attached polymer layers. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3487–3496, 2005     

Shear-induced structural transformation of pentaethylene glycol <Emphasis Type="Italic">n</Emphasis>-dodecyl ether and lithium perfluorooctane sulfonate mixed-surfactant lamellar solution

The viscoelastic behavior of the shear-induced structural transformation from the lamellar phase to multilamellar vesicles (MLVs) of a mixed-surfactant system was investigated. The transformation was divided into two processes on the basis of the strain dependence of the apparent viscosity. The first stage is a lamellar-to-intermediate structure transformation. It was found that a strain, not an applied shear rate, governed this process. The second stage is an intermediate-to-MLV phase transformation, which was not controlled by the strain. These structure developments were found in the shear-thickening viscosity regime. The MLV phase formed by applying shear flow exhibited shear-thinning viscosity behavior and reversible response to shear flow. The viscoelastic properties of the MLV phase were investigated by dynamic viscoelastic measurements. Under oscillating shear deformation, the amplitude dependence of the dynamic modulus indicated that the viscoelasticity of the MLV depended on the initial structure, such as the number of vesicle shells and the size of the MLV, which is governed by the preshear rate.     

Dynamic bulk and shear relaxation in glassy polymers. I. Experimental techniques and results on PMMA

In this paper the authors describe in detail the experimental techniques for the simultaneous measurement of the dynamic Young's modulus and the dynamic Poisson's ratio, from which the dynamic bulk and shear moduli can be calculated. Experimental results are presented on the effects of temperature, frequency, and tensile strain on these properties of poly(methyl methacrylate) (PMMA). The temperature and frequency effects indicate that the β relaxation in PMMA is not a purely internal motion but is coupled to the bulk.     

Complex shear modulus of concentrated suspensions of solid spherical particles

Starting from the complex shear modulus equation for a dilute suspension system, three new equations are developed for the complex shear modulus of concentrated suspensions of solid spheres. The continuous phase (matrix) and the dispersed particles are treated as viscoelastic materials in the derivation. Complex shear modulus data on suspensions of spherical glass beads in polymeric liquid were obtained experimentally and compared with the predictions of the proposed equations. The proposed equations describe the experimental data reasonably well.     

The instantaneous shear modulus in the shoving model

We point out that the instantaneous shear modulus G(∞) of the shoving model for the non-Arrhenius temperature dependence of viscous liquids' relaxation time is the experimentally accessible high-frequency plateau modulus, not the idealized instantaneous affine shear modulus that cannot be measured. Data for a large selection of metallic glasses are compared to three different versions of the shoving model. The original shear-modulus based version shows a slight correlation to the Poisson ratio, which is eliminated by the energy-landscape formulation of the model in which the bulk modulus plays a minor role.     

Rheological and relaxation properties of MQ copolymers

The rheological properties of MQ copolymer melts are investigated under steady-state shear flow and dynamic oscillatory shear within a wide temperature range. The MQ copolymers are highly branched polycyclic compounds (densely crosslinked nanosized networks) incapable of further intermolecular interactions. The samples have identical chemical compositions, but their detailed molecular structures are different. The polymers under consideration show Newtonian behavior in a wide shear-stress range. The values of viscosity vary considerably with the molecular structure of the copolymers. The generalized frequency dependence of complex dynamic modulus components is constructed with the use of the temperature-frequency superposition method. In a first approximation, the viscoelastic behavior of the materials is satisfactorily described by the Maxwell model with a single relaxation time. In this respect, the studied materials are similar to micellar colloids. The relaxation spectra of the copolymers distinguished by narrow distributions are calculated.     

Compression and shear surface rheology in spread layers of beta-casein and beta-lactoglobulin

We investigate the surface viscoelasticity of beta-lactoglobulin and beta-casein spread surface monolayers using a recently discovered method. Step compressions are performed, and the surface pressure is measured as a function of time. This is a common experiment for surface monolayers. However in our experiments the pressure is recorded by two perpendicular sensors, parallel and perpendicular to the compression direction. This enables us to clearly measure the time relaxation of both the compression and shear moduli, at the same time, in a single experiment, and with a standard apparatus. beta-Lactoglobulin and beta-casein monolayers are interesting because of their importance in food science and because they exhibit universally slow dynamical behavior that is still not fully understood. Our results confirm that the compressional modulus dominates the total viscoelastic response in both proteins. Indeed for beta-casein we confirm that the shear modulus is always negligible, i.e., the layer is in a fluid state. In beta-lactoglobulin a finite shear modulus emerges above a critical concentration. We emphasize that in Langmuir trough dynamic experiments the surface pressure should be measured in both the compression and the perpendicular directions.     

Phase Behavior and Morphology of Poly(Methyl Methacrylate)/Poly(α‐Methyl Styrene‐co‐Acrylonitrile) Blends Under Quiescent and Shear Flow

The kinetics of spinodal decomposition (SD) for the binary blend poly(methyl methacrylate), PMMA, and Poly(α‐methylstyrene‐co‐acrylonitrile), PαMSAN, with 31 wt% AN content (LCST‐type phase diagram) has been thoroughly studied using a time‐resolved light scattering technique. The early stage SD was dominated by a diffusion process and can be well described within the framework of the linearized Cahn‐Hilliard theory. The spinodal temperature could be evaluated from the analysis of the early stage SD based on the Cahn theory. In addition, viscoelastic properties of this system have been systematically investigated at temperatures below and above the LCST phase diagram. The linear viscoelastic properties of the blends were found to be greatly changed by phase separation in the two‐phase regime. This change in the linear viscoelastic properties attributed to an additional contribution of concentration fluctuations to the material functions at the phase separation temperatures. The phase diagram of the blends was also estimated rheologically through the dynamic temperature ramps of G′, G″ and η*. Furthermore, the phase behavior and morphology of this system has been studied under different shear rates using simple shear apparatus and transmission electron microscopy (TEM), respectively.     

Bulk and shear rheology of a symmetric three‐arm star polystyrene

The bulk and shear rheological properties of a symmetric three‐arm star polystyrene were measured using a self‐built pressurizable dilatometer and a commercial rheometer, respectively. The bulk properties investigated include the pressure–volume–temperature behavior, the pressure‐dependent glass transition temperature (T_g), and the viscoelastic bulk modulus and Poisson's ratio. Comparison with data for a linear polystyrene indicates that the star behaves similarly but with slightly higher T_gs at elevated pressures and slightly higher limiting bulk moduli in glass and rubbery states. The Poisson's ratio shows a minimum at short times similar to what is observed for the linear chain. The horizontal shift factors above T_g obtained from reducing the bulk and shear viscoelastic responses are found to have similar temperature dependence when plotted using T ? T_g scaling; in addition, the shift factors also exhibit a similar temperature dependence to linear polystyrene. The retardation spectra for the bulk and shear responses are compared and show that the long time molecular mechanisms available to the shear response are unavailable to the bulk. At short times, the two spectra have similar slopes, but the short‐time retardation spectrum for the shear response is significantly higher than that for the bulk, a finding that is, as yet, unexplained. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Nonlinear Viscoelasticity Raised at Low Temperatures by Intermolecular Cooperation of Bulk Amorphous Polymers

We performed dynamic Monte Carlo simulations of stress relaxation in parallel-aligned and uniaxially stretched bulk amorphous polymers at low temperatures.We observed an extra-slowing down in the early stage of stress relaxation,which causes nonlinear viscoelasticity as deviated from Debye relaxation and Arrhenius-fluid behaviors observed previously at high temperatures.Meanwhile,fluctuation analysis of stress relaxation revealed a substantial increase in the stretch fractions of polymers at the transient periods of high-temperature Debye relaxation.Structural analysis of free volume further revealed the scenario that,at low temperatures,the modulus of polymer entropy elasticity decreases with temperature and eventually loses its competition to the imposed modulus (Deborah number becomes larger than one),and hence upon stress relaxation under constant strains,monomers are firstly accumulated nearby two stretching ends of polymers,resulting in tentative global jamming like physical cross-linking there,and thus retarding the coming transient state of stress relaxation.We concluded that intermolecular cooperation raises physical crosslinking for nonlinear viscoelasticity of polymer stress relaxation as well as the rubbery states unique to bulk amorphous polymers.The new microscopic mechanism of the fluid-rubbery transition of polymers may bring insights into the intermolecular cooperation mechanism of glass transition of small molecules,if the fluid-rubbery transition is regarded as an extrapolation of glass transition from low to high molecular weights.     

Normal stress and shear stress in a viscoelastic liquid under oscillatory shear flow

Normal stress and shear stress of concentrated polystyrene solutions in a chlorinated diphenyl were measured under steady flow and oscillatory shear flow in a Weissenberg rheogoniometer. The normal stress difference was observed to oscillate at double the frequency of the applied shear strain with amplitude proportional to the square of the applied amplitude, while the shear stress was found to oscillate at the same frequency with amplitude proportional to the applied amplitude. A theoretical relation between the displacement of the oscillatory normal stress difference from zero level and the dynamic modulus derived by Lodge and other investigators was confirmed experimentally, and the theoretical predictions of Coleman and Markovitz concerning the relation among steady-flow normal stress difference and dynamic modulus were also confirmed. However, the theoretical predictions of Lodge, of Spriggs, Huppler and Bird, and of Williams on the relation between the amplitude and phase of oscillatory normal stress and those of oscillatory shear stress did not agree with experimental results.     

A New Molecular Theory of Non‐Linear Viscoelasticity for Vitrifiable (or Crystallizable) Thermoplastic Polyurethane Elastomers

The molecular theory of non‐linear viscoelasticity for vitrifiable thermoplastic polyurethane elastomers (VTPUE) is a refinement and extension of viscoelastic theory of thermoplastic elastomers and polyurethanes to glassy transition, a structural model and a mechanism of vitrification for glassy polymers were proposed. Five kinds of constituent chains with Nagai chain constraint consisting of soft‐domains, hard‐domains, and entanglements are used as the elementary structural and statistical ensemble units for the correlation of molecular and phase‐domain structures to the static and dynamic mechanical behaviors. So the influences of non‐Gaussian in character, the phase separation of domain, the network topology of structure, the affined deformation of constituent chains, and the thermal history are all taken into account in the constituent chains of the theory. Free energies of deformation for the VTPUE segment copolymer were calculated by the statistical mechanics with the probability distribution functions of the sizes for the five kinds of constituent chains. Then the static constitutive equations and modulus of four types of deformation and the dynamic shear viscosity, modulus and loss tangent of VTPUE are derived from the proposed theory. The theory is successful in relating the molecular chain parameters C₁₀₀, C₀₂₀, and C₂₀₀ to the constitutive equations and modulus under large deformations and the micro‐domain structure to the complex shear viscosity and modulus and the loss tangent. The dynamic shear modulus and loss tangent of VTPUE are related to the domain structures through the fraction of hard segments (W_h), the molecular weight of soft segment (M_ns), and the growth dimensional parameters of hard and soft domains (β). Two series of linear VTPUE copolymers (ES and ET) with different fractions(W_h) of hard segments and molecular weight (M_ns) of soft segments were prepared. Their static and dynamic mechanical properties were studied by uni‐axial extension and dynamic analysis tests. Then the constitutive equation at uni‐axial extension and the expressions of shear modulus and loss tangent are verified by these experimental data, and excellent agreement between the theory and experiments is achieved. It is shown, that the proposed theory can predict the viscoelastic behavior of vitrifiable thermoplastic polyurethanes.     

Multiscale modeling of viscoelastic properties of polymer nanocomposites

A methodology for simple multiscale modeling of mechanical properties of polymer nanocomposites has been developed. This methodology consists of three steps: (1) obtaining from molecular dynamics simulations the viscoelastic properties of the bulklike polymer and approximating the position-dependent shear modulus of the interfacial polymer on the basis of the polymer-bead mean-square displacements as a function of the distance from the nanoparticle surface, (2) using bulk- and interfacial-polymer properties obtained from molecular dynamics simulations and performing stress–relaxation simulations of the nanocomposites with material-point-method simulations to extract the nanocomposite viscoelastic properties, and (3) performing direct validation of the average composite viscoelastic properties obtained from material-point-method simulations with those obtained from the molecular dynamics simulations of the nanocomposites. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1005-1013, 2005     

Local Transient Jamming in Stress Relaxation of Bulk Amorphous Polymers

Bulk amorphous polymers become stretched and parallel-aligned under loading stress,and their intermolecular cooperation slows down the subsequent stress relaxation process.By means of dynamic Monte Carlo simulations,we employed the linear viscoelastic Maxwell model for stress relaxation of single polymers and investigated their intermolecular cooperation in the stress relaxation process of stretched and parallel-aligned bulk amorphous polymers.We carried out thermal fluctuation analysis on the reproduced Debye relaxation and Arrhenius fluid behaviors of bulk polymers.We found a transient state with stretch-coil coexistence among polymers in the stress relaxation process.Further structure analysis revealed a scenario of local jamming at the transient state,resulting in an entropy barrier for stretch-coil transition of partial polymers.The microscopic mechanism of intermolecular cooperation appears as unique to polymer stress relaxation,which interprets the hydrodynamic interactions as one of essential factors raising a high viscosity in bulk amorphous polymers.Our simulations set up a platform of molecular modeling in the study of polymer stress relaxation,which brought new insights into polymer dynamics and the related mechanical/rheological properties.     

Transport Coefficients Of Ar—Kr Mixtures by Molecular Dynamics Computer Simulation

Abstract

Equilibrium molecular dynamics computer simulations have been used to determine the transport coefficients of model Ar—Kr mixtures, which are represented by Lennard-Jones pair potentials with Lorentz—Berthelot rules for the cross-species interactions. The component self-diffusion and mutual-diffusion coefficients are calculated from time correlation functions and mean square displacements. Time correlation functions are used to evaluate the shear and bulk viscosity, thermal conductivity and the thermal diffusion coefficient (Soret/Dufour coefficient). In the case of the thermal transport coefficients, the partial enthalpy of the two species is required at each state point to define the heat flux rigorously. We obtain this and the partial volume (and species resolved chemical potential) using particle-exchange (and particle insertion) techniques implemented in separate [NPT] simulations at the same state point.

The viscoelasticity of the fluids is characterised by the relaxation times for bulk and shear stress relaxation. The results are for dense liquids close to the triple point temperature and density. Agreement with experiment and previous simulation is particularly good for the density of the mixtures, the shear modulus, shear viscosity, shear stress relaxation time and thermal conductivity. As for the single component noble gas fluids (simulated and experiment) there is a significant qualitative difference in the temperature and, for mixtures, composition dependence of the bulk viscosity.     

Viscoelastic Effects on the Dynamics of Spinodal Decomposition in Binary Polymer Mixtures

Numerical simulations based on the modified time‐dependent Ginzburg‐Landau (TDGL) equation have been performed on the domain growth dynamics of binary polymer mixtures. An elastic relaxation term was introduced into the equation to take the entanglement effects of the polymer chains into account. A cell dynamical scheme (CDS) is employed in this paper to improve the computing efficiency. The dynamics of the phase separation in polymer blends was investigated through to a very late stage. In the system without viscoelastic effects, there exists an apparent early stage, and in the late stage the modified Lifshitz‐Slyozov law and dynamical scaling law are satisfied very well. In the system with viscoelastic effects, there are some unique characteristics. A morphology with a rough interface between the domains is obtained and suppression of order‐parameter fluctuations is observed. The growth behavior of domains was altered, and there exits an intermediate stage between the early and late stage, in which the growth rate of domains slows down drastically. The intermediate stage was prolonged with enhanced entanglement effects. Entanglement effects also enhance the quench‐depth effects on the correlation and diminish the discrimination of correlation induced by criticality. After the relaxation of entanglements, the growth exponents with the model employed in this paper are independent of entanglements and are essentially consistent with the modified Lifshitz‐Slyozov law. In addition, the pair correlation function and the structure function are shown to exhibit the dynamical scaling law at the late stage.