Linear viscoelasticity of a two-dimensional glass-former by stress-fluctuation formalism

Viscoelastic properties of dense colloids are investigated using the stress-fluctuation formalism and equilibrium molecular dynamics simulations. The focus is on a two-dimensional (2D) non-additive Lennard-Jones binary mixture, which is a glass-former. Its behaviour is compared with that of a one-component Lennard-Jones system, which forms a 2D crystal with triangular lattice at low temperatures. The systems are under fixed pressure and temperature conditions. The effects of the mixing, the temperature and the pressure are studied. Calculated functions include the shear modulus relaxation function, the dynamic moduli (storage modulus and loss modulus), the complex compliance and the dynamic viscosity. Both the liquid and the solid (crystal and glass) states are investigated. Qualitative aspects are discussed in the light of simple rheological models.     

Small-angle X-ray scattering from styrene-butadiene-styrene block copolymers

Abstract

A new type of time-dependent and strain-history-dependent viscoelasticity was discovered in semidilute polymer solutions. Dynamic moduli G′ and G″ of 20% and 10% nitrile butadiene rubber (NBR) solutions were recorded as a function of time while oscillatory shear deformations were maintained. The moduli decrease with time was observed only at lower frequencies. The time dependence of G′ was more pronounced than that of G″. At a higher temperature, the time dependence was extended toward higher frequencies also, and the time dependence became stronger. Lowering the concentration of solution gave a similar effect as increasing temperature. After the cessation of oscillations, a slow recovery was observed. The recovery was somewhat faster at the higher temperature. The time-dependent moduli and their recovery were explained by the change and recovery of structures associated with long branches and gels in the NBR. The structure change occurred at higher frequencies also, but it was not observed during the application of oscillation. Only in subsequent measurements at lower frequencies could the structure change be detected. Thus, the change may be regarded as strain history dependent. The mechanism of the structural change was explained with either the entanglement or osmotic pressure models, depending on concentration.     

高压对食品胶溶液流变特性的影响

 经高压处理后,卡拉胶、琼胶、高甲氧基果胶、海藻酸钠、黄原胶和瓜尔豆胶等六种食品胶溶液的粘度变化不同。卡拉胶和琼胶溶液的粘度显著增加,高甲氧基果胶、海藻酸钠和瓜尔豆胶溶液的粘度变化较小,而黄原胶溶液的粘度明显降低。动态粘弹性测量表明,卡拉胶和琼胶溶液的贮藏模量（G′）在高压处理后明显减小,而且G′变得小于G″,这表明卡拉胶和琼胶溶液的弹性变小。高甲氧基果胶、海藻酸钠和瓜尔豆胶溶液的损耗正切值（tan δ=G″/G′）在处理后几乎没有变化,黄原胶溶液的tan δ略微减小。高压处理后食品胶溶液流变特性的不同变化表明,高压处理对食品胶的影响因其种类、胶分子的结构和胶在水溶液中的构象而异。文中对造成这些变化差异的可能原因进行了探讨。     

Linear hydrodynamics and viscoelasticity of nematic elastomers

We develop a continuum theory of linear viscoelastic response in oriented monodomain nematic elastomers. The expression for the dissipation function is analogous to the Leslie-Ericksen version of anisotropic nematic viscosity; we propose the relations between the anisotropic rubber moduli and new viscous coefficients. A new dimensionless number is introduced, which describes the relative magnitude of viscous and rubber-elastic torques. In an elastic medium with an independently mobile internal degree of freedom, the nematic director with its own relaxation dynamics, the model shows a dramatic decrease in the dynamic modulus in certain deformation geometries. The degree to which the storage modulus does not altogether drop to zero is shown to be both dependent on frequency and to be proportional to the semi-softness, the non-ideality of a nematic network. We consider the most interesting geometry for the implementation of the theory, calculating the dynamic response to an imposed simple shear and making predictions for effective moduli and (exceptionally high) loss factors. Received 16 October 2000 and Received in final form 10 December 2000     

Ultrasound-assisted extraction of polysaccharides from Rhododendron aganniphum: Antioxidant activity and rheological properties

In this study, we aimed to optimize the extraction of polysaccharides from the leaves of Rhododendron aganniphum and investigate its rheological properties and antioxidant activity. After optimizing the operating parameters using a Box-Behnken design (BBD), the results showed that the optimal ultrasound-assisted extraction conditions were as follows: extraction temperature, 55 °C; liquid-solid ratio, 25:1; extraction time, 2.2 h; and ultrasound treatment power, 200 W. The optimized experimental yield of polysaccharides by ultrasound-assisted extraction (PUAE) was 9.428%, higher than that obtained by hot water extraction (PHWE) for 12 h at the same liquid-solid ratio and extraction temperature. In the in vitro antioxidant activity tests, PUAE had higher positive radical scavenging activity for hydroxyl, superoxide and 1,1-diphenyl-2-picrylhydrazyl (DPPH) radicals than PHWE. However, PUAE and PHWE solutions had similar intermolecular interactions in the steady-shear flow and dynamic viscoelasticity tests, resulting in similar macroscopic behaviour. With respect to the apparent viscosity, storage modulus (G′) and loss modulus (G″) of PUAE were lower at the same shear rate or angular frequency. All PUAE solutions exhibited non-Newtonian shear-thinning pseudoplastic behaviour that was accurately described by the Carreau model but was better fit by the power-law model at high shear rates (≥1/s), which demonstrated that the variation in the apparent viscosity dependence was greater at higher concentrations and shear rates. The G′ and G″ of the solutions increased as the experimental frequency increased from 0.05 to 500 rad/s under all experimental concentrations, and the modulus crossover point decreased gradually with increasing PUAE concentration. The above results demonstrated that the ultrasound-assisted extraction methods gave a higher yield of polysaccharides from the leaves of R. aganniphum with a shorter extraction time than the hot water extraction method, which could affect the apparent viscosity and dynamic viscoelasticity. PUAE presented good radical scavenging activity for DPPH, superoxide and hydroxyl radicals in vitro and could be used as a natural antioxidant in the food and medical industries.     

Preparation and Rheology of Isocyanate Functionalized Graphene Oxide/Thermoplastic Polyurethane Elastomer Nanocomposites

Using monomer-functionalized nanofiller to prepare polymeric nanocomposites is a promising strategy toward achieving enhanced performance. In this study toluene-2,4-diisocyanate (TDI), one of the monomers used for synthesizing polyurethane, was covalently functionalized on graphene oxide (GO) and then the functionalized GO (TDI-GO) was polymerized with polycaprolactone diol (PCL) via in-situ polymerization, leading to chemically linked polyurethane nanocomposites through the covalent bonds between the isocyanate groups on GO and the hydroxyl-terminated PCL. Fourier transform infrared spectroscopy (FTIR), X-ray photoelectron spectroscopy (XPS), X-ray diffraction (XRD) and dispersion experiments of the nanofillers demonstrated that the TDI was successfully grafted onto the GO. The rheological properties were investigated to establish the structure-property relationships of the nanocomposites. The storage moduli (G’), loss moduli (G”) and complex viscosity (η*) of the samples increased monotonically with TDI-GO content, which is attributed to the strong polymer-filler interactions and the effective dispersion of the nanofillers. Additionally, the tan δ variation with frequency, the intersection of G’ and G”, Han plots, van Gurp-Palmen plots and Cole-Cole plots all showed that the incorporation of TDI-GO decreased the degree of microphase separation and improved the elastic properties of the nanocomposites. We suggest this is related to the enhanced interactions between the polymer and nanofillers, which strongly restricted the mobility and relaxation of the polymer chains.     

High-frequency stress relaxation in semiflexible polymer solutions and networks

We measure the linear viscoelasticity of sterically entangled and chemically cross-linked networks of actin filaments over more than five decades of frequency. The high-frequency response reveals rich dynamics unique to semiflexible polymers, including a previously unobserved relaxation due to rapid axial tension propagation. For high molecular weight, and for cross-linked gels, we obtain quantitative agreement with predicted shear moduli in both amplitude and frequency dependence.     

Micro-Structure and Fracture Behavior of High-Melt-Strength PPs Prepared by Reactive Extrusion

In this study, high-melt-strength polypropylenes (PPs) were prepared by reactive extrusion of PP and varied amount of divinylbenzene in the presence of dicumyl peroxide and an antioxidant, and the dynamic rheological behavior, crystalline morphology, and fracture behavior of the resultant materials were investigated. It was found that at relatively low frequency, with the cross-linking and branching structures increasing, the complex viscosity of the melt of the modified PP increased significantly and then leveled off. The modulus of the melt, particularly the storage modulus, increased. The storage moduli of the melts with higher content of cross-linking and branching structures were higher than the loss modulus in the whole range of testing frequency, indicative of a completely elastic behavior. The crystallinity and the size of spherulites of the modified PP decreased, while the number of spherulites increased. The specific essential work of fracture and the specific non-essential work of fracture of the modified PP were found to be reduced compared with pure PP, but the specific essential work of fracture showed an increasing trend with the cross-linking and branching structures increasing.     

Structural and rheological properties of chitosan semi-interpenetrated networks

The local structure and the viscoelastic properties of semi-interpenetrated biopolymer networks based on cross-linked chitosan and poly(ethylene oxide) (PEO) were investigated by Small Angle Neutron Scattering and rheological measurements. The specific viscosity and the entanglement concentration of chitosan were first determined, respectively, by capillary viscosimetry and steady-state shear rheology experiments performed at different polymer concentrations. Mechanical spectroscopy was then used to study the gelation process of chitosan/PEO semi-interpenetrated networks. By fitting the frequency dependence of the elastic and loss moduli with extended relations of relaxation shear modulus around the sol-gel transition, it was shown that the addition of PEO chains had a significant effect on the viscoelastic properties of aqueous chitosan networks but no effect on the gelation time. The improvement of mechanical properties was in accordance with the correlation length decrease deduced from Small Angle Neutron Scattering experiments.     

Comments on frequency dependent AC conductivity in polymeric materials at low frequency regime

The AC conductivity response in a broad frequency range of disordered materials is of great interest not only for technological applications, but also from a theoretical point of view. The Jonscher's power exponent value, and its temperature dependence, is a very important parameter in dielectric data analysis as well as the physical interpretation of conduction mechanisms in disordered materials. In some cases the power exponent of AC conductivity has been reported to be greater than 1 at the low frequency regime. This fact seems to contradict the universal dynamic response. The present work focuses on the analysis of dielectric spectroscopy measurements in polymeric materials, below ～100 MHz. The apparent power exponent n gets values in the range 0 < n < 1 and is directly related to the characteristics of mobile charges at shorter time scales, in the case of the occurrence of DC conduction and the slowest polarization mechanism that is due to the charge motions within sort length scales, in logε''-logω plot. The emergence of apparent n values in the range 1 ≤ n ≤ 2, for a relatively narrow frequency range, may be attributed to an additional molecular dipolar relaxation contribution at higher frequencies, in logε''-logω plot. The appearance of apparent n values in the range 1 < n ≤ 2, can be assigned to the existence of a well defined minimum between DC conductivity contribution and a molecular dipolar dispersion or between two well separated dielectric loss mechanisms, in logε''-logω plots, above the crossover frequency. In these latter cases, the apparent power exponent n is merely related to the Havriliak-Negami equation shape parameters of the higher frequencies molecular dipolar relaxations.     

Dynamic rheological and dynamic thermomechanical properties of poly(trimethylene terephthalate)/short carbon fibre composites

The dynamic rheology and thermomechanical properties of poly(trimethylene terephthalate) (PTT)/short carbon fibre (CF) composites at different mechanical states were investigated by a rotational rheometer and a dynamic mechanical analyzer (DMA). At molten state, the composite melts were pseudo-plastic fluids, and the complex viscosity of the composite melts decreased much with increasing CF content because of the poor adhesion at the fiber/matrix interface. The viscous behavior was predominant rather than elastic behavior in the composites melt and viscous behavior was increased with increasing CF at low shearing frequency. An apparent slope change in storage modulus and loss modulus plot suggested that a structure change occurred in the melt that was dependent on shearing frequency. At glassy state, the storage modulus increased with increasing CF content, suggesting that CFs had good reinforcing effect on PTT. At glass transition region, the increasing loss modulus indicated a better toughness of the composites, and the elastic behavior was predominant rather than viscous behavior. Moreover, the glass-transition temperatures of the composites increased with 10% CF content. The composites have larger cold-crystallization rate than pure PTT.     

Rayleigh wave at the boundary of an inhomogeneous nonlinear viscoelastic half-space

In the approximation of weak nonlinearity and weak viscosity of the medium, we obtain an equation describing the spectral density of the particle horizontal velocity for a Rayleigh wave propagating along the boundary of a half-space. The coefficients of nonlinear interaction between the wave harmonics are found on the assumption that the third-order elastic moduli arbitrarily depend on the depth. We find expressions for the complex correction to the wave frequency due to small relaxation corrections to the elastic moduli and small variations in the medium density, which arbitrarily depend on the depth as well. The imaginary part of this correction to the frequency determines the decay of the linear Rayleigh wave due to small relaxation corrections to the elastic moduli arbitrarily dependent on the depth. Using numerical simulation (with allowance for the interaction of 500 harmonics), we study distortions of an initially harmonic Rayleigh wave for a particular dependence of variations in the nonlinear moduli on the depth. An integral equation is derived for the nonlinear elastic moduli as functions of the depth. It is shown that for independent spatio-temporal distributions of the viscous moduli, functions determining the dependence of the viscosity on the depth are described by an analogous integral equation. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 3, pp. 212–226, March 2007.     

An elastic,plastic, viscous model for slow shear of a liquid foam

We suggest a scalar model for deformation and flow of an amorphous material such as a foam or an emulsion. To describe elastic, plastic and viscous behaviours, we use three scalar variables: elastic deformation, plastic deformation rate and total deformation rate; and three material-specific parameters: shear modulus, yield deformation and viscosity. We obtain equations valid for different types of deformations and flows slower than the relaxation rate towards mechanical equilibrium. In particular, they are valid both in transient or steady flow regimes, even at large elastic deformation. We discuss why viscosity can be relevant even in this slow shear (often called “quasi-static”) limit. Predictions of the storage and loss moduli agree with the experimental literature, and explain with simple arguments the non-linear large amplitude trends.     

Thermal Cross‐Linking of Poly(Vinyl Methyl Ether). I. Effect of Cross‐Linking Process on the Viscoelastic Properties

Abstract

Thermal cross‐linking of poly(vinyl methyl ether) (PVME) in the absence of cross‐linking agent, was detected rheologically. The linear viscoelastic properties of PVME were found to be greatly changed by the onset of the cross‐linking process. The viscoelastic material functions, such as dynamic shear moduli, G′ and G″, complex shear viscosity, η*, and loss tangent, tan δ, were found to be sensitive to the structure changes during the cross‐linking process and the formation of a three‐dimensional polymer network. At the onset temperature of the cross‐linking process, an abrupt increase in G′, G″, and η* (several orders of magnitude) during dynamic temperature ramps (2°C/min heating rate) was observed with some frequency dependence. The temperature dependence of tan δ was found to be frequency independent at the gel‐point, T _gel, that is, the crossover in tan δ regardless of the value of frequency can be taken as an accurate method for determination of T _gel. The coincidence of G′ and G″ at the gel‐point cannot be considered a general method for evaluation of T _gel due to its high frequency dependence, that is, T _gel determined from the crossover of G′ and G″ in the dynamic temperature ramp at 1 rad/sec is about 20°C less than at 100 rad/sec. Furthermore, a dramatic increase in η₀ above the minimum (“v” shape) was observed at T = T _gel in agreement with the value obtained from tan δ vs. T (190°C). The time–temperature‐superposition principle was found to be valid only for temperatures lower than the T _gel (190°C); the principle failed at T ≥ 190°C. This was clearly seen in the low‐frequency region as a deviation from the terminal slope in the G′ curve. Similar behavior was observed in the modified Cole–Cole analyses (G″ vs. G′) that is, the curves start to deviate at 190°C.     

Measurements of the complex shear modulus of polymers under hydrostatic pressure usina the quartz resonator method

Abstract

The quartz resonator method measures the complex shear modulus or compliance of viscoelastic materials in the frequency range from 50 kHz to 140 MHz at temperatures between ?150°C and 300°C and pressures up to 1 GPa. This method can be applied to viscous fluids or polymer melts -even in their glassy or seminystalline regime.

The phase diagram of poly(diethylsiloxane) PDES (a mesophase polymer) was determined for two samples with different molecular weight at pressures up to 400 MPa and temperatures between 20°C and 100°C. Phase transitions are indicated by a sharp bend in the shear compliance although the volume effect of the mesophase-isotropic transition vanishes around 80 MPa.

The pressure dependence of the glass relaxation process (in PVAc), was studied by measuring the change of the complex shear modulus with pressure at constant temperatures between 95°C and 145°C and pressures up to 600 MPa. Additionally to the relaxation process, also the pressure dependence of the real part of the shear modulus in the glassy region can be determined for testing the dislocation concept in the meandermodell by W. Pechhold.     

Errata

Gelatin/1-allyl-3-methylimidazolium chloride solutions with different gelatin concentrations were prepared by using the ionic liquid 1-allyl-3-methylimidazolium chloride [AMIM]Cl as a solvent. Rheological properties of the gelatin ionic liquid solutions were investigated by steady shear and oscillatory shear measurements. In the steady shear measurements, all gelatin solutions showed a shear-thinning behavior at low shear rates, which we suggest reflect the characteristics of solvent [AMIM]Cl. In the oscillatory shear measurements, the effects of concentration and temperature on solution viscoelasticity were determined. The results show that the storage modulus G′ of gelatin solutions was essentially independent of gelatin concentration and temperature at all frequencies, while the solution viscosity greatly depended on polymer concentration and temperature. The loss modulus G″ increased with increase in concentration and decreased with rising temperature. This indicated that physical origins of elastic and dissipative behaviors were completely different. The influence of dissolved gelatin on the elasticity of solutions seemed to be minor.     

LJ流体非牛顿现象的分子动力学模拟

使用非平衡分子动力学模拟方法研究了单原子LJ流体的非牛顿流变行为,并在系统中分别施加稳态Couette流场和振荡剪切流场.在Couette流场的模拟中,流体出现剪切变稀和法向应力差效应,不同剪切率下的径向分布函数反映了流体分子由于剪切所导致的微观结构变化,通过分析势能函数发现当剪切率增大时,分子间排斥作用增强,吸引作用减弱.在振荡剪切流场的模拟中,发现剪切应力和剪切率之间的相位差随频率增加而增加,随频率增加复数粘度的实部先增大再减小,虚部单调增加,导致虚部粘度相对实部粘度比例增大,弹性模量和粘性模量之比也随频率增加而增加.这三点现象表明LJ流体出现粘弹性行为,且在高频率下,弹性所占比重增大.     

Thermal Cross‐Linking of Poly(Vinyl Methyl Ether). II. Rheological Behavior at the Gel Point

Abstract

Isothermal time evolution measurements at different constant temperatures (170°C, 180°C, and 190°C) over a wide range of frequency for the thermal cross‐linking process of poly(vinyl methyl ether), PVME, have been investigated rheologically. At the onset of cross‐linking (t _onset) the elastic storage modulus, G′, increases abruptly. The magnitude of the elevation in G′ and the value of t _onset were found to be temperature‐dependent. Similar behavior was observed for both the viscous loss modulus, G″ and the complex dynamic viscosity, η*; however, the value of G″ shows a very low sensitivity to the cross‐linking process compared to G′ and η* at the same experimental conditions. The gel point, t _gel, was evaluated from the point of intersection in plots of tan δ vs. curing time for different constant shear frequencies. At the gel point tan δ is no longer frequency‐dependent, and all curves cross‐over, indicating the validity of the Winter–Chambon criterion. The value of t _gel obtained from the coincidence of G′ and G″ was about 10 min longer than that determined from tan δ vs. t, indicating that the crossover of G′ and G″ is not be considered as a general method for evaluation of t _gel. The value of the apparent activation energy of gelation determined from the temperature dependence of t _gel was 74 kJ mol^?1 in good agreement with literature values for other different systems. At the gel point G′ and G″ showed a power law with shear frequency, i.e., G′ ～ G″ ～ ω _n with critical exponents equal to 0.64 and 0.75, respectively, in close agreement with the percolation theory (n = 2/3). The zero shear viscosity, η₀, and the equilibrium shear modulus, G _eq, can also be expressed in power low scaling functions with the relative distance from the gel point, ? i.e., η₀ ～ ?^?k and G _eq ～ ? ^z with k = 1.3 and z = 2.4 in good agreement with the predicted values based on the percolation theory.     

The Great Myths of Rheology Part III: Elasticity of the Network of Entanglements

The dynamic data of polymer melts are analyzed in a novel way, presenting new correlations between the viscosity, G′ and G′′ (the elastic and loss moduli), and strain rate and the implications of the new formulas on our understanding of melt entanglement network elasticity are discussed. In the two previous articles of this series, Part I and Part II, we showed that the existing models valid in the linear viscoelastic deformation range were not adequate to extrapolate to the nonlinear regime, suggesting that the stability of the network of entanglements was at the center of the discrepancies. In this article, we introduce new tools for the analysis of the dynamic data and suggest new ideas for the understanding of melt deformation based on this different focus. In particular, we express classical concepts, such as shear-thinning, melt diffusion or melt elasticity and viscosity, in a different context, that of the existence of a dual-phase interaction, essential to our treatment of the statistics of interaction of the bonds responsible for the system coherence and cohesion. It is within this framework that viscoelasticity parameters emerge and the new view of the deformation of a polymer melt results in a different definition of the entanglement network.