Structural relaxation and rheological response of a driven amorphous system

The interplay between the structural relaxation and the rheological response of a simple amorphous system {a 80:20 binary Lennard-Jones mixture [W. Kob and H. C. Andersen, Phys. Rev. Lett. 73, 1376 (1994)]} is studied via molecular dynamics simulations. In the quiescent state, the model is well known for its sluggish dynamics and a two step relaxation of correlation functions at low temperatures. An ideal glass transition temperature of Tc=0.435 has been identified in the previous studies via the analysis of the system's dynamics in the framework of the mode coupling theory of the glass transition [W. Kob and H. C. Andersen, Phys. Rev. E 51, 4626 (1995)]. In the present work, we focus on the question whether a signature of this ideal glass transition can also be found in the case where the system's dynamics is driven by a shear motion. Indeed, the following distinction in the structural relaxation is found: In the supercooled state, the structural relaxation is dominated by the shear at relatively high shear rates gamma, whereas at sufficiently low gamma the (shear-independent) equilibrium relaxation is recovered. In contrast to this, the structural relaxation of a glass is always driven by shear. This distinct behavior of the correlation functions is also reflected in the rheological response. In the supercooled state, the shear viscosity eta decreases with increasing shear rate (shear thinning) at high shear rates, but then converges toward a constant as the gamma is decreased below a (temperature-dependent) threshold value. Below Tc, on the other hand, the shear viscosity grows as eta proportional, etax 1/gamma, suggesting a divergence at gamma=0. Thus, within the accessible observation time window, a transition toward a nonergodic state seems to occur in the driven glass as the driving force approaches zero. As to the flow curves (stress versus shear rate), a plateau forms at low shear rates in the glassy phase. A consequence of this stress plateau for Poiseuille-type flows is demonstrated.     

Influence of strain on transport in dense Lennard-Jones systems

We study the shear stress relaxation and temperature dependence of the diffusion coefficient, viscosity, and thermal conductivity along a high-density Lennard-Jones isochore of the reduced density of 1.0, as it crosses the freezing and melting lines, in equilibrium and under constant strain.     

Electrorheological fluids based on glycerol-activated titania gel particles and silicone oil with high yield strength

This article describes an electrorheological (ER) fluid based on glycerol-activated titania organic-inorganic hybrid gel particles and silicone oil with high yield strength. Based on a physical picture of a water-activated ER system, glycerol that has a high dielectric constant and boiling point is in situ prepared in the amorphous titania gel during the sol-gel processing. A small amount of ionic surfactant hexadecyltrimethylammonium bromide (CTAB) is employed to enhance charge carriers in particles. FTIR and XRD techniques are used to determine the nature and structure of the hybrid gel. Rheology test results show that a large static yield stress greater than 12.6 kPa is obtained when 3 kV/mm dc electric field is applied. This value is close to the value predicted by H. Conrad (MRS Bull. 8 (1998) 35) in theory. Furthermore, dynamic shear stress as a function of shear rate and temperature is also investigated. This ER fluid exhibits strong temperature dependence and a wide working temperature range from 0 to 120 degrees C, while its leaking current density is still low. More interesting is that the glycerol content is demonstrated to have an influence on ER effect and temperature dependence. Measurement of the dielectric properties of ER fluids shows enhancement of the dielectric constant and dielectric loss due to addition of glycerol and a regular dependence of them on temperature, which well explains the strong ER effect.     

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.     

Two-Gaussian excitations model for the glass transition

We develop a modified "two-state" model with Gaussian widths for the site energies of both ground and excited states, consistent with expectations for a disordered system. The thermodynamic properties of the system are analyzed in configuration space and found to bridge the gap between simple two-state models ("logarithmic" model in configuration space) and the random energy model ("Gaussian" model in configuration space). The Kauzmann singularity given by the random energy model remains for very fragile liquids but is suppressed or eliminated for stronger liquids. The sharp form of constant-volume heat capacity found by recent simulations for binary mixed Lennard-Jones and soft-sphere systems is reproduced by the model, as is the excess entropy and heat capacity of a variety of laboratory systems, strong and fragile. The ideal glass in all cases has a narrow Gaussian, almost invariant among molecular and atomic glassformers, while the excited-state Gaussian depends on the system and its width plays a role in the thermodynamic fragility. The model predicts the possibility of first-order phase transitions for fragile liquids. The analysis of laboratory data for toluene and o-terphenyl indicates that fragile liquids resolve the Kauzmann paradox by a first-order transition from supercooled liquid to ideal-glass state at a temperature between T(g) and Kauzmann temperature extrapolated from experimental data. We stress the importance of the temperature dependence of the energy landscape, predicted by the fluctuation-dissipation theorem, in analyzing the liquid thermodynamics.     

Lattice Boltzmann simulation of particles agglomeration and rheology in a particulate flow

The dynamics and rheology of particles in a Newtonian fluid subjected to shear are simulated using Lattice Boltzmann Method. A computationally-efficient Smoothed Profile Method is used to resolve fluid-solid interactions, and the Lennard-Jones inter-particle potential is implemented to account for inter-particle forces. The use of a bi-periodic computational domain with Lees-Edward boundary conditions allows simulation for systems consisting of a large number of particles under shear. The method is validated for single and dual particle problems and an analysis is performed for multi-particle problems under a range of shear rates and particle fractions. The introduction of particle-particle interactions, which are physically important in many engineering processes, is found to have a considerable impact on the dynamics, agglomeration and rheology. The total stress exhibits high unsteadiness primarily due to the solid component contribution, at higher particle fractions. The simulations underscore the complex interplay between shear, interparticle forces and agglomeration and the complex dependencies of the rheological properties.     

The origin of persistent shear stress in supercooled liquids

The persistence of shear stress fluctuations in viscous liquids is a direct consequence of the non-zero shear stress of the local potential minima which couples stress relaxation to transitions between inherent structures. In simulations of 2D and 3D glass forming mixtures, we calculate the distribution of this inherent shear stress and demonstrate that the variance is independent of temperature and obeys a power law in density. The inherent stress is shown to involve only long wavelength fluctuations, evidence of the central role of the static boundary conditions in determining the residual stress left after the minimization of the potential energy. A temperature T(η) is defined to characterise the crossover from stress relaxation governed by binary collisions at high temperatures to low temperature relaxation dominated by the relaxation of the inherent stress. T(η) is found to coincide with the breakdown of the Stokes-Einstein scaling of diffusion and viscosity.     

Modified free volume theory of self-diffusion and molecular theory of shear viscosity of liquid carbon dioxide

In previous work on the density fluctuation theory of transport coefficients of liquids, it was necessary to use empirical self-diffusion coefficients to calculate the transport coefficients (e.g., shear viscosity of carbon dioxide). In this work, the necessity of empirical input of the self-diffusion coefficients in the calculation of shear viscosity is removed, and the theory is thus made a self-contained molecular theory of transport coefficients of liquids, albeit it contains an empirical parameter in the subcritical regime. The required self-diffusion coefficients of liquid carbon dioxide are calculated by using the modified free volume theory for which the generic van der Waals equation of state and Monte Carlo simulations are combined to accurately compute the mean free volume by means of statistical mechanics. They have been computed as a function of density along four different isotherms and isobars. A Lennard-Jones site-site interaction potential was used to model the molecular carbon dioxide interaction. The density and temperature dependence of the theoretical self-diffusion coefficients are shown to be in excellent agreement with experimental data when the minimum critical free volume is identified with the molecular volume. The self-diffusion coefficients thus computed are then used to compute the density and temperature dependence of the shear viscosity of liquid carbon dioxide by employing the density fluctuation theory formula for shear viscosity as reported in an earlier paper (J. Chem. Phys. 2000, 112, 7118). The theoretical shear viscosity is shown to be robust and yields excellent density and temperature dependence for carbon dioxide. The pair correlation function appearing in the theory has been computed by Monte Carlo simulations.     

Statistical-mechanical theory of rheology: Lennard-Jones fluids

The generalized Boltzmann equation for simple dense fluids gives rise to the stress tensor evolution equation as a constitutive equation of generalized hydrodynamics for fluids far removed from equilibrium. It is possible to derive a formula for the non-Newtonian shear viscosity of the simple fluid from the stress tensor evolution equation in a suitable flow configuration. The non-Newtonian viscosity formula derived is applied to calculate the non-Newtonian viscosity as a function of the shear rate by means of statistical mechanics in the case of the Lennard-Jones fluid. For that purpose we have used the density-fluctuation theory for the Newtonian viscosity, the modified free volume theory for the self-diffusion coefficient, and the generic van der Waals equation of state to compute the mean free volume appearing in the modified free volume theory. Monte Carlo simulations are used to calculate the pair-correlation function appearing in the generic van der Waals equation of state and shear viscosity formula. To validate the Newtonian viscosity formula obtained we first have examined the density and temperature dependences of the shear viscosity in both subcritical and supercritical regions and compared them with molecular-dynamic simulation results. With the Newtonian shear viscosity and thermodynamic quantities so computed we then have calculated the shear rate dependence of the non-Newtonian shear viscosity and compared it with molecular-dynamics simulation results. The non-Newtonian viscosity formula is a universal function of the product of reduced shear rate (gamma*) times reduced relaxation time (taue*) that is independent of the material parameters, suggesting a possibility of the existence of rheological corresponding states of reduced density, temperature, and shear rate. When the simulation data are reduced appropriately and plotted against taue*gamma* they are found clustered around the reduced (universal) non-Newtonian viscosity formula. Thus we now have a molecular theory of non-Newtonian shear viscosity for the Lennard-Jones fluid, which can be implemented with a Monte Carlo simulation method for the pair-correlation function.     

Nonequilibrium dynamics in amorphous Si3B3N7

We present extensive numerical investigations of the structural relaxation dynamics of a realistic model of the amorphous high-temperature ceramic a-Si3B3N7, probing the mean-square displacement of the atoms, the bond survival probability, the average energy, the specific heat, and the two-point energy average. Combining the information from these different sources, we identify a transition temperature Tc approximately 2000 K below which the system is no longer ergodic and physical quantities observed over a time t(obs) show a systematic parametric dependence on the waiting time t(w), or age, elapsed after the quench. The aging dynamics "stiffens" as the system becomes older, which is similar to the behavior of highly idealized models such as Ising spin glasses and Lennard-Jones glasses.     

Orientation effects and rheology of short glass fiber-reinforced thermoplastics

The rheology of polyolefines, polyamide 6, and polystyrene-acrylonitrile filled with glass fibers of different concentrations and aspect ratios have been investigated in simple shear flow, capillary rheometry, and uniaxial elongation. A comparison is made with unfilled and glass bead-filled melts. Fiber orientation was investigated by X-ray microradiography.Steady-state viscosities are obtained on fibers aligned parallel to the direction of flow. Entrance pressure losses, the shape of the viscosity function, and the appearance of a yield stress are depending on the fiber aspect ratio. The temperature dependence of the viscosity function is not significantly different from that of the unfilled melt.Transient shear stresses were measured on samples of different initial orientations of the fibers. The change of fiber orientation during shear flow gives rise to a pronounced overshoot of shear stress and normal stress difference. Elastic strains in shear are increased by the fibers but elastic elongational strains are reduced. Mechanisms are proposed to explain the experimental observations.Dedicated to Dr. D. Heinze on the occasion of his 60th birthday.     

Colloids on the frontier of ferrofluids. Rheological properties

This paper is devoted to the steady-state rheological properties of two new kinds of ferrofluids. One of these was constituted by CoNi nanospheres of 24 nm in diameter, whereas the other by CoNi nanofibers of 56 nm in length and 6.6 nm in width. These ferrofluids were subjected to shear rate ramps under the presence of magnetic fields of different intensity, and the corresponding shear stress values were measured. From the obtained rheograms (shear stress vs shear rate curves) the values of both the static and the dynamic yield stresses were obtained as a function of the magnetic field. The magnetoviscous effect was also obtained as a function of both the shear rate and the magnetic field. The experimental results demonstrate that upon magnetic field application these new ferrofluids develop yield stresses and magnetoviscous effects much greater than those of conventional ferrofluids, based on nanospheres of approximately 10 nm in diameter. Besides some expected differences, such as the stronger magnetorheological effect in the case of ferrofluids based on nanofibers, some intriguing differences are found between the rheological behaviors of nanofiber ferrofluids and nanosphere ferrofluid. First, upon field application the rheograms of nanofiber ferrofluids present N-shaped dependence of the shear stress on the shear rate. The decreasing part of the rheograms takes place at low shear rate. These regions of negative differential viscosity, and therefore, unstable flow is not observed in the case of nanosphere ferrofluids. The second intriguing difference concerns the curvature of the yield stress vs magnetic field curves. This curvature is negative in the case of nanosphere ferrofluid, giving rise to saturation of the yield stress at medium field, as expected. However, in the case of nanofiber ferrofluid this curvature is positive, which means a faster increase of the yield stress with the magnetic field the higher the magnitude of the latter. These interesting differences may be due to the existence of strong interparticle solid friction in the case of nanofiber ferrofluids. Finally, theoretical models for the static yield stress of the ferrofluids were developed. These models consider that upon field application the ferrofluid nanoparticles are condensed in drops of dense phase. These drops tend to be aligned along the field direction, opposing the flow of the ferrofluids and being responsible for the static quasielastic deformation and the yield-stress phenomena. By considering the existence of interparticle dry friction only in the case of nanofiber ferrofluids, the developed models predicted quite well not only the magnitude of the static yield stress but also the differences in curvature of the yield stress vs magnetic field curves.     

“Belt-loop” model of chain entanglement

A simple model of an entangled chain is proposed. Statistical properties of the model are examined based on the partition function derived to include geometrical constraints imposed by entanglements. The model chain statistics results, for long chains, in a modified Gaussian function. The new statistics applied in the affine network theory yield stress-strain dependence, which qualitatively agrees with experimental data obtained for uniaxial extension and compression. Non-linear Mooney-Rivlin plots with a maximum appearing in the compression region are predicted for unswollen networks. With increasing swelling, non-linearity decreases. The proposed explanation of these phenomena is based on the restraints imposed on entangled chains, rather than on network junctions, unlike in the Flory-Erman theory. No arbitrary parameters are involved in the model.     

Interfacial rheology of an ultrathin nanocrystalline film formed at the liquid/liquid interface

We report the interfacial properties of monolayers of Ag nanoparticles 10-50 nm in diameter formed at the toluene-water interface under steady as well as oscillatory shear. Strain amplitude sweep measurements carried out on the film reveal a shear thickening peak in the loss moduli (G") at large amplitudes followed by a power law decay of the storage (G') and loss moduli with exponents in the ratio 2:1. In the frequency sweep measurements at low frequencies, the storage modulus remains nearly independent of the angular frequency, whereas G" reveals a power law dependence with a negative slope, a behavior reminiscent of soft glassy systems. Under steady shear, a finite yield stress is observed in the limit of shear rate .gamma going to zero. However, for .gamma > 1 s-1, the shear stress increases gradually. In addition, a significant deviation from the Cox-Merz rule confirms that the monolayer of Ag nanoparticles at the toluene-water interface forms a soft two-dimensional colloidal glass.     

Rheology of concentrated carbon nanotube suspensions

The rheological properties of non-Brownian carbon nanotube suspensions are measured over a range of nanotube volume fractions spanning the transition from semidilute to concentrated. The polymer-stabilized nanotubes are "sticky" and form a quiescent elastic network with a well-defined shear modulus and yield stress that both depend strongly on nanotube volume fraction with different but related critical exponents. We compare controlled-strain-rate and controlled-stress measurements of yielding in shear flow, and we study the effect of slow periodic stress reversal on yielding and the arrest of flow. Our measurements support a universal scaling of both the linear viscoelastic and steady-shear viscometric response. The former allows us to extract the elastic shear modulus of semidilute nanotube networks for values that are near or below the resolution limit of the rheometers used, while the latter provides a similar extrapolation of the yield stress. A simple scaling argument is used to model the dependence of yield stress and elastic modulus on concentration.     

Microscopic in situ observation of the plastic deformation of polybutene-1 films under simple shear

Optical micrographs were obtained in situ during the course of simple shear tests operated on thin films of isotactic polybutene-1 (modification I) and the stress-strain curves were recorded simultaneously. A detailed observation of individual spherulites showed that the radial crystallites perpendicular to the major principal tensile axis of stress are separated by bending and that those inclined on this axis participate in the plastic deformation. It is demonstrated that the simple shear test cannot be performed on polymer films without being perturbated by plastic buckling and by a deformation of the material in the grips. These artefacts do not seriously affect the results concerning the microstructure dependence of the yield stress but make questionable the quantitative interpretation of the plastic regime. A geometric criterion is proposed for the design of shear samples which could undergo the plastic shear strain without side effects.     

The role of pressure in rubber elasticity

We describe a series of molecular dynamics computations that reveal an intimate connection at the atomic scale between difference stress (which resists stretches) and pressure (which resists volume changes) in an idealized elastomer, in contrast to the classical theory of rubber elasticity. Our simulations idealize the elastomer as a "pearl necklace," in which the covalent bonds are stiff linear springs, while nonbonded atoms interact through a Lennard-Jones potential with energy epsilon(LJ) and radius sigma(LJ). We calculate the difference stress t(11)-(t(22)+t(33))/2 and mean stress (t(11)+t(22)+t(33))/3 induced by a constant volume extension in the x(1) direction, as a function of temperature T and reduced density rho(*)=Nsigma(IJ) (3)/nu. Here, N is the number of atoms in the simulation cell and nu is the cell volume. Results show that for rho(*)<1, the difference stress is purely entropic and is in good agreement with the classical affine network model of rubber elasticity, which neglects nonbonded interactions. However, data presented by van Krevelen [Properties of Polymers, 3rd ed. (Elsevier, Amsterdam, 1990), p. 79] indicate that rubber at standard conditions corresponds to rho(*)=1.2. For rho(*)>1, the system is entropic for kT/epsilon(LJ)>2, but at lower temperatures the difference stress contains an additional energy component, which increases as rho(*) increases and temperature decreases. Finally, the model exhibits a glass transition for rho(*)=1.2 and kT/epsilon(LJ) approximately 2. The atomic-scale processes responsible for generating stress are explored in detail. Simulations demonstrate that the repulsive portion of the Lennard-Jones potential provides a contribution sigma(nbr)>0 to the difference stress, the attractive portion provides sigma(nba) approximately 0, while the covalent bonds provide sigma(b)<0. In contrast, their respective contributions to the mean stress satisfy Pi(nbr)<0, Pi(nba)>0, and Pi(b)<0. Analytical calculations, together with simulations, demonstrate that mean and difference stresses are related by sigma(nbr)=-APi(nbr)P(2)(theta(b)), sigma(b)=BPi(b)P(2)(theta(b)), where P(2)(theta(b)) is a measure of the anisotropy of the orientation of the covalent bonds, and A and B are coefficients that depend weakly on rho(*) and temperature. For high values of rho(*), we find that [sigma(nbr)]>[sigma(b)], and in this regime our model predicts behavior that is in good agreement with experimental data of D.L. Quested et al. [J. Appl. Phys. 52, 5977 (1981)] for the influence of pressure on the difference stress induced by stretching solithane.     

Tuning polymer melt fragility with antiplasticizer additives

A polymer-diluent model exhibiting antiplasticization has been developed and characterized by molecular dynamics simulations. Antiplasticizer molecules are shown to decrease the glass transition temperature Tg but to increase the elastic moduli of the polymeric material in the low-temperature glass state. Moreover, the addition of antiplasticizing particles renders the polymer melt a stronger glass-forming material as determined by changes in the characteristic temperatures of glass formation, the fragility parameter D from fits to the Vogel-Folcher-Tamman-Hesse equation, and through the observation of the temperature dependence of the size of cooperatively rearranging regions (strings) in each system. The length of the strings exhibits a weaker temperature dependence in the antiplasticized glass-forming system than in the more fragile pure polymer, consistent with the Adam-Gibbs model of glass formation. Unexpectedly, the strings become increasingly concentrated in the antiplasticizer particles upon cooling. Finally, we discuss several structural indicators of cooperative dynamics, and find that the dynamic propensity (local Debye-Waller factor p) does seem to provide a strong correlation with local molecular displacements at long times. The authors also consider maps of the propensity, and find that the antiplasticized system exhibits larger fluctuations over smaller length scales compared to the pure polymer.