Rheology of polymer brush under oscillatory shear flow studied by nonequilibrium Monte Carlo simulation

The rheological behaviors of polymer brush under oscillatory shear flow were investigated by nonequilibrium Monte Carlo simulation. The grafted chain under oscillatory shear flow exhibited a waggling behavior like a flower, and the segments were found to have different oscillatory phases along the chain contour. Stress tensor was further obtained based on the statistics of sampled configuration distribution functions. The simulation reproduced the abrupt increase of the first normal stress difference N(1) with the flow velocity over a critical value, as observed in the experiment of Klein et al. [Nature (London) 352, 143 (1991)]. However, our simulation did not reproduce the brush thickening with shear velocity increased, which was suggested to be responsible for the abrupt increase of N(1) in the above-mentioned paper. This simulation demonstrates that the increase of normal stress might be an inherent behavior of polymer brush due to chain deformation under flow.     

Multiparticle collision dynamics modeling of viscoelastic fluids

In order to investigate the rheological properties of viscoelastic fluids by mesoscopic hydrodynamics methods, we develop a multiparticle collision (MPC) dynamics model for a fluid of harmonic dumbbells. The algorithm consists of alternating streaming and collision steps. The advantage of the harmonic interactions is that the integration of the equations of motion in the streaming step can be performed analytically. Therefore, the algorithm is computationally as efficient as the original MPC algorithm for Newtonian fluids. The collision step is the same as in the original MPC method. All particles are confined between two solid walls moving oppositely, so that both steady and oscillatory shear flows can be investigated. Attractive wall potentials are applied to obtain a nearly uniform density everywhere in the simulation box. We find that both in steady and oscillatory shear flows, a boundary layer develops near the wall, with a higher velocity gradient than in the bulk. The thickness of this layer is proportional to the average dumbbell size. We determine the zero-shear viscosities as a function of the spring constant of the dumbbells and the mean free path. For very high shear rates, a very weak "shear thickening" behavior is observed. Moreover, storage and loss moduli are calculated in oscillatory shear, which show that the viscoelastic properties at low and moderate frequencies are consistent with a Maxwell fluid behavior. We compare our results with a kinetic theory of dumbbells in solution, and generally find good agreement.     

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.     

Shear viscosity of the ionic liquid 1-n-butyl 3-methylimidazolium hexafluorophosphate [bmim][pf6] computed by reverse nonequilibrium molecular dynamics

Reverse nonequilibrium molecular dynamics and equilibrium molecular dynamics simulations were carried out to compute the shear viscosity of the pure ionic liquid system [bmim][PF 6] at 300 K. The two methods yielded consistent results which were also compared to experiments. The results showed that the reverse nonequilibrium molecular dynamics (RNEMD) methodology can successfully be applied to computation of highly viscous ionic liquids. Moreover, this study provides a validation of the atomistic force-field developed by Bhargava and Balasubramanian ( J. Chem. Phys. 2007, 127, 114510 ) for dynamic properties.     

Non-linear Viscoelastic Rheological Properties of PCC/PEG Suspensions

The shear thinning and shear thickening rheological properties of PCC/PEG suspension were investigated with the increase of oscillatory amplitude stress at different constant frequencies. The results show that the complex viscosity was initially independent of stress amplitude and obvious shear thinning occurred, then dramatic shear thickening took place after reaching the minimum viscosity. Typically, in a constant frequency of 5 rad/s, the elastic modulus, viscous modulus, and tanδ （δ is the out-of-phase angle） vs. the stress amplitude was investigated. It is found that the elastic modulus initially appeared to be independent of stress amplitude and then exhibited a rapid decrease, but the viscous modulus was independent of amplitude stress at lower amplitude stress. After reaching the minimum value the viscous modulus showed a rapid increase. On the other hand, tanδ increased from 0.6 to 92, which indicates that the transition from elastic to viscous had taken place and tanδ showed a steep increase when shear thickening occurred. Lissajous plots are shown for the dissipated energy vs. different maximum stress amplitude in the shear thinning and shear thickening regions. The relationship of dissipated energy vs. maximum stress amplitude was determined, which follows a power law. In the shear thinning region the exponent was 1.91, but it steeply increases to 3.97 in the shear thickening region.     

Study on Non-Newtonian Behaviors of Lennard-Jones Fluids via Molecular Dynamics Simulations

Using nonequilibrium molecular dynamics simulations, we study the non-Newtonian rheological behaviors of a monoatomic fluid governed by the Lennard-Jones potential. Both steady Couette and oscillatory shear flows are investigated. Shear thinning and normal stress effects are observed in the steady Couette flow simulations. The radial distribution function is calculated at different shear rates to exhibit the change of the microscopic structure of molecules due to shear. We observe that for a larger shear rate the repulsion between molecules is more powerful while the attraction is weaker, and the above phenomena can also be confirmed by the analyses of the potential energy. By applying an oscillatory shear to the system, several findings are worth mentioning here:First, the phase difference between the shear stress and shear rate increases with the frequency. Second, the real part of complex viscosity first increases and then decreases while the imaginary part tends to increase monotonically, which results in the increase of the proportion of the imaginary part to the real part with the increasing frequency. Third, the ratio of the elastic modulus to the viscous modulus also increases with the frequency. These phenomena all indicate the appearance of viscoelasticity and the domination of elasticity over viscosity at high oscillation frequency for Lennard-Jones fluids.     

Study of a shear thickening fluid: the suspensions of monodisperse polystyrene microspheres in polyethylene glycol

The monodisperse polystyrene (PS) microspheres were prepared by dispersion polymerization. The rheological properties of shear thickening fluid (STF) based on PS microspheres dispersing in polyethylene glycol with different concentrations were studied through the steady and oscillatory shear at different temperatures, respectively. All suspensions successively present the first shear thinning, the shear thickening, and the second shear thinning. The experimental results indicate that the shear thickening behavior of STF is controlled by the concentration of PS microspheres and temperature, as changed from continuous shear thickening (CST) to discontinuous shear thickening (DST) with increasing solid content or decreasing temperature. The STF is affected by shear rate, temperature, and the viscosity of the dispersed medium, and it is reversible absolutely and presents transient response ability. Both CST and DST behave as dilatancy. The PS microsphere aggregations formed under shear stress may result in the shear thickening in STFs.     

Kinetics of the shear-induced isotropic-to-lamellar transition of an amphiphilic model system: a nonequilibrium molecular dynamics simulation study

The shear-induced isotropic-to-lamellar phase transition in the amphiphilic systems in the vicinity of the quiescent order-to-disorder transition point is investigated by the large-scale parallel nonequilibrium molecular dynamics simulations of simple amphiphilic model systems. There is a shear-induced upward shift of the ordering temperature. The initial isotropic phase orders into a lamellar phase perpendicular to the shear vorticity. The phase diagram as a function of temperature and shear rate is established. The dependency of the ordering transition on interaction strength and shear rate is rationalized by the competition between shear rate and chain relaxation. The time evolution of morphology reveals that the shear-induced ordering proceeds via nucleation and growth, a signature of a first-order phase transition. At low shear rate, a single ordered domain grows after an incubation period. With increasing shear rate ordering speeds up, but eventually develops in a lamellar system with disordered shear bands. The time dependence of the order parameter follows that of the mean-squared end-to-end distance, shear viscosity, and bulk pressure, and follows an Avrami scheme with an Avrami exponent between 2 and 4.     

Shear viscosity of liquid copper at experimentally accessible shear rates: application of the transient-time correlation function formalism

We report on nonequilibrium molecular dynamics (NEMD) simulations results on the shear viscosity of liquid copper, modeled by a many-body embedded-atoms model potential. Because conventional NEMD methods are restricted to very high shear rates (at least of the order of 10(10) s(-1), that is several orders of magnitude larger than those accessible by experiment), previous work only provided access to the response of the fluid in the shear-thinning regime. Using the transient-time correlation function formalism, we show how NEMD simulations can be extended to study the rheological properties of liquid copper subjected to low, experimentally accessible, shear rates. Our results provide a full picture of the rheology of the system, in the Newtonian regime as well as in the shear-thinning regime.     

Shear thinning and shear dilatancy of liquid n-hexadecane via equilibrium and nonequilibrium molecular dynamics simulations: Temperature, pressure, and density effects

Equilibrium and nonequilibrium molecular dynamics (MD) simulations have been performed in both isochoric-isothermal (NVT) and isobaric-isothermal (NPT) ensemble systems. Under steady state shearing conditions, thermodynamic states and rheological properties of liquid n-hexadecane molecules have been studied. Between equilibrium and nonequilibrium states, it is important to understand how shear rates (gamma) affect the thermodynamic state variables of temperature, pressure, and density. At lower shear rates of gamma<1 x 10(11) s(-1), the relationships between the thermodynamic variables at nonequilibrium states closely approximate those at equilibrium states, namely, the liquid is very near its Newtonian fluid regime. Conversely, at extreme shear rates of gamma>1 x 10(11) s(-1), specific behavior of shear dilatancy is observed in the variations of nonequilibrium thermodynamic states. Significantly, by analyzing the effects of changes in temperature, pressure, and density on shear flow system, we report a variety of rheological properties including the shear thinning relationship between viscosity and shear rate, zero-shear-rate viscosity, rotational relaxation time, and critical shear rate. In addition, the flow activation energy and the pressure-viscosity coefficient determined through Arrhenius and Barus equations acceptably agree with the related experimental and MD simulation results.     

Molecular Dynamics of Polymer Composites Using Rheology and Combined RheoNMR on the Example of TiO2-Filled Poly(n-Alkyl Methacrylates) and Trans-1,4-Polyisoprene

The determination of the interplay between polymeric matrices and filler particles in composites is of great interest to understand structure-property relationships and develop predictive theories. To study the molecular dynamics of polymers in composites, model systems based on poly(n-alkyl methacrylates), trans-1,4-polyisoprene (gutta percha), and titania (TiO₂) were prepared and characterized using rheometry and a combined RheoNMR technique. Apparent entanglement molecular weights were obtained from small amplitude oscillatory shear (SAOS) experiments, which are related to the increasing physical cross-link density as a function of the filler content. Large amplitude oscillatory shear (LAOS) experiments were performed and analyzed within the FT-rheometry framework. The filler had a strong impact on the scaling behavior of the normalized third harmonic. A combined RheoNMR technique was used to simultaneously study the molecular dynamics via NMR and the corresponding mechanical response via rheometry. A strong correlation between the macroscopic mechanical properties and microscopic molecular dynamics was found, which might lead to a new understanding of polymer melt dynamics.     

Viscoelasticity of Shear Thickening Fluid Based on Silica Nanoparticles Dispersing in 1-butyl-3-methylimidizolium Tetrafluoroborate

The viscoelasticity of shear thickening fluid (STF), a crucial property in the protective composite applications, with different silica nanoparticle concentrations in ionic liquid, 1-butyl-3-methylimidizolium tetrafluoroborate ([C₄min]BF₄), was studied at different temperatures and with shear frequencies through oscillatory shear, respectively. All STFs present strain thickening behavior. With increasing silica nanoparticle concentration, the critical shear strain for the onset of strain thickening decreased, while the complex viscosity, storage modulus, and loss modulus increased significantly. The critical shear strain increased with an increase of temperature, while the complex viscosity, storage modulus, and loss modulus decreased notably. The critical shear strain was constant with increasing the frequency of strain, while the complex viscosity decreases slightly. The storage modulus and loss modulus were independent with frequency in the strain thickening region. Nanoparticle clusters leading to strain thickening were demonstrated. The viscoelastic response of STFs to varying silica nanoparticle content, temperature, and frequency investigated here will help to design the specific application of STFs in soft protective composites and damping devices.     

Effect of molecular topology on the transport properties of dendrimers in dilute solution at Theta temperature: a Brownian dynamics study

Structure and transport properties of dendrimers in dilute solution are studied with the aid of Brownian dynamics simulations. To investigate the effect of molecular topology on the properties, linear chain, star, and dendrimer molecules of comparable molecular weights are studied. A bead-spring chain model with finitely extensible springs and fluctuating hydrodynamic interactions is used to represent polymer molecules under Theta conditions. Structural properties as well as the diffusivity and zero-shear-rate intrinsic viscosity of polymers with varied degrees of branching are analyzed. Results for the free-draining case are compared to and found in very good agreement with the Rouse model predictions. Translational diffusivity is evaluated and the difference between the short-time and long-time behavior due to dynamic correlations is observed. Incorporation of hydrodynamic interactions is found to be sufficient to reproduce the maximum in the intrinsic viscosity versus molecular weight observed experimentally for dendrimers. Results of the nonequilibrium Brownian dynamics simulations of dendrimers and linear chain polymers subjected to a planar shear flow in a wide range of strain rates are also reported. The flow-induced molecular deformation of molecules is found to decrease hydrodynamic interactions and lead to the appearance of shear thickening. Further, branching is found to suppress flow-induced molecular alignment and deformation.     

Operator splitting algorithm for isokinetic SLLOD molecular dynamics

We apply an operator splitting method to develop a simulation algorithm that has complete analytical solutions for the Gaussian thermostated SLLOD equations of motion [D. J. Evans and G. P. Morriss, Phys. Rev. A 30, 1528 (1984)] for a system under shear. This leads to a homogeneous algorithm for performing both equilibrium and nonequilibrium isokinetic molecular dynamics simulation. The resulting algorithm is computationally efficient. In particular, larger integration time steps can be used compared to simulations with regular Gaussian thermostated SLLOD equations of motion. The utility and accuracy of the algorithm are demonstrated through application to the Weeks-Chandler-Anderson fluid. Although strict conservation of the kinetic energy suppresses thermal fluctuations in the system, this algorithm does not allow simulations at lower shear rates than those normally afforded by older nonequilibrium molecular dynamics simulations.     

Vibrational energy relaxation of a diatomic molecule in a room-temperature ionic liquid

Vibrational energy relaxation (VER) dynamics of a diatomic solute in ionic liquid 1-ethyl-3-methylimidazolium hexafluorophosphate (EMI(+)PF(6) (-)) are studied via equilibrium and nonequilibrium molecular dynamics simulations. The time scale for VER is found to decrease markedly with the increasing solute dipole moment, consonant with many previous studies in polar solvents. A detailed analysis of nonequilibrium results shows that for a dipolar solute, dissipation of an excess solute vibrational energy occurs almost exclusively via the Lennard-Jones interactions between the solute and solvent, while an oscillatory energy exchange between the two is mainly controlled by their electrostatic interactions. Regardless of the anharmonicity of the solute vibrational potential, VER becomes accelerated as the initial vibrational energy increases. This is attributed primarily to the enhancement in variations of the solvent force on the solute bond, induced by large-amplitude solute vibrations. One interesting finding is that if a time variable scaled with the initial excitation energy is employed, dissipation dynamics of the excess vibrational energy of the dipolar solute tend to show a universal behavior irrespective of its initial vibrational state. Comparison with water and acetonitrile shows that overall characteristics of VER in EMI(+)PF(6) (-) are similar to those in acetonitrile, while relaxation in water is much faster than the two. It is also found that the Landau-Teller theory predictions for VER time scale obtained via equilibrium simulations of the solvent force autocorrelation function are in reasonable agreement with the nonequilibrium results.     

Dynamics of attractive vesicles in shear flow

A nonequilibrium molecular dynamics (NEMD) method is employed to study the dynamics of two identical vesicles with attractive interactions immersed in shear flow. The dynamics behaviors of attractive vesicles depend on the attractive interactions and the shear rates simultaneously. There are four motion types for attractive vesicles in shear flow: a coupled-tumbling (CTB) motion, a coupled-trembling (CTR) motion, a collision/rotation mixture (CRM) motion and a separated-tank-treading (STT) motion, which are determined by the competition between the shear flow and the attractive interactions. Furthermore, the dynamics behavior of an individual vesicle shows three main motion types such as tumbling, trembling and tank-treading motions, and relies mainly on the shear rates. Meanwhile, comparisons with rigid vesicles for the dynamics behaviors are made, and the collision/rotation mixture (M) motion isn’t observed for rigid vesicles.     

Static and dynamic properties of the interface between a polymer brush and a melt of identical chains

Molecular-dynamics simulations of a short-chain polymer melt between two brush-covered surfaces under shear have been performed. The end-grafted polymers which constitute the brush have the same chemical properties as the free chains in the melt and provide a soft deformable substrate. Polymer chains are described by a coarse-grained bead-spring model, which includes excluded volume and backbone connectivity of the chains. The grafting density of the brush layer offers a way of controlling the behavior of the surface without altering the molecular interactions. We perform equilibrium and nonequilibrium molecular-dynamics simulations at constant temperature and volume using the dissipative particle dynamics thermostat. The equilibrium density profiles and the behavior under shear are studied as well as the interdigitation of the melt into the brush, the orientation on different length scales (bond vectors, radius of gyration, and end-to-end vector) of free and grafted chains, and velocity profiles. The obtained boundary conditions and slip length show a rich behavior as a function of grafting density and shear velocity.     

Linear Viscoelastic Behavior of Unentangled Polymer Melts via Non‐Equilibrium Molecular Dynamics

Summary: We present and assess the use of non‐equilibrium molecular dynamics (NEMD) simulation method for the direct study of the linear viscoelastic behavior of polymer melts. The polymer melt is modeled by a collection of repulsive, anharmonic multibead chains subjected to small amplitude oscillatory shear flow. We present results for chain lengths below the critical entanglement length and obtain good agreement with theoretical results for the viscoelastic behavior of melts of low molecular weight. The range of oscillation frequencies attainable in the simulation is of a few decades. Thus we use, as in experiments, a time‐temperature superposition rule to extend the frequency domain. As a side result, we confirm the so‐called Cox‐Merz rule.

Snapshot from a non‐equilibrium molecular dynamics (3D) simulation of a polymer melt with 100 chains and 40 beads.     

Molecular dynamic simulations of systems undergoing shear

Non-equilibrium molecular dynamics have been used to simulate, at a molecular level, fluids undergoing planar Couette flow. The results give a microscopic picture of the processes involved in viscoelasticity, shear dilatancy, shear birefringence, normal stress effects and shear thinning behavior. The calculations prove that shear dilatant fluids are not necessarily shear thickening. The results also suggest that the constitutive relations governing non-Newtonian behavior are non-analytic functions of strain rate.The calculations have led directly to the development of non-linear irreversible thermodynamics. This generalization of thermodynamics provides a macroscopic understanding of such processes as shear induced phase changes and the relation of shear dilatancy to shear induced energy changes.