Results Of Nonequilibrium Molecular Dynamics Research Articles

Analyzing and Predicting the Viscosity of Polymer Nanocomposites in the Conditions of Temperature, Shear Rate, and Nanoparticle Loading with Molecular Dynamics Simulations and Machine Learning

Predicting the viscosity (η) of polymer nanocomposites (PNCs) is of critical importance as it governs a dominant role in PNCs' processing and application. Machine-learning (ML) algorithms, enabled by pre-existing experimental and computational data, have emerged as robust tools for the prediction of quantitative relationships between feature parameters and various physical properties of materials. In this work, we employed nonequilibrium molecular dynamics (NEMD) simulation with ML models to systematically investigate the η of PNCs over a wide range of nanoparticle (NP) loadings (φ), shear rates (γ̇), and temperatures (T). With the increase in γ̇, shear thinning takes place as the value of η decreases on the orders of magnitude. In addition, the φ dependence and T dependence reduce to the extent that it is not visible at high γ̇. The value of η for PNCs is proportional to φ and inversely proportional to T below the intermediate γ̇. Using the obtained NEMD results, four machine-learning models were trained to provide effective predictions for the η. The extreme gradient boosting (XGBoost) model yields the best accuracy in η prediction under complex conditions and is further used to evaluate feature importance. This quantitative structure-property relationship (QSPR) model used physical views to investigate the effect of process parameters, such as T, φ, and γ̇, on the η of PNCs and paves the path for theoretically proposing reasonable parameters for successful processing.

First law of thermodynamics on the boundary for flow through a carbon nanotube.

The definition of boundary at the nanoscale has been a matter of dispute for years. Addressing this issue, the nonequilibrium molecular dynamics (NEMD) simulations in this work investigate the flow characteristics of a simple liquid in a single-walled carbon nanotube (SWCNT), and equilibrium molecular dynamics simulations support the range of the NEMD results. The inconsistencies in defining the flow boundary at the nanoscale are understood through the first law of thermodynamics: Local thermodynamic properties (the effects of the density distribution, pressure, viscosity, and temperature) define the boundary. We have selected different boundary positions in the CNT to demonstrate the probability of density distribution that also indicates the coexistence of multiple thermodynamic states. Altering the interaction parameters, we produce convergence between the NEMD result and the no-slip Hagen-Poiseuille assumptions. Meanwhile, the results indicate that the boundary position varies between the innermost solid wall and peak density position of the CNT as a function of the input energy or work done in the system. Finally, we reveal that the ratio between the potential energy barrier and the kinetic energy is proportional to the shift of the boundary position away from the innermost solid wall.

Time reversal symmetry breaking and odd viscosity in active fluids: Green–Kubo and NEMD results

Active fluids, which are driven at the microscale by non-conservative forces, are known to exhibit novel transport phenomena due to the breaking of time reversal symmetry. Recently, Epstein and Mandadapu [arXiv:1907.10041 (2019)] obtained Green-Kubo relations for the full set of viscous coefficients governing isotropic chiral active fluids, including the so-called odd viscosity, invoking Onsager's regression hypothesis for the decay of fluctuations in active non-equilibrium steady states. In this Communication, we test these Green-Kubo relations using molecular dynamics simulations of a canonical model system consisting of actively torqued dumbbells. We find the resulting odd and shear viscosity values from the Green-Kubo relations to be in good agreement with values measured independently through non-equilibrium molecular dynamics flow simulations. This provides a test of the Green-Kubo relations and lends support to the application of the Onsager regression hypothesis in relation to viscous behaviors of active matter systems.

SYNERGISTIC TRIBOLOGICAL PROPERTIES OF SYNTHETIC MAGNESIUM SILICATE HYDROXIDE COMBINED WITH AMPHIPHILIC MOLECULES

This paper reports the synthesis of magnesium silicate hydroxide (MSH) nanoparticles and their synergistic tribological properties combined with amphiphilic molecules (AMs) as additives in base oil. This combination reduces wear losses substantially due to the formation of a double well-arranged molecular layer or tribofilm on the rubbing surfaces under certain test conditions. From the results of nonequilibrium molecular dynamics (NEMD) simulations, lamellate MSH nanoparticles provide a medium for the adsorption of AMs thus further decreasing the contact of rough peaks. In addition, with the increase of load, a tribofilm containing element Mg, Si, O forms on the worn surfaces and greatly improves the anti-wear property of base oil.

Extraction of the solid-liquid friction coefficient between a water-methanol liquid mixture and a non-polar solid crystal surface by Green-Kubo equations

Using equilibrium molecular dynamics (EMD), we analyzed the friction between water-methanol liquid mixtures and a non-polar solid wall. Specifically, we calculated the friction coefficient (FC) from the autocorrelation of the shear force exerted on a liquid from a solid wall using two Green-Kubo (GK) equations proposed by Bocquet and Barrat (BB) [Physical Review E, Vol. 49, (1994), 3079], and Huang and Szulfarska (HS) [Physical Review E, Vol. 89 (2014), 032119], and compared these FC values with those obtained in our previous non-equilibrium molecular dynamics (NEMD) work. Both GK equations reproduced the FC dependence on the methanol concentration in the first adsorption layer XaMeOH observed with NEMD, but the BB method gave a better estimate of the NEMD results with a difference of 20 % at largest. The independent molecular FCs of water and methanol, which were only extractable with the HS method from EMD simulations, corresponded qualitatively well with the NEMD results regarding the dependency on XaMeOH. Though certain discrepancies were observed between the EMD and NEMD results, the EMD had a considerable advantage regarding the computational time required to calculate the FC with a comparable error: the EMD computational time was about 20 times shorter than the NEMD time in the present system.

Simulating the superheating of nanomaterials due to latent heat release in surface reconstruction

Surface reconstruction and phase transformation in nanomaterials can result in a significant rise in temperature due to the release of stored energy called “latent heat.” To simulate this behavior, we propose a hybrid continuum partial differential equation for non-Fourier heat transfer with a stochastic source term modeled using a kinetic Monte Carlo (KMC) algorithm for time-dependent rates to account for the latent heat release as the temperature is changing. The parameters required for the method are obtained through independent atomistic calculations. This includes energy barriers for KMC rates obtained using nudged elastic band calculations, and the non-Fourier thermal parameters obtained using a novel thermal parameter identification scheme described in this paper. As a demonstration of the approach, we study the superheating of silicon nanobeams observed in non-equilibrium molecular dynamics (NEMD) simulations. In these simulations, silicon (001) surfaces undergo a reconstruction from the ideal diamond crystalline surface to a reconstructed structure involving the formation of rows of dimers along a 〈110〉 direction. This reconstruction is accompanied by latent heat release that causes the nanobeam to dramatically superheat. The evolution of the nonuniform temperature profile along the nanobeam predicted by the continuum–KMC method is in excellent agreement with the NEMD results. A logarithmic dependence of the superheating temperature on nanobeam length is observed and theoretically discussed.

Characteristics of thermal conductivity in classical water models

The thermal conductivities of common water models are compared using equilibrium (EMD) and non-equilibrium molecular dynamics (NEMD) simulation. A complete accounting for electrostatic contributions to the heat flux was found to resolve the previously reported differing results of NEMD and EMD Green-Kubo measurements for the extended simple point-charge (SPC/E) model. Accordingly, we demonstrate the influence of long-range electrostatics on the thermal conductivity with a simple coulomb cutoff, Ewald summation, and by an extended particle-particle particle-mesh method. For each water model, the thermal conductivity is computed and decomposed in terms of frequency-dependent thermodynamic and topological contributions. The rigid, three-site SPC, SPC/E, and transferable intermolecular potential (TIP3P-Ew) water models are shown to have similar thermal conductivity values at standard conditions, whereas models that include bond stretching and angle bending have higher thermal conductivities.

Equilibrium molecular dynamics determination of thermal conductivity for multi-component systems

We perform the equilibrium molecular dynamics (EMD) determination of thermal conductivity via the Green-Kubo method for several multi-component systems including gas and liquid mixtures, solid nanoparticle liquid suspension (nanofluids), and a solid alloy. The results are compared against those obtained with the application of the heat source and sink and determination of thermal conductivity from non-equilibrium molecular dynamics (NEMD) and the Fourier's Law. We demonstrate that the proper definition of the heat current in the equilibrium simulations leads to the consistency between the results obtained using the equilibrium and non-equilibrium simulations. In particular, EMD simulations, in agreement with NEMD results, do not predict any significant thermal conductivity enhancement for well-dispersed nanofluids.

Shear viscosity of the Lennard-Jones chain fluid in its gaseous, supercritical, and liquid states

Extensive nonequilibrium molecular dynamics (NEMD) simulations have been carried out in order to estimate the Newtonian shear viscosity of a fluid composed of short chains (up to 16 segments) of jointed spheres [Lennard-Jones chain (LJC)] over a large range of thermodynamic conditions. Using the NEMD results, it is shown that the zero-density contribution decreases with the chain length for a given temperature and is simply proportional to N-1/2 , where N is the number of spheres composing the chain. In addition, it has been noticed that the residual shear viscosity is proportional to the chain length. Then, using these results, a relation is proposed to correlate the shear viscosity of the LJC fluid using the LJ fluid (the monomer) as a reference. It is shown that this correlation is able to provide an excellent estimation of the LJC fluid viscosity compared to NEMD results for N<or=16 over the domain 0<or=rho <or=1.1 and 0.7<or=T <or=6 . Finally, it is shown that the LJC model is unambiguously more efficient than a simple LJ approximation when applied to estimate the shear viscosity of n -butane, if only the sphere or segment diameter is used as an adjustable parameter in both models.

Molecular dynamics of shock-wave induced structural changes in silica glasses

We seek to model the shock wave induced structural changes in silicate glass at the atomic scale. We use both direct shock propagation with nonequilibrium molecular dynamics (NEMD) and bulk simulations in the Hugoniot ensemble to characterize the structure and topology of the shocked glass. Despite the lack of long-range interactions in our model, the close agreement between our structures and those obtained by experimental and simulation studies alike underlines the importance of the role played by first neighbor interactions on the structure of silicate glass. The results obtained from this study show that, in agreement with experimental work, the structure and topology of the shock-induced densified phase is unique in its structure as can be revealed by medium-range order measurements. The modifications include a reduction of the average tetrahedra size and an increase in the proportion of 3--4 and 8--10 membered Si-rings. Application of a Hugoniostat method based on constraint dynamics shows near-perfect agreement with the NEMD results. Besides validating the former method, this opens the prospect of studying shock-induced effects at a fraction of the cost required to run large scale shock simulations while using much more complicated potentials and setups.

Structural and Transport Properties of an SPC/E Electrolyte in a Nanopore

Equilibrium (EMD) and nonequilibrium molecular dynamics (NEMD) simulations were conducted to investigate the effects of confinement on the structural and transport properties of an electrolyte in a nanopore. The extended simple point charge (SPC/E) model was used to model water molecules in a 0.5 M KCl electrolyte. The cylindrical nanopore was smooth, structureless, and hydrophobic with a radius that varied from 4.75 to 15.8 Å. Changes in energies and structures were observed as the nanopore radius varied. The ion−ion, ion−water, and water−water interaction energies, the ion−ion and ion−water pair distribution functions, the density profiles of H and O atoms, and the water orientation about the vertical axis and around an ion were calculated in the simulations. Because of confinement in the radial direction in a narrow pore, there was incomplete solvation of ions, evidenced by less negative ion−water energy and less alignment of water molecules with the field of the ion. With a stronger confinement, H-bonding decreased, whereas the external field had a stronger influence on the orientation of the water molecules. Both EMD and NEMD results showed a decrease of ionic conductivity with decreasing pore radius, but there was an appreciable discrepancy between the conductivities obtained by the two methods for the cases of smaller pore diameters.

Rheological properties of self-associating polymer systems: nonequilibrium molecular dynamics simulation

Abstract We present the results of nonequilibrium molecular dynamics (NEMD) studies of self-associating polymer systems composed of flexible linear telechelic chains with strongly attracting end-groups. Formation of micellar aggregates, their structure and structural characteristics of associative polymer network (micellar gel) are studied under the influence of external shearing forces. Interconnection between structural and rheological properties of the steady-state system is discussed. We find that a critical factor in the shear behavior of self-associating polymers is the space distribution (topology) of chain «bridgesa connecting micellar aggregates. Depending on the topology of the bridges, the system may exhibit shear thickening or shear thinning. Furthermore, the applied external force may cause transitions from continuous (space-filling) associative network, which spans the whole space, to fibrous textures — threadlike objects which align along the shear field. These structural reorganizations lead to dramatic changes in the shear dependent steady-state viscosity.

Distribution functions of a simple fluid under shear: low shear rates.

Anisotropic pair distribution functions for a simple, soft sphere fluid at moderate and high density under shear have been calculated by nonequilibrium molecular dynamics, by equilibrium molecular dynamics with a nonequilibrium potential, and by a nonequilibrium distribution function theory [H. H. Gan and B. C. Eu, Phys. Rev. A 45, 3670 (1992)] and some variants. The nonequilibrium distribution function theory consists of a nonequilibrium Ornstein-Zernike relation, a closure relation, and a nonequilibrium potential and is solved in spherical harmonics. The distortion of the fluid structure due to shear is presented as the difference between the nonequilibrium and equilibrium pair distribution functions. From comparison of the results of theory against results of equilibrium molecular dynamics with the nonequilibrium potential at low shear rates, it is concluded that, for a given nonequilibrium potential, the theory is reasonably accurate, especially with the modified hypernetted chain closure. The equilibrium molecular-dynamics results with the nonequilibrium potential are also compared against the results of nonequilibrium molecular dynamics and suggest that the nonequilibrium potential used is not very accurate. In continuing work, a nonequilibrium potential better suited to high shear rates [H. H. Gan and B. C. Eu, Phys. Rev. A 46, 6344 (1992)] is being tested.

Simulation of self-associating polymer systems. I. Shear-induced structural changes

We present the results of nonequilibrium molecular dynamics (NEMD) studies of self-associating polymer systems composed of flexible telechelic chains with associating end-groups (“stickers”). Formation of micellar aggregates, their structure and structural characteristics of associative polymer network (micellar gel) are studied under the influence of external shearing forces. When the association energy εc is quite large (εc⩾εc*, where εc* is a critical association energy corresponding to the gelation transition at rest), the spatial organization of the system as a whole is characterized by a typical network architecture with bridging chains connecting different micellar aggregates. The shearing forces cause only a slight perturbation in the structural properties of the sol (at εc&amp;lt;εc*). However, when the association energy εc becomes quite large (εc≳εc*), we observe sharp structural variations as the shear force is increased. At sufficiently strong attraction between stickers, the shear flow facilitates development of the aggregation process: even at rather weak shearing forces, the cluster-size distribution functions become considerably wider when the association energy is close to εc*. Thus, aggregation processes become considerably more pronounced under shear, as compared to the same system at rest. As the shear force increases, the content of looplike chains decreases while the fraction of bridgelike chains rises. This process is accompanied by stretching of the chains. However, under a condition of high shear, many chains belonging to the associative network tend to be coiled up. This leads to the redistribution of structural elements in favor of loop chains. This exchange process can decrease the internal stress in the associative network which is mainly determined by the number and spatial topology of elastically active bridgelike chains.

Thermodynamics of ideal gases under shear: a maximum-entropy approach

The maximum-entropy formalism is used here as a basis of a thermodynamic description of ideal gases under shear. We have obtained expressions for the entropy and the equations of state in nonequilibrium steady states characterized by a given shear viscous pressure and have identified in physical terms the Lagrange multiplier conjugated to the viscous pressure. Our results for those thermodynamic quantities generalize previous expressions which were limited to second order in the shear viscous pressure. These results show a reduction of the shear viscosity at high shear rates and also show how previous results of nonequilibrium molecular dynamics could be compatible with our thermodynamic analysis.

Non-equilibrium molecular dynamics (NEMD) simulations and the rheological properties of liquid n-hexadecane

Non-equilibrium molecular dynamics (NEMD) simulations of liquid n-hexadecane have been performed and its rheological properties have been studied in detail. The Ryckaert and Bellemans model of hydrocarbons has been adopted and extended by using appropriate bond-stretching and angle-bending harmonic potentials. The so-called SLLOD equations of motion which impose and maintain a homogeneous shear rate have been employed in conjunction with an iterative algorithm for determining the Gaussian thermostatting multiplier which maintains the kinetic energy explicitly constant. A number of phenomena have been observed (shear thinning, shear dilatancy, normal stress effects and molecular alignment) and studied in detail using standard rheological viscometric functions and appropriate geometrical analysis parameters. NEMD results have been compared with theoretical and empirical expectations from polymer rheology and indicate that a large-n(e.g. n= 16) liquid alkane has some striking similarities to polymer melts with appropriately scaled molecular weights.

Shear-rate dependence of the viscosity of the Lennard-Jones liquid at the triple point.

High-precision molecular-dynamics (MD) data are reported for the shear viscosity \ensuremath{\eta} of the Lennard-Jones liquid at its triple point, as a function of the shear rate \ensuremath{\epsilon}\ifmmode \dot{}\else \.{}\fi{} for a large system (N=2048). The Green-Kubo (GK) value \ensuremath{\eta}(\ensuremath{\epsilon}\ifmmode \dot{}\else \.{}\fi{}=0)=3.24\ifmmode\pm\else\textpm\fi{}0.04 is estimated from a run of 3.6\ifmmode\times\else\texttimes\fi{}${10}^{6}$ steps (40 nsec). We find no numerical evidence of a ${\mathit{t}}^{\mathrm{\ensuremath{-}}3/2}$ long-time tail for the GK integrand (stress-stress time-correlation function). From our nonequilibrium MD results, obtained both at small and large values of \ensuremath{\epsilon}\ifmmode \dot{}\else \.{}\fi{}, a consistent picture emerges that supports an analytical (quadratic at low shear rate) dependence of the viscosity on \ensuremath{\epsilon}\ifmmode \dot{}\else \.{}\fi{}.

Flow Properties and Shear‐induced Structural Changes in Fluids: A Case Study on the Interplay between Theory, Simulation, Experiment and Application

AbstractThe interrelation between the flow properties of fluids and the shear‐induced changes of their structure is discussed and the methods for their study are reviewed. The fruitful interaction between (conventional) theory, simulation, experiment and application is emphasized. Results are presented for simple fluids where the distortion of the local (short range) order, as described by the pair‐correlation function or the static structure factor, is found to be in good agreement with kinetic theory predictions. Experimental data are compared with results of nonequilibrium molecular dynamics (NEMD) computer simulations which are also used to study the non‐newtonian flow behavior of simple fluids. The spectacular long range positional order found in NEMD simulations at high shear rates is reviewed and interpreted as a hydrodynamic instability.