Parametric dependence on shear viscosity of SPC/E water from equilibrium and non-equilibrium molecular dynamics simulations

A parametric dependent study is crucial for the accurate determination of transport coefficients such as shear viscosity. In this study, we calculate the shear viscosity of extended simple point charge water using a transverse current auto-correlation function (TCAF) from equilibrium molecular dynamics (EMD) and the periodic perturbation method from non-equilibrium molecular dynamics (NEMD) simulations for varying coupling time and system sizes. Results show that the shear viscosity calculated using EMD simulations with different thermostats varies significantly with coupling times and system size. The use of Berendsen and velocity-rescale thermostats in NEMD simulations generates a significant drift from the target temperature and results in an inconsistent shear viscosity with coupling time and system size. The use of Nosé–Hoover thermostat in NEMD simulations offers thermodynamic stability which results in a consistent shear viscosity for various coupling times and system sizes.     

Calculating the bulk modulus for a lipid bilayer with nonequilibrium molecular dynamics simulation

Nonequilibrium molecular dynamics (NEMD) computer simulations are used to calculated the bulk modulus for a dimyristoylphosphatidylcholine bilayer. A methodology is developed whereby NEMD can be effectively used to calculate material properties for complex systems that undergo long time-scale conformational changes. It is found that the bulk modulus upon expansion from a zero stress state agrees well with experimental estimates. However, it is also found that the modulus upon contraction from a zero stress state is larger. From a molecular perspective, it is possible to explain this phenomena by examining the molecular origins of the pressure response. The finding that the two moduli are not equal upon compression and expansion is in apparent contradiction to osmotic stress experiments where the area modulus was found to be the same upon expansion and contraction. This issue is addressed.     

Computer Simulation of Isothermal Mass Transport in Graphite Slit Pores

Abstract

Results are presented from a simulation study of the mass transport of oxygen and nitrogen through graphite slit pores. The work is motivated by an attempt to understand the molecular origins of the kinetic selectivity displayed when air is separated into its major components using pressure swing adsorption. A combination of non-equilibrium molecular dynamics (NEMD), equilibrium molecular dynamics (EMD) and grand canonical Monte Carlo methods has been employed in our study to extract the maximum information. Transport diffusivities, self-diffusivities, permeabilities and Darken thermodynamic factors have been calculated as a function of pore width and temperature for pure component oxygen and nitrogen. In addition, new EMD simulation data for an 80:20 mixture of nitrogen and oxygen is reported, including a direct calculation of the Stefan-Maxwell coefficients. The results are discussed in terms of the oxygen selectivity and the possible mechanisms, which increase or decrease this quantity.

We find that the pore width behaviour of the diffusion coefficients consists of three distinct regimes: a regime at larger pore widths in which single component diffusion coefficients are largely independent of pore width, an optimum pore width at which both diffusivities increase substantially but the slit pore is selective towards nitrogen, and a regime at very low pore widths at which the diffusivities decrease sharply, but the slits are selective towards oxygen. The mechanism behind each of these regimes is discussed in terms of “entropic” effects and potential barrier heights.

We have also found that permeability selectivity is substantially reduced in a mixture of the two gases with a composition similar to that of air. Cross diffusion coefficients in the mixture have been calculated and shown to be non-negligible.     

Simulation Performance of a Non-Equilibrium Molecular Dynamics Method Using Density Difference as Driving Force

Abstract

The simulation performance of two NEMD algorithms, the constant density difference (DD) and the constant chemical potential difference (CPD) methods, has been compared in fluctuations of molar flux for He and CH₄ permeation across the ZSM-5 membrane. The CPD method and the DD method are found to give almost the same performance; however, the former seems slightly superior to the latter in terms of low fluctuations of molar flux though the former needs more CPU time than the latter. An advantage of the DD method is that it can simulate the mixed-gas permeation through a membrane under the specification of high and low pressures and the composition of feed gas. It is shown that the density profile of permeating gas could provide important information about the relative resistance at the entrance, inside, and exit regions for permeation.     

Atomistic simulations of liquid–liquid coexistence in confinement: comparison of thermodynamics and kinetics with bulk

We review a few simulation methods and results related to the structure and non-equilibrium dynamics in the coexistence region of immiscible symmetric binary fluids, in bulk as well as under confinement, with special emphasis on the latter. Monte Carlo methods to estimate interfacial tensions for flat and curved interfaces have been discussed. The latter, combined with a thermodynamic integration technique, provides contact angles for coexisting fluids attached to the wall. For such three-phase coexistence, results for the line tension are also presented. For the kinetics of phase separation, various mechanisms and corresponding theoretical expectations have been discussed. A comparative picture between the domain growth in bulk and confinement (including thin-film and semi-infinite geometry) has been presented from molecular dynamics simulations. Applications of finite-size scaling technique have been discussed in both equilibrium and non-equilibrium contexts.     

Accurate determination of normal stress differences via transient-time correlation function – non-equilibrium molecular dynamics (TTCF–NEMD) simulations

When a non-Newtonian liquid undergoes shear flow, differences between the values taken by the diagonal elements of the pressure tensor arise. These differences, known as normal stress differences, are notoriously difficult to compute accurately. In this work, we propose to apply the transient-time correlation function (TTCF) formalism together with non-equilibrium molecular dynamics (NEMD) simulations to determine normal stress differences, as well as the corresponding normal stress coefficients, in an atomic fluid undergoing shear flow. Our results shed light on the dependence of normal stress differences and coefficients on the applied shear.     

Mixing of nanofluids: molecular dynamics simulations and modelling

In this paper we study a mixing scheme, which has recently been proposed for microfluids, on the nanoscale. We do this by performing a series of nonequilibrium molecular dynamics simulations. On the nanoscale the chaotic mixing regime is captured. We discover a new phenomenon where the two mixing fluids exchange positions after leaving the mixing intersection. The results from the molecular dynamics simulations also reveal complex spatio-temporal stream velocity profiles generated by the mixing device. We find that these profiles can be modelled through an approximate analytical solution to the Navier–Stokes equation.     

Gibbs-Ensemble Molecular Dynamics: A New Method for Simulations Involving Particle Exchange

We discuss a novel simulation method suitable for simulating phenomena involving particle exchange. The method is a molecular dynamics version of the Gibbs-Ensemble Monte Carlo technique, which has been developed some years ago for the direct simulation of phase equilibria in fluid systems. The idea is to have two separate simulation boxes, which can exchange particles or molecules in a thermodynamically consistent fashion. We discuss the general idea of the Gibbs-Ensemble Molecular Dynamics technique and present examples for different simple atomic and molecular fluids. Specifically we will discuss Gibbs-Ensemble Molecular Dynamics simulations of gas-liquid and liquid-solid equilibria in Lennard-Jones systems and in hexane as well as an application of the method to adsorption.     

The dynamic stress responses to area change in planar lipid bilayer membranes

The viscoelastic properties of planar phospholipid (dimyristoylphosphatidylcholine) bilayer membranes at 308 K are studied, many of them for the first time, using the nonequilibrium molecular dynamics simulation (NEMD) method for membrane area change. First, we present a unified formulation of the intrinsic three-dimensional (3D) and apparent in-plane viscoelastic moduli associated with area change based on the constitutive relations for a uniaxial system. The NEMD simulations of oscillatory area change process are then used to obtain the frequency-domain moduli. In the 4-250 GHz range, the intrinsic 3D elastic moduli of 20-27 kbar and viscous moduli of 0.2-9 kbar are found with anisotropy and monotonic frequency dispersion. In contrast, the apparent in-plane elastic moduli (1-9 kbar) are much smaller than, and the viscous moduli (2-6 kbar) comparable to, their 3D counterparts, due to the interplay between the lateral and normal relaxations. The time-domain relaxation functions, separately obtained by applying stepwise strains, can be fit by 4-6 exponential decay modes spanning subpicosecond to nanosecond timescale and are consistent with the frequency-domain results. From NEMD with varying strain amplitude, the linear constitutive model is shown to be valid up to 6 and 20% area change for the intrinsic 3D elastic and viscous responses, respectively, and up to 20% area change for the apparent in-plane viscoelasticity. Inclusion of a gramicidin A dimer (approximately 1 mol %) yields similar response properties with possibly smaller (<10%) viscous moduli. Our results agree well with available data from ultrasonic experiments, and demonstrate that the third dimension (thickness) of the planar lipid bilayer is integral to the in-plane viscoelasticity.     

Controllers for imposing continuum-to-molecular boundary conditions in arbitrary fluid flow geometries

We present a new parallelised controller for steering an arbitrary geometric region of a molecular dynamics (MD) simulation towards a desired thermodynamic and hydrodynamic state. We show that the controllers may be applied anywhere in the domain to set accurately an initial MD state, or solely at boundary regions to prescribe non-periodic boundary conditions (PBCs) in MD simulations. The mean molecular structure and velocity autocorrelation function remain unchanged (when sampled a few molecular diameters away from the constrained region) when compared with those distributions measured using PBCs. To demonstrate the capability of our new controllers, we apply them as non-PBCs in parallel to a complex MD mixing nano-channel and in a hybrid MD continuum simulation with a complex coupling region. The controller methodology is easily extendable to polyatomic MD fluids.     

The Rheology of 6-Propyl Duodecane and 5-Dibutyl Nonane by Non-Equilibrium Molecular Dynamics Simulations

Abstract

In recent papers, we reported non-equilibrium molecular dynamics (NEMD) simulations of planar Couette flow for liquid n- and i-butane, and liquid n-decane and 4-propyl heptane, using two collapsed atom models and an atomistically detailed model. It was found that the collapsed atom models predict the viscosities of the n-butane and n-decane quite well, and that the atomistically detailed model does not yield quantitative agreement with the viscosity of the n-alkanes or the branched alkanes, but it does have the one positive feature that the calculated viscosities of the branched alkanes are higher than these of the n-alkanes. In the present paper, we report results of NEMD simulations of planar Couette flow for liquid 6-propyl duodecane and 5-dibutyl nonane at 296 K and 0.782 g/cc, using an expanded collapsed atom model for simplicity. The strain rate dependent viscosity shows three different regions—two shear thinning ones and a Newtonian one. The slopes of the log-log plot for the branched-chain alkanes at high strain rate are different from those at intermediate strain rate, which is characterized as a rheological behavior of branched-chain alkanes. The Newtonian viscosity of the branched-chain alkanes can be extrapolated from the plateau value of the strain rate dependent viscosity at low strain rate as for straight-chain alkanes [J. Chem. Phys., 105, 1214 (1996)]. The results indicate that more-branched alkanes have a larger viscosity than less-branched C₁₇ alkanes.     

Non-Ewald methods: theory and applications to molecular systems

Several non-Ewald methods for calculating electrostatic interactions have recently been developed, such as the Wolf method, the reaction field method, the pre-averaging method, and the zero-dipole summation method, for molecular dynamics simulations of various physical systems, including biomolecular systems. We review the theories of these approaches and their potential applications to molecular simulations, and discuss their relationships.     

Silica xerogel/aerogel-supported lipid bilayers: Consequences of surface corrugation

The objective of this paper was to review our recent investigations of silica xerogel and aerogel-supported lipid bilayers. These systems provide a format to observe relationships between substrate curvature and supported lipid bilayer formation, lipid dynamics, and lipid mixtures phase behavior and partitioning. Sensitive surface techniques such as quartz crystal microbalance and atomic force microscopy are readily applied to these systems. To inform current and future investigations, we review the experimental literature involving the impact of curvature on lipid dynamics, lipid and phase-separated lipid domain localization, and membrane-substrate conformations and we review our molecular dynamics simulations of supported lipid bilayers with the atomistic and molecular information they provide.     

Molecular simulations of physical and chemical adsorption under gas and liquid environments using force field- and quantum mechanics-based methods

Here we review our simulations of adsorption on metal–organic frameworks (MOFs) and platinum (Pt) catalysts, focusing on the modelling methods required to understand these two very different systems. MOFs are porous, crystalline materials with large surface areas, which are promising for a variety of adsorption applications. We review our simulations of gas uptake in PCN-53 (porous coordination network) as well as gas storage in MOFs functionalised with metal alkoxide sites. While fluid–solid interactions in both systems can be modelled quite well using algebraic force fields, the alkoxide sites in the functionalised MOFs require specialised versions, in order to describe the stronger adsorption energies. We discuss grand canonical Monte Carlo (GCMC) simulations of both systems. Pt is a common catalyst, and simulations have proven quite useful for providing molecular level details to understand its functionality. This involves understanding adsorption phenomena, which often requires quantum mechanical calculations. We describe our periodic boundary condition density functional theory (DFT) simulations of Pt-catalysed NO oxidation, focusing on adsorbate geometries and coverage effects. Finally, we describe one of the current ‘grand challenges’ in molecular simulations of adsorption, modelling catalytic activity in aqueous phase, which requires a combination of algebraic force fields, DFT and GCMC.     

Statistical prediction and molecular dynamics simulation

We describe a statistical approach to the validation and improvement of molecular dynamics simulations of macromolecules. We emphasize the use of molecular dynamics simulations to calculate thermodynamic quantities that may be compared to experimental measurements, and the use of a common set of energetic parameters across multiple distinct molecules. We briefly review relevant results from the theory of stochastic processes and discuss the monitoring of convergence to equilibrium, the obtaining of confidence intervals for summary statistics corresponding to measured quantities, and an approach to validation and improvement of simulations based on out-of-sample prediction. We apply these methods to replica exchange molecular dynamics simulations of a set of eight helical peptides under the AMBER potential using implicit solvent. We evaluate the ability of these simulations to quantitatively reproduce experimental helicity measurements obtained by circular dichroism. In addition, we introduce notions of statistical predictive estimation for force-field parameter refinement. We perform a sensitivity analysis to identify key parameters of the potential, and introduce Bayesian updating of these parameters. We demonstrate the effect of parameter updating applied to the internal dielectric constant parameter on the out-of-sample prediction accuracy as measured by cross-validation.     

Computational modeling of membrane trafficking processes: From large molecular assemblies to chemical specificity

In the last decade, molecular dynamics (MD) simulations have become an essential tool to investigate the molecular properties of membrane trafficking processes, often in conjunction with experimental approaches. The combination of MD simulations with recent developments in structural biology, such as cryo-electron microscopy and artificial intelligence-based structure determination, opens new, exciting possibilities for future investigations. However, the full potential of MD simulations to provide a molecular view of the complex and dynamic processes involving membrane trafficking can only be realized if certain limitations are addressed, and especially those concerning the quality of coarse-grain models, which, despite recent successes in describing large-scale systems, still suffer from far-from-ideal chemical accuracy. In this review, we will highlight recent success stories of MD simulations in the investigation of membrane trafficking processes, their implications for future research, and the challenges that lie ahead in this specific research domain.     

Viscosity of heptane-toluene mixtures. Comparison of molecular dynamics and group contribution methods

Three methods of molecular dynamics simulation [Green–Kubo (G–K), non-equilibrium molecular dynamics (NEMD) and reversed non-equilibrium molecular dynamics (RNEMD)], and two group contribution methods [UNIFAC–VISCO and Grunberg–Nissan (G–N)] were used to calculate the viscosity of mixtures of n-heptane and toluene (known as heptol). The results obtained for the viscosity and density of heptol were compared with reported experimental data, and the advantages and disadvantages of each method are discussed. Overall, the five methods showed good agreement between calculated and experimental viscosities. In all cases, the deviation was lower than 9%. It was found that, as the concentration of toluene increases, the deviation of the density of the mixture (as calculated with molecular dynamics methods) also increases, which directly affects the viscosity result obtained. Among the molecular simulation techniques evaluated here, G–K produced the best results, and represents the optimal balance between quality of result and time required for simulation. The NEMD method produced acceptable results for the viscosity of the system but required more simulation time as well as the determination of an appropriate shear rate. The RNEMD method was fast and eliminated the need to determine a set of values for shear rate, but introduced large fluctuations in measurements of shear rate and viscosity. The two group contribution methods were accurate and fast when used to calculate viscosity, but require knowledge of the viscosity of the pure compounds, which is a serious limitation for applications in complex multicomponent systems.     

Pressure effects in confined nanophases

In this article, we review how pressure effects in pores affect both the physics of the confined fluid and the properties of the host porous material. Molecular simulations in which high-pressure effects were observed are first discussed; we will see how the strong dependence on bulk phase pressure of the freezing temperature of a fluid confined in nanopores can be explained by important variations of the pressure within the pore. We then discuss recent works in which direct calculations of the pressure tensor of fluids confined in pores provide evidence for large pressure enhancements. Finally, practical applications of these pressure effects in which gas adsorption in microporous solids (pore size < 2 nm) was found to enhance their mechanical properties by increasing the elastic modulus by a factor 4 are discussed.