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.     

Homogeneous non-equilibrium molecular dynamics simulations of viscous flow: techniques and applications

We provide a review of the literature for non-equilibrium molecular dynamics (NEMD) simulations of homogeneous fluids. Our review focuses on techniques for simulations of shear and elongational flows in viscous fluids and covers the formulation and application of NEMD algorithms for atomic and molecular fluids. We provide a set of expositions that can be effectively used as guidelines to formulate the relevant equations of motion, periodic boundary conditions and thermostats. We also provide a survey of applications in a convenient tabular form as an aid to researchers who wish to use NEMD to study transport phenomena.     

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.     

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.     

The Rheology of Liquid Pentane Isomers by Non-Equilibrium Molecular Dynamics Simulations

Abstract

In this paper, non-equilibrium molecular dynamics (NEMD) simulations of planar Couette flow are reported for an expanded collapsed atom model for liquid pentane isomers at 273.15 K. The strain rate dependent viscosity for liquid pentane isomers exhibits shear-thinning and a linear dependence on γ^1/2. Newtonian viscosities for liquid pentane isomers obtained by a linear extrapolation to zero strain rate are: 0.256cP for normal pentane, 0.219cP for isopentane, and 0.168cP for neopentane. The strain rate dependent pressure difference and normal stress difference vary nearly linearly with the γ^3/2 law and the γ law, respectively, for all three liquid pentane isomers. The overall trend of the square of radius of gyration and end-to-end distance for normal pentane is a linear increase with strain rate. For isopentane, the trend hardly changes for the range of shear rate in this study. The alignment angle decreases with increasing strain rate and the alignment angle of the straight chain alkane is less than that of the branched chain alkane. The average percentage of C?C?C?C trans for normal pentane as a function of strain rate is in excellent correlation with the square of the radius of gyration and the average end-to-end distance. Applying the strain rate in the x-direction, the alignment angle is forced to decrease and the percentage of C?C?C?C trans increases with increasing strain rate.     

On the prediction of transport properties of ionic liquid using 1-n-butylmethylpyridinium tetrafluoroborate as an example

The Green–Kubo and Einstein–Helfand approaches are examined for calculating diffusion coefficient, electronic conductivity and shear viscosity of ionic liquid using 1-n-butylmethylpyridinium tetrafluoroborate [C₄PY][BF₄] as an example. Both methods suffer numerical errors accumulated at long simulation time, resulting divergences in the integrated autocorrelation time (IAT) and nonlinearity in the mean square displacement (MSD). The numerical errors can be reduced using smaller time step in the simulation. By identifying a converged plateau in IAT and a linear segment in MSD both approaches yield consistent predictions. Using a validated force field, the predicted diffusion coefficient and electrical conductivity agree reasonably well with the experimental data. However, the shear viscosity is significantly underestimated. Analysis of the simulation data indicates that a much slow relaxation in the pressure tensor must be considered, which is unfortunately infeasible due to the accumulated numerical error. Alternatively, the non-equilibrium periodic perturbation method shows promising improvement in the prediction.     

Shear viscosity and thermal conductivity of quadrupolar real fluids from molecular simulation

In the present work, equilibrium molecular dynamics was used with the Green-Kubo formalism to simultaneously calculate shear viscosity and thermal conductivity of ten real fluids, i.e. F₂, N₂, O₂, CO₂, C₂H₆, C₂H₄, C₂F₆, C₃H₄, C₃H₆ and SF₆. The fluids were consistently described by the two-center Lennard–Jones plus point quadrupole (2CLJQ) pair potential, whose parameters were adjusted to vapor–liquid equilibria only [J. Phys. Chem. B, 2001, 105, 12126–12133]. The predicted shear viscosities and thermal conductivities show an overall average deviation of only about 10% from correlations of experimental data where comparison was possible.

At low temperature and high density state points, the Green–Kubo integral for shear viscosity shows slow convergence. This problem can be overcome by a new approach developed in the present work. It is based on the adjustment of a suitable function describing the long time behavior of the autocorrelation function and yields reliable results without the need of excessively long simulation runs.     

influence of concentration and mannuronate/guluronate [correction of gluronate] ratio on steady flow properties of alginate aqueous systems.

Steady flow properties were measured at various concentrations for aqueous systems of alignates with different mannuronate/gluronate (M/G) ratios using a cone-plate type rheometer. The flow curve (a plot of shear stress vs. shear rate) shows a plateau region, which is ascribed to a heterogeneous structure, at low shear rate. This plateau region is more noticeable in the G-rich systems than in the M-rich systems. On the other hand, the flow curves for the systems with the same molecular weight but different M/G ratios are congruent in the high shear rate region. The zero shear viscosity can be reduced by the segment contact parameter, cMw, for the alginates with the same M/G ratio but different molecular weights. The zero shear viscosity is proportional to cMw in a low concentration region and is proportional to (cMw)3.4 at relatively high concentrations. The critical value of cMw for which the zero shear viscosity changes from proportionality with cMw to proportionality with (cMw)3.4 is ca. 900.     

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.     

Studying the Unfolding Kinetics of Proteins under Pressure Using Long Molecular Dynamic Simulation Runs

The usefulness of computational methods such as molecular dynamics simulation has been extensively established for studying systems in equilibrium. Nevertheless, its application to complex non-equilibrium biological processes such as protein unfolding has been generally regarded as producing results which cannot be interpreted straightforwardly. In the present study, we present results for the kinetics of unfolding of apomyoglobin, based on the analysis of long simulation runs of this protein in solution at 3 kbar (1 atm = 1.01325, bar = 101 325 Pa). We hereby demonstrate that the analysis of the data collected within a simulated time span of 0.18 μs suffices for producing results, which coincide remarkably with the available unfolding kinetics experimental data. This not only validates molecular dynamics simulation as a valuable alternative for studying non-equilibrium processes, but also enables a detailed analysis of the actual structural mechanism which underlies the unfolding process of proteins under elusive denaturing conditions such as high pressure.     

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.     

Simulating the rheology of surfactant solution using dissipative particle dynamics

Reverse non-equilibrium (RNE) method is applied to investigate the rheological properties of surfactant solutions by using dissipative particle dynamics algorithm. Results show that the surfactant solutions exhibit a shear-thinning behaviour. With the strengthening of shear, the worm-like micelles are gradually oriented in the x direction and then broken up into small spherical micelles. The process is also shown by the decrease of viscosity, which starts quickly, levels off for moderate shear rates and speeds up again over a critical value. We find that this critical value is independent of surfactant concentration. Compared with the shear flow method, the RNE method is credible for moderate shear rate and has more computational efficiency.     

一种改进型体液表观粘度函数测量仪

本文介绍一种性能较好的体液表观粘度函数快测系统,它是在较严密的流变学理论基础上通过较精细的硬、软件设计而研究成功的.其前身为L-1型粘度计,但作了重要改进.它的最大特点是能在一次测量过程完后得到不同切变率下的表观粘度;同时能在通常认为困难却十分重要的“低剪切”段令人满意地工作.     

Intermonolayer friction and surface shear viscosity of lipid bilayer membranes

The flow behavior of lipid bilayer membranes is characterized by a surface viscosity for in-plane shear deformations, and an intermonolayer friction coefficient for slip between the two leaflets of the bilayer. Both properties have been studied for a variety of coarse-grained double-tailed model lipids, using equilibrium and nonequilibrium molecular dynamics simulations. For lipids with two identical tails, the surface shear viscosity rises rapidly with tail length, while the intermonolayer friction coefficient is less sensitive to the tail length. Interdigitation of lipid tails across the bilayer midsurface, as observed for lipids with two distinct tails, strongly enhances the intermonolayer friction coefficient, but hardly affects the surface shear viscosity. The simulation results are compared against the available experimental data.     

Rheology of synovial fluid

After a discussion of the role of synovial fluid as a joint lubricant, rheological measurements are described with both normal (healthy) synovial fluids and pathological ones. Shear stress and first normal stress difference are measured as a function of shear gradient to calculate the apparent shear viscosity eta 1 and the apparent normal viscosity psi 7 as well as an apparent shear modulus G'. It is found, that in case of diseased synoviae all rheological parameters deteriorate. Most significant changes are observed with the zero shear viscosity eta 0, the shear modulus G', and a characteristic time theta 1, which is the reciprocal of the critical shear rate Dc which determines the onset of shear thinning. The rheological deterioration of synovial fluids is explained in terms of solute structure, whereby a molecular mass of the backbone hyaluronic acid of at least 10(7) g.mol-1 is required for satisfactory function. A theory of the rheological performance of normal synovial fluid as well as its pathological deterioration is proposed.     

Methods for molecular dynamics simulations of protein folding/unfolding in solution

All atom molecular dynamics simulations have become a standard method for mapping equilibrium protein dynamics and non-equilibrium events like folding and unfolding. Here, we present detailed methods for performing such simulations. Generic protocols for minimization, solvation, simulation, and analysis derived from previous studies are also presented. As a measure of validation, our water model is compared with experiment. An example of current applications of these methods, simulations of the ultrafast folding protein Engrailed Homeodomain are presented including the experimental evidence used to verify their results. Ultrafast folders are an invaluable tool for studying protein behavior as folding and unfolding events measured by experiment occur on timescales accessible with the high-resolution molecular dynamics methods we describe. Finally, to demonstrate the prospect of these methods for folding proteins, a temperature quench simulation of a thermal unfolding intermediate of the Engrailed Homeodomain is described.     

Aggregation of poly(γ-benzyl-α,L-glutamate)

The aggregation of poly(γ-benzyl-α,L -glutamate) and its enantiomer in toluene has been investigated by following the viscosity as a function of temperature, concentration, molecular weight, molecular-weight distribution, helix chirality, and shear rate. The temperature and concentration data for a 138,000-molecular-weight sample was fitted to an open, reversible end-to-end aggregation model. The aggregation numbers resulting from this fit were consistent with the sudden onset in non-Newtonian flow resulting from only a 0.2-wt% increase in concentration. The association equilibrium constant was then used to predict viscosity for comparison with other data, in particular, the effect of molecular weight and molecular-weight distribution. A mixture of right-and left-handed helices showed the aggregation was not chiral selective. The stiffness of end-to-end aggregated (hydrogen-bonded) molecules differed little from their covalent counterparts, at least below a molecular weight of ～10⁶. We conclude that polybenzylglutamate aggregation in toluene can be described by an open end-to-end aggregation model.     

Multiscale simulation for thermo-hydrodynamic lubrication of a polymeric liquid between parallel plates

Thermo-hydrodynamic lubrication of a polymeric liquid composed of short chains between parallel plates is analysed by a multi-scale simulation, i.e. the synchronised molecular dynamics simulation via macroscopic heat and momentum transfer, which has been recently developed by us. The rheological properties and conformation of polymer chains coupled with the temperature rise caused by local viscous heating are investigated with a non-dimensional parameter, i.e. the Nahme–Griffith number, which is defined by the ratio of the viscous heating to the thermal conduction at the characteristic temperature required to sufficiently change the viscosity. The present simulation demonstrates that strong shear thinning and transitional behaviour of the conformation of the polymer chains occurs with a rapid temperature rise when the Nahme–Griffith number exceeds unity.     

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.