Periodic Perturbation Method Research Articles

Implementation of probe rheology simulation technique in atomistically detailed molecular dynamics simulations

The probe rheology simulation technique is a technique for measuring the viscosity of a fluid by measuring the motion of an inserted probe particle. This approach has the benefit of greater potential accuracy at a lower computational cost than other conventional simulation techniques used for the calculation of mechanical properties, such as the Green-Kubo approach and nonequilibrium molecular dynamics simulations, and the potential to allow for sampling local variations of properties. This approach is implemented and demonstrated for atomistically detailed models. The viscosity of four different simple Newtonian liquids is calculated from both the Brownian motion (passive mode) and the forced motion (active mode) of an embedded probe particle. The probe particle is loosely modeled as a nano-sized diamond particle: a rough sphere cut out of an FCC lattice made of carbon atoms. The viscosities obtained from the motion of the probe particle are compared with those obtained from the periodic perturbation method, and good agreement between the two sets of values is observed once the probe-fluid interaction strength (i.e., in the pair-wise Lennard-Jones interaction) is two times higher than their original values, and the artificial hydrodynamic interactions between the probe particle and its periodic images are accounted for. The success of the proposed model opens new opportunities for applying such a technique in the rheological characterization of local mechanical properties in atomistically detailed molecular dynamics simulations, which can be directly compared with or help guide experiments of similar nature.

Amplitude modulation control method for bursting dynamics under time-delayed feedback

Time-delayed feedback control is one of the important active control methods for complex dynamical behaviors in nonlinear systems. Yet its relationship and effectiveness on multiple time scale dynamics need to be further explored. As a purpose to gain insight into such complexity, we investigate the effectiveness of amplitude modulation in controlling (suppressing or enhancing) bursting oscillations in a classical mechanical oscillator with time-delayed feedback. It is shown how the presence of delay can change the amplitude of the singular cycle oscillations, or suppress them altogether. The results are compared to the conventional periodic perturbation method. In many cases, the amplitudes of periodic solutions under delayed feedback are easier to satisfy the technical requirements. If the delayed feedback is added, stable periodic bursting can be easily accomplished. Therefore, we demonstrate that an effective vibration modulation for bursting dynamics is possible if appropriate time delay and feedback gains are chosen.

Comparison and Validation of Force Fields for Deep Eutectic Solvents in Combination with Water and Alcohol Dehydrogenase

Deep eutectic solvents (DESs) have become popular as environmental-friendly solvents for biocatalysis. Molecular dynamics (MD) simulations offer an in-depth analysis of enzymes in DESs, but their performance depends on the force field chosen. Here, we present a comprehensive validation of three biomolecular force fields (CHARMM, Amber, and OPLS) for simulations of alcohol dehydrogenase (ADH) in DESs composed of choline chloride and glycerol/ethylene glycol with varying water contents. Different properties (e.g., protein structure and flexibility, solvation layer, and H-bonds) were used for validation. For two properties (viscosity and water activity) also experiments were performed. The viscosity was calculated with the periodic perturbation method, whereby its parameter dependency is disclosed. A modification of Amber was identified as the best-performing model for low water contents, whereas CHARMM outperforms the other models at larger water concentrations. An analysis of ADH's structure and interactions with the DESs revealed similar predictions for Amber and CHARMM.

Viscosities of polyethylene glycol monolaurate in alcohol solvents from non-equilibrium molecular dynamics (NEMD) simulation

Non-equilibrium molecular dynamic (NEMD) simulation was carried out to calculate the shear viscosities based on the periodic perturbation method. Six binary systems composed of polyethylene glycol monolaurate (PEGML) in aliphatic alcohols were studied, namely PEGML with methanol, ethanol, 2-propanol, 2-butanol, tert-butanol, and 1-pentanol, respectively. The simulated systems were subjected to an external shear-stress acceleration field which induces a velocity gradient of the liquid, and the shear viscosity was further determined from the resulting velocity. Different values of shear-stress acceleration in the range of (0.005 to 0.08) nm ps2 were used to perform an independent simulation. The viscosity was further calculated for each of shear-stress acceleration rate and then extrapolated to obtain the zero-shear rate viscosity. It is found that the shear viscosity follows the order of PEGML + tert-butanol > PEGML + 1-pentanol > PEGML + 2-butanol > PEGML + 2-propanol > PEGML + ethanol > PEGML + methanol, respectively.

Extension of the CL&Pol Polarizable Force Field to Electrolytes, Protic Ionic Liquids, and Deep Eutectic Solvents.

The polarizable CL&Pol force field presented in our previous study, Transferable, Polarizable Force Field for Ionic Liquids (J. Chem. Theory Comput. 2019, 15, 5858, DOI: http://doi.org/10.1021/acs.jctc.9b0068910.1021/acs.jctc.9b00689), is extended to electrolytes, protic ionic liquids (PIL), deep eutectic solvents (DES), and glycols. These systems are problematic in polarizable simulations because they contain either small, highly charged ions or strong hydrogen bonds, which cause trajectory instabilities due to the pull exerted on the induced dipoles. We use a Tang-Toennies (TT) function to dampen, or smear, the interactions between charges and induced dipole at a short range involving small, highly charged atoms (such as hydrogen or lithium), thus preventing the "polarization catastrophe". The new force field gives stable trajectories and is validated through comparison with experimental data on density, viscosity, and ion diffusion coefficients of liquid systems of the above-mentioned classes. The results also shed light on the hydrogen-bonding pattern in ethylammonium nitrate, a PIL, for which the literature contains conflicting views. We describe the implementation of the TT damping function, of the temperature-grouped Nosé-Hoover thermostat for polarizable molecular dynamics (MD) and of the periodic perturbation method for viscosity evaluation from non-equilibrium trajectories in the LAMMPS MD code. The main result of this work is the wider applicability of the CL&Pol polarizable force field to new, important classes of fluids, achieving robust trajectories and a good description of equilibrium and transport properties in challenging systems. The fragment-based approach of CL&Pol will allow ready extension to a wide variety of PILs, DES, and electrolytes.

Insight into the Relationship between Viscosity and Hydrogen Bond of a Series of Imidazolium Ionic Liquids: A Molecular Dynamics and Density Functional Theory Study

The viscosity of ionic liquids (ILs) is an important factor for their industrial applications, which determines mass transfer efficiency. In this work, the relationship between molecular structures and viscosity for three imidazolium-based ILs is investigated by molecular dynamics simulations and density functional theory. The shear viscosity was calculated by using periodic perturbation method, and accurate viscosities are obtained with less than 13% errors as compared to experimental values. Radial distribution functions and space distribution functions reveal that viscosities are correlated strongly to the local structures of ion pairs. Especially, the local aggregation of anions in certain sites of cations prevents movements of the ion pairs, which increase the viscosities of ILs. DFT calculations were further performed to analyze the effects of hydrogen bonds on the viscosities. The results show that asymmetrically distributed interaction sites lead to the high viscosities, which could be used as a rule of thumb for the future design of ILs with target viscosity.

Supra-molecular structure and rheological aspects of liquid terminal 1,n‑diols from ethylene glycol, 1,3‑propandiol, 1,4‑butanediol to 1,5‑pentanediol

A structural and rheological study of terminal 1,n‑diols from etane‑1,2‑diol to pentane‑1,5‑diol at 25 °C was performed using a combination of the experimental small- and wide-angle X-ray scattering (SWAXS) technique and theoretical TraPPE-UA force-field model-based molecular dynamics (MD) simulations. Our already well-established complemented-system approach was used to calculate the SWAXS intensities from the simulation data needed to validate the accuracy of the theoretical results by comparing them with the experimental SWAXS data. Next, a simulated analogue of the contrast-matching method was used to reveal the supra-molecular structural details of the studied diols, which were then further discussed in a comparison with those of the basic primary mono-ols from our previous study (Tomšič M., et al., J. Phys. Chem B, 2007). This revealed the important structural differences arising from the influence of an additional –OH group in the molecule and an increasing diol alkyl chain length. The additional –OH group enhances the H-bonding and leads to a more compact supra-molecular structure that is increasingly locally inhomogeneous with an increasing diol alkyl chain length. Furthermore, the shear-rate-dependent viscosities were calculated for the modelled 1,n‑diols at 25 °C using the non-equilibrium MD periodic perturbation method and the extrapolated zero-shear viscosities were compared with the experimental data. We directly related the effect of the revealed structural details to the viscosity of diols. The level of H-bonding in the system seems to affect the viscosity less than the type of structural details and the molecular conformations. Allowing the modelled system to occupy a higher degree of stretched molecular conformations was in turn reflected in the greatly increased viscosity of the system. Terminal 1,n‑diols exhibit much higher viscosities than the basic mono-ols due to a more rigid cross-linking between the sequentially H-bonded OH-aggregates in the system.

Molecular dynamics simulation for the test of calibrated OPLS-AA force field for binary liquid mixture of tri-iso-amyl phosphate and n-dodecane.

Tri-isoamyl phosphate (TiAP) has been proposed to be an alternative for tri-butyl phosphate (TBP) in the Plutonium Uranium Extraction (PUREX) process. Recently, we have successfully calibrated and tested all-atom optimized potentials for liquid simulations using Mulliken partial charges for pure TiAP, TBP, and dodecane by performing molecular dynamics (MD) simulation. It is of immense importance to extend this potential for the various molecular properties of TiAP and TiAP/n-dodecane binary mixtures using MD simulation. Earlier, efforts were devoted to find out a suitable force field which can explain both structural and dynamical properties by empirical parameterization. Therefore, the present MD study reports the structural, dynamical, and thermodynamical properties with different mole fractions of TiAP-dodecane mixtures at the entire range of mole fraction of 0-1 employing our calibrated Mulliken embedded optimized potentials for liquid simulation (OPLS) force field. The calculated electric dipole moment of TiAP was seen to be almost unaffected by the TiAP concentration in the dodecane diluent. The calculated liquid densities of the TiAP-dodecane mixture are in good agreement with the experimental data. The mixture densities at different temperatures are also studied which was found to be reduced with temperature as expected. The plot of diffusivities for TiAP and dodecane against mole fraction in the binary mixture intersects at a composition in the range of 25%-30% of TiAP in dodecane, which is very much closer to the TBP/n-dodecane composition used in the PUREX process. The excess volume of mixing was found to be positive for the entire range of mole fraction and the excess enthalpy of mixing was shown to be endothermic for the TBP/n-dodecane mixture as well as TiAP/n-dodecane mixture as reported experimentally. The spatial pair correlation functions are evaluated between TiAP-TiAP and TiAP-dodecane molecules. Further, shear viscosity has been computed by performing the non-equilibrium molecular dynamics employing the periodic perturbation method. The calculated shear viscosity of the binary mixture is found to be in excellent agreement with the experimental values. The use of the newly calibrated OPLS force field embedding Mulliken charges is shown to be equally reliable in predicting the structural and dynamical properties for the mixture without incorporating any arbitrary scaling in the force field or Lennard-Jones parameters. Further, the present MD simulation results demonstrate that the Stokes-Einstein relation breaks down at the molecular level. The present methodology might be adopted to evaluate the liquid state properties of an aqueous-organic biphasic system, which is of great significance in the interfacial science and technology.

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.

Calculations of shear viscosity, electric conductivity and diffusion coefficients of aqueous sodium perchlorate solutions from molecular dynamics simulations

In this paper the shear viscosity, electric conductivity and diffusion coefficients under ambient conditions of sodium perchlorate solutions in two water models (tip3p and tip4p/2005) are evaluated using the classical molecular dynamics. While using the Green–Kubo formalism, the influence of simulation trajectory length and integration limit was examined. The obtained results are compared with the experimental data. The best results were obtained for shear viscosity calculations of tip4p/2005 solutions by means of the periodic perturbation method. In the case of electric conductivity the best agreement with the experimental data was obtained using tip3p and the Green–Kubo formula. Finally, perchlorate diffusion coefficients calculated using the mean square displacement depend linearly on the inverse of the length of simulation box. It allows to calculate the correction for the finite system-size dependence of diffusion coefficients.

Dynamic properties of methanol–water mixtures at the temperatures up to 476.2 K and at high pressures via molecular dynamics simulation

Viscosities and self-diffusion coefficients of methanol–water mixtures were calculated via molecular dynamics simulation from 298.2 to 476.2 K and at pressures up to 40 MPa. The periodic perturbation method (non-equilibrium molecular dynamics) and the Green-Kubo method with three-site flexible potential models were adopted for evaluating the viscosities and the diffusion coefficients, respectively. The calculated viscosities and diffusion coefficients of methanol–water mixtures agreed qualitatively with literature experimental values. The three-site flexible potential models used in this study provided similar performance to the previous studies that used rigid models. Results correlated with the Stokes–Einstein relation show the possibility that the effective hydrodynamic radii were approximately constant for the studied condition and might be little affected by the clathrate-type structure at lower methanol compositions.

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.

The shear viscosities of common water models by non-equilibrium molecular dynamics simulations

We have performed non-equilibrium molecular dynamics simulations to simulate the shear viscosity of five commonly used water models, SPC, SPC/E, TIP3P, TIP4P and TIP5P, using the periodic perturbation method. By comparing the computed viscosities of the water models, we find that the viscosities of SPC/E and TIP5P are in better agreement with the experimental value than the others. Furthermore, we have systematically investigated the effects of system size, acceleration amplitude, electrostatic treatment and cut-off length on the viscosities of the SPC/E and TIP5P models. Finally, by simulating the viscosity of water as a function of temperature, our work suggests that the SPC/E and TIP5P models reasonably reproduce the water viscosity vs. temperature experimental profile from 283 to 373 K at 1 bar, although SPC/E gives a better viscosity at high temperatures and TIP5P reproduces closer viscosity values at low temperatures.

On the accuracy of predicting shear viscosity of molecular liquids using the periodic perturbation method

Non-equilibrium molecular dynamics simulations are performed to calculate shear viscosities of 16 representative molecular liquids using the periodic perturbation method (PPM). A perturbation index is defined to measure the strength of the perturbation. It is identified that the predictions are systematically underestimated using PPM. The origin of the underestimate is the acoustic wave in the liquid density, which is persistent in the simulation box unless the perturbation is completely removed. However, there is a linear correlation between the perturbation indexes and the apparent viscosities, which can be utilized to accurately predict the shear viscosities. Finally, it is demonstrated that general force fields derived based on equilibrium properties can be used to predict the shear viscosities of small molecular liquids with relative errors less than 10%.

Prediction of shear viscosities using periodic perturbation method and OPLS force field

The periodic perturbation method is applied to predict shear viscosities of liquid 1,4-butanediol, 1,3-butanediol, 1,2-butanediol, 2-methyl-1,3-propanediol and 1,2,4-butanetriol under two thermodynamical conditions: T = 373 K, P = 0.1 MPa and T = 373 K, P = 250 MPa. A linear dependence of the calculated shear viscosities with respect to the applied perturbation forces is identified. Based on this finding, extrapolation of the calculated viscosities to zero perturbation force is applied to estimate the shear viscosities for the “undisturbed” fluids. The uncertainties of the estimates are calculated using the block average method. The predicted values compare favorably with the experimental data. Although the force field is optimized using equilibrium properties (liquid densities and vaporization enthalpies), calculated results demonstrate that the force field can be used to predict the kinetic properties accurately. The force field parameters are well transferable among different state points. However, transferring parameters among different molecules should be executed with caution.

Lennard-Jones Viscosities in Wide Ranges of Temperature and Density: Fast Calculations Using a Steady–State Periodic Perturbation Method

A method for fast calculation of viscosity from molecular dynamics simulation is revisited. The method consists of using a steady-state periodic perturbation. A methodology to choose the amplitude of the external perturbation, which is one of the major practical issues in the original technique of Gosling et al. [Mol. Phys. 26: 1475 (1973)] is proposed. The amplitude of the perturbation required for fast caculations and the viscosity values for wide ranges of temperature and density of the Lennard-Jones (LJ) model fluid are reported. The viscosity results are in agreement with recent LJ viscosity calculations. Additionally, the simulations demonstrate that the proposed approach is suitable to efficiently generate viscosity data of good quality.

Control and suppression of chaos in flared laser systems: a numerical analysis

Numerical analysis of control and suppression of chaos in flared laser systems is presented. In order to stabilize the chaotic output of such systems, both the periodic perturbation method and the proportional feedback method are examined with good results. Several variations of the proportional feedback method are presented. A certain rule of thumb for tuning the different control algorithms is demonstrated to be fruitful.