Green-Kubo Formalism Research Articles

Fick and Maxwell-Stefan diffusion of the liquid mixture cyclohexane + toluene + acetone + methanol and its subsystems

Transport diffusion of the quaternary mixture cyclohexane + toluene + acetone + methanol and most of its binary and ternary subsystems at ambient conditions of temperature and pressure is studied by molecular dynamics simulation. Liquid-liquid phase separation of cyclohexane + methanol extends into the according ternary and quaternary mixtures, rendering them highly non-ideal. Maxwell-Stefan diffusion and intradiffusion coefficients are predicted with the Green-Kubo formalism, while the thermodynamic factor is sampled with Kirkwood-Buff integration. From these data, the Fick diffusion coefficient is determined and thoroughly compared with experimental literature values. Given that the simulation results for all binaries, one of the ternaries and the quaternary mixture are successfully validated, it can be assumed that the results for the three remaining ternary mixtures, for which no experimental data exist, are sound, too. These three ternaries exhibit non-idealities that entail Maxwell-Stefan diffusion coefficient maxima that are accompanied by Fick diffusion coefficient minima due to the thermodynamic factor. Particularly the very different nature of cyclohexane and methanol molecules, where the latter strongly self-associate, leads to anomalies. The predictive models by Li et al. (2001) and Allie-Ebrahim et al. (2018) for binary and ternary mixtures, respectively, are found to yield good results for predicting the Fick diffusion coefficient of these challenging systems.

Phonon modal analysis of thermal transport in ThO2 with point defects using equilibrium molecular dynamics

Defects can significantly degrade the thermal conductivity of ThO2, an advanced nuclear fuel material as well as a surrogate for other fluorite-structured materials. We investigate how point defects in ThO2 impact phonon mode-resolved thermal transport. By incorporating phonon modes from lattice dynamics, we decompose the trajectory and heat flux to phonon normal mode space and extract key phonon properties, including phonon relaxation times and their contributions to thermal conductivity. We implement two methods. The first method is based on the Green Kubo formalism to resolve the contribution of each phonon mode to thermal conductivity. The second resolves the lifetime of individual phonon modes and the thermal conductivity is calculated using the Boltzmann transport equation within relaxation time approximation. Notably, a lower contribution of acoustic modes is revealed compared to perturbative approaches considering only three-phonon scattering processes. The effects of four types of point defects are evaluated. The strongest impact on a reduction in thermal conductivity is from Th interstitials, followed by Th vacancies. O interstitials/vacancies have a similar impact, albeit smaller than defects on the thorium sublattice. These observations are consistent with previous studies.

Numerical characterization of thermal transport in hexagonal tungsten disulfide (WS2) nanoribbons

In this study, we have investigated the thermal transport characteristics of single-layer tungsten disulfide, WS2 nanoribbons (SLTDSNRs) using equilibrium molecular dynamics simulations with the help of Green-Kubo formulation. Using Stillinger-Weber (SW) inter-atomic potential, the calculated room temperature thermal conductivities of 15 nm × 4 nm pristine zigzag and armchair SLTDSNRs are 126 ± 10 W m−1K−1 and 110 ± 6 W m−1K−1, respectively. We have explored the dependency of thermal conductivity on temperature, width, and length of the nanoribbon. The study shows that the thermal conductivity of the nanoribbon decreases with the increase in temperature, whereas the thermal conductivity increases with an increase in either the width or length of the ribbon. The thermal conductivity does not increase uniformly as the size of the ribbon changes. We have also observed that the thermal conductivity of SLTDSNRs depends on edge orientations; the zigzag nanoribbon has greater thermal conductivity than the armchair nanoribbon, regardless of temperature or dimension variations. Our study additionally delves into the tunable thermal properties of SLTDSNRs by incorporating defects, namely vacancies such as point vacancy, edge vacancy, and bi-vacancy. The thermal conductivities of nanoribbons with defects have been found to be considerably lower than their pristine counterparts, which aid in enhanced values for the thermoelectric figure of merit (zT). We have varied the vacancy concentration within a range of 0.1% to 0.9% and found that a point vacancy concentration of 0.1% leads to a 64% reduction in the thermal conductivity of SLTDSNRs. To elucidate these phenomena, we have calculated the phonon density of states for WS2 under different aspects. The findings of our work provide important understandings of the prospective applications of WS2 in nanoelectronic and thermoelectric devices by tailoring the thermal transport properties of WS2 nanoribbons.

Investigation of the thermal conductivity of shape-modulated silicon nanowires by the Monte Carlo method combined with Green–Kubo formalism

Investigation of the thermal conductivity of shape-modulated silicon nanowires by the Monte Carlo method combined with Green–Kubo formalism

The Impact of Chemical Modifications on The Ionic Conductivity of Ionic Liquid Encapsulated in Carbon Nanotubes, Potential Application in Aluminum Ion Battery

The transport and thermodynamic properties of 1-ethyl-3methyl imidazolium hexafluorophosphate ([EMIM][PF6]) ionic liquid encapsulated in carbon nanotubes or graphite represent a significant challenge in the development of Aluminum-ion batteries. To achieve high energy density in Aluminum-ion batteries, it is explored the use of ionic liquid solvents as electrolytes to enhance the ionic conductivity of the ionic liquid when encapsulated in carbon nanotubes as electrodes. The doping effects of sulfur and boron atoms in single-walled carbon nanotubes (SWCNTs) have been investigated to determine their impact on the ionic transfer number of the ionic liquid encapsulated in SWCNTs. The Green-Kubo formalism has been employed to calculate the ionic transfer number and electrical conductivity of the ionic liquid when encapsulated in SWCNTs doped with sulfur and boron atoms. The results obtained using the Green-Kubo formalism indicate that sulfur doping in SWCNTs, particularly in those with a larger radius, serves as a selective porous electrode material, significantly enhancing the electrical conductivity of the confined ionic liquid. Furthermore, the radial distribution function between the carbon alkyl groups in the ionic liquid and the carbon wall of the carbon nanotube, which is doped with sulfur and boron atoms, demonstrates that the doping effect does not alter the radial distribution function. The Green-Kubo result obtained for the electrical conductivity of the ([EMIM][PF6]) ionic liquid demonstrates excellent agreement with the experimental data.

Interpreting pore-scale fluctuations: Predicting transport coefficients in multiphase flow through porous media using the Green–Kubo formulation—An experimental investigation

Flow fluctuations that are commonly associated with multiphase flow in porous media are studied using concepts from non-equilibrium thermodynamic and statistical mechanics. We investigate how the Green–Kubo formulation of the fluctuation dissipation theorem can be used to predict the transport coefficient from the two-phase extension of Darcy's law. Flow rate-time series data are recorded at the millisecond timescale using a novel experimental setup that allows for the determination of flow fluctuation statistics. By using Green–Kubo relations, a transport coefficient is predicted based on the integrated autocorrelation function. Notably, this coefficient aligned closely with the total effective phase mobility computed using Darcy's equation for multiphase flow, particularly in scenarios where a linear relationship between flow rate and pressure gradient was observed. Our results open a new field of coefficient explorations where microscale fluctuations during multiphase flow are directly linked to macroscale parameters.

Thermal transport characterization of monolayer GaN nanoribbon doped with group IV materials: An equilibrium molecular dynamics study

Bulk gallium nitride (GaN) has been considered as one of the prominent materials for a long time in the application of laser, LED and transistors. Due to its superior electrical characteristics, its low-dimensional hexagonal counterpart is currently drawing attention like graphene. In this study, we have investigated the effect of impurity atoms on the heat energy conduction within this honeycomb nanostructure of GaN to explore its scope of applications. The room temperature thermal conductivity of zigzag GaN nanoribbon (ZGaNNR) is found to be ∼ 11 Wm−1K−1 using the molecular dynamics approach with the Green-Kubo formulation. Various group IV elements namely- carbon, silicon, germanium and tin, have been incorporated within the pristine structure in four distinct doping patterns; like- point (Type-I and Type-II), pair and delta doping, to explore the thermal transport in chemically doped nanostructures. A gradual enhancement in the thermal conductivity is observed for the increasing concentration of carbon and silicon as dopants. On the other hand, selection of germanium and tin as impurity atoms suppresses the heat conduction within the crystal due to the increased low frequency phonon scattering. In all cases, Type-I point doping affects the thermal transport of ZGaNNR significantly. The narrower ribbons impede the phonon transportation due to the strong boundary effects resulting in a lower thermal conductivity. Moreover, phonon transportation is largely suppressed, and heat energy is observed to flow at a slower rate as the temperature of the ribbon rises. We have also studied these doped structures under the influence of point, edge and pair vacancies and observed a decreasing trend in thermal conductivity for each type of vacancy defect patterns introduced in the crystal. Such a study would promote the rising interest in properly characterizing the heat transport of low dimensional nanostructures and it can be an effective technique to tune the thermal conductivity of ZGaNNR for improving thermoelectric performance and thermal management in nanoscale devices.

Shear viscosity of OPC and OPC3 water models.

Water is a unique and abundant substance in biological and chemical systems. Considering its importance and ubiquity, numerous water models have been developed to reproduce various properties of bulk water in molecular simulations. Therefore, selecting an appropriate water model suitable for the properties of interest is crucial for computational studies of water systems. The four-point Optimal Point Charge (OPC) and three-point OPC (OPC3) water models were developed in 2014 and 2016, respectively. These models reproduce numerous properties of bulk water with high accuracy, such as density, dielectric constant, heat of vaporization, self-diffusion coefficient, and surface tension. In this study, we evaluated the shear viscosities of the OPC and OPC3 water models at various temperatures ranging from 273 to 373K using the Green-Kubo formalism to assess their performance. The evaluated viscosities of both models were very close to each other at all the examined temperatures. At temperatures above 310K, the calculated shear viscosities were in excellent agreement with the experimental results. However, at lower temperatures, the water models systematically underestimated the shear viscosity, with the calculated values at 273 and 298K being 20% and 10% lower than the experimental values, respectively. Despite this limitation, the OPC and OPC3 water models outperformed other widely used water models.

Unraveling the pressure-viscosity behavior and shear thinning in glycerol using atomic scale molecular dynamics simulations

In order to increase the usage and explore new applications of glycerol as a replacement for fossil-based lubricants its properties needs to be known at the fundamental level. In this study, the viscosity of pure glycerol at high pressures and strain rates has been investigated using of molecular dynamics (MD) simulations, utilizing both the Green-Kubo (GK) formalism and the SLLOD algorithm. Although the viscosity acquired by the GK method is in agreement with the corresponding experimental values at low pressure, a significant distinction was identified between the viscosity obtained by the GK method and the experimental values at higher pressures (P > 0.5 GPa). This results in a clear difference between the viscosity-pressure coefficient attained by the GK method and the corresponding experimental value. The SLLOD method using a non-equilibrium MD (NEMD) platform was exploited to take into account the simultaneous effects of strain rate and pressure on viscosity. As a result, the pressure-viscosity coefficient acquired by the SLLOD algorithm approaches the experimental value. By combining the experimental outputs for viscosity at low strain rates (γ̇ < 104 s−1) with the SLLOD outputs at higher rates (γ̇ > 105 s−1), the evolutions of glycerol viscosity with pressure and strain rate were ultimately achieved. Implementing this computational platform depicts the shear thinning process in pure glycerol in a wide range of pressures and strain rates.

Molecular dynamics modeling of thermodiffusion in solids with charged defects using uranium dioxide as the case study

Although thermodiffusion is generally much less efficient than diffusion for chemical species transport, this phenomenon can sometimes have a significant impact on natural or technological systems. More specifically, oxygen thermodiffusion is reported as a key mechanism for nuclear fuel evolution during high power transients in nuclear plant operation.To contribute to our understanding and characterization of this phenomenon, oxygen thermodiffusion in UO2 is simulated by molecular dynamics (MD) in order to evaluate the oxygen heat of transport. Specific formulae for the heat flux are derived to take into account the non-pairwise embedded atom model (EAM) term of the empirical potential used. No electronic defects are considered and a specific strategy is built to address this flaw, including the way to ensure electroneutrality with a background charge compensating for the deviation from stoichiometry. A specific thermodynamic model is designed, including the effect of the background charge and each point defect contribution.Five MD techniques are tested and compared, among which the Green-Kubo formalism and the imposed electric field give similar results. The results are interpreted in terms of the defect heats of transport whose combination yields the complete oxygen heat of transport, which is a function of the oxygen potential. The calculated ranges of the heats of transport for the oxygen vacancy and interstitial are [0.20,0.86] eV and [-3.75,-2.60] eV, respectively.

Pseudo hard-sphere viscosities from equilibrium Molecular Dynamics

Transport coefficients like shear, bulk and longitudinal viscosities are sensitive to the intermolecular interaction potential and finite size effects when are numerically determined. For the hard-sphere (HS) fluid, such transport properties are determined almost exclusively with computer simulations. However, their systematic determination and analysis throughout shear stress correlation functions and the Green-Kubo formalism can not be done due to discontinuous nature of the interaction potential. Here, we use the pseudo hard-sphere (PHS) potential to determine pressure correlation functions as a function of volume fraction in order to compute mentioned viscosities. Simulation results are compared to available event-driven molecular dynamics of the HS fluid and also used to propose empirical corrections for the Chapman–Enskog zero density limit of shear viscosity. Moreover, we show that PHS potential is a reliable representation of the HS fluid and can be used to compute transport coefficients. The molecular simulation results of the present work are valuable for further exploration of HS-type fluids or extend the approach to compute transport properties of hard-colloid suspensions.

Magnetic Field-Controlled Electrical Conductivity in AA Bilayer Graphene

We consider the effect of the external magnetic field on the in-plane conductivity in the AA-stacked bilayer graphene system in the strong excitonic condensate regime. We include the effects of the applied inter-layer electric field and the Coulomb interactions. The on-site and inter-layer Coulomb interactions were treated via the bilayer Hubbard model. Using the solutions for the physical parameters in the system, we calculate the in-plane conductivity of the bilayer graphene. By employing the Green-Kubo formalism for the polarization function in the system, we show that the conductivity in the AA bilayer system is fully controlled by the applied magnetic field. For the partial filling in the layers, the electrical conductivity is different for different spin orientations, and, at the high values of the magnetic field, only one component remains with the given spin orientation. Meanwhile, for the half-filling limit, there is no spin-splitting observed in the conductivity function. The theory evaluated here shows the new possibility for spin-controlled electronic transport in the excitonic bilayer graphene system.

Insight into the structural and transport properties of methyl and benzyl triphenyl phosphonium based deep eutectic solvents using molecular dynamics simulations

Molecular dynamics simulation of twelve phosphonium based DESs based on methyl triphenyl phosphonium bromide and benzyl triphenyl phosphonium chloride as hydrogen bond acceptors (HBA) with glycerol, ethylene glycol, triethylene glycol and trifluoroacetamide as hydrogen bond donors (HBDs) are carried out with the Generalized Amber Force Field between 25 °C and 95 °C at 1 atm pressure. Isobaric-isothermal ensemble is used for predicting the structural properties, namely, radial distribution function and coordination number. Further, time resolved trajectory data is correlated to predict the transport properties such as, self-diffusivity, binary-diffusivity, ionic conductivity and viscosity. The temperature dependence of predicted density is observed with 4.96 × 10−2 absolute average deviations from experimental dataset. Further, the self-diffusivities are predicted using Einstein's approach and ionic conductivity is calculated from Nernst-Einstein equation as well as Green-Kubo formulation. Further, the viscosity is also predicted using the Green-Kubo formulation. The predicted ionic conductivities and viscosities are fitted in the Vogel-Fulcher-Tammann (VFT) equation to calculate the VFT parameters for the respective DESs.

Sampling the Bulk Viscosity of Water with Molecular Dynamics Simulation in the Canonical Ensemble.

The bulk viscosity, a transport coefficient in the Navier-Stokes equation, is often neglected in the continuum mechanics of Newtonian fluids. Recently, however, the role of the bulk viscosity is highlighted in the area of surface and interface-related phenomena, in systematic model up-scaling and as an important quantity for the interpretation of acoustic sensor data. The prediction of the bulk viscosity usually employs molecular dynamics and the Green-Kubo linear response theory, which is used to sample transport properties in general from molecular trajectories. Since simulations are usually carried out at specified state points in concert with the evaluation of other thermodynamic properties, the role of thermostats in molecular dynamics needs to be explored systematically. In this work, we carefully investigate the role of thermostatting schemes and numerical implementations of the Green-Kubo formalism, in particular in the canonical ensemble, using two popular water force field models. It turns out that the sampling of the bulk and shear viscosities is a delicate challenge since details of thermostatting and numerical subtleties may have an influence on the results beyond statistical uncertainties. Based on the present findings, we conclude with hints on how to construct robust sampling in the canonical ensemble for the bulk viscosity.

A study of the thermal, ionic conductivities and thermotransport of calcia and gadolinia doped zirconia using molecular dynamics simulations

In the present study, 10 mol% concentrations of calcium and gadolinium oxides were chosen as dopants to stabilise zirconium oxide (ZrO2). The main goals of this research were to study the lattice thermal conductivity, oxygen diffusion coefficient, oxygen ionic conductivity and thermotransport of these materials. Therefore, molecular dynamics (MD) simulations based on the Green-Kubo formalism were applied over a wide temperature range (from 800 K to 1800 K) to calculate the thermal and ionic conductivities and thermotransport. These calculations employed a reliable Buckingham type interatomic potential. The integration of an autocorrelation function was applied to calculate the ionic conductivity and, (approximately) the oxygen tracer diffusion coefficient. It was found that the results were in reasonable agreement with available experimental data. The Onsager cross-coefficients (LOq = LqO) were estimated by using the Green-Kubo formalism as well. The results were also compared with the findings of our previous study on yttria-stabilised zirconia (YSZ).

Experimental and molecular dynamics approach to evaluate the thermo-rheological properties of CuO nanofluids for heat transfer application

The experimental and Molecular Dynamics (MD) simulation studies of nanofluids have substantially gained traction among many researchers in recent years as both studies complement each other. The main aim of this work is to investigate the stability, thermal conductivity (TC) and rheological behavior of copper oxide (CuO) based nanofluids at different particle concentrations (0.1–2.0%) and temperatures (20–60 °C) with the use of experimental and atomistic study. Nanofluid appears as a non-Newtonian fluid with a shear rate between 12 and 232 s−1 and they exhibit shear thickening behavior. MD study has confirmed the presence of nanolayer and enhanced self-diffusion coefficient of water which have been attributed to the viscosity and TC enhancement of the nanofluid. The maximum enhancement of TC is found to be 7% for CuO-SDS nanofluid over the base fluid at the highest concentration and temperature. The percentage of TC enhancement increases with temperature and concentration. MD study has also confirmed the same with a maximum error of 11% at the lowest temperature. Viscosity ratio of nanofluid increases with temperature and concentration. The same has been investigated using Green-Kubo formalism via MD and observed a maximum error of 8% at the lowest temperature.

Density and viscosity of liquid mixtures formed by n-hexane, ethanol, and cyclopentyl methyl ether

• Experimental data of density and viscosity of liquid mixtures. • Theoretical modeling of density and viscosity of liquid mixtures. • Equilibrium Molecular Dynamics of density and viscosity of liquid mixtures • SAFT VR Mie EoS couple to FVT for ternary mixtures. Experimental determination, theoretical modeling, and molecular simulation have been combined to describe atmospherical density and viscosity for liquid n-hexane, ethanol, and cyclopentyl methyl ether pure compounds as a function of temperature and all the corresponding binary and ternary liquid mixtures at 298.15 K over the whole mole fraction range. Experimental determinations are carried out using a Stabinger viscosimeter. The reported density and viscosity data are modeled with the Statistical Associating Fluid Theory of Variable Range employing a Mie potential (SAFT-VR-Mie) equation of state coupled to the free volume theory (FVT). All-Atom molecular simulations employ equilibrium molecular dynamics (EMD) to obtain the corresponding densities from Isobaric-Isothermal (NPT) ensemble and viscosities from the microcanonical (NVE) and using the Green–Kubo formulation. According to the results, density and viscosity decrease with temperature for pure liquid fluids. For the case of liquid mixtures, densities and viscosities negatively deviate from the corresponding linear trend, and no ternary stationary points are detected under the explored conditions. The experimental data of both properties in binary mixtures are well correlated by a Redlich–Kister polynomial, and the ternary mixture is acceptably correlated by only using binary parameters. From a theoretical perspective, densities of binary and ternary mixtures are excellently predicted from the SAFT-VR-Mie EoS, whereas viscosities of the binary mixtures are well correlated from SAFT-VR-Mie EoS + FVT, while the viscosities of the ternary mixture are well predicted using the same framework. EMD accurately describes the density of pure fluids and mixtures, but it exhibits more significant deviations in viscosity predictions. Moreover, the qualitative viscosity trend with temperature and composition is maintained. Finally, SAFT-VR-Mie and EMD are used to describe the hydrogen bond (HB) network formed within the mixtures at different alcohol compositions, which is also used to validate the selected association scheme. HB formation varies with respect to ethanol concentration, and the results show a negative deviation from compositions linearity, showing good agreement between both approaches.

Many-body Green's function approach to lattice thermal transport

Recent progress in understanding thermal transport in complex crystals has highlighted the prominent role of heat conduction mediated by interband tunneling processes, which emerge between overlapping phonon bands (i.e., with energy differences smaller than their broadenings). These processes have recently been described in different ways, relying on the Wigner or Green-Kubo formalism, leading to apparently different results, which question the definition of the heat-current operator. Here, we implement a full quantum approach based on the Kubo formula, elucidating analogies and differences with the recently introduced Wigner or Green-Kubo formulations, and extending the description of thermal transport to the overdamped regime of atomic vibrations, where the phonon quasiparticle picture breaks down. We rely on first-principles calculations on complex crystals with ultralow conductivity to compare numerically the thermal conductivity obtained within the aforementioned approaches, showing that at least in the quasiparticle regime the differences are negligible for practical applications.

Temperature guided behavioral transitions in confined helium: Gas-wall interaction effects on dynamics and transport in the cryogenic limit

The low-temperature dynamics and transport of a real gas He, in confined condition are studied employing molecular dynamics simulations. Characterization of the gaseous properties at varying temperatures (T) in the range 30 - 150 K, is carried out employing velocity autocorrelation function (VACF), mean squared displacement (MSD), and the transport properties such as, self-diffusion coefficient (D) and thermal conductivity (λ) are determined. In the confined system, gas-wall interactions are found to dictate the above properties, and near-wall accumulation of molecules is observed. Further, depending upon T, the effect of wall-mediated forces is found on the distant gas particles. At very short timescales (t* < 0.1), gas-wall interactions result in faster decay of VACF and shorter ballistic phase in MSD along the confining direction, which are most prominent at higher T, compared to those for the unconfined directions. Whereas, at short timescales (t*∼ 0.5) non-thermal gas-wall collisions are observed, leading to a minimum in VACF along the confining direction depending upon T. At longer timescales (t* > 1), gas-wall particle collisions lead to the sub-diffusive behavior of the confined gas along the confinement, which is most prominent at higher T. The results are compared with those for the bulk He to quantify the confining effect on the gas. Reasonably good agreement of the bulk transport properties with numerically calculated quantum mechanical results for LJ potential and existing results from literature (experimental and quantum mechanical) has been found. In the confined system, the parallel self-diffusion coefficient and thermal conductivity (D∥ and λ∥) are found to be close to the bulk values. Additionally, λ is estimated from direct heat flux measurements using the Green-Kubo (G-K) formalism and non-equilibrium method for the confined system, and the results are compared. The findings of this work have far-reaching consequences in investigating complex systems.

Tunable rheological behaviour of magnetized complex plasma

The shear viscosity (η) of a 3D liquid dusty plasma has been estimated as a function of magnetic field (B) and normalized ion flow velocity (M) from the simulation data using Green–Kubo formalism with the help of Langevin dynamics simulation. It has been shown that in the strongly correlated liquid state, complex plasma may exhibit sharp changes in viscosity with magnetic field and ion drift velocity. In presence of ion drift, an oscillatory and attractive wake potential develops among charged dust particles immersed in a plasma. The amplitude of this wake potential can be modulated by applying an external magnetic field. In this work, we explore how an external magnetic field influences the rheological properties of complex plasma via anisotropic wake potential. It is observed that the rheological property of such plasma depends on the dominant interaction operating among the particles and can be controlled by applying an external magnetic field. A novel regime of magnetic field is observed in which strongly correlated complex plasma liquid exhibits a sharp response to an external magnetic field. Due to this unique property, complex plasma may be used as a platform to study magneto-rheological characteristics of soft matter and there is a possibility of using dusty plasma as a magneto-rheological material in near future.