Green-Kubo Method Research Articles

A molecular dynamics study of the effect of nanoparticles coating on thermal conductivity of nanofluids

Nanofluids have become the subject of theoretical and experimental researches over the last few decades due to their enhanced heat transfer performance. In this study, thermal conductivity of copper argon nanofluids containing coated and non-coated copper particles is determined through MD simulation. Coating over the nanoparticles is applied to provide long-term stable dispersion and also to enhance the heat transfer performance. Thermal conductivity of nanofluids depends on the types of coating applied over the nanoparticles. The role of surface coating over the nanoparticles in enhancing thermal properties of the nanofluids is discussed and compared to that of non-coated particles. The silver coating is applied over the copper nanoparticles. Green Kubo method is employed to determine the thermal conductivity of the nanofluids. Result shows that, for volume fraction 3% and 86 K system temperature, thermal conductivity enhancement of nanofluid containing coated particle is 17% compared to that of base fluid and without coating, thermal conductivity enhancement is 12%. The mechanism of increased heat transfer performance for surface coating over the nanoparticles is discussed in this paper.

Molecular dynamics simulation on vegetable oil modified model asphalt

Vegetable oil is a common waste in the food and hospitality industries. It has been proposed as a modifier for asphalt to improve its performance on road pavement. In order to understand the functional mechanism of vegetable oil modifying the properties of model asphalt mixture, investigating the chemical composition, microstructure and property relationship of vegetable oil modified asphalt mixture in a wide temperature range is important. To understand the mechanism with molecular details, molecular dynamics (MD) simulations have been conducted on major fatty acid components in waste vegetable oil (WVO) (including linoleic acid, oleic acid, palmitic acid) and their mixture with model asphalt at different temperatures. One model WVO ternary mixture was built based on the literature data of the chemical composition of three kinds of fatty acids. Major properties such as density, diffusion coefficient, radial distribution function, thermal conductivity, molecular correlation functions, and viscosity were calculated. It was found that oleic acid, linoleic acid and palmitic acid have similar densities, diffusion activation energies, diffusion coefficient prefactors, and thermal conductivities from the room temperature to the hot-mix asphalt temperature. The bulk viscosities of fatty acids predicted using Green-Kubo method are similar as well, and are close to available literature data. All three kinds of fatty acids and their mixture can mix well with components in model asphalt mixture at different temperatures, and can help components in asphalt to mix more homogeneously. The zero-shear-rate viscosities of fatty acids modified asphalts at 443 K, 400 K, and 358 K were calculated running non-equilibrium MD simulations, while the viscosity at the room temperature was predicted using the Debye-Stoke-Einstein equation based on the correlation function and relaxation time calculation. Based on result in this project, implementing vegetable oil improves the density of model asphalt mixture and the mixing of components in asphalt. It does not change the viscosity of asphalt significantly at high temperature but decreases the viscosity at low temperature. The thermal conductivities of pure fatty acids, model vegetable oil ternary mixture, and model vegetable oil modified asphalt mixtures are very similar and show negligible dependence on temperature. The findings in this project suggest the functional mechanism of vegetable oil on asphalt that implementing vegetable oil can improve the performance of asphalt by facilitating the mixing of components in asphalt mixture and reorientation relaxation of asphalt at low temperatures but not at high temperatures, thus reducing the viscosity of mixture at low temperatures while having negligible effect at high temperatures.

Laser fabrication of Cu nanoparticles based nanofluid with enhanced thermal conductivity: Experimental and molecular dynamics studies

Nanofluids are engineered colloidal suspensions of solid nanoparticles in aqueous and non-aqueous base fluids with enhanced thermo-physical characteristics compared to conventional heat transfer fluids (HTFs). In this study, we report on the fabrication of copper nanoparticles-ethylene glycol (CuNPs-EG) nanofluid by using a simple one-step pulsed Nd:YAG laser ablation method to ablate the surface of a pure copper target in EG base fluid under ambient conditions. Structural and morphological analysis confirmed the fabrication of pure spherical shaped CuNPs with average diameter of ~7 nm. Thermal conductivity (k) investigations of CuNPs-EG nanofluid were conducted by using a computational approach where Equilibrium Molecular Dynamics (EMD) simulations integrated with Green-Kubo (EMD-GK) method was used. The obtained EMD-GK results for k were confirmed experimentally through a guarded hot-plate technique within the temperature ranges of 298–318 K. Interestingly, a relative enhancement (η) in the percentage of thermal conductivity of CuNPs-EG nanofluids obtained after an ablation time ta = 5 min was 15% at 318 K, while sample obtained after ta = 30 min showed an enhancement of ~24% in thermal conductivity. These obtained results confirmed the suitability of using a laser based ablation method to fabricate highly efficient nanofluids which could be used as alternatives for conventional HTFs in various heat transfer applications.

Influence of Missing Linker Defects on the Thermal Conductivity of Metal-Organic Framework HKUST-1.

Although metal-organic frameworks (MOFs) are promising materials for gas storage and separation applications, the heat released during the exothermic adsorption process can potentially negatively impact their practical utility. Thermal transport in MOFs has not been widely studied, and among the relatively few reports on the topic, MOFs have either been assumed to be defect free or the presence of defects was not discussed. However, defects naturally exist in MOFs and can also be introduced intentionally. Here, we investigate the effect of missing linker defects on the thermal conductivity of HKUST-1 using molecular dynamics (MDs) simulation and the Green-Kubo method. We found that missing linker defects, even at low concentrations, substantially reduce the thermal conductivity of HKUST-1. If not taken into account, the presence of defects could lead to significant discrepancies between experimentally measured and computationally predicted thermal conductivities.

Chirality effects on an electron transport in single-walled carbon nanotube

In our work, we investigate characteristics of conductivity for single-walled carbon nanotubes caused by spin–orbit interaction. In the case study of chirality indexes, we especially research on the three types of single-walled carbon nanotubes which are the zigzag, the chiral, and the armchair. The mathematical analysis employed for our works is the Green-Kubo Method. For the theoretical results of our work, we discover that the chirality of single-walled carbon nanotubes impacts the interaction leading to the spin polarization of conductivity. We acknowledge such asymmetry characteristics by calculating the longitudinal current–current correlation function difference between a positive and negative wave vector in which there is the typical chiral-dependent. We also find out that the temperature and the frequency of electrons affect the function producing the different characteristics of the conductivity. From particular simulations, we obtain that the correlation decrease when the temperature increase for a low frequency of electrons. For high frequency, the correlation is nonmonotonic temperature dependence. The results of the phenomena investigated from our study express different degrees of spin polarization in each chiral of single-walled carbon nanotube and significant effects on temperature-dependent charge transport according to carrier backscattering. By chiral-induced spin selectivity that produces different spin polarization, our work could be applied for intriguing optimization charge transport.

Efficient anharmonic lattice dynamics calculations of thermal transport in crystalline and disordered solids

Understanding heat transport in semiconductors and insulators is of fundamental importance because of its technological impact in electronics and renewable energy harvesting and conversion. Anharmonic lattice dynamics provides a powerful framework for the description of heat transport at the nanoscale. One of the advantages of this method is that it naturally includes quantum effects due to atoms vibrations, which are needed to compute the thermal properties of semiconductors widely used in nanotechnology, like silicon and carbon, even at room temperature. While the heat transport picture substantially differs between amorphous and crystalline semiconductors from a microscopic standpoint, a unified approach to simulate both crystals and glasses has been devised. Here, we introduce a unified workflow, which implements both the Boltzmann Transport equation and the quasi-harmonic Green-Kubo methods. We discuss how the theory can be optimized to exploit modern parallel architectures, and how it is implemented in κALDo: a versatile and scalable open-source software to compute phonon transport in solids. This approach is applied to crystalline and partially disordered silicon-based systems, including bulk silicon and clathrates, and on silicon–germanium alloy clathrates with largely reduced thermal conductivity.

Computing the Heat Conductivity of Fluids from Density Fluctuations.

Equilibrium molecular dynamics simulations, in combination with the Green-Kubo (GK) method, have been extensively used to compute the thermal conductivity of liquids. However, the GK method relies on an ambiguous definition of the microscopic heat flux, which depends on how one chooses to distribute energies over atoms. This ambiguity makes it problematic to employ the GK method for systems with nonpairwise interactions. In this work, we show that the hydrodynamic description of thermally driven density fluctuations can be used to obtain the thermal conductivity of a bulk fluid unambiguously, thereby bypassing the need to define the heat flux. We verify that, for a model fluid with only pairwise interactions, our method yields estimates of thermal conductivity consistent with the GK approach. We apply our approach to compute the thermal conductivity of a nonpairwise additive water model at supercritical conditions, and of a liquid hydrogen system described by a machine-learning interatomic potential, at 33GPa and 2000K.

Ionic and thermal conductivity of pure and doped ceria by molecular dynamics

Numerous parametrizations of pair potentials have been developed to investigate various properties of pure and doped ceria in recent decades. In this paper, we assess frequently applied sets of pair potentials for pure and gadolinia doped ceria with respect to the prediction of the bulk properties lattice parameter, bulk modulus, and thermal expansion coefficient as well as defect properties including defect formation energies, defect interactions and anion migration energy. We furthermore apply molecular dynamics simulations to obtain the thermal and ionic conductivity of the material using the Green-Kubo and electric field methods, respectively. We found that none of the applied potentials is able to reproduce all of the monitored properties correctly. Nonetheless, we provide a recommendation of suitable potential sets for different applications.

Shear viscosity to entropy density ratio of Hagedorn states

The fireball concept of Rolf Hagedorn, developed in the 1960's, is an alternative description of hadronic matter. Using a recently derived mass spectrum, we use the transport model GiBUU to calculate the shear viscosity of a gas of such Hagedorn states, applying the Green-Kubo method to Monte-Carlo calculations. Since the entropy density is rising ad infinitum near $T_H$, this leads to a very low shear viscosity to entropy density ratio near $T_H$. Further, by comparing our results with analytic expressions, we find a nice extrapolation behavior, indicating that a gas of Hagedorn states comes close or even below the boundary $1/4\pi$ from AdS-CFT.

Potential energy and atomic stability of H2O/CuO nanoparticles flow and heat transfer in non-ideal microchannel via molecular dynamic approach: the Green–Kubo method

It is interesting to investigate the number of nanoparticle (NP) and temperature effects on H2O/CuO nanofluid thermal conductivity and the atomic manner in a non-ideal microchannel. The outcomes of the physical features of these structures were supposed using molecular dynamic (MD) method and LAMMPS simulation package. For the study of dynamic properties of nanofluid microchannel system, parameters such as temperature profiles, velocity, density, and potential energy of H2O/CuO atomic structures were calculated. Furthermore, the thermal conductivity of these structures was estimated by the Green–Kubo method in the final step. This simulation shows that nanoparticle number is a crucial parameter in nanofluid movement in a microchannel. Theoretically, via adding CuO nanoparticle to H2O fluid, the maximum rate of velocity, density, temperature, and thermal conductivity of base fluid increases to 0.106 g cm−3, 29.810 A ps−1, 549.217 K, and 0.81 W mK−1 rates, respectively. Moreover, the temperature increase of Cu microchannel increases the rate of density, velocity, temperature, and thermal conductivity of CuO nanofluids.

Measurement and prediction of kinematic viscosity for linear ethers.

Using the methods of equilibrium and non-equilibrium molecular dynamics alongside capillary viscometer experiments, we explore differences between united and all-atom models of a series of linear ethers. The models are based on two transferable force fields, and changes in viscosity and diffusion are studied across a wide range of temperatures and shear rates. We analyze diffusivity and viscosity data by means of the rotational relaxation time and Arrhenius equation. Rotational relaxation times are calculated explicitly from the ether chain's end-to-end vectors, and self-diffusion values are calculated from the mean square displacement. We find an increase in orientational alignment as temperature drops in both models and consistent differences in activation energies across the models and experiment. A clear relationship is observed between viscosity, rotational relaxation time, and diffusion time. These time constants also impact the reliability of the viscosity value determined by the Green-Kubo method. We also study the trends in zero-shear viscosity as chain length increases and force field performance relative to experiment as this length changes.

Effect of resin/asphaltene ratio on the rheological behavior of asphaltene solutions in a de-asphalted oil and p-xylene: A theoretical–experimental approach

This study focuses on understanding the effect of the resin/asphaltene mass ratio (R/A) on the rheological behavior of asphaltene solutions. To this aim, two cases were evaluated experimentally and theoretically. The first case comprised asphaltenes dissolved in a de-asphalted oil (DAO) at asphaltene concentrations of 2, 10, and 16.5% of mass fraction, with R/A ratios of 3, 6, and 31 being obtained. The second case consisted of asphaltenes dissolved in p-xylene, at an asphaltene mass fraction of 1 and 18%, and adding resins to obtain low R/A ratios (0, 0.125, 0.5, 1, and 1.5). The viscosities measured experimentally were reproduced by molecular dynamics (MD) simulations, using the Green-Kubo method and non-equilibrium MD (NEMD) for estimating the viscosity of solutions with Newtonian and non-Newtonian behavior, respectively. In all cases, the experimental measurements were accurately reproduced by MD. Further, the asphaltene-asphaltene and asphaltene-resin coordination number (CN), the asphaltene-asphaltene and asphaltene-solvent interaction energies, the radius of gyration, and the volumetric fraction for asphaltene aggregates were calculated. Theoretical results evidence that the asphaltene molecules dissolved in DAO exhibited repulsive interaction energies between them, whereby the asphaltene is mainly dispersed for R/A ratios higher than 3 in DAO. This result indicates that the viscosity of the heavy oil is not only dependent on the asphaltene aggregation, but that the resin plays a key role in the rheological behavior of this type of crude oil. This latter suggestion was evidenced in the viscosity measurements due to the DAO viscosity (1776 cP) being considerably higher compared to the individual viscosity of the other compounds of the mixture (i.e., saturates and aromatics), which were at least two orders of magnitude lower. In the experimental evaluations of rheological behavior, varying the resin amount in asphaltene dissolved in p-xylene, a minimum viscosity point was obtained for a specific R/A ratio. The MD results indicated that the resins inhibit the asphaltene aggregation, reducing the volumetric fraction and, therefore, the viscosity decreased. Understanding the physical principles of the effect of the resin on the asphaltenes' aggregation, from an atomistic point of view, is a valuable contribution for designing inhibitors that can be used for the specific molecular characteristics of any crude oil.

Mesoscale structure-based investigation of polyurea dynamic modulus and shock-wave dissipation

Polyurea is a block copolymer with excellent shock absorption. It has a unique phase separation structure, yet there are few reports on how the mesoscale structure affects the dynamic mechanical properties. In this paper, the effect of two-phase structure on the dynamic modulus and shock-wave dissipation of polyurea is investigated by coarse-grained molecular dynamics. Shear relaxation modulus is calculated by the Green-Kubo method. Pulse load is applied by non-equilibrium molecular dynamics. The two-phase structure improves the dynamic modulus by restricting the segment movement. Shock-wave energy is dissipated by heat dissipation, viscous retardation, and plastic dissipation. The two-phase structure must obey deformation coordination, which results in more strain energy and internal friction. Hydrogen bond dissociation and structure destruction occur during the impact. Furthermore, the simulations results are verified by AFM, X-ray diffraction, and DMA experiments.

Effect of copper nanoparticles on thermal behavior of water flow in a zig-zag nanochannel using molecular dynamics simulation

Molecular dynamics (MD) simulation is one of the most common simulation methods which predict the dynamical and thermodynamical properties of atomic structures based on classical Newton's laws. In this study, the effect of copper nanoparticles on the thermal behavior of the fluid in zig-zag nanochannel was investigated using molecular dynamics simulation. In our simulations, water molecules were used to model the base fluid, and platinum atoms were used to model the nanochannel walls. To investigate the effects of copper nanoparticles on the base fluid, physical quantities such as potential energy, density, velocity, temperature profiles, and finally, the thermal conductivity has been reported. The results show that, by adding nanoparticles to the base fluid, the maximum density increases. On the other hand, the maximum velocity decreases from0.22°A/ps to 8°A/ps to. From the velocity behavior of the fluid particles, the temperature decreases from 363 K to 330 K. Furthermore, a study of the thermal conductivity of the simulated system by using the Green-Kubo method showed an increase in the thermal conductivity of water up to 0.679 W m−1 K−1. The increase of the nanofluid thermal conductivity is consistent with the increase in heat transfer, which can be a promising parameter in industrial applications.

Single trajectory transport coefficients and the energy landscape by molecular dynamics simulations.

The Green-Kubo (GK) method is widely used to calculate the transport coefficients of model liquids by Molecular Dynamics (MD) simulation. A reformulation of GK was proposed by Heyes et al. [J. Chem. Phys. 150, 174504 (2019)], which expressed the shear viscosity in terms of a probability distribution function (PDF) of "single trajectory (ST) viscosities," called "viscuits." This approach is extended here to the bulk viscosity, thermal conductivity, and diffusion coefficient. The PDFs of the four STs expressed in terms of their standard deviations (calculated separately for the positive and negative sides) are shown by MD to be statistically the same for the Lennard-Jones fluid. This PDF can be represented well by a sum of exponentials and is independent of system size and state point in the equilibrium fluid regime. The PDF is not well reproduced by a stochastic model. The PDF is statistically the same as that derived from the potential energy, u, and other thermodynamic quantities, indicating that the transport coefficients are determined quantitatively by and follow closely the time evolution of the underlying energy landscape. The PDFs of out-of-equilibrium supercooled high density states are quite different from those of the equilibrium states.

Development of a Polarizable Interatomic Potential for Molten Lithium, Sodium, and Potassium Nitrate.

A polarizable interatomic potential is developed for atomistic simulations of molten MNO3 (M = Li, Na, K) salts. The potential is parametrized using a force matching method relying on the adjustment of parameters such that density functional theory generated forces, stress tensors, and dipole moments are reproduced. Simulations conducted using the new potential are used to estimate physical parameters of the melt, which are then compared with available experimental results. The average calculated densities of NaNO3 and KNO3 are within 2% of the experimental value within the temperature range studied, while that of LiNO3 is within 3%. Thermal conductivities and viscosities are estimated using equilibrium calculations and the Green-Kubo method. The thermal conductivity values of NaNO3 and KNO3 are found to match well with experimental data, while that of LiNO3 is approximately 20% larger than experimentally determined values throughout the temperature ranges simulated. The calculated viscosities are also in good agreement with experimentally determined values. The (NaxK1-x)NO3 mixture is also investigated, with densities, thermal conductivities, and viscosities determined and compared with experimentally determined values where available. Additionally, radial and angular distribution function data is presented for all salts, revealing details of the atom-level structures present in the melts. We have found that the new interatomic potential is effective for atom scale modeling of the physical properties of molten nitrate salts.

Molecular Dynamics Determination of the Lattice Thermal Conductivity of the Cubic Phase of Hafnium Dioxide

The wide range of industrial applications is the main reason for an increased interest in dioxides such as HfO2. In this study, classical molecular dynamic simulations were performed to calculate the lattice thermal conductivity of the cubic phase of HfO2, over a temperature range of 100-3000 K, based on the Green-Kubo fluctuation method. In this research, the heat current autocorrelation function and lattice thermal conductivity were calculated in the a-direction. The lattice thermal conductivity of the cubic phase of HfO2 was found to be a result of three contributions. These were the optical and acoustic short-range and long-range phonon modes. Comparisons between the results of the research and experimental data when available indicate good agreement. Keywords: lattice thermal conductivity, molecular dynamics, Green-Kubo formalism, heat current autocorrelation function, hafnium dioxid

Thermal conductivity reduction in carbon nanotube by fullerene encapsulation: A molecular dynamics study

Single-walled carbon nanotubes (SWCNTs) in their pristine form have high thermal conductivity whose further improvement has attracted a lot of interest. Some theoretical studies have suggested that the thermal conductivity of a (10,10) SWCNT is dramatically enhanced by C60 fullerene encapsulation. However, recent experiments on SWCNT bundles show that fullerene encapsulation leads to a reduction rather than an increase in thermal conductivity. Here, we employ three different molecular dynamics methods to study the influence of C60 encapsulation on heat transport in a (10,10) SWCNT. All the three methods consistently predict a reduction of the thermal conductivity of (10,10) SWCNT upon C60 encapsulation by 20%−30%, in agreement with experimental results on bundles of SWCNTs. We demonstrate that there is a simulation artifact in the Green-Kubo method which gives anomalously large thermal conductivity from artificial convection. Our results show that the C60 molecules conduct little heat compared to the outer SWCNT and reduce the phonon mean free paths of the SWCNT by inducing extra phonon scattering. We also find that the thermal conductivity of a (10,10) SWCNT monotonically decreases with increasing filling ratio of C60 molecules.

EQUILIBRIUM MOLECULAR DYNAMICS CALCULATIONS OF THERMAL CONDUCTIVITY: A “HOW-TO” FOR THE BEGINNERS

The ready availability of codes such as LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) for molecular dynamics simulations has opened up the realm of atomistic modelling to novice code users with an interest in computational materials modelling but who lack the appropriate theoretical or computational background. As such, there is significant risk of the “user effect” having a negative impact on the quality of results obtained using such codes. Here, we present a “how-to” procedure for equilibrium molecular dynamics-based nuclear fuel thermal conductivity calculations using the Green–Kubo method with an interatomic potential developed by Cooper et al. [ 1 ]. The various steps of the simulation are identified and explained, along with criteria to assess the quality of the intermediate and final results, discussion of some problems that can arise during a simulation, and some inherent limitations of the method. Calculated thermal conductivities for UO2 and ThO2 will be compared with the available experimental data and also with similar thermal conductivity calculations using nonequilibrium molecular dynamics, reported in the open literature.

Self-diffusion coefficient of fe, pb, ni and Cr by molecular dynamics simulation using the potential morse

The molecular dynamics simulation using the Morse potential has been applied to calculate the value of self-diffusion coefficients D(T) of some pure metals as Pb, Cr, Ni, and Fe. The simulation then was done using the MOLDY molecular dynamics program. The procedure to calculate these coefficients following several steps: first, determining the Morse potential parameters as , a and r 0; second, simulating the material under consideration using Moldy based on the appropriate ensemble; third, diffusion coefficient calculation using the Green-Kubo method for specific temperature; and fourth, the temperature-dependent diffusion coefficient D(T) based on the Arrhenius. The simulation work has obtained the best results as following: for Pb metal the Morse potential parameter (a = 1.4795 A−1, r 0 = 3.733 Å, and ) with ; for Cr metal the potential parameters (, a = 1.1005 A−1, and r 0 = 2.2032 Å), with ; for Ni metal the Morse potential parameter (, a = 1.0649 A−1, r 0 = 2.085 Å), with ; and for Fe metal the potential parameter (, a = 1.5974 A−1, r 0 = 2.840 Å) with . The calculated diffusion coefficients of the work have significant application as for the corrosion study of steels in nuclear reactor design.