Molecular dynamics thermal conductivity from

Another approach to calculate thermal conductivity is equilibrium molecular dynamics (EMD) [125] that uses the Green-Kubo relation derived from linear response theory to extract thermal conductivity from heat current correlation functions. The thermal conductivity X is calculated by integrating the time autocorrelation function of the heat flux vector and is given by... 

Recently, an interesting study of the molecular dynamics calculation of the wavevector dependence of the viscosity and the thermal conductivity of a Lennard-Jones fluid was reported [202]. The transport properties were found to decrease rapidly as the value of the wavevector k was increased from zero, and they were nearly zero when kxs is larger than 5. However, we are not aware of any mode coupling theory calculation of this interesting behavior. In fact, most of the theoretical expressions exist, but the numerical calculation is formidable. 

In the hydrate lattice structure, the water molecules are largely restricted from translation or rotation, but they do vibrate anharmonically about a fixed position. This anharmonicity provides a mechanism for the scattering of phonons (which normally transmit energy) providing a lower thermal conductivity. Tse et al. (1983, 1984) and Tse and Klein (1987) used molecular dynamics to show that frequencies of the guest molecule translational and rotational energies are similar to those of the low-frequency lattice (acoustic) modes. Tse and White (1988) indicate that a resonant coupling explains the low thermal conductivity. 

Sewell and co workers [145-148] have performed molecular dynamics simulations using the HMX model developed by Smith and Bharadwaj [142] to predict thermophysical and mechanical properties of HMX for use in mesoscale simulations of HMX-containing plastic-bonded explosives. Since much of the information needed for the mesoscale models cannot readily be obtained through experimental measurement, Menikoff and Sewell [145] demonstrate how information on HMX generated through molecular dynamics simulation supplement the available experimental information to provide the necessary data for the mesoscale models. The information generated from molecular dynamics simulations of HMX using the Smith and Bharadwaj model [142] includes shear viscosity, self-diffusion [146] and thermal conductivity [147] of liquid HMX. Sewell et al. have also assessed the validity of the HMX flexible model proposed by Smith and Bharadwaj in molecular dynamics studies of HMX crystalline polymorphs. 

Molecular dynamics simulations entail integrating Newton s second law of motion for an ensemble of atoms in order to derive the thermodynamic and transport properties of the ensemble. The two most common approaches to predict thermal conductivities by means of molecular dynamics include the direct and the Green-Kubo methods. The direct method is a non-equilibrium molecular dynamics approach that simulates the experimental setup by imposing a temperature gradient across the simulation cell. The Green-Kubo method is an equilibrium molecular dynamics approach, in which the thermal conductivity is obtained from the heat current fluctuations by means of the fluctuation-dissipation theorem. Comparisons of both methods show that results obtained by either method are consistent with each other [55]. Studies have shown that molecular dynamics can predict the thermal conductivity of crystalline materials [24, 55-60], superlattices [10-12], silicon nanowires [7] and amorphous materials [61, 62]. Recently, non-equilibrium molecular dynamics was used to study the thermal conductivity of argon thin films, using a pair-wise Lennard-Jones interatomic potential [56]. 

For temperatures below the Debye temperature (9d), quantum corrections must be applied to the temperature and thermal conductivity obtained from molecular dynamics. These quantum corrections are negligible for T 0, where the system behaves classically. A quantum correction for the temperature can be estimated by equating the ensemble s total energy to the phonons total energy [10, 57, 61] as ... 

Figure 7 (a). In-plane silicon thermal conductivity predicted by molecular dynamics at 376K ( ), predicted from BTE for pure (dashed lines) and natural (solid lines) silicon, and available experimental data ( ) [53] and (A) [80] at300K. 

Figure 7 (b). In-plane silicon thermal conductivity at lOOOK predicted by molecular dynamics ( ), and from BTE (solid lines). 

Che, J., T. Qagin, W. Deng, and W.A. Goddard, Thermal Conductivity of Diamond and Related Materials from Molecular Dynamics Simulations. Journal of Chemical Physics, 2000. 113(16) p. 6888-6900. 

A molecular dynamics calculation was performed for thorium mononitride ThN(cr) in the temperature range from 300 to 2800 K to evaluate the thermophysical properties, viz. the lattice parameter, linear thermal expansion coefficient, compressibility, heat capacity (C° ), and thermal conductivity. A Morse-type function added to the Busing-Ida type potential was employed as the potential function for interatomic interactions. The interatomic potential parameters were semi-empirically determined by fitting to the experimental variation of the lattice parameter with temperature. 

What is the thermal conductivity of silicon nanowires, n-alkane single molecules, carbon nanotubes, or thin films How does the conductivity depend on the nanowiie dimension, nanotube chirality, molecular length and temperature, or the film thickness and disorder More profoundly, what are the mechanisms of heat transfer at the nanoscale, in constrictions, at low tanperatures Recent experiments and theoretical studies have dononstrated that the thermal conductivity of nanolevel systems significantly differ from their macroscale analogs [1]. In macroscopic-continuum objects, heat flows diffusively, obeying the Fourier s law (1808) of heat conduction, J = -KVT, J is the current, K is the thermal conductivity and VT is the temperature gradient across the structure. It is however obvious that at small scales, when the phonon mean free path is of the order of the device dimension, distinct transport mechanisms dominate the dynamics. In this context, one would like to understand the violation of the Fourier s... 

THERMAL CONDUCTIVITY AND SPECIFIC HEAT OF AMORPHOUS POLYMERS BETWEEN 0.4 AND 4 K. FROM MOLECULAR DYNAMICS AND STRUCTURE OF SOLIDS. 

Here is the appropriate microscopic current and tlim denotes the thermodynamic limit. (For reviews of this theory, see Zwanzig and Steele. ) We will here focus our attention on the self-diffusion process, both because it is the simplest case from a pedagogical standpoint and because it is the one that has been most extensively studied by means of molecular dynamics calculations. Calculations of the coefficients of viscosity and thermal conductivity and the associated time-correlation functions have been reported by Alder et for hard spheres. 

Several transport properties can be evaluated from equilibrium simulations with use of linear response theory, which relates correlation fimctions of spontaneously fluctuating molecular properties to phenomenological transport coefficients. These relations can be used to evaluate diffusion coefficients, thermal conductivities, viscosities, IR spectra, and so on. However, most of these properties are evaluated more directly using appropriately devised techniques of nonequilibrium molecular dynamics. Particularly challenging for polymers is the direct... 

An alternative NEMD method has been developed that is much simpler to implement than is the SLLOD method, particularly for charged systems such as ionic liquids. The method is called reverse nonequilibrium molecular dynamics (RNEMD) and was first developed as a means for computing thermal conductivity but has also been applied to viscosity. It differs from conventional equilibrium and nonequilibrium methods where the cause is an imposed shear rate and the measured effect is a momentum flux/stress. RNEMD does the opposite it imposes the difficult to compute quantity (the momentum flux or stress) and measures the easy to compute property (the shear rate or velocity profile). The method is very simple to implement because it only requires periodic swapping of momenta between atoms at different positions in the box. These swaps set up a velocity profile in the system (i.e., a shear rate). By tracking the frequency and amount of momentum... 

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