Argon interatomic potential

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]. 

This formula can be used to calculate the surface energy of a liquid when both the intermolecular potential and the distribution function are known. Thus, the distribution function of liquid argon obtained by Eisenstein and Gingrich10 and the known intermolecular potential give Ucaic = 27 erg/cm2, while the observed value, that is, the value obtained from the observed values of surface tension by Eq. 11.12, is U0bs = 35 erg/cm2. For mercury the distribution functions obtained by Boyd and Wake-ham5 and the interatomic potential obtained by Hildebrand, Wakeham, and Boyd16 can be used. The calculated value is Ucaie = 490 erg/cm2, which can be compared with the observed value Uohs = 500 erg/cm2. 

Aziz R A 1993 A highly accurate interatomic potential for argon J. Chem. Phys. 99 4518-25... 

In spite of the inherent limitations of the infinite density series, its theoretical significance has grown. In fact, at the present time, theoretical calculations of the second virial coefficient, e.g., for argon from an interatomic potential, are purported to be more accurate than values obtained from the best experimental data. For fluids of more complicated mole-... 

B°d and C2D, have been evaluated using the Lennard-Jones 6-12 interatomic potential and for argon using the exp-six potential to describe adsorbate self-interactions. 

Aziz, R. A. (1987). Accurate thermal conductivity coefficients for argon based on a state-of-the-art interatomic potential. Int. J. Thermophys., 8,193-204. 

Find the value of the Lennard-Jones representation of the interatomic potential function of argon at interatomic distances equal to each of the effective hard-sphere diameters of argon at different temperatures in Table A. 15 of Appendix A. Explain the temperature dependence of your values. 

The usual procedure is to define to be positively infinite in this region. Find the values of a, b, and c in the 6-exponential representation of the interatomic potential of argon that matches the Lennard-Jones representation such that c = 4sa and such that the minimum is at the same value of r as the minimum of the Lennard-Jones representation. 

An empirical and useful rule of thumb considers the velocities of particles. In particular, the time step is chosen based on how particle distances change in comparison to the interatomic potential range. For example, argon atoms at room temperature in a low-density state have a most probable velocity of 353 ms . With this speed, a time step of 10 s would result in two particles colliding (placed on top of one another) in the next time step, if they were originally at a distance of 2.5a (there are no interactions at this distance) and moving in opposite... 

Plot the attractive and repulsive potential energies. [Note not shown in answers at the end of this book.] Estimate the minimum potential energy of the pair, which can be considered the bonding energy of a molecule of argon, and the interatomic separation of this molecule. 

To see how the equipartition theorem works, first consider the simple case of a monatomic ideal gas (which would be a good model for argon or neon at low pressure). We saw in Section 5.4 that each of the N atoms in this system contributes 3/2 k T to the total translational kinetic energy (Equation 5.34), where is Boltzmann s constant. Because the system is ideal and there are no interatomic interactions, the potential energy is zero and the total energy of the gas is... 

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