Fluid density, molecular dynamics simulations

Figure 5. Molecular dynamics simulation of the decay forward and backward in time of the fluctuation of the first energy moment of a Lennard-Jones fluid (the central curve is the average moment, the enveloping curves are estimated standard error, and the lines are best fits). The starting positions of the adiabatic trajectories are obtained from Monte Carlo sampling of the static probability distribution, Eq. (246). The density is 0.80, the temperature is Tq — 2, and the initial imposed thermal gradient is pj — 0.02. (From Ref. 2.)...

Figure 8 Compressibility factor P/fiksT versus density p = pa3 of the hard-sphere system as calculated from both free-volume information (Eq. [8]) and the collision rate measured in molecular dynamics simulations. The empirically successful Camahan-Starling84 equation of state for the hard-sphere fluid is also shown for comparison. (Adapted from Ref. 71).

Substantial evidence suggests that in highly asymmetric supercritical mixtures the local and bulk environment of a solute molecule differ appreciably. The concept of a local density enhancement around a solute molecule is supported by spectroscopic, theoretical, and computational investigations of intermolecular interactions in supercritical solutions. Here we make for the first time direct comparison between local density enhancements determined for the system pyrene in CO2 by two very different methods-fluorescence spectroscopy and molecular dynamics simulation. The qualitative agreement is quite satisfactory, and the results show great promise for an improved understanding at a molecular level of supercritical fluid solutions. 

In this chapter, we have reviewed some of our own work on solvation properties in supercritical fluids using molecular dynamics computer simulations. We have presented the main aspects associated with the solvation structures of purine alkaloids in CO2 under different supercritical conditions and in the presence of ethanol as co-solvent, highlighting the phenomena of solvent density augmentation in the immediate neighborhood of the solute and the effects from the strong preferential solvation by the polar co-solvent. We have also presented a summary of our results for the structure and dynamics of supercritical water and ammonia, focusing on the dielectric behavior of supercritical water as functions of density and temperature and the behavior of excess solvated electrons in aqueous and non-aqueous associative environments. 

Figure 1.38. Molecular dynamics simulation of the density profiles for spherical molecules in a cylinder, mimicking SFg in controlled pore glass (CPG-10). Fluid-fluid and fluid-wall interaction modelled by Lennard-Jones interactions. Reference A. de Keizer. T. Michalski and G.H. Findenegg, Pure Appl. Chem. 63(1991) 1495.

It can be seen from Eqs. (2) and (3) that the potential of mean force zv(r) is not the true potential w(r). Figure 1 shows a comparison between ii(r) and zv(r) based on our own molecular dynamic simulations with a simple monatomic fluid system. Only when the particle density of the system p is approaching 0, that is, when two particles that are apart at a fixed distance r are not affected by the remaining N — 2 particles, w r) — u r). 

Unfortunately, previous work is almost exclusively concerned with the inversion temperature in the limit of vanishing gas density, Ti y (0). The inversion temperature can be linked to the second virial coefficient, which can be measured [210] or computed from rigorous statistical physical expressions [211] with moderate effort. Currently, only the fairly recent study of Heyes and Llaguno is concerned with the density dependence of the inversion temperature from a molecular (i.c., statistical physical) perspective [212]. These authors compute the inversion temperature from isothermal isobaric molecular dynamics simulations of the LJ (12,6) fluid over a wide range of densities and analyze their results through various equations of state. 

Orientational structure at a liquid vapor-interface of diatomic interaction site fluids has been studied extensively by Gubbins and Thompson using both thermodynamic perturbation theory and molecular dynamics simulation, and by Tarazona and Navascues using perturbation theory. Chacon et al. have applied density-functional theories to these systems. The theoretical methodology and results are reviewed in a comprehensive article by Gubbins, to which the reader is directed for more complete details. 

HMX (1,3,5, 7-tetranitro-l, 3,5,7-tetraazacyclooctane) is widely used as an ingredient in various explosives and propellants. A molecular solid at standard state, it has four known pol5miorphs, one of which, the 8 phase is comprised of six molecules per unit cell, as depicted in Fig. 10. We study the chemical decomposition of the dense fluid of this phase by conducting a high-density and temperature (p = 1.9 g/cm, T = 3500 K) quantum mechanical based molecular dynamics simulation. [50] To our knowledge, this is the first reported ab initio based/molecular dynamics study of an explosive material at extreme conditions for extended reaction times of up to 55 picoseconds, thus allowing the formation of stable product molecules. 

We conducted a quantiun-based molecular dynamics simulation of HMX at a density of 1.9 g/cm and temperature of 3500 K for up to 55 picoseconds has been conducted. These are conditions similar to those encountered at the Chapman-Jouget detonation state. Thus, although we do not model the entire shock process, we can provide some insight into the nature of chemical reactivity under similar conditions. Under the simulation conditions HMX was found to be in a highly reactive dense supercritical fluid state. We estimated effective reaction rates for the production of H2O, N2, CO2, and CO to be 0.48,... 

The collision frequency t must be obtained from some model for the liquid. If an effective hard sphere radius for the molecules can be chosen, the collision rate can then be obtained from Enskog theory or from molecular dynamics simulations of the hard sphere fluid. An alternative that has been popular is to use a cell model for the liquid." In its simplest form a molecule moves in a cell created by fixed neighbors located on a lattice. For a cubic lattice, the distance between neighbors is where p is the hquid-state number density. The central molecule then moves a distance 2p / —2a between collisions, if its effective diameter is a. The time between collision is then... 

Readers might have seen a similar picture from a result of a molecular dynamics simulation. If you look carefully, there are places where molecules are densely crowded, while in some places molecules are scarce. If one takes the average of the number of molecules over the entire volume of the container, N/V = p, it is of course a constant, and it does not include useful information with respect to the structure and dynamics of the fluid. However, if one takes a product of densities at two different places r and r, and takes a thermal average over configurations, namely, u r)u r )) = p(r,r ), it then contains ample information about the structure and dynamics of liquids. The quantity is called density-density pair correlation function . When the fluid is uniform, the quantity can be expressed by a function of only the distance between the two places, such that p(r, F) p( r — r ). 

Figure 7. Time dependence of the wavelength of the fastest growing density fluctuation (Affiax) during a molecular dynamics simulation of isothermal liquid-vapor spinodal decomposition in the three-dimensional Lennard-Jones fluid kT/e = 0.8 p

In order to ascertain whether the 3-regime behavior observed in the experimental vibrational lifetimes is indeed a result of local density enhancements, Goodyear and Tucker [12] computed both vibrational lifetimes and local density enhancements from molecular dynamics simulation for a model solute-solvent SCF solution. These authors considered a diatomic solute in a 2-dimensional supercritical Lennard-Jones fluid of 1150 atoms (Fig. 1). In this model, each of the solute atoms was designated as a Lennard-Jones site, and the Lennard-Jones parameters between solute and solvent atoms were taken to be the same as those between solvent atoms. The vibrational lifetimes were computed using the standard, classical Landau-Teller expression [69,70,72,73,78], i.e. 

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