Fluids dense, molecular simulations

An analogy may be drawn between the phase behavior of weakly attractive monodisperse dispersions and that of conventional molecular systems provided coalescence and Ostwald ripening do not occur. The similarity arises from the common form of the pair potential, whose dominant feature in both cases is the presence of a shallow minimum. The equilibrium statistical mechanics of such systems have been extensively explored. As previously explained, the primary difficulty in predicting equilibrium phase behavior lies in the many-body interactions intrinsic to any condensed phase. Fortunately, the synthesis of several methods (integral equation approaches, perturbation theories, virial expansions, and computer simulations) now provides accurate predictions of thermodynamic properties and phase behavior of dense molecular fluids or colloidal fluids [1]. 

Tmskett and Dill (2002) proposed a two-dimensional water-like model to interpret the thermodynamics of supercooled water. This model is consistent with model (1) for liquid water. Cage-like and dense fluid configurations correspond to transient structured and unstructured regions, observed in molecular simulations of water (Errington and Debenedetti, 2001). Truskett and Dill s model provides a microscopic theory for the global phase behavior of water, which predicts the liquid-phase anomalies and expansion upon freezing. 

An example drawn from Deitrick s work (Fig. 2) shows the chemical potential and the pressure of a Lennard-Jones fluid computed from molecular dynamics. The variance about the computed mean values is indicated in the figure by the small dots in the circles, which serve only to locate the dots. A test of the thermodynamic goodness of the molecular dynamics result is to compute the chemical potential from the simulated pressure by integrating the Gibbs-Duhem equation. The results of the test are also shown in Fig. 2. The point of the example is that accurate and affordable molecular simulations of thermodynamic, dynamic, and transport behavior of dense fluids can now be done. Currently, one can simulate realistic water, electrolytic solutions, and small polyatomic molecular fluids. Even some of the properties of micellar solutions and liquid crystals can be captured by idealized models [4, 5]. 

Although experimental transport properties are measured at different temperatures and pressures, it is the density, or molar volume, which is the theoretically important variable. So, for the prediction of transport properties, it is necessary to convert data at a given temperature and pressure to the corresponding temperature and density, or vice versa, by use of a reliable equation of state. Accordingly, an account is given in this volume of the most useful equations of state to express these relationships for gases and liquids. For dense fluids, it is possible to calculate transport properties directly by molecular simulation techniques under specified conditions when the molecular interactions can be adequately represented. A description is included in this book of these methods, which are significant also for the results which have aided the development of transport theory. 

In the first problem class mentioned above (hereinafter called class A), a collection of particles (atoms and/or molecules) is taken to represent a small region of a macroscopic system. In the MD approach, the computer simulation of a laboratory experiment is performed in which the "exact" dynamics of the system is followed as the particles interact according to the laws of classical mechanics. Used extensively to study the bulk physical properties of classical fluids, such MD simulations can yield information about transport processes and the approach to equilibrium (See Ref. 9 for a review) in addition to the equation of state and other properties of the system at thermodynamic equilibrium (2., for example). Current activities in this class of microscopic simulations is well documented in the program of this Symposium. Indeed, the state-of-the-art in theoretical model-building, algorithm development, and computer hardware is reflected in applications to relatively complex systems of atomic, molecular, and even macromolecular constituents. From the practical point of view, simulations of this type are limited to small numbers of particles (hundreds or thousands) with not-too-complicated inter-particle force laws (spherical syrmetry and pairwise additivity are typically invoked) for short times (of order lO" to 10 second in liquids and dense gases). 

We turn then to dense fluids and outline the main approaches used for them, which we classify into three main categories Molecular Simulation, Perturbation, and Semiempirical. More emphasis is given to the last one which, using results from the other two approaches, leads to semiempirical equations of state. 

Under the simulation conditions, the HMX was found to exist in a highly reactive dense fluid. Important differences exist between the dense fluid (supercritical) phase and the solid phase, which is stable at standard conditions. One difference is that the dense fluid phase cannot accommodate long-lived voids, bubbles, or other static defects, whereas voids, bubbles, and defects are known to be important in initiating the chemistry of solid explosives.107 On the contrary, numerous fluctuations in the local environment occur within a time scale of tens of femtoseconds (fs) in the dense fluid phase. The fast reactivity of the dense fluid phase and the short spatial coherence length make it well suited for molecular dynamics study with a finite system for a limited period of time chemical reactions occurred within 50 fs under the simulation conditions. Stable molecular species such as H20, N2, C02, and CO were formed in less than 1 ps. 

Molecular dynamics. The spectroscopy of dense fluids is closely related to the dynamics of the many-body system. For that reason, molecular dynamics and other computer simulations of many-body dynamics have been used to compute spectral moments and line shapes of dense fluids. Such simulations are important for liquids or highly compressed gases (Frenkel 1980). 

Here ji(qa) is the spherical Bessel function of order l,g(a) is the radial distribution function at contact, and f = /fSmn/Anpo2g a) is the Enskog mean free time between collisions. The transport coefficients in the above expressions are given only by their Enskog values that is, only collisional contributions are retained. Since it is only in dense fluids that the Enskog values represents the important contributions to transport coefficient, the above expressions are reasonable only for dense hard-sphere fluids. Earlier Alley, Alder, and Yip [32] have done molecular dynamics simulations to determine the wavenumber-dependent transport coefficients that should be used in hard-sphere generalized hydrodynamic equations. They have shown that for intermediate values of q, the wavenumber-dependent transport coefficients are well-approximated by their collisional contributions. This implies that Eqs. (20)-(23) are even more realistic as q and z are increased. 

The perturbation theories [2, 3] go a step beyond corresponding states the properties (e.g., Ac) of some substance with potential U are related to those for a simpler reference substance with potential Uq by a perturbation expansion (Ac = Aq + A + Aj + ). The properties of the simple reference fluid can be obtained from experimental data (or from simulation data for model fluids such as hard spheres) or corresponding states correlations, while the perturbation corrections are calculated from the statistical mechanical expressions, which involve only reference fluid properties and the perturbing potential. Cluster expansions involve a series in molecular clusters and are closely related to the perturbation theories they have proved particularly useful for moderately dense gases, dilute solutions, hydrogen-bonded liquids, and ionic solutions. 

Figure 2.5. Molecular D)oiainics simulation of self-diffusion in a dense fluid of "soft" spherical particles near a "hard" solid wail. The "wall" exerts no force on the particles but reverses the z-component of the velocity if a molecule attempts to cross it a is the length parameter in the repulsive part of the Lennard-Jones interaction. (Redrawm from J.N. Cape. J. Chem. Soc., Faraday Trans. II 78 (1982) 317.)...

W. Loose and G. Ciccotti, Phys. Rev. A., 15, 3859 (1992). Temperature and Temperature Control in Nonequilibrium Molecular Dynamics Simulations of the Shear Flow in Dense Fluids. 

The empirical determination of potential parameters has usually been performed assuming pairwise additivity for the molecular interactions, that is, that the total interaction energy is a summation of the interactions over all pairs of molecules. However, for many fluids such as water, methanol, and other highly polar molecules, pairwise additivity does not properly describe molecular interactions, especially in dense phases. This is why an approximate potential with one set of empirically adjusted or effective parameters cannot be made to reproduce a wide range of experimental data. Until recently, most simulations used the assumption of pairwise additivity. 

On the theoretical front, the use of molecular dynamics simulations in combination with first principle, semi empirical, or classical fields have also emerged as viable tools to access the short time scale for chemical events of dense fluids at high-temperature. These methods not only complement experimental work, but also predict the early... 

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,... 

If a fiVT ensemble simulation can be turned into a ( quasi ) NPT ensemble-type simulation (e.g., a pseudo- FT ensemble), the inverse transformation (a pseudo-NPT ensemble) is also possible. The key relationship for a pseudo-NPT ensemble technique is Eq. (5.1) [78]. Such a reverse strategy can be practical only if molecular insertion and deletion moves can be performed efficiently for the system under study (e.g., by expanded ensemble moves for polymeric fluids). Replacing volume moves by particle insertions can be advantageous for polymeric and other materials that require simulation of a large system (due to the sluggishness of volume moves for mechanical equilibration of the system) such an advantage has been clearly demonstrated for a test system of dense, athermal chains [78]. 

The physics of motion in a layer adjacent to the solid surface is quite different from the bulk motion described by the Stokes equation. This generates effective slip at a microscopic scale comparable with intermolecular distances. The presence of a slip in dense fluids it is confirmed by molecular dynamics simulations [17, 18] as well as experiment [19]. The two alternatives are shp conditions of hydrodynamic and kinetic type. The version of the slip condition most commonly used in fluid-mechairical theory is a linear relation between the velocity component along the solid surface and the shear stress... 

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 ). 

Although it turned out that a number of essential features concerning dynamics of molecular liquids can be well captured by the theory of the previous subsection (see Secs. 3 and 5), an intense investigation through experimental, theoretical, and molecular-dynamics simulation studies for simple liquids has revealed that the microscopic processes underlying various time-dependent phenomena cannot be fully accounted for by a simplified memory-function approach [18, 19, 20]. In particular, the assumption that the decay of memory kernels is ruled by a simple exponential-type relaxation must be significantly revised in view of the results of the kinetic framework developed for dense liquids (see Sec. 5.1.4). This motivated us to further improve the theory for dynamics of polyatomic fluids. 

The principal advantage of the time correlation function method is that it provides a new set of microscopic functions for a fluid, the time correlation functions, which can be studied directly by experimental observations of the fluidt or by computer-simulated molecular dynamics. The time correlation functions depend even more sensitively on the microscopic properties of the fluid molecules than the transport coefficients, which are expressed as time integrals of the correlation functions. Thus, a further test of kinetic theory has been found it must not only lead to expressions for the transport coefficients for dilute and dense gases that are in agreement with experiment, but also describe the dependence of the time correlation functions on both time and the density of the gas. One of the principal successes of kinetic theory is that it provides a quantitatively correct description of the short- and long-time... 

As we discussed earlier, the generalized Boltzmann equation leads to a density expansion of the transport coefficients of a dense gas. However, general expressions for transport coefficients of a fluid that are not in the form of an expansion can be derived by another technique, the time correlation function method. This approach has provided a general framework by means of which one can make detailed comparisons between theoretical results, the results of computer-simulated molecular dynamics,and experimental results. ... 

In Sections 2 and 3, we set up a formalism for dealing with the dynamics of dense fluids at the molecular level. We begin in Section 2 by focusing attention on the phase space density correlation function from which the space-time correlation functions of interest in scattering experiments and computer simulations can be obtained. The phase space correlation function obeys a kinetic equation that is characterized by a memory function, or generalized collision kernel, that describes all the effects of particle interactions. The memory function plays the role of an effective one-body potential and one can regard its presence as a renormalization of the motions of the particles. 

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