Fluid density, molecular dynamics

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. 

In Fig. III-7 we show a molecular dynamics computation for the density profile and pressure difference P - p across the interface of an argonlike system [66] (see also Refs. 67, 68 and citations therein). Similar calculations have been made of 5 in Eq. III-20 [69, 70]. Monte Carlo calculations of the density profile of the vapor-liquid interface of magnesium how stratification penetrating about three atomic diameters into the liquid [71]. Experimental measurement of the transverse structure of the vapor-liquid interface of mercury and gallium showed structures that were indistinguishable from that of the bulk fluids [72, 73]. 

The simulations to investigate electro-osmosis were carried out using the molecular dynamics method of Murad and Powles [22] described earher. For nonionic polar fluids the solvent molecule was modeled as a rigid homo-nuclear diatomic with charges q and —q on the two active LJ sites. The solute molecules were modeled as spherical LJ particles [26], as were the molecules that constituted the single molecular layer membrane. The effect of uniform external fields with directions either perpendicular to the membrane or along the diagonal direction (i.e. Ex = Ey = E ) was monitored. The simulation system is shown in Fig. 2. The density profiles, mean squared displacement, and movement of the solvent molecules across the membrane were examined, with and without an external held, to establish whether electro-osmosis can take place in polar systems. The results clearly estab-hshed that electro-osmosis can indeed take place in such solutions. 

Equilibrium Systems. Magda et al (12.) have carried out an equilibrium molecular dynamics (MD) simulation on a 6-12 Lennard-Jones fluid In a silt pore described by Equation 41 with 6 = 1 with fluid particle Interactions given by Equation 42. They used the Monte Carlo results of Snook and van Me gen to set the mean pore density so that the chemical potential was the same In all the simulations. The parameters and conditions set In this work were = 27T , = a, r = 3.5a, kT/e = 1.2, and... 

To compare molecular theoretical and molecular dynamics results, we have chosen the same wall-particle potential but have used the 6 - oo fluid particle potential. Equation 14, Instead of the truncated 6-12 LJ potential. This Is done because the molecular theory Is developed In terms of attractive particles with hard sphere cores. The parameter fi n Equation 8 Is chosen so that the density of the bulk fluid In equilibrium with the pore fluid Is the same, n a = 0.5925, as that In the MD 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).

The local density augmentation caused by the large isothermal compressibility of the fluid may conceivably influence k i or ka. We assume that the lifetime of the clusters is extremely short and thus there is no effect on kd, based on the molecular dynamics study of Petsche and Debenedetti (29) and experimental measurements of binary diffusion coefficients near the critical point. It seems more likely that a higher local density would affect k i due to an increase in the number of... 

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. 

The second contribution spans an even larger range of length and times scales. Two benchmark examples illustrate the design approach polymer electrolyte fuel cells and hard disk drive (HDD) systems. In the current HDDs, the read/write head flies about 6.5 nm above the surface via the air bearing design. Multi-scale modeling tools include quantum mechanical (i.e., density functional theory (DFT)), atomistic (i.e., Monte Carlo (MC) and molecular dynamics (MD)), mesoscopic (i.e., dissipative particle dynamics (DPD) and lattice Boltzmann method (LBM)), and macroscopic (i.e., LBM, computational fluid mechanics, and system optimization) levels. 

Molecular dynamics calculations of Hoover and Ree (25) have indicated that a fluid-solid transition occurs in a system of hard spheres even in the absence of attractive forces. The fluid exists for particle volume fractions up to a value rj = 0.49 and at this point, a solid phase with ij = 0.55 is predicted to coexist in equilibrium with the fluid phase. When the particle volume fraction lies in the range 0.55 < jj < 0.74, the solid phase is stable. The upper limit for ij corresponds to the density at closest packing for a face-centered-cubic (fee) arrangement of the particles. 

The principal tools have been density functional theory and computer simulation, especially grand canonical Monte Carlo and molecular dynamics [17-19]. Typical phase diagrams for a simple Lennard-Jones fluid and for a binary mixture of Lennard-Jones fluids confined within cylindrical pores of various diameters are shown in Figs. 9 and 10, respectively. Also shown in Fig. 10 is the vapor-liquid phase diagram for the bulk fluid (i.e., a pore of infinite radius). In these examples, the walls are inert and exert only weak forces on the molecules, which themselves interact weakly. Nevertheless,... 

Figure 10. Vapor-liquid equilibria for an argon-krypton mixture (modeled as a Lennard-Jones mixture) for the bulk fluid (R = >) and for a cylindrical pore of radius R = / /Oaa = 2.5. The dotted and dashed lines are from a crude form of density functional theory (the local density approximation, LDA). The points and solid lines are molecular dynamics results for the pore. Reprinted with permission from W. L. Jorgensen and J. Tirado-Rives, J. Am. Chem. Soc.

The kinetic equations serve as a bridge between the microscopic domain and the behavior of macroscopic irreversible processes through the description of hydrodynamics in terms of intermolecular collisions. Hydrodynamics can specify a large number of nonequilibrium states by a small number of reproducible properties such as the mass, density, velocity, and energy density of a fluid conserved during the collision of molecules. Therefore, the hydrodynamic equations can describe a wide range of relaxation processes of nonequilibrium states to equilibrium state. We call such processes decay processes represented by phenomenological equations, such as Fourier s law of heat conduction. The decay rates are determined by the transport coefficients. Reliable transport coefficients provide microscopic and macroscopic information, and validate the results of molecular dynamics. 

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.

The transport of a sub-critical Lennard-Jones fluid in a cylindrical mesopore is investigated here, using a combination of equilibrium and non-equilibrium as well as dual control volume grand canonical molecular dynamics methods. It is shown that all three techniques yield the same value of the transport coefficient for diffusely reflecting pore walls, even in the presence of viscous transport. It is also demonstrated that the classical Knudsen mechanism is not manifested, and that a combination of viscous flow and momentum exchange at the pore wall governs the transport over a wide range of densities. 

The simplest possible case of a gas-solid interaction for physical adsorption is that of a molecule interacting with a smooth hard wall. The wall can be planar, as for a free surface or a slit pore, or it can be cylindrical or some other shape for a pore. These cases have been extensively studied by Monte Carlo and molecular dynamics with results that show that such a gas-solid interaction gives a strongly structured fluid that can be best described as a series of layers that follow the contour of the wall. The sharpness of the density variations that define these layers increases as the overall density of the adsorbed film increases and decreases with increasing distance from the wall. 

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