Monte Carlo simulations fluid models

Cummings PT, Cochran HD, Simorrson JM, Mesmer RE, Karabomi S (1991) Simrrlation of supercritical water and of supercritical aqueous solutiorrs. J Chem Phys 94 5606-5621 Dang LX, Pettitt BM (1987) Simple intermolecular model potentials for water. J Phys Chem 91 3349-3354 De Jong PHK, Neilson GW (1997) Hydrogen-bond structme in an aqueous solution of sodiiun chloride at sub- and supercritical conditions. J Chem Phys 107 8577-8585 De Pablo JJ, Prausnitz JM (1989) Phase equilibria for fluid mixtures from Monte Carlo simulation. Fluid Phase Equil 53 177-189... 

Orkoulas G and Panagiotopoulos A Z 1999 Phase behavior of the restricted primitive model and square-well fluids from Monte Carlo simulations in the grand canonical ensemble J. Chem. Phys. 110 1581... 

Mesoscale simulations model a material as a collection of units, called beads. Each bead might represent a substructure, molecule, monomer, micelle, micro-crystalline domain, solid particle, or an arbitrary region of a fluid. Multiple beads might be connected, typically by a harmonic potential, in order to model a polymer. A simulation is then conducted in which there is an interaction potential between beads and sometimes dynamical equations of motion. This is very hard to do with extremely large molecular dynamics calculations because they would have to be very accurate to correctly reflect the small free energy differences between microstates. There are algorithms for determining an appropriate bead size from molecular dynamics and Monte Carlo simulations. 

V, ip, x, and t) in the PDF transport equation makes it intractable to solve using standard discretization methods. Instead, Lagrangian PDF methods (Pope 1994a) can be used to express the problem in terms of stochastic differential equations for so-called notional particles. In Chapter 7, we will discuss grid-based Eulerian PDF codes which also use notional particles. However, in the Eulerian context, a notional particle serves only as a discrete representation of the Eulerian PDF and not as a model for a Lagrangian fluid particle. The Lagrangian Monte-Carlo simulation methods discussed in Chapter 7 are based on Lagrangian PDF methods. 

Figure 7.8 For the unit-diameter hard sphere fluid at p = 0.277, comparison of the Poisson distribution (solid curve) with primitive quasi-chemical distribution Eq. (7.27) (dashed curve). This is the dense gas thermodynamic suggested in Fig. 4.2, p. 74, and the dots are the results of Monte Carlo simulation (Gomez et al, 1999). The primitive quasi-chemical default model depletes the probability of high- and low- constellations and enhances the probability near the mode.

Grand Canonical Monte Carlo simulation is used to investigate the properties of water (fluid of most importance) confined in mesoporous Controled Porous Glass (Vycor-like) numerically obtained by the off-lattice method developed by P. Levitz [Adv. Coll. Int. Sci. 76-77 (1998), 71]. We first outline the interaction model and give the adsorption isotherm obtained at 300 K. Good agreement is found with available experimental results. 

Fig. 2. Adsorption isotherms in all four model systems. F is the Gibbs excess adsoiption. The pressures corresponding to the three configurations shown in Figure 3 are marked with arrows. The pressure is plotted relative to the vapor pressure of the model fluid, as determined by independent Gibbs Ensemble Monte Carlo simulations. Chemical potentials were converted to pressures using a virial equation of state.

Orkoulas, G. and Panagiotopoulos, A.Z. Free energy and phase equilibria for the restricted primitive model of ionic fluids from monte carlo simulations. J. Chem. Phys., 1994,101, p. 1452-1459. 

In the current example, cerebral spinal fluid (CSF) lactate concentration was considered to be the biomarker. A model linking the PK exposure to the biomarker and another model linking biomarker to clinical response were estimated and then applied by Monte Carlo simulation to evaluate competing clinical trial designs for a Phase 3 study. 

Thus, if we know the dielectric constant of the fluid, then Eq. (3.3.15) could be used to improve the results obtained from the SSOZ-MSA approximation, for example. This has been done for dipolar hard dumbbell fluid by Lee and Rasaiah using Monte Carlo simulation results for the dielectric constant (Morriss ), and by Rossky, Pettitt and Stell. However, this approach does not seem to have any value as a predictive tool. Moreover, in the case of some interaction site models, notably hard linear triatomics, the site-site direct correlation function is not a short-range function but in fact increases with increasing r. This notwithstanding, the Cummings-Stell analysis remains an important contribution to our understanding of the SSOZ equation. 

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