Gibbs-ensemble Monte Carlo simulation

Panagiotopoulos A Z 1987 Adsorption and oapillary oondensation of fluids in oylindrioal pores by Monte Carlo simulation in the Gibbs ensemble Mol. Phys. 62 701-19... 

Esoobedo F A and de Pablo J J 1996 Expanded grand oanonioal and Gibbs ensemble Monte Carlo simulation of polymers J. Chem. Phys. 105 4391-4... 

Fig. 3.23 The Gibbs ensemble Monte Carlo simulation method uses one box for each of the two plwses. Three types < move are permitted translations within either box volume changes (keeping the total volume constant) and transfer a particle from one box to the other.

The simulation of a first-order phase transition, especially one where the two phases have a significant difference in molecular area, can be difficult in the context of a molecular dynamics simulation some of the works already described are examples of this problem. In a molecular dynamics simulation it can be hard to see coexistence of phases, especially when the molecules are fairly complicated so that a relatively small system size is necessary. One approach to this problem, described by Siepmann et al. [369] to model the LE-G transition, is to perform Monte Carlo simulations in the Gibbs ensemble. In this approach, the two phases are simulated in two separate but coupled boxes. One of the possible MC moves is to move a molecule from one box to the other in this manner two coexisting phases may be simulated without an interface. Siepmann et al. used the chain and interface potentials described in the Karaborni et al. works [362-365] for a 15-carbon carboxylic acid (i.e. pen-tadecanoic acid) on water. They found reasonable coexistence conditions from their simulations, implying, among other things, the existence of a stable LE state in the Karaborni model, though the LE phase is substantially denser than that seen experimentally. The re-... 

FIG. 24 Monolayer G-LE coexistence conditions from the simulations of Siepmann et al. (Ref. 369) on a pentadecanoic acid model using Gibbs ensemble Monte Carlo simulation. The filled circles are the simulation results. Experimental results are also shown from Ref. 370 (triangles), Ref. 14 (squares), and Ref. 15 (diamonds). (Reproduced with permission from Ref. 369. Copyright 1994 American Chemical Society.)... 

Medeiros M, Costas ME (1997) Gibbs ensemble Monte Carlo simulation of the properties of water with a fluctuating charges model. J Chem Phys 107(6) 2012-2019... 

Monte Carlo simulations were carried out to determine the free energy curve for the reaction in solution. The simulations were executed for the solute surrounded by 250 water molecules (or 180 DMF molecules) in the isothermal-isobaric ensemble at 25 °C and 1 atm, including periodic boundary conditions. As a consequence, the Gibbs free energy is obtained in this case. There is sufficient solvent to adequately represent the bulk participation in the chemical reaction. 

Nuclear and Electronic Sampling Monte Carlo Simulations in the Gibbs Ensemble Application to Polarizable Force Fields for Water. 

S. T. Cui, P. T. Cummings, and H. D. Cochran, Fluid Phase Equilibria, 141, 45 (1997). Configurational Bias Gibbs Ensemble Monte Carlo Simulation of Vapor-Liquid Equilibria of Linear and Short-Branched Alkanes. 

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.

Gibbs-Ensemble Monte Carlo Simulations of Phase Equilibria in Supercritical Fluid Mixtures... 

Simulations essentially extend possibility to study supercooled liquid water, as crystallization may be suppressed. However, there is no water model, which adequately reproduces phase diagram of water and its properties even in the thermodynamic region, where experimental data are available. In such situation, only comparative analysis of the results, obtained for various water models, can give information, relevant for the behaviour of real water in supercooled region. Additional complication appears due to the necessity to use sophisticated simulation methods, appropriate for the studies of the phase transitions, such as Monte Carlo simulations in the grand canonical or in the Gibbs ensemble (see Refs.7,16 for more details). Note, that simulations in the simple constant-volume or constant-pressure ensembles, widely used in the studies of supercooled water (see, for example Refs. 17,18), are not appropriate for the location of the phase transitions. 

Although the mechanism of the melting transition is still not clear, but the phase diagram is now fairly well known. In particular, the triple point temperature is located at 7) = 0.40 0.01 and the triple point density is equal to about p = pa 0.79 [167]. A little more controversial is the location of the critical point. Barker et al. [165] have obtained T 0.56, while more recent Monte Carlo simulation [169] has given a somewhat lower value of 0.50T0.02. The differences in the values of the critical point temperature obtained by different authors are not surprizing, however. The recent Monte Carlo simulations in the Gibbs ensemble [170,171] have clearly demonstrated that the way one cuts the interaction potential considerably influences the estimated critical temperature. It appears that the tail of the interaction potential (beyond the assumed cut-off distance) has a big influence on the obtained results. 

Fig. 10. Schematic of the Gibbs ensemble Monte Carlo simulation method for calculation of phase equilibria of confined fluids [22].

I ic. 11. Relationship between the pore filling pressure and the pore width predicted by the modified Kelvin equation (MK). the Horvath-Kawazoe method (HK), density functional theory (DFT). and Gibbs ensemble Monte Carlo simulation (points) for nitrogen adsorption in carbon slit pores at 77 K [11]. 

Abstract The use of configurational-bias Monte Carlo simulations in tbe Gibbs ensemble allows for the sampling of phenomena that occur on vastly different time and length scales. In this review, applications of this simulation approach to probe retention in gas and reversed-phase liquid chromatographic systems are discussed. These simulations provide an unprecedented view of the retention processes at the molecular-level and show excellent agreement with experimental retention data. 

Ungerer P, Wender A, Demoulin G et al (2004) Application of Gibbs ensemble and NPT Monte Carlo simulation to the development of improved processes for H2S-rich gases. Mol Simul 30 631-648... 

Abstract Configurational-bias Monte Carlo simulations in the Gibbs ensemble have been carried out to determine the vapor-liquid coexistence curve for a pentadecanoic acid Langmuir monolayer. Two different force fields were studied (i) the original monolayer model of Karaborni and Toxvaerd including anisotropic interactions between alkyl tails, and (ii) a modified version of this model which uses an isotropic united-atom description for the methylene and methyl groups and includes dispersive interactions between the tail segments and the water surface. 

Gibbs ensemble Monte Carlo simulation is predominantly used to simulate phase equilibrium for fluids and mixtures. Two fluid phases are simulated simultaneously allowing for particle moves between each phasel . 

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