Gibbs ensemble Monte Carlo molecular simulation

The most striking news that one learns when studying vapor-liquid phenomena is that not only does the vapor need to nucleate a liquid droplet to condense, but that also the liquid needs to nucleate a gas bubble to evaporate [24]. On the theoretical side, the simulation is made easier because the vapor is relatively simple to handle, on the experimental side, vapor pressure measurements in vapor-liquid equilibrium are fairly easy to perform. The Gibbs ensemble Monte Carlo method (Section 9.8) can be applied to the vapor-liquid equilibrium with considerable success vapor pressure curves, second virial coefficients, and other equilibrium properties can be calculated by molecular simulation, and, remarkably, good results can apparently be obtained by highly accurate ab initio quantum mechanical potentials [25a] or by simple empirical potentials [25b]. 

MC techniques are applied in practice. The methodology is rather general and in principle can be applied to any molecular liquid [82] or spin system. It also has advantages over techniques like Gibbs ensemble Monte Carlo [83] because it can be combined with finite-size scaling in the vicinity of the critical point. In addition, the method yields interfadal properties. Our presentation follows Reference [47]. Simulations are typically performed in the grand canonical pVT ensemble with periodic boundary conditions, that is, we fix the chemical volume and temperature but allow for particle insertions or deletions. For a simple Lennard-Jones liquid, Eq. (1.13) becomes ... 

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-... 

The reported results for equilibrium properties were obtained by means of the standard Monte Carlo (MC), molecular dynamics (MD), and Gibbs ensemble (GE) simulation methods [23, 24], For the trial systems of a finite range the simple spherical cutoff was used, whereas in simulations of the full systems either the Ewald summation or the reaction field method were used. For further technical details we refer the reader to the original papers. 

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. 

A new molecular simulation technique is developed to solve the perturbation equations for a multicomponent, isothermal stured-tank adsorber under equilibrium controlled conditions. The method is a hybrid between die Gibbs ensemble and Grand Canonical Monte Carlo methods, coupled to macroscopic material balances. The bulk and adsorbed phases are simulated as two separate boxes, but the former is not actually modelled. To the best of our knowledge, this is the first attempt to predict the macroscopic behavior of an adsorption process from knowledge of the intermolecular forces by combining atomistic and continuum modelling into a single computational tool. 

Once the force field is chosen, a proper simulation method needs to be selected. Molecular dynamics simulations are applied to determine the solvation behaviour of ionic liquids by means of solving the Newtonian equations of motion for all molecules in the presence of a gradient in potential energy. Ionic liquid phase equilibria are determined by using Monte Carlo simulations in the isothermal isobaric Gibbs ensemble, grand canonical ensemble or osmotic ensemble with clever sampling schemes. 

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