Monte Carlo techniques grand-canonical

In the last section we have assumed that we perform our simulation for a fixed number, N, of particles at constant temperature, T, and volume, V, the canonical ensemble. A major advantage of the Monte Carlo technique is that it can be easily adapted to the calculation of averages in other thermodynamic ensembles. Most real experiments are performed in the isobaric-isothermal (constant- ) ensemble, some in the grand-canonical (constant-pFT) ensemble, and even fewer in the canonical ensemble, the standard Monte Carlo ensemble, and near to none in the microcanonical (constant-NFE) ensemble, the standard ensemble for molecular-dynamics simulations. 

Simulations of water in contact with metal surfaces have been performed in a number of ensembles, including the microcanonical (NVE), canonical (NVT), and grand canonical (p-VT) ensembles. The implementation of these ensembles differs for molecular dynamics and for Monte Carlo techniques. The NVT ensemble is convenient because the temperature of the system is maintained along with the number of particles and the volume. However, with the NVE and NVT ensembles care must be exercised to ensure that the density of the water in the system is consistent with the desired equilibrium state. For... 

In closing, we would like to mention some applications of the GEMC/CBMC approach and very much related combination of CBMC and the grand canonical Monte Carlo technique to other complex systems prediction of structure and transfer free energies into dry and water-saturated 1-octanol [72], prediction of the solubility of polymers in supercritical carbon dioxide [73], prediction of the upper critical solution pressure for gas-expanded liquids [74], investigation of the formation of multiple hydrates for a pharmaceutical compound [75], exploration of multicomponent vapor-to-particle nucleation pathways [76], and investigations of the adsorption of articulated molecules in zeolites and metal organic frameworks [77, 78]. 

This review discusses a newly proposed class of tempering Monte Carlo methods and their application to the study of complex fluids. The methods are based on a combination of the expanded grand canonical ensemble formalism (or simple tempering) and the multidimensional parallel tempering technique. We first introduce the method in the framework of a general ensemble. We then discuss a few implementations for specific systems, including primitive models of electrolytes, vapor-liquid and liquid-liquid phase behavior for homopolymers, copolymers, and blends of flexible and semiflexible... 

The acceptance rates for insertions and deletions can be exceedingly low, making it impractical to employ this technique in many cases. However, for water under ambient conditions this technique can be successfully utilized at the cost of increased computational time. Where applicable, grand canonical Monte Carlo simulations enable constant volume simulations to attain the appropriate densities. This is particularly useful when one is simulating a system in which the appropriate density is not known a priori, as is often the case for inhomogeneous systems. 

For the case of equilibrium methods, for mesoporous materials gas porosimetry is complemented by Small Angle Neutron Scattering to obtain information on pore size distribution. For microporous membranes the extraction of structural information from the equilibrium sorption measurements can be based on techniques like Grand Canonical Monte Carlo Simulation. 

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. 

To capture more accurately the behavior of the adsorbates in micropores, it is often necessary to model them as non-spherical molecules with electrostatic interactions. Given the limited capabilities of DFT in this context, molecular simulation based on the Grand Canonical Monte Carlo (GCMC) technique has been established for the generation of adsorption isotherms in carbons [15,16, 17] and the determination of PSDs [18, 19, 20, 21, 22,23, 24, 25, 26]. A review on both methods is given in [27]. 

In this paper, we review our experimental and simulation work [5-7] and include new results on the solid - liquid phase behavior of mixtures confined in nanopores. Dielectric relaxation spectroscopy (DRS) was used to study the experimental phase diagram of CClVCaHn mixtures confined in activated carbon fibers (ACF). Grand Canonical Monte Carlo (GCMC) simulations with the parallel tempering technique were used to model the freezing of Lennard-Jones mixtures in slit pores. Mixtures having a simple solid solution or... 

The grand canonical Monte Carlo simulation technique was used to model the gas absorption process in SWNT bundles. The paramters used in the simulation are as follows ... 

Baeurle, Sa Grand canonical auxiliary field Monte Carlo a new technique for simulating open systems at high density. Comput. Phys. Commun. 157, 201-206 (2004). doi 10.1016/j. comphy.2003.11.001... 

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