Zeolites Monte Carlo method

For adsorption in zeolites, the biased Monte Carlo method as developed by Smit is an excellent method to determine the free energies of molecules adsorbed on zeolites [9bj. This method can be used to compute the concentration of molecules adsorbed on zeolites, as we discuss below. 

Metropolis Monte Carlo method sorption on zeolites, 42 62, 66 MgO... 

The configurational-bias Monte Carlo method (CB-MC) (112) was developed to overcome these sorts of problems. Instead of a random insertion into the zeolite host, the guest molecule is grown atom by atom within the host in a way that avoids unfavorable overlap with the zeolite atoms. 

Yashonath etal. (46) used a Metropolis Monte Carlo method to simulate the infinite-dilution adsorption of methane in NaY zeolite. The lattice had a Si/Al ratio of 3.0 and was treated as rigid, whereas methane was modeled... 

The shape of a zeolite sorption uptake isotherm, a quantitation of the amount of a given sorbate taken up as a function of its partial pressure in the gas phase in equilibiitun with the zeolite sorbent, depends both on the zeolite sorbate interaction and on the sorbate - sorbate interactions. Simulation of such isotherms for one or more sorbates is accomplished by the Grand Canonical Monte Carlo method. Additional to the molecular reorientation and movement attempts is a particle creation or annihilation, the probability of which scales with the partial pressure [100,101]. This procedure thus simulates the eqmlibrium between the sorbed phase in the zeolite and an infinite gas / vapor bath. Reasonable reproduction of uptake isotherms for simple gases has been achieved for a small number of systems (e.g. [100,101]), and the molecular simulations have, for example, explained at a molecular level the discontinuity observed in the Ar - VPI-5 isotherm. 

Transition state theory can also be employed to calculate diffusion coefficients in hopping processes. Adsorbates prefer to reside at particular places in a zeolite and because an energy barrier is present between them, they do not transfer easily from one site to another. The possible adsorption sites are located via a Monte Carlo method, and the transition state via migration path analyses. A rate constant can be associated with jumps from site i to siteA surface can be defined that separates sites i and and contains the top of the energy... 

In the grand-canonical Monte Carlo method, the system volume, temperature, and chemical potential are kept fixed, while the number of particles is allowed to fluctuate.There exist three types of trial move (1) displacement of a particle, (2) insertion of a particle, and (3) removal of a particle. These trial moves are generated at random with equal probability. The acceptance probability of the Metropolis method can be used for the trial moves of type (1). For the two other types, the acceptance probabilities are different. Regarding zeolites, an adsorption isotherm can be calculated with the grand-canonical Monte Carlo method by running a series of simulations at varying chemical potentials. 

For ab initio modelling of extra-framework cations, when only the framework structure is known, it becomes convenient to use a Monte Carlo method, as described above. Recent calculations by Newsam et al. (1996) (discussed in greater detail in Chapter 5) have demonstrated the efficacy of this approach, by correctly reproducing the distribution of Na + in zeolite A, and also predicting the (as yet unknown) location of Li+ in Li-ABW. 

Such methods of analysing and describing adsorption data have considerable merit in describing microporosity in porous carbons, which are not crystalline, or for microporous solids of unknown structure, but for zeolites of known structure they add little to our understanding. In such cases, the form of the adsorption isotherms can be modelled by computer simulation using Grand Canonical Monte Carlo methods. In this approach all the parameters are known or can be measured or calculated (see Section 4.5.1) so that the adsorption isotherm can be simulated using a physically well-characterised model. 

In a molecular simulation, a zeolite is described by its geometry and the interactions among atoms (namely, the force fields). This atomic or molecular level information then needs to be translated into measurable macroscopic quantities so that computations can be validated against experiments. Statistical-modeling techniques, such as the classical Monte Carlo method, can be used to accurately compute the static properties of zeolites, provided the force fields assigned to the system are accurate enough and are based on experimental data. Dynamic properties, such as thermal conductivity or mass diffusivity, are most readily computed using classical MD. 

A series of SIM data is compared with those Irom simulation experiments using Monte Carlo methods, and excellent agreement has been achieved. The energetic heterogeneity of sorbents due to specific interactions between molecules of various gases, e.g., carbou dioxide, and specific sorption centers in zeolites, is quantified by characteristic concentration dependences of the thermodynamic functions. 

Af/ads is the heat of adsorption from the gas phase, which takes into account the dispersion interaction of hexene with the oxygen atoms in the wall of the zeolite pores. This energy depends both on the size of the reactant (hexene in this case) and the size o .the pores in the zeolite (Figure 8a and 8b) and is estimated with the configurational-bias Monte Carlo method (CB-MC). - The CB-MC method differs from conventional Monte Carlo (see Monte Carlo Simulations for Polymers) in so far as.ti guest species is grown atom by atom inside the host rather than inserted as a complete molecule. ... 

A moment analysis of Si MAS spectra of zeolites is shown to provide direct information on the number of second-nearest-neighbor Al-Al pairs. Monte Carlo computer calculations are described of randomized A1 distributions in zeolite frameworks, under restrictions of Loewenstein s and Dempsey s rules. The method is applied to a hypothetical square planar lattice which allows the various A1 distribution patterns to be visualized in simple displays, and to the zeolite X and Y framework. The results are compared with experimental data taken from the literature. 

The complexity of xylene adsorption over zeolites is too high to predict the selectivity from the chemical properties of the zeolite only (electronegativity of the cations, charge of the framework oxygens). The interactions between xylenes and the zeolite must necessarily be considered, which explains the important development of molecular simulation methods. This is supported by the work of V. Lachet et al. (18) who succeeded in reproducing the inversion of selectivity between KY and NaY with Grand Canonical Monte Carlo Simulations. 

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