Approaches to Zeolite Modeling

During the last two decades, the number of molecular modeling studies on zeolites published annually has grown enormously. As a result of advances in both the development of computational methodologies and new computer architectures, modeling has become an important tool in zeolite research. It can provide useful insight into the structure and reactivity of zeolites and into the sorption of molecules in zeolites. This section gives a brief introduction to computational approaches, as well as a short overview on applications in zeolite research. 

Although there are many ways to describe a zeolite system, models are based either on classical mechanics, quantum mechanics, or a mixture of classical and quantum mechanics. Classical models employ parameterized interatomic potentials, so-called force fields, to describe the energies and forces acting in a system. Classical models have been shownto be able to describe accurately the structure and dynamics of zeolites, and they have also been employed to study aspects of adsorption in zeolites, including the interaction between adsorbates and the zeolite framework, adsorption sites, and diffusion of adsorbates. The forming and breaking of bonds, however, cannot be studied with classical models. In studies on zeolite-catalyzed chemical reactions, therefore, a quantum mechanical description is typically employed where the electronic structure of the atoms in the system is taken into account explicitly. 

Conventional methods based on quantum mechanical models use matrix diagonalization to find a self-consistent solution of the time-independent Schrodinger equation. Unfortunately, the cost of matrix diagonalization grows extremely rapidly with the number of atoms in the system. Consequently, methods based on quantum mechanical models tend to be computationally expensive. As a result, the zeolite framework is often treated as a cluster instead of as a periodical system. To overcome this obstacle, hybrid models have been put forward in which the problem is circumvented the reaction center is described in a quantum mechanical way, whereas the surroundings are described in a classical way.  

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Figure 3 Approaches to zeolite modeling depicted in a three-dimensional graph.

Another approach to mathematical modeling of contact-sorption drying that was used to simulate drying of com by mixing with zeolite particles (Alighani, 1990) is based on the following simplified system of Luikov s differential equations for heat and mass transfer (Luikov, 1966 Luikov and Mikhailov, 1961) ... 

In order to illustrate the general applicability of the methodology we have extended our approach to other large zeolite crystals, such as SAPO-34, SAPO-5 and ZSM-5. Our study on the rhombic SAPO-34 crystals reveals a four-pointed star fluorescence pattern at 445 K, which is transformed into a square-shaped feature at 550 K. This is illustrated in Figure 4a. Confocal fluorescence slices, summarized in Figures 4b-d, recorded at different temperatures show the cubical pattern, which proceed from the exterior of the crystal inwards. Both observations are consistent with a model which involves six components of equal tetragonal pyramids as illustrated in Figure 3b. 

In summary while conceptually appealing, the application of complex multi-solute models for Sr sorption to zeolite is in the early stages of development. While preliminary results are encouraging, additional work is required to develop more efficient computational methods and develop an improved database for parameter estimation. The remainder of this section focuses on the simpler retardation factor approach. 

The deactivation of a lanthanum exchanged zeolite Y catalyst for isopropyl benzene (cumene) cracking was studied using a thermobalance. The kinetics of the main reaction and the coking reaction were determined. The effects of catalyst coke content and poisoning by nitrogen compounds, quinoline, pyridine, and aniline, were evaluated. The Froment-Bischoff approach to modeling catalyst deactivation was used. 

This new approach to the nitration of deactivated aromatics has been successfully applied to a range of substrates and details have recently been published.17 As indicated above, the approach was modelled on the successful nitration of moderately activated substrates using nitric acid, acetic anhydride and zeolite 3 that we had developed earlier.11 However, commercial organisations appear reluctant to adopt that new technology despite its greatly superior selectivity and potential environmental impact. Therefore, we continue to look for alternative methods of achieving selective nitrations. 

The state and capabilities of quantum chemical modeling of silicon dioxide framework structures (silica, aluminosilicates, zeolites) are discussed by Zhido-mirov and Kazansky. Here are basic theoretical approaches to a class of catalytic compositions which contribute the probably most massive quantities of catalysts used by man s (petroleum and chemical) industries. 

Pressure Swing Adsorption (PSA) unit is a dynamic separation process. In order to create a precise model of the process and thus an accurate design, it is necessary to have a good knowledge of the mixture s adsorption behaviour. Consequently, the dilAision rates in the adsorbent particles and the mixture isotherms are extremely vital data. This article intends to present a new approach to study the adsorption behaviour of isomer mixtures on zeolites. In a combined simulation and experimental project we set out to assess the sorption properties of a series of zeolites. The simulations are based on the configurational-bias Monte Carlo technique. The sorption data are measured in a volumetric set-up coupled with an online Near Infra-Red (NIR) spectroscopy, to monitor the bulk composition. Single component isotherms of butane and iso-butane were measured to validate the equipment, and transient volumetric up-take experiments were also performed to access the adsorption kinetics. 

There is an already impressive literature on the application of various first principles and semi-empirical approaches to aspects of zeolite chemistry (see, e.g., [104-107]). Even a cursory overview of this aspect of zeolite modeling and simulation would be beyond the scope of the present paper. However, two recent development areas are noted. 

First principles approaches are important as they avoid many of the pitfalls associated with using parameterized descriptions of the interatomic interactions. Additionally, simulation of chemical reactivity, reactions and reaction kinetics really requires electronic structure calculations [108]. However, such calculations were traditionally limited in applicability to rather simplistic models. Developments in density functional theory are now broadening the scope of what is viable. Car-Parrinello first principles molecular dynamics are now being applied to real zeolite models [109,110], and the combined use of classical and quantum mechanical methods allows quantum chemical methods to be applied to cluster models embedded in a simpler description of the zeoUte cluster environment [105,111]. 

This conversational and somewhat subjective overview of computational approaches in zeolite chemistry has illustrated that the field is very diverse, and expanding rapidly. Modeling and simulation at the atomistic or electronic structural level clearly contribute at various levels to practical zeolite research and development programs. Characterization and zeolite physical and chemical property prediction are the most prominent application domains at present. 

Many computational approaches have been applied in zeolite modeling. Each uses a different combination of the description of the system (model) and the technique (method) that may be suited for a particular problem (application) (see Figure 3). This section mentions briefly the frequently encountered models and methods in zeolite modeling, to provide a basic understanding. In the following sections, they are discussed in more detail. 

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