**1. Introduction**

Zeolites are excellent catalysts due to the presence of acid sites on the framework. These catalyze a number of reactions such as hydrocarbon isomerization, hydrocarbon cracking or transformation. In recent times, there have been considerable increase in investigations pertaining to various aspects of zeolites [1–13]. There have been several studies aimed at clarifying the mechanism involved in the reactions catalyzed by zeolites. Boronat and Corma have discussed the changes in energy on proton exchange between zeolite and an adsorbate. They attempt to compute the contribution due to the van der Waals interaction between the zeolite and the adsorbate, which can be significant when the molecules are of size similar to the pore [1]. Davis and coworkers have attempted synthesis of enantiomerically enriched molecular sieve. Recently they succeeded in such a synthesis and this has been discussed in a recent article [11, 13]. Corma and coworkers have discussed various novel approaches to the synthesis of zeolites [3]. Dusselier and Davis have discussed at length the synthesis and the use in catalysis of small pore zeolites [12]. Corma and coworkers have discussed the synthesis of a new all-silica polymorph ITQ-55, which is highly efficient in the separation of ethane and ethylene with a high selectivity of 100 [4]. Prashant Kumar et al. [9] have pointed out the novel synthesis of MFI nanosheets with sandwiched MEL. Zeolite can be used for separation of xylene isomers with a high degree of separation [8]. From these it is evident that many new and novel aspects of zeolites are still being discovered and zeolites continues to be an exciting field of research with a bounty of surprises.

argon in NaCaA is higher than xenon in NaY, further investigations were carried out to find the reasons for this. To start with the energy barrier at the bottleneck was computed. This is shown in **Figure 1** [27]. From the figure it is seen that the energy barrier for xenon at the window in Y is positive while the barrier at the window is negative for argon in A zeolite. This explains why the diffusivity of argon in A zeolite is higher than xenon in Y zeolite. The trends seen in the observed barrier appears to be due to the strong interaction of argon with the oxygens of the 8-ring window. As argon is about the same diameter as the window, its strength of interaction with the oxygens is optimum being close to ϵ, which occurs at a distance at which the Lennard-Jones curve is minimum in energy. This is not the case for xenon in zeolite Y where xenon can be close to only some of the oxygens of the 12-ring window. This is the first indication that nongeometrical factors can

*Anomalous Diffusivity in Porous Solids: Levitation Effect*

*DOI: http://dx.doi.org/10.5772/intechopen.92685*

influence the diffusivity. This study shows that sorbate-zeolite interaction plays an

This study suggests that an understanding of diffusivity as a function of the diameter of the guest species might show something interesting. Such a study was carried out and the results were indeed found to be interesting [28]. A molecular dynamics study of monatomic guest molecules confined to zeolite NaY and NaCaA were carried out in which the diameter of the guest molecule was varied. The diffusivities of the guest species was computed from the time evolution of the mean square displacements. A plot of diffusivity as a function of the reciprocal of square of the guest diameter is shown in **Figure 2** for guests in both zeolites Y and A [28]. It is seen that the diffusivities decrease linearly with increase in the reciprocal of the square of the diameter of the guest molecule for small diameters. This is referred to as the linear regime (LR). As the diameter increases, it is seen that the diffusivity suddenly increases and later decreases sharply exhibiting a maximum in diffusivity. This is referred to as the anomalous regime (AR). This increase followed by a decrease in diffusivity was surprising and needed further investigations.

As can be seen the location of the guest diameter at which the maximum occurs is different in both zeolite Y and A (see **Figure 3** [28]). In order to understand the reasons for the maximum in diffusivity we have tried to search in literature any report that refers to such an observation. Derouane and coworkers have reported a finding arrived at through a theoretical analysis. They showed that the nesting

*Potential energy landscape of (a) xenon in zeolite NaY at 190 K and (b) argon in zeolite NaCaA at 140 K. the*

*energy landscapes are computed from molecular dynamics simulations.*

important role.

**Figure 1.**

**55**

Zeolites are porous aluminosilicates capable of accommodating molecules within the pores. They are well known for their catalytic, ion-exchange, and separation properties. They are widely used in petrochemical industries for processing hydrocarbons. Hydrocarbon cracking, transformation, isomerization, etc. are achieved with the help of zeolites [14, 15]. Zeolites are also used in separating hydrocarbon molecules of various sizes [16]. Larger hydrocarbons such as C15 and with still higher number of carbon atoms diffuse slowly through the pores and hence reach the bottom of a zeolite column last. Small molecules such as C1-C5 diffuse fast and exit from the column first [17, 18]. Other molecules of intermediate size have values of diffusivity in between those of C15 and C1-C5 and exit at intermediate times. Thus the various fractions from crude can be separated. This separation is much more energy efficient as compared to separation by distillation.

Another application of zeolites is its use for ion-exchange and water softening [19, 20]. Ions such as Ca2+ can be exchanged with Na+ already present in the zeolites, thus removing these ions from water. Zeolites are therefore used in detergents for washing clothes.

Apart from the use of zeolite for separation based on the size of the molecule, it is also of considerable use for separations based on the shape of the molecules. This property of zeolites is often referred to as shape selectivity [21]. The pore dimensions of zeolites, which are not always of regular shape, make this possible. An oft quoted example is the separation of xylenes (p-, m-, and o-xylenes) using silicate or ZSM-5 [22, 23]. At sufficiently high temperatures, o-xylene will convert to p-xylene and ZSM-5 also acts as a catalyst.

Zeolites and other host materials also exhibit interesting properties. They exhibit window effect, single file diffusion, and levitation effect [24–26]. Here we will focus on the levitation effect, which refers to the dependence of diffusivity on the guest or diffusant diameter.
