Diffusion In Porous Solids : Void Disorder, Orientation And Rotation, Reaction And Separation, And Levitation Effect
Diffusion in bulk has been well studied and our understanding may be said to be adequate if not complete. Similarly, surface diffusion has been investigated by a number of workers and a fair understanding of it has emerged. When guest particles are confined within the micropores of solids such as zeolites, the resulting phase is neither bulk nor an adsorbed phase but something in between. Properties of such a phase have not been understood sufficiently. Such phase found within these porous solids display rich variety in their property. In part, such a variety arises from the large number of factors that determine their properties. Present thesis attempts to study the relationship of some of these factors, viz., the pore size and the disorder in the pore sizes, the sorbate sizes, the role of orienta-tional motion, the inhomogeneities in temperature etc. to diffusion of the guest molecules in porous solids. Chapter 1 gives a brief overview of the literature and the present understanding in the field of diffusion of spherical atoms and small molecules in microporous materials with special attention to zeolites.,The discussion is focussed on the experimental, theoretical and computer simulation results reported in the last few years. In chapter 2 an analytic expression is derived for the diffusion coefficient of a sorbate in a crystalline porous solid with bottlenecks. This is done by assuming a situation of quasiequi-Hbrium and by applying some elementary results of kinetic theory of gases. The diffusion coefficients obtained from the analytic expression is found to agree well with the molecular dynamics results. Further, it is found to reproduce the diffusion anomaly and its temperature dependence for different zeolites such as Y, A and p. The present calculations provide a strong theoretical support for the levitation effect obtained so far purely from molecular dynamics calculations. The computational effort involved in evaluating the derived expression is at least an order of magnitude less as compared to the molecular dynamics simulations. Levitation effect is found to exist in crystalline porous solids, irrespective of the geometry and topology of the void network of the host - the zeolite. Does levitation effect exist in non-crystalline porous solids where a distribution of pore sizes is seen instead of a single size? Chapter 3 attempts to answer this question via detailed molecular dynamics simulations on zeolite Y whose perfectly crystalline pore structure has been modified by introducing disorder. A normal distribution characterized by its width <TQ of 12-ring window diameters has been generated. Investigation of motion of spherical sorbates within such a disordered host suggests that levitation effect persists although the intensity of the anomalous peak is reduced compared to crystalline faujasite. Further, there is a breakdown of the linear relationship between the self-diffusivity D and 1 /^ where a99 is the sorbate diameter in the disordered host. Comparison of similarity between the effect of temperature and that of disorder are discussed. Chapter 4 investigates the role of orientation on diffusion of methane in zeolite NaCaA during intercage and intracage migration. In this work, diffusion of a five site model of methane within porous zeolite A has been investigated by molecular dynamics simulation. Methane exhibits interesting orientational preference during its passage through the 8-membered window, the rate determining step for overall diffusion: (2+2) (or scissor) orientation is preferred to (1+3) (or inverted umbrella) orientation. This suggests strong translational-orientational coupling. This is supported by ab initio mixed basis calculations thereby suggesting that the results are not a consequence of the classical potential employed. Partial freezing of certain rotational degrees of freedom is observed during the passage of methane through the 8-ring window. Intracage motion of methane shows that methane performs a rolling motion rather than a sliding motion within the supercage. In Chapter 5, diffusion of methane and neopentane through the pores of zeolite NaY has been investigated by means of molecular dynamics simulation. Intercage motion consisting of diffusion through 12-ring window of zeolite NaY is seen to occur with strong orientational preference for (2+2) orientation in the case of neopentane but not methane. Comparison of the result with methane diffusion through the 8-ring window of zeolite NaCaA reported in chapter 4 suggests that such a preferential orientation is a typical characteristic of systems whose levitation parameter is close to unity. Temperature dependence of translational-orientational coupling during the passage through the bottleneck has been obtained. As seen earlier, partial freezing of certain rotational degrees of freedom also exists. Little or no freezing is observed around the molecular axis of symmetry parallel to the vector, ft, perpendicular to the window plane since it does the orientation of the molecule with respect to fi. Analysis of intracage motion suggests existence of rolling motion in preference to sliding motion both in methane and neopentane. It is suggested that globular molecules show a predominance of rolling motion in comparison to anisotropic molecules such as benzene. Chapter 6 reports results from molecular dynamics(MD) simulations and its comparison to the quasi-elastic neutron scattering (QENS) measurements of the diffusion of propane, NaY zeolite, at different temperatures and at a relatively high loading. The contributions to S(Q, cu) from ballistic and diffusive motions are analysed. The self-diffusivity D has been calculated from mean squared displacement (MSD) as well as from the dynamic structure factor (S(Q,cu)) computed from the MD simulation. Both the values are consistent with each other. Also, they are in reasonable agreement with the experimental QENS results. The MD results indicate a fixed jump length diffusion process, whereas, the QENS data fits well to a jump diffusion model with a Gaussian distribution of jump lengths. Diffusion is often accompanied by a reaction or sorption which in turn can induce temperature inhomogeneities. In chapter 7 Monte Carlo simulations of Lennard-Jones atoms in zeolite NaCaA are reported for the presence of a hot zone presumed to be created by a reaction. Our simulations show that the presence of localized hot regions can alter both the kinetic and transport properties such as diffusion. An enhancement in diffusion coefficient is seen in the presence of a local hot spot. Further, the enhancement of the diffusion constant is greater for systems with larger barrier height, a surprising result that may be of considerable significance to many chemical and biological processes. We find an unanticipated coupling between reaction and diffusion due to the presence of hot or cold zone in addition to that which normally exists between them via concentration. Chapter 8 explores the possibility of exploiting a judicial combination of levitation effect and blow-torch effect for the separation of mixtures. In this study, Monte Carlo simulations have been carried out for three different binary mixtures in zeolite NaCaA with hot spot placed just before the position of the window along one direction. The binary mixture consisting of two types of particles both of which are from the linear regime does not separate well while the separation achieved of the mixture with one component from the linear regime and another from the anomalous regime is excellent. The separation factors obtained in the case of the latter mixture is more than an order of magnitude larger than that of the conventional separation methods. In the case of Ne-Ar mixture in NaCaA also, where Ne is in the linear regime and Ar is in the anomalous regime, the separation attained is excellent. These results suggest that a combination of levitation and blow-torch effects can be used to obtain extraordinary separation. Here the levitation effect specifies the sign and the magnitude of the energy barrier. The blow-torch drives the component in positive or negative direction depending on the energy barrier of the guest species. An appendix describes an additional but unrelated work carried out: a Monte Carlo study of the orthorhombic(fJ), monoclinic(ct) and liquid phases of toluene in the isobaric isothermal ensemble employing variable shape simulation cell. The structure has been characterized in terms of the radial distribution functions and orientational correlation functions. The transition from the orthorhombic low temperature (3-phase to the high temperature monoclinic cc-phase has been successfully simulated. The transition is first order and lies between 140 and 145K in agreement with experiment. The reverse transition from the a-to the (3-phase does not take place in agreement with experiment. The liquid phase density and the heat of vapourization are in good agreement with the experimental values.