Diffusion is a fundamental process which occurs in a wide variety of phases. It plays an important role in chemistry, physics, biology, materials science etc. In recent times, diffusion in confined systems has been widely investigated. Porous aluminosilicates such as zeolites, carbon nano tubes and metal organic frameworks(MOF) provide confined regions within which small molecules can diffuse. Indeed, diffusion within these materials have attracted considerable attention in the past few decades (see for example, “Diffusion in Zeolites and Other Microporous Solids”, J. Ka¨rger and D..M. Ruthven, John Wiley &Sons, NewYork,1992). Diffusion in confined spaces exhibits rich variety. For example, single file diffusion, window effect, levitation effect (LE), super-and sub-diffusive motion have all been observed in confined regions.
Levitation effect provides an explanation for the dependence of self-diffusivity on the diameter of the diffusant. Consider a diffusant diffusing within a porous material. The pore network provided by the pore material may be characterized by the void and the neck distribution where the necks are the narrower regions interconnecting larger voids. It has been seen that diffusivity is maximum when the size of the diffusant is large and when it is comparable to the diameter of the bottleneck of the pore network. Recently it has been demonstrated that the levitation effect also exists in dense liquids such as water and dense solids. These developments essentially unify our understanding of diffusion in widely differing condensed matter phases. These results show that there is fundamentally no difference between porous substances and dense media at least with regard to dependence of self-diffusivity on the diameter of the diffusant.
Chapter 1 provides a brief introduction to the subject of hydrocarbons confined within zeolites and ionic conductivity in polar solvents. We have given a description of the different applications of zeolites in the area of catalysis, separation etc. Window effect, single file diffusion, levitation effect and enhancement of viscosity of confined fluids are described. A brief review of various computational studies of hydrocarbons confined within zeolites is given. This is followed by a discussion of different experimental techniques and their use in the study of diffusion and adsorption within zeolites by many different groups in the last few decades. In the last section of the chapter we have discussed the anomalous size dependence of ionic conductivity in polar solvents which presumably has its origin in the Levitation Effect(LE). We have explained different theories proposed previously to understand the non-monotonic behavior of ionic conductivity as a function of ionic radius.
A molecular dynamics(MD) investigation and quasi-elastic neutron scattering (QENS) study of pentane isomers in zeolite NaY is pre-sented in Chapter 2. QENS provides the first direct experimental evidence for LE. In an earlier study, a maximum in diffusivity as a function of the diameter of the diffusant for monatomic sorbates confined within zeolite NaY was observed by MD simulation. Since LE has been invoked to explain the diffusion in a wide variety of condensed matter phases, an experimental evidence of the levitation effect would be of great value. QENS measurements were carried out by Dr. Herve Jobic. Surprisingly we found that neopentane shows higher diffusivity than n-pentane and isopentane although its cross-sectional diameter perpendicular to the long molecular axis is larger compared to isopentane and n-pentane in agreement with predictions of LE. There is an excellent agreement between QENS results and MD simulation. LE predicts that the isomer with high diffusivity has low activation energy. The activation energies have been calculated from the Arrhenius plots using QENS as well as MD data. These follow the order Ea(n−pentane)>Ea(isopentane)>Ea(neopentane). Various other properties such as potential energy barrier at the bottleneck, velocity auto correlation function, intermediate scattering function, k dependence of the width of the dynamic structure factor have been computed. These provide additional insights into the nature of the motion of these isomers. They suggest that the barrier at the 12-ring window depends on the molecular diameter and levitation parameter of isomer.
In Chapter 3, we report molecular dynamics simulation study of n-hexane and 2,2-dimethylbutane(DMB) mixture confined within the pores of zeolite NaY. We have taken an equimolar composition of the mixture consisting of n-hexane and DMB. The total number of hydrocarbon molecules in the system is 128. The simulations were carried out at various temperatures of 170, 200, 250 and 300 K. We have computed the self-diffusivities from the slope of the mean square displacement. It is found that the diffusivity of DMB is 0.82 ×10−9 m2/sec and that of n-hexaneis0.38 ×10−9 m2/sec. All previous studies of linear hydrocarbon and its branched analogue in different zeolites in the literature suggest that it is the linear member which has higher self-diffusivity. The cross-sectional diameter of DMB perpendicular to the long molecular axis is higher than that of n-hexane. Thus, DMB should have lower diffusivity. In order to understand this behavior of diffusivity we have computed the activation energies from the Arrhenius plots. The activation energy of DMB is found to be lower than that of n-hexane. This is inconformity with the levitation effect which states that the molecule with larger diameter comparable to that of the bottleneck diameter has low activation energy. We have also computed the potential energyprofileatthe12-ring window. The potential energy profile shows a barrier for n-hexane and a minimum for DMB at the window. This is in agreement with the previous results on monatomic species. We have computed other properties such as velocity auto correlation function, intermediate scattering function as well as wave number dependence of full width at half maximum of dynamic structure factor. These properties explain in detail the motion of n-hexane and DMB within NaY zeolite.
In Chapter 4 molecular dynamics investigation into diffusion of n-decane and 3-methylpentane mixture within zeolite NaY. We have studied an equimolar mixture of n-decane and 3-methylpentane (36 of each) in the supercages of NaY zeolite in such a way that the con-centration is one molecule for every three cages. Simulations were performed at four different temperatures : 300, 350, 400 and 450 K. The distribution and orientation of the molecules inside the cage and at the window plane have been studied. Inside the cage, 3-methylpentane stays more close to the inner surface of the zeolite whereas n-decane prefers to stay close to the center of the cage. Both the species prefer to stay with their long molecular axis parallel to the surface of the zeolite. During passage through the window, 3-methylpentane is closer to the window center than n-decane. The distribution of the angle subtended by the end-to-end vector of the molecule with the normal to the window plane, while the molecular center is in the window plane, shows that 3-methylpentane samples a larger range of orientation than n-decane. This may lead to an entropic barrierfor n-decane. We have computed the diffusivity of both the molecules. Diffusivity of 3-methylpentane is found to be higher than n-decane. This behavior is consistent with the observations made in the last two chapters. The activation energy of 3-methylpentane is found to be 3.17 kJ/mol and forn-decaneitis6.0kJ/mol. This agrees with the prediction of levitation effect. The energy profile a the window shows shallow minimum for both n-decane and 3-methylpentane. Therefore, the energy profile does not describe the nature of motion of the molecules. We have computed the the dihedral angle distribution when the molecule is at the adsorption site and when it is at the window plane. The distributions essentially remain same for 3-methylpentane whereas a considerable change in the distributions is seen for n-decane. The gauche population of n-decane increases at the cost of trans population when it goes from the adsorption site to the window. The lower diffusivity of n-decane can be partly attributed to the change in the dihedral angle. Also, the orientational entropic barrier may be another cause of the slow motion of n-decane. Thus, in the present study the slow motion of n-decane is partly explained by levitation effect and partly by the change in the dihedral angle as well as the entropic barrier. Overall, the results in the last three chapters leads to the main conclusion that the branched isomer will diffuse faster than a linear hydrocarbon in zeolites with 12-ring window such as zeolite NaY.
In Chapter 5, diffusion of pentane isomers in zeolites NaX and NaY has been investigated using pulsed field gradient nuclear magnetic resonance(PFG-NMR) and molecular dynamics(MD) techniques respectively. Temperature as well as concentration dependence of diffusivity have been studied. The diffusivities obtained from NMR are roughly an order of magnitude smaller than those obtained from MD. The dependence of diffusivity on loading at high temperatures exhibits a type I behavior according to the classification of K¨arge rand Pfeifer. NMR diffusivities of the isomers exhibit the order D(n−pentane)>D(isopentane)>D(neopentane). The results from MD are in agreement with the QENS results where the diffusivities of the isomers follow the order D(n-pentane)<D(isopentane)<D(neopentane). The activation energies from NMR show Ea(n-pentane)<Ea(isopentane) <Ea(neopentane) whereas those from MD suggest the order Ea(n-pentane) >Ea(isopentane) >Ea(neopentane). The latter follows the predictions of levitation effect whereas those of NMR appears to be due to the presence of defects in the zeolite crystals. The differences between NMR and MD are attributed to the long time and length scales over which NMR samples are probed compared to MD or QENS. Th eresults from these studies suggests that although branched isomer intrinsically have higher diffusivities than linear hydrocarbons in zeolites such as NaY, the presence of defects can effectively annul this higher diffusivity of the branched isomer.
Correlation of self-diffusivity and entropy of monatomic sorbates con-fined within zeolite NaY has been investigated in Chapter 6. We have carried out molecular dynamics simulation on monatomic sor-bates within zeolite NaY at 150, 110 and 90 K. As suggested by the Levitation Effect, the self-diffusivity shows a non-monotonic behavior as a function of the diameter of the sorbates. We have computed the entropy of the sorbates of various sizes ranging from 3.07˚
A to 7.0˚
A using the method proposed by Goddard and his co-workers as well as from the radial distribution function. The variation of entropy with the diffusant diameter exhibits a behavior similar to that of the self-diffusivity on diffusant diameter, thereby showing a strong correlation between the entropy and diffusivity. The loss of entropy on adsorption is a minimum for the diffusant with maximum diffu-sivity. This is in agreement with the experimental measurements of Kemball. Thus, entropy follows the prediction of the levitation effect. With decrease in temperature both self-diffusivity as well as entropy show more pronounced maximum as a function of the diameter of the sorbate. The dimensionless diffusivity from three different isotherms follow a Rosenfeld type of excess entropy scaling rule, D∗= Aexp(αSe) where A and α are the scaling coefficients.
In Chapter 7 we have investigated the self-diffusivity as well as cor-rected diffusivity of pure methane in faujasite NaY combining quasi elastic neutron scattering experiment and molecular dynamics simu-lation. The QENS experiment carried out at 200 K led to an unex-pected dependence of self-diffusivity on loading for pure methane with the presence of a maximum at 32 CH4/unit cell. This is at variance with previous reports. Typically, diffusivity of a polar species such as methane in a zeolite such as NaY exhibits a monotonic decrease with loading. Molecular dynamics simulation was performed to reproduce this experimentally observed behavior. We could reproduce the diffusivity behavior qualitatively with a maximum at 16 CH4/unit cell. The corrected diffusivities obtained from both experiment as well simulation show similar behavior as the self-diffusivity with maximum at an intermediate loading. The experimental behavior was reproduced only when the interaction of methane with the sodium cation is in-creased suggesting that this interaction may be important.
In Chapter8 we have investigated the role of attractive interaction on size dependent diffusivity maximum of ions in water. We have per-formed molecular dynamics simulation of mode lions in water. Earlier study of systems interacting only through van der Waals interaction shows that the size dependent diffusivity maximum or the levitation effect disappears when the attractive term(r−6 term) of the Lennard-Jones potential is put equal to zero. It is not clear whether the absence of the dispersion interaction in a system where there is electrostatic attraction will lead to a size dependent diffusivity maximum. There-fore, two sets of simulations with and without dispersion interaction between the ion and water have been carried out at700Kinorderto understand the influence of the attractive interaction. It is found that the self-diffusivity of the ions indeed exhibits an anomalous maximum as a function of the vanderWaals diameter for both the sets, viz., with dispersion and without dispersion interaction. In fact, the diffusivity maximum is seen to be more pronounced when there is no dispersion interaction. This existence of the maximum in self diffusivity when there is no dispersion interaction between the ion and the water is attributed to the attractive term from electrostatic interactions. De-tailed analysis shows that the solvent shell is more well defined in the presence of dispersion interactions. The velocity auto correlation function shows undulation at short times for the smaller ions indicating rattling motion inside the cage formed by the surrounding water molecules. Smaller ion exhibits a bi-exponential decay while a single exponential decay is seen for the ion with maximum diffusivity in the intermediate scattering function. The solvent structure appears to determine much of the dynamics of the ion. Interesting trends are seen in the activation energies and these can be understood in terms of the Levitation Effect.
| Identifer | oai:union.ndltd.org:IISc/oai:etd.ncsi.iisc.ernet.in:2005/1921 |
| Date | 08 1900 |
| Creators | Borah, Bhaskar J |
| Contributors | Yashonath, S |
| Source Sets | India Institute of Science |
| Language | en_US |
| Detected Language | English |
| Type | Thesis |
| Relation | G24450 |
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