Cationic Motion in Dehydrated Zeolites
The exchangeable cations in dehydrated zeolites, types X and Y, are located on several energetically and coordinatively different sites. The number of vacant sites is of the same orde; of magnitude as the number of occupied sites. As a result, the motions of the cations as evidenced by the dielectric relaxation and electrical conductivity, are highly correlated. The dielectric relaxation can be described in terms of a dipole moment per cubooctahedron, the magnitude of which depends on the number of cations in the cubooctahedron. The ionic conduction due to the movement of the cations in the supercages, requires the introdaction of an ionic conductivity correlation factor besides the classical geometrical correlation factor in the Nernst-Einstein equation. 1 . Introduction. In dehydrated, synthetic zeolites, types X and Y, the exchangeable cations occupy well-defined sites. These sites are distinguished in' two aspects : the coordination offered by the lattice oxygens and their place in the cavities [I]. Table I gives a survey and figure 1 shows a general view of the structure. The numljer of exchangeable cations depends on the Si : A1 ratio and is typically 86 for X-type and 56 for Y-type zeolites. This is less than the number of available sites. Consequently, specific cationic distribution patterns exist, depending on the properties of the exchangeable cations and the site characteristics [2]. The mobility of the exchangeable cations was measured with the electrical conductivity technique in the frequency range 200-3 x lo6 Hz and up to 750 K. Ionic relaxations and ionic' conduction are revealed and assigned to specific cationic motions. The ionic relaxations around room temperature are Table I. Description of exchangeable cation sites for zeolites X and Y . Number of coordinating Number of sites Site oxygens per unit cell Cavity I 6 16 hexagonal prism I' 3 32 cubooctahedron 11' 3 32 cubooctahedron I1 3 32 supercage 111 4 48 supercage Flg. 1. Schemat~c drawlng of the structure of ieolites X and Y. due to local motion of-cations in the vicinity of sites I11 between two occupied sites 11. 1on.k relaxations above 400 K are ascribed to @tionic'jumps inside the cubooctahedra, while ionic conduction was due to migration of exchangeable cations in the superArticle published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980666 C6-262 R. A. SCHOONHEYDT cages. The arguments for these assignments are given in the original papers [3-51. ow ever when it comes to an analysis of these movements in terms of elementarry jump processes, the nature of the system imposes a physically important boundary condition : the inumber of available vacant sites is of the same ord~er of magnitude as the number of diffusing cations. As a consequence, every cationic jump disturbs the equilibrium configuration of exchangeable cations in its surroundings and highly correlated motions result. The situation is similar to that of such superionic conductors as b-alumina. In the following paragraphs these correlations are taken into account to explain the cationic mobility in these systems. 2. Ionic relaxation. In one cubooctahedron 4 sites I' and 4 sites 11' are available, but in dehydrated zeolites only sites I' are oocupied. Correlations between site occupancies arc: derived from the fact that because of electrostatic repulsions sites I and I' on one hand and sites 11' and I1 on the other hand cannot be occupied simultaneously 161. The potential energy of cations on the sites I' depends on the occupancy of seighbouring sites but also on the Si4+ and AI3+ distributions in the lattice and the coordinating properties of the exchangeable cation under investigation. On the atomic scale every cation in the cubooctahedron faces an energetically heterogeneous surface. Consequently, the e1eme;ritary ionic diffusion or local electrical conductivity .varies from site to site. The resulting relaxation prcxess will be characterized by a distribution d relaxa.ti'on times [7, 81. The elementary dipole is formed betweenthe cation on site I' and the negatively charged lattice. The dipole moment length is, not the cation-oxygen distance or the jump distance, But the statistical average of the projections of all the possible cationic orientations on the electric, hJd axis [9]. Thus, the experimentally measured dipole m.oment is not the dipole moment per c a t i ~ n in the cubooctahedron, but the average dipole moment pe.r cubooctahedron. Only with one exchangeable cation per cubooctahedron the two dipole moments are equal. When there is more than one cation in the cubooctahedron, the dipole moment of the cubooctal~edron is the vectorial sum of the dipole moments associated with the individual cations. When one catiojn jumps to a neighbouring site, the other adapts itself to the new situation and the individual dipole moments cannot be resolved. Clearly, when there are no exchangeable cations in the cuboocta'hedron, or when all the sites are occupied, there is no net dipole moment and no ionic relaxation. To substanti.ate these ideas the dipole moment per cubooctahedron was czstimated from the experimental intensities of thie ionic relaxations [3-51 and the cation occupancies [2, 10, 111 with neglect of the distribution of relaxation times. Thle Onsager-Kirkwood relation [12] was used : The experimental data are summarized in table I1 together with the calculated dipole moments, peff. When they are plotted as a function of the number of elementary positive charges per cubooctahedron a plot is obtained which satisfies the theoretical deductions (Fig. 2). At zero and full occupancies of site I' the dipole moment per cubooctahedron approaches zero. Table 11. Dipole monventsper cubooctahedron. Cations per T Perf Sample cubooctahed~:on K 8, E , cm x lo2' *NaF5 2.37 519 5.3 29.0 2.87 NaHFS(1) 1.40 640 3.0 37.0 4.12 NaHFS(2) 0.50 631 4.7 10.0 0.79 CaF5 0.325 627 2.9 21.9 1.52 CuF5 1.40 625 5.6 18.6 1.76 LaF2.5 1 .OO 800 3.0 23.0 1.06 * The chemical symbol clenotes the exchangeable cation in the cubooctahedron, F the zeolites and the number following this sample symbol is the SiO, :. A1203 ratio. C;harges/ Sodalite Cage Fig. 2. The dipole moment per cubooctahedron as a functlon of the number of cha.rges (in terms of number of monovalent cations) per cubooctahedron. It is maximum when 2 out of the 4 sites I' are occupied by monovalent cations. Divalent and trivalent cations fit the cun7e of figure 2 when they are taken equivalent to 2 atla' 3 monovalent cations respectively. Thus, the idea of a dipole moment per cubooctahedron has a physi.cal meaning. CATIONIC MOTION IN DEHYDRATED ZEOLITES C6-263 The following picture emerges when a large temperature domain is investigated. Below 400 K the cationic jump frequency is too low to obtain a measurable relaxation intensity. As the temperature raises and thus the jump frequency, the relaxational intensity increases. Above a fixed temperature, characteristic for the zeolite and the type of exchangeable cation, the migration is no longer restricted to the cubooctahedra but jumps between cubooctahedra and supercages become possible. They do not contribute to the relaxation process. A dynamic equilibrium is established between cubooctahedra and supercages. The relaxational intensity is at maximum intensity or decreases slightly. This behavior was experimentally verified [4, 51. In conclusion, it is clear that this picture of a cationic relaxation, restricted inside a cubooctahedron can be generalized to any cation moving between 2 closely spaced boundaries. This is the case, for instance, for Naf on sites I11 in the supercages, around room temperature [3]. These Na+ ions move between 2 sites I1 occupied by Na+. As the mobility of Naf on I1 is low with respect to Naf on 111, the occupied sites I1 constitute at room temperature unsurmountable barriers and Na+ on I11 oscillates around site 111, giving rise to an ionic relaxation. The corresponding average dipole moment was calculated to be 3.32 x cm. 3. Ionic conduction. The ionic conduction in dehydrated zeolites X and Y is governed by the cations on sites I1 in the supercages. The elementary jump processes can be envisaged as I1 -t I11 + I1 [3-51. This system of sites in the supercages constitutes a superlattice structure. Every cationic jump in the superlattice disturbs the equilibrium distribution of the exchangeable cations. It necessitates the introduction in the Nernst-Einstein relation of a supplementary correlation factor f , , besides the structural correlation factor [13-151 : The room temperature cation distribution of a homogeneous series of K+-saturated zeolites has Table 111. Correlation coeflcients for ionic conductivity in K + -zeolites. F48.2 F54.7 F69.8 F86.5 P o 0.816 0.838 0.903 0.800 40 0.033 0.092 0.310 0.796 f (300 K) 0.366 8 0.422 6 0.526 9 0.921 5 A (300 K) 0.391 3 0.489 9 0.765 0 1 W (kJmol-') 9.66 7.22 4.38 1.74 po, occupancy of sites I1 ; go, occupancy of sites I11 ; W, the potentxal energy difference of Kf on sites I1 and I11 ; f;, is the ionic conductivity correlation factor and A the geometrical correlation factor. The number after the sample F is the number of kT per unit cell. been published [6] together with an analysis of the potential energy difference between the exchange sites [16]. This allows a calculation of the correlation factors with the path probability method [13-151. Table I shows the ionic conductivity correlation factor A and the geometrical correlation factor f. FI increases monotonically with site occupation p[= 1/2Cpo + q,)] to reach the value 1 for nearly equal occupancies of the 2 sites i.e. no potential energy difference between sites I1 and 111'. Such a behavior satisfies the theoretical predictions [13-151. F is composed of the individual correlation coefficients of the 2 migration processes : Its value depends on the diffusion mechanism. In the limit of p -+ 1 this mechanism is an interstitialcy mech
Fundamental aspects of water methane separation in zeolites
The main objective of this thesis was to use molecular dynamics to investigate the methane interactions with zeolite, specifically the Linde Type A-3A, alongside with an investigation into the use of polynomial path integration for water in zeolite. This thesis is a part of a larger collaboration between the separation group at the University of Bergen and Statoil, with the main goal of explaining the reduced lifetime of zeolites. This thesis continued from the work done by the separation group at the University of Bergen. The then used model was suspect to wrongly describe the methane zeolite interactions. Consequently, a new model was tried in order to correctly describe the interactions. The obtained diffusion coefficients for the old and new model, have been compared to reported literature values for a counter-ion free zeolite A. The new model shows an excellent agreement with these values, for a loading of 8 molecules/cavity or more. A simulation using the new model in Linde Type A-3A zeolite, shows that potassium blocks all methane motion in the structure. Furthermore, it was observed that potassium motion, at 500 K under the influence of methane, can lead to unblocking of the 8T-window. This leads us to formulate a hypothesis for the reduced lifetime of LTA-3A zeolite. Polynomial path integration was performed for water in zeolite. This was computational difficult, due to the different forces in the multi-specie system. The results revealed that different paths from ideal gas towards real gas gave large differences in the estimated excess Helmholtz energy. Other methods can thus be better suited for this purpose, for example the particle insertion method.
New method for analysis of enzymatic reactions: Thermolysin-catalyzed synthesis of aspartame precursor
Aspartame is an artificial sweetener which is 200 times sweeter than sucrose. A precursor of aspartame, N-(benzyloxycarbonyl)-l-aspartyl-l-phenylalanine methyl ester (Z-APM) was synthesized and hydrolyzed with thermolysin in an aqueous monophasic system. Graphical plotting methods and/or nonlinear regression have been used to analyze enzymatic reactions because of the nonlinearity of enzymatic rate equations. There are, however, problems: the former require accurate measurement of the initial reaction rate and the latter gives no analytical information. The authors proposed a method to solve the nonlinear enzymatic rate equations with respect to the concentration of a product with the Taylor expansion, especially for the reversible Theorell-Chance mechanism (Murakami, Y., Hirata, M., and Hirata, A., J. Ferment. Bioeng., 82, 246–252, 1996). This solution, however, is complex for practical use. In this paper, a simpler solution to explain the thermolysin-catalyzed synthesis of Z-APM is obtained. New methods to determine the kinetic parameters, especially for the reversible Theorell-Chance mechanism, based on the approximated solution are proposed. The results calculated using the obtained kinetic parameters can satisfactorily explain the experimental results, which demonstrates the effectiveness of the proposed analysis. We must know the relation between the concentrations of substrates and a product, and accurately evaluate of the result obtained using Taylor expansion when we determine the kinetic parameters using our newly developed methods. The methods to determine the kinetic parameters of the reversible Theorell-Chance mechanism described in this paper is, however, expected to be applied to general enzymatic reactions.