Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-15T05:22:40.168Z Has data issue: false hasContentIssue false
  • English
  • Français

A First-Order Markov-Chain Model of Zeolite Crystallization

Published online by Cambridge University Press:  02 April 2024

Daniel B. Hawkins
Daniel B. Hawkins*
Affiliation:
Department of Geology/Geophysics, The University of Alaska Fairbanks, Fairbanks, Alaska 99775
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A method using a finite, first-order Markov chain is presented to estimate rate constants for zeolite formation from experimental nuclear magnetic resonance (NMR) data on the abundance of different silica oligomers. An experimental design is suggested by which this method can be implemented. The method uses weighted least squares to estimate transition probabilities from aggregate NMR data. Rate constants, equilibrium constants, and free energies of elementary zeolite-forming reactions can be estimated. Hypothetical zeolite-forming reactions can also be modeled. An example of modeling, using hypothetical data, shows how zeolite formation can result from reactions involving mainly silica cyclic tetramers.

Keywords

CrystallizationMarkov-chain modelRate constantsSilica oligomersZeolites
Type
Research Article
Information
Clays and Clay Minerals , Volume 37 , Issue 5 , October 1989 , pp. 433 - 438
Copyright
Copyright © 1989, The Clay Minerals Society

Footnotes

1

Presented at Symposium on the Geology, Genesis, Synthesis, and Use of Zeolites at 38th annual meeting of The Clay Minerals Society, Jackson, Mississippi, October 1986, convened by R. J. Donahoe. Manuscript reviewing and editing coordinated by R. J. Donahoe and R. A. Sheppard.

References

Bruns, W., Motoc, I. and O’Drisco, U. K. F., 1981 Monte Carlo Applications in Polymer Science New York Springer-Verlag.CrossRefGoogle Scholar
Cary, L. W., de Jong, B H W S and Dibble, W. E., 1982 A 29Si NMR study of silica species in dilute aqueous solution Geochim. Cosmochim. Acta 46 1317 – 1321.Google Scholar
Carman, C.J. Harrington, R. A. and Wilkes, C. E., 1977 Monomer sequence distribution in ethylene-propylene rubber measured by l3C NMR. 3. Use of reaction probability model Macromolecules 10 536 – 544.CrossRefGoogle Scholar
Cheng, H. N., 1982 Markovian statistics and Simplex algorithm for carbon-13 nuclear magnetic resonance spectra of ethylene-propylene copolymers Anal. Chem 54 1828 – 1833.CrossRefGoogle Scholar
Daniels, F. and Alberty, R. A., 1966 Physical Chemistry 3rd ed. New York Wiley.Google Scholar
Davis, J. C., 1986 Statistics and Data Analysis in Geology 2nd ed. New York Wiley.Google Scholar
Donahoe, R. J. and Liou, J. G., 1985 An experimental study on the process of zeolite formation Geochim. Cosmochim. Acta 49 2349 – 2360.CrossRefGoogle Scholar
Formosinho, S. J. and Miguel, M M daG, 1979 Markov chains for plotting the course of complex reactions J. Chem. Ed 56 582 – 586.Google Scholar
Harbaugh, J. W. and Bonham-Carter, G., 1970 Computer Simulation in Geology New York Wiley.Google Scholar
Hawkins, D. B., 1981 Kinetics of glass dissolution and zeolite formation under hydrothermal conditions Clays & Clay Minerals 29 331 – 340.CrossRefGoogle Scholar
Hayhurst, D. T. and Sand, L. B. (1977) Crystallization kinetics and properties of Na, K-phillipsites: in Proc. 4th Int. Zeolite Conf., Chicago, 1977, Katzer, J. R., ed., Amer. Chem. Soc, Symp. Series 40, 219–232.Google Scholar
Kalbfleisch, J. D. and Lawless, J. F., 1984 Least-squares estimation of transition probabilities from aggregate data Can. Jour. Statistics 12 169 – 182.CrossRefGoogle Scholar
Kemeny, J. G. and Snell, J. L., 1976 Finite Markov Chains New York Springer-Verlag.Google Scholar
Lin, C. and Harbaugh, J. W., 1984 Graphic Display of Two-and Three-Dimensional Markov Computer Models in Geology New York Van Nostrand Reinhold.Google Scholar
Lowry, G. G., 1970 Markov Chains and Monte Carlo Calculations in Polymer Science New York Dekker.Google Scholar
Strang, G., 1976 Linear Algebra and Its Applications New York Academic Press.Google Scholar