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Modelling crystal growth in zeolite A
Zeolites and Related Materials: Trends, Targets and Challenges Proceedings of 4th International FEZA Conference A. Gédéon, P. Massiani and F. Babonneau (Editors) © 2008 Elsevier B.V. All rights reserved.
705
Modelling crystal growth in zeolite A Ayako Umemura, Pablo Cubillas, Michael W. Anderson, and Jonathan R. Agger Centre for Nanoporous Materials. School of Chemistry. The University of Manchester Oxford Road, M13 9PL. Manchester, U.K. +44 (0)161 306 2770.
Abstract Zeolite A is one of most widely used and studied zeolites owing to its cation-exchange properties. Here, we present a computer program that simulates morphology as well as surface topology for zeolite A crystals. Results from simulations were compared with scanning electron microscopy and atomic force microscopy images on the {100}, {110} and {111} faces of synthetic crystals. This allowed to further refine the program by varying the relative attachment/detachment probabilities of individual growth sites. Keywords: zeolite A, Monte Carlo simulation, atomic force microscopy
1. Introduction Zeolites and other microporous materials have been the subject of a great number of studies in the last century owing to their applications in many industrial processes.1-3 Nevertheless, only recently have studies been performed to understand the fundamental aspects involved in the nucleation and growth of these materials.4,5 Nucleation is affected under high supersaturation and the end product of the synthesis is a function of the equilibrium state. The use of Monte Carlo simulation methods proposes a good prediction of the real crystal growth processes. The aim of the study is to gain further understanding about the thermodynamics and kinetics of these processes by simulating the morphology and topology of zeolite A.
2. Methods 2.1. Algorithm for Zeolite A Crystal Growth and Dissolution Events in Solution A Monte Carlo program has been written to coarse grain the crystal growth into 1.2 nm, which is half unit cell of LTA structure. The choice of 1.2 nm growth units was based on measurements of individual step heights on AFM studies on zeolite A. 4 Each site is defined by considering 24 first and second coordination neighbours (Fig.1a). This yielded a total of 223 different site types. Nevertheless only 192 site types were actually considered during the simulation, since bulk sites where not allowed to grow or dissolve. The first sphere coordination considers six sites and is based in the Kossel model (Fig. 1b), whereas the second sphere of coordination takes into account 18 different sites. Addition of the second sphere of coordination was due to the inability to simulate beveled edges and/or truncated structures using only the Kossel model.6 Each site was assigned with a certain probability of crystal growth and dissolution creating sets of probabilities that will, ultimately, simulate different growth modes with different rates. By considering the probabilities and the population of each site type, either crystal growth or dissolution is randomly chosen at each iteration during the
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A. Umemura et al.
Figure 1. a) First and b) second sphere coordination sites around an individual growth unit. c) Ideal crystal surface showing the six different types of sites considered by the Kossel model. calculation. The local coordination is then changed at every iteration as the growth or dissolution affects the coordination of their neighbouring sites. In designing the program, we focused on creating an efficient simulation as CPU time consumption and memory usage could hamper its utility and flexibility. For this reason surface diffusion is not currently considered in the program. 2.2. Computing and Rendering Environment The simulation program was written in Fortran 90 and rendered with Surface Evolver7. The calculation was executed on a 264 bit Intel Xeon processor running at 3GHz with 4GB of RAM. This cluster, called the Epsilon, is supported by the Research Support Group of the faculty of Engineering and Physical Sciences at the University of Manchester. The Epsilon provides Intel£ Fortran Compiler, which was reported almost twice as fast of any other compilers on the market by Polyhedron8. Images were rendered on the Intel Core Duo processor with 2.16 GHz and 1GB of RAM. 2.3. Comparison with Synthetic Crystals The results obtained from the simulation program were iteratively compared with atomic force microscopy (AFM) images of synthetic zeolite A crystals. Synthesis of zeolite A crystals was carried out following the method by Thompson9. Scanning electron micrographs where obtained using an FEI Quanta 200. AFM images were obtained using a Nanowizard II BioAFM from JPK Instruments AG. Images were taken using both contact and intermittent contact scanning modes.
3. Results and Discussion The computation was performed with about two minutes of CPU time at 20 million iterations, which represents ca. 0.3 × 0.3 × 0.3 μm3 of zeolite A. Further optimisation would come from running the program in a bigger memory environment. The program was used to simulate the growth of a crystal of zeolite A after nucleation has taken place. This was accomplished by selecting two different probability sets (applied at two different crystal sizes), which reproduced two different “growth modes” expected at high and low supersaturation respectively. Fig. 2 shows a typical evolution of crystal fraction and supersaturation as a function of time compared with three
Modelling crystal growth in zeolite A
707
Figure 2. a) Typical crystal size and supersaturation evolution as a function of time for zeolite A synthesis. Inset picture shows typical zeolite A crystal produced in the synthesis. Image size 2.5 μm. b), c) and d) show ca. 0.3 × 0.3 × 0.3 μm3 sized zeolite A crystals simulated at time intervals 1, 2 and 3, respectively. renderings of the simulation, corresponding to the highlighted time intervals (1, 2 and 3). The SEM image in Fig. 2a shows the typical final product of synthesis of zeolite A. It can be noted that this preparation yielded crystals with {100}, {110} and {111} faces clearly exposed. At interval 1 supersaturation is maximum and hence nucleation is high on all of the crystal surfaces, creating rough surfaces full of nuclei as depicted in Fig. 2b. At interval 2 the supersaturation starts to decrease, and nucleation becomes less frequent. Spread of nuclei takes over and the edges of terraces become less ragged (Fig. 2c). Finally, at interval 3, when supersaturation is close to equilibrium, nucleation is non-existent and the spread of terraces is very slow, resulting in straight edges (Fig. 2d). It can be seen that the crystal habit from the simulation matches that of the synthesis product, validating the choice of the probability set used in the simulation. The final topology observed in the simulations was compared to that observed by AFM on the different faces of synthetic zeolite A crystals. Fig. 3 shows this comparison for the {110} and {111} faces. It can be seen that the simulation successfully simulated the rectangular shaped terraces for the {110} (Fig. 3a and 3b) face as well as the triangular shaped terraces for the {111} face (Fig. 3c and 3d).
4. Conclusion and Further Study A new program to model zeolite A crystal growth has been developed. The program has succeeded in replicating morphology and surface topology of real zeolite A crystals studied by SEM and AFM. The simulation program could be used to study the crystal growth mechanism under high supersaturation as well as at the equilibrium state. The
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A. Umemura et al.
Figure 3. a) AFM deflection image (1 × 2 μm2) on (110) of zeolite A, and b) its corresponding simulation image (ca. 0.15 × 0.3 μm2). c) AFM deflection image (450 × 450 nm2) on (111) of zeolite A, and d) its corresponding simulation image (ca. 65 × 65 nm2). corresponding simulation images provide a determination of kinetics and thermodynamics of zeolite A crystal growth process. Further refinement of the program should be done by comparing habit and topology determined with synthetic crystals produced at different synthesis conditions. This will lead to more approximate values on activation energies of the different mechanisms.
Acknowledgements This work has been financially supported by EPSRC and ExxonMobil.
References [1] F.D. Renzo, Catalysis Today 41 (1998) 37-40. [2] M.J. Schwuger and H.G. Smolka, Colloid & Polymer Sci. 254 (1976) 1062-1069. [3] L. Bonetto, M.A. Camblor, A. Corma and J. Perez-Pariente, Applied Catalysis A: General 82 (1992) 37-50. [4] J.R. Agger, N. Pervaiz, A.K. Cheetham and M.W. Anderson, J. Am. Chem. Soc. 120 (1998) 10754-10759. [5] M.W. Anderson, J.R. Agger, N. Hanif, O. Terasaki and T. Ohsuna, Solid State Sciences 3 (2001) 809-819. [6] A.A. Chernov, J. Mater. Sci.: Materials in Electronics 12 (2001) 437-449. [7] Surface Evolver, version 2.26 (August 20, 2005) http://www.susqu.edu/brakke/evolver/evolver.html [accessed in January 2007]. [8] http://www.polyhedron.com/ [Accessed in June 2007] [9] R.W. Thompson and M.J. Huber, Cryst. Growth 56 (1982) 711.
705
Modelling crystal growth in zeolite A Ayako Umemura, Pablo Cubillas, Michael W. Anderson, and Jonathan R. Agger Centre for Nanoporous Materials. School of Chemistry. The University of Manchester Oxford Road, M13 9PL. Manchester, U.K. +44 (0)161 306 2770.
Abstract Zeolite A is one of most widely used and studied zeolites owing to its cation-exchange properties. Here, we present a computer program that simulates morphology as well as surface topology for zeolite A crystals. Results from simulations were compared with scanning electron microscopy and atomic force microscopy images on the {100}, {110} and {111} faces of synthetic crystals. This allowed to further refine the program by varying the relative attachment/detachment probabilities of individual growth sites. Keywords: zeolite A, Monte Carlo simulation, atomic force microscopy
1. Introduction Zeolites and other microporous materials have been the subject of a great number of studies in the last century owing to their applications in many industrial processes.1-3 Nevertheless, only recently have studies been performed to understand the fundamental aspects involved in the nucleation and growth of these materials.4,5 Nucleation is affected under high supersaturation and the end product of the synthesis is a function of the equilibrium state. The use of Monte Carlo simulation methods proposes a good prediction of the real crystal growth processes. The aim of the study is to gain further understanding about the thermodynamics and kinetics of these processes by simulating the morphology and topology of zeolite A.
2. Methods 2.1. Algorithm for Zeolite A Crystal Growth and Dissolution Events in Solution A Monte Carlo program has been written to coarse grain the crystal growth into 1.2 nm, which is half unit cell of LTA structure. The choice of 1.2 nm growth units was based on measurements of individual step heights on AFM studies on zeolite A. 4 Each site is defined by considering 24 first and second coordination neighbours (Fig.1a). This yielded a total of 223 different site types. Nevertheless only 192 site types were actually considered during the simulation, since bulk sites where not allowed to grow or dissolve. The first sphere coordination considers six sites and is based in the Kossel model (Fig. 1b), whereas the second sphere of coordination takes into account 18 different sites. Addition of the second sphere of coordination was due to the inability to simulate beveled edges and/or truncated structures using only the Kossel model.6 Each site was assigned with a certain probability of crystal growth and dissolution creating sets of probabilities that will, ultimately, simulate different growth modes with different rates. By considering the probabilities and the population of each site type, either crystal growth or dissolution is randomly chosen at each iteration during the
706
A. Umemura et al.
Figure 1. a) First and b) second sphere coordination sites around an individual growth unit. c) Ideal crystal surface showing the six different types of sites considered by the Kossel model. calculation. The local coordination is then changed at every iteration as the growth or dissolution affects the coordination of their neighbouring sites. In designing the program, we focused on creating an efficient simulation as CPU time consumption and memory usage could hamper its utility and flexibility. For this reason surface diffusion is not currently considered in the program. 2.2. Computing and Rendering Environment The simulation program was written in Fortran 90 and rendered with Surface Evolver7. The calculation was executed on a 264 bit Intel Xeon processor running at 3GHz with 4GB of RAM. This cluster, called the Epsilon, is supported by the Research Support Group of the faculty of Engineering and Physical Sciences at the University of Manchester. The Epsilon provides Intel£ Fortran Compiler, which was reported almost twice as fast of any other compilers on the market by Polyhedron8. Images were rendered on the Intel Core Duo processor with 2.16 GHz and 1GB of RAM. 2.3. Comparison with Synthetic Crystals The results obtained from the simulation program were iteratively compared with atomic force microscopy (AFM) images of synthetic zeolite A crystals. Synthesis of zeolite A crystals was carried out following the method by Thompson9. Scanning electron micrographs where obtained using an FEI Quanta 200. AFM images were obtained using a Nanowizard II BioAFM from JPK Instruments AG. Images were taken using both contact and intermittent contact scanning modes.
3. Results and Discussion The computation was performed with about two minutes of CPU time at 20 million iterations, which represents ca. 0.3 × 0.3 × 0.3 μm3 of zeolite A. Further optimisation would come from running the program in a bigger memory environment. The program was used to simulate the growth of a crystal of zeolite A after nucleation has taken place. This was accomplished by selecting two different probability sets (applied at two different crystal sizes), which reproduced two different “growth modes” expected at high and low supersaturation respectively. Fig. 2 shows a typical evolution of crystal fraction and supersaturation as a function of time compared with three
Modelling crystal growth in zeolite A
707
Figure 2. a) Typical crystal size and supersaturation evolution as a function of time for zeolite A synthesis. Inset picture shows typical zeolite A crystal produced in the synthesis. Image size 2.5 μm. b), c) and d) show ca. 0.3 × 0.3 × 0.3 μm3 sized zeolite A crystals simulated at time intervals 1, 2 and 3, respectively. renderings of the simulation, corresponding to the highlighted time intervals (1, 2 and 3). The SEM image in Fig. 2a shows the typical final product of synthesis of zeolite A. It can be noted that this preparation yielded crystals with {100}, {110} and {111} faces clearly exposed. At interval 1 supersaturation is maximum and hence nucleation is high on all of the crystal surfaces, creating rough surfaces full of nuclei as depicted in Fig. 2b. At interval 2 the supersaturation starts to decrease, and nucleation becomes less frequent. Spread of nuclei takes over and the edges of terraces become less ragged (Fig. 2c). Finally, at interval 3, when supersaturation is close to equilibrium, nucleation is non-existent and the spread of terraces is very slow, resulting in straight edges (Fig. 2d). It can be seen that the crystal habit from the simulation matches that of the synthesis product, validating the choice of the probability set used in the simulation. The final topology observed in the simulations was compared to that observed by AFM on the different faces of synthetic zeolite A crystals. Fig. 3 shows this comparison for the {110} and {111} faces. It can be seen that the simulation successfully simulated the rectangular shaped terraces for the {110} (Fig. 3a and 3b) face as well as the triangular shaped terraces for the {111} face (Fig. 3c and 3d).
4. Conclusion and Further Study A new program to model zeolite A crystal growth has been developed. The program has succeeded in replicating morphology and surface topology of real zeolite A crystals studied by SEM and AFM. The simulation program could be used to study the crystal growth mechanism under high supersaturation as well as at the equilibrium state. The
708
A. Umemura et al.
Figure 3. a) AFM deflection image (1 × 2 μm2) on (110) of zeolite A, and b) its corresponding simulation image (ca. 0.15 × 0.3 μm2). c) AFM deflection image (450 × 450 nm2) on (111) of zeolite A, and d) its corresponding simulation image (ca. 65 × 65 nm2). corresponding simulation images provide a determination of kinetics and thermodynamics of zeolite A crystal growth process. Further refinement of the program should be done by comparing habit and topology determined with synthetic crystals produced at different synthesis conditions. This will lead to more approximate values on activation energies of the different mechanisms.
Acknowledgements This work has been financially supported by EPSRC and ExxonMobil.
References [1] F.D. Renzo, Catalysis Today 41 (1998) 37-40. [2] M.J. Schwuger and H.G. Smolka, Colloid & Polymer Sci. 254 (1976) 1062-1069. [3] L. Bonetto, M.A. Camblor, A. Corma and J. Perez-Pariente, Applied Catalysis A: General 82 (1992) 37-50. [4] J.R. Agger, N. Pervaiz, A.K. Cheetham and M.W. Anderson, J. Am. Chem. Soc. 120 (1998) 10754-10759. [5] M.W. Anderson, J.R. Agger, N. Hanif, O. Terasaki and T. Ohsuna, Solid State Sciences 3 (2001) 809-819. [6] A.A. Chernov, J. Mater. Sci.: Materials in Electronics 12 (2001) 437-449. [7] Surface Evolver, version 2.26 (August 20, 2005) http://www.susqu.edu/brakke/evolver/evolver.html [accessed in January 2007]. [8] http://www.polyhedron.com/ [Accessed in June 2007] [9] R.W. Thompson and M.J. Huber, Cryst. Growth 56 (1982) 711.