(173d) Anisotropic Diffusion in Zeolites and Metal-Organic Frameworks: Calculation of Diffusion Tensors

Microporous materials, such as zeolites and metal-organic frameworks, are composed of complex porous networks that give rise to intracrystalline diffusion anisotropy. Although the phenomenon is well-understood, experimental measurements of diffusion anisotropy are difficult to obtain. Computational techniques, which typically rely on molecular simulations or simplified lattice models, are also challenging. With recently developed pore characterization methods ZEOMICS [1] and MOFomics [2], it is now possible to exploit the exact geometry and connectivity of microporous networks and calculate energetic barriers to transport through various pathways [3-6]. We have developed a novel methodology [7] to estimate full diffusion tensors based on these detailed descriptions.

We have validated our approach through a number of computational studies that demonstrate good agreement with experimental and computational results reported in the literature. A comprehensive examination involving approximately 200 zeolite framework types elucidates classifications based on a number of anisotropy metrics.

The power of characterizing materials based on diffusion tensors is illustrated in the context of microporous membranes. In such membranes, the orientation of crystals is crucial because it controls transport along the desired direction. We have formulated mathematical optimization models that determine an orientation of a porous network to maximize the throughput of a species or the separation between two species of interest. These models are solved to global optimality using ANTIGONE [8-9], a branch-and-bound solver for general mixed-integer nonlinear models.

References:

1. First EL, Gounaris CE, Wei J, and Floudas CA. Computational characterization of zeolite porous networks: an automated approach. Phys. Chem. Chem. Phys. 13:17339-17358, 2011.
2. First EL and Floudas CA. MOFomics: Computational pore characterization of metal-organic frameworks. Micropor. Mesopor. Mater. 165:32-39, 2013.
3. Gounaris CE, Floudas CA, and Wei J. Rational design of shape selective separation and catalysis-I: Concepts and analysis. Chem. Eng. Sci. 61:7933-7948, 2006.
4. Gounaris CE, Wei, J, and Floudas CA. Rational design of shape selective separation and catalysis-II: Mathematical model and computational studies. Chem. Eng. Sci. 61:7949-7962, 2006.
5. Gounaris CE, Wei J, Floudas CA, Ranjan R, and Tsapatsis M. Rational design of shape selective separations and catalysis: Lattice relaxation and effective aperture size. AIChE J. 56:611-632, 2009.
6. First EL, Gounaris CE, and Floudas CA. Predictive framework for shape-selective separations in three-dimensional zeolites and metal-organic frameworks. Langmuir 29:5599-5608, 2013.
7. Gounaris CE, First, EL, and Floudas CA. Estimating diffusion anisotropy in microporous crystalline materials. Submitted for publication.
8. Misener R and Floudas CA. ANTIGONE: Algorithms for continuous / integer global optimization of nonlinear equations. Submitted for publication.
9. Misener R and Floudas CA. A framework for globally optimizing mixed-integer signomial programs. Submitted for publications.