Material Informatics

Towards controlling porosity in crystalline materials: Algorithms for characterization and design of nanoporous structures

Maciek Haranczyk

Porous materials, typically inorganic crystals, are currently used in a wide range of applications including petroleum cracking, detergents, and molecular separations, and account for billions of dollars of the world economy. However, over the last two decades there has been a surge of interest in the potential design and application of advanced new classes of material which combine both organic and inorganic building blocks; these novel materials include metal-organic frameworks (MOFs), covalent organic frameworks (COFs), porous polymeric networks (PPNs) and porous organic cages (POCs). Due to the organic (i.e. molecular) nature of the components used to assemble these materials, they offer potentially limitless control over their pore geometry, size, and chemical functionality. Furthermore, these advanced porous materials hold great promise for application in many energy-related technologies, most prominently in separations (e.g. separating carbon dioxide from other gases in power plant exhaust) and catalysis. The staff and users at The Molecular Foundry are currently devoting a considerable effort to the synthesis, characterization and understanding of the structure and design principles of these materials. The ultimate goal of these efforts is to establish precise control over the size, shape and chemical character of pores by careful selection of material building blocks. This development will enable the design of next-generation porous materials with highly controlled reactive environments for catalysis and chemical separation.

The shape and geometry of the pores in these materials, as well as the topology of their open (void) space, is controlled by the three-dimensional arrangement of their constituent building blocks. These building blocks are typically rigid organic molecules or organic-inorganic cations with a number of connection sites by which they bond covalently to one another. These connections define the possible topologies of the resulting material. The huge space of possible organic molecules, along with these simple, tinkertoy-like building principles, gives rise to a vast combinatorial space of possible materials. Novel mathematics that would allow us to describe and efficiently explore this complex space will facilitate studies of these materials and ultimately enable the deliberate design of porous framework materials with controlled properties. In particular, the research activities taking place at the Molecular Foundry would greatly benefit from developing the abilities in three main areas: a) building 3D models of materials; b) pore structure characterization and comparison; and c) advanced pore design via optimization algorithms. The challenges in these areas are outlined below.

Building material modelsThe inability to grow adequate single crystals of many framework materials makes determining (solving) the structure of materials by single-crystal X-ray diffraction techniques very challenging or even impossible. This situation can usually be resolved by using powder X-ray diffraction; however, structure solutions from polycrystalline powders are extremely difficult and time consuming, especially in systems with increasing complexity and large numbers of atoms and/or low symmetry. Stagnant experimental methods create a serious bottleneck in the discovery rate of new materials, and so computational simulation of structures constitutes a valuable means of phase identification. The molecular nature of these materials warrants the development of new algorithms to enumerate possible frameworks from a predefined set of building blocks, and construct corresponding low-strain 3D structure models; the latter preserve both the geometry of building blocks and their connections. One big challenge is the enumeration of possible structures, which often involves a combinatorial explosion of possibilities. Our algorithms have to handle this problem by, for example, constraining enumeration only to structurally diverse materials and/or satisfying crystal symmetry constraints. Success will lend to the solution of structures of newly synthesized materials, as powder patterns obtained from simulated structures can be used for rapid phase identification relaxing the synthetic requirement to achieve single crystal growth. Further, based on a set of predefined building blocks, these methods can be utilized for the design of new materials in advance of their actual synthesis.



Pore characterization/comparison Given a material structure, either predicted computationally or from crystallography experiments, researchers would like to be able to fully characterize its pore structure, for example, estimate its internal surface area and volume, determine its diffusion limiting pore diameters as well as analyze the connectivity and shape of its pores. Moreover, they would like capabilities by which different materials’ pore systems can be compared in terms of their geometry and topology. Such a capability will allow collection of knowledge over diverse families of materials and lead to development of novel design approaches via the concept of scaffold hopping, i.e. searching for chemically diverse frameworks that give rise to very similar pore structures (a concept utilized in the pharmaceutical drug discovery process). For example, this technique can provide a means to identify new materials with pore structures similar to a well-known material with the optimal performance for a particular application, but constructed from cheaper building blocks and/or easier synthesis routes. Scaffold hopping may be of particular interest in the design of materials hosting catalytic sites; for example, researchers can search through all families of MOFs, COFs, etc. to identify all material scaffolds that can nest a given catalytic site.



Pore design algorithms Finally, the holy grail of the porous framework field is to predict for any desired pore structure the building blocks needed to generate it. Major advances toward this goal of ‘inverse pore design’ can be achieved by utilizing both bottom-up and top-down approaches. In the first approach, researchers explore the kinds of pores that can be built from simple building blocks, and how the characteristics of these building blocks affect the resulting material/pore structures. Constructing a material would require combining and aligning these discrete building blocks to achieve a framework with the requested porosity. In the latter, top-down approach, researchers would operate in a continuous space describing geometrical parameters of a material and its voids, and then project it onto the discrete space of realistic building block molecules. The latter approach can be very powerful tool when exploring frontiers of possible materials. For example, a continuous geometrical model of porous materials can be optimized to identify shapes that guarantee the largest surface areas. Then, they can be projected onto real molecular frameworks.





To effectively pursue and enable the outlined desired abilities, we use and combine many mathematical methods. For example, we use computational geometry and PDE-based techniques to analyze material structures and the associated data describing their pores. We utilize graph algorithms in analysis of materials and their void space topology. We employ optimization algorithms to design pore structures and to select systems to undergo characterization, as well as machine learning tools to control data collection, build property-predicting models and perform analysis on sets of molecules or materials. In particular, by combining the Molecular Foundry priorities and our current experience, we have given the highest priority to the following areas:



  • Algorithms for void space analysis, segmentation and representation. We are developing new algorithms for structure and void space analysis and representation. Here, we would like to achieve the ability to automatically analyze and deconstruct any given material and its void space to fundamental building blocks: pores, cages, channels etc. Then, we would like to extend our structure and void space representations to enable similarity comparison between them. Moreover, we would like to achieve the ability to track changes in these building blocks in a time-series representing material evolution. Moreover, our initial work involves looking towards data-mining for material design principles, which correlates structure of material building blocks with characteristics of the void space. For example, models that correlate geometry (distances, angles) of building blocks with possible sizes of pores constructed from these blocks.

  • Customizable 3D structure model builders. Here we are working to provide efficient algorithms to construct realistic sets of 3D structures from provided building blocks. Such a tool will be used by Molecular Foundry users, or as a component of pore design workflows based on optimization algorithms. We would like these tools to construct 3D models within a set of constraints set by symmetry, requested topology etc.

  • Optimization-based pore design approaches. Here we are building upon our prototype algorithms for designing high-surface area MOFs, and exploring multiobjective optimization with a number of target properties.



Our short term plans involve development of tools enabling characterization of structures currently under investigation at the Molecular Foundry as well as other labs. These tools provide functionality to analyze topology and geometry of pores, and can provide information on how particular factors in material chemistry affect the porosity of a material. The mid-term goal is to provide sustainable packages of algorithms for structure enumeration and characterization. This will enable the researchers at the Molecular Foundry to incorporate our tools into their own work processes and use them without our involvement. Moreover, we aim to provide unique functionality enabling the analysis of structure data representing a material’s time-evolution. This will provide information on pore dynamics, which control many phenomena such as guest-diffusion. Finally, in the long term, we would like to extend these tools with new capabilities for material design. Here, we will combine 3D structure model construction and characterization with optimization algorithms. This will result in tools for navigated searches through the complex material space.

New Mathematics for Chemical Informatics