Material porosity and permeability

Several projects on which I have worked related to understanding the structure of materials, and how that influences the ability of fluids and gases to flow through them. I've made use of both discrete techniques, where individual atoms and particles are modeled, as well as continuum techniques, where flow can be analyzed via partial differential equations.

Voro++: A 3D Voronoi cell software library in C++

Voronoi tessellation in a sphere

I have written an open source software library called Voro++ for carrying out the Voronoi tessellation. Voro++ works differently from most established libraries, and calculates the Voronoi cell for each point individually, as a polyhedron surrounding the point. This makes it well-suited to applications that rely on cell-based statistics, where features of Voronoi cells (e.g. volume, centroid, number of faces) can be used to analyze a system of points or particles.

The library is structured around several C++ classes, making it straightforward to modify and incorporate into other programs; a large number of example programs are available on the library website. The library is downloaded several thousand times a year and is referenced in a number of peer-reviewed publications. The most common area of application is in condensed matter physics and materials science, although there are many other examples, including mesh generation, solidification patterns, biological cell modeling, and the dynamics of object shattering.


  1. Voro++ website.
  2. C. H. Rycroft, Voro++: A three-dimensional Voronoi cell library in C++, Chaos 19, 041111 (2009). [Link]
  3. C. H. Rycroft, Voro++: A three-dimensional Voronoi cell library in C++, January 23rd 2009, Lawrence Berkeley National Laboratory, Paper LBNL-1430E. [Paper]
  4. C. H. Rycroft, Multiscale modeling in granular flow, submitted to MIT, September 2007. [More information]
  5. C. M. Freeman, K. L. Boyle, M. Reagan, J. Johnson, C. H. Rycroft, G. J. Moridis, MeshVoro: A three-dimensional Voronoi mesh building tool for the TOUGH family of codes, Computers & Geosciences 70, 26–34 (2014). [Link]

High-throughput screening of crystalline porous materials

A path through an atomic system along the Voronoi network

I have carried out a collaboration at the Lawrence Berkeley Laboratory to create new tools for high-throughput screening of crystalline porous materials such as zeolites. These materials contain complex networks of void channels, which can be exploited in many industrial applications as molecular filters. A key requirement of the success of any nanoporous material is that the pore topology must be optimal for a given application. However, this is a difficult task, since the number of pore topologies is extremely large: thousands of materials have been synthesized and databases of millions of hypothetical structures are available. The Voronoi tessellation provides a map of the channels within a given structure, and can be used to determine whether a given molecule can propagate between the atoms, and I adapted the Voro++ library to carry out these computations. Particular attention was paid to zeolites with non-orthogonal unit cells, which requires a careful consideration of the periodic images of each atom that may influence the Voronoi calculation.

Voronoi tessellation of JBW zeolite Voronoi tessellation of YUG zeolite Voronoi tessellation of AFX zeolite

Once the Voronoi tessellation has been computed, it can be used to calculate several geometrical indicators of each material, such as the surface area accessible to a given molecular probe.


  1. Zeo++ website.
  2. T. F. Willems, C. H. Rycroft, M. Kazi, J. C. Meza, and M. Haranczyk, Algorithms and tools for high-throughput geometry-based analysis of crystalline porous materials, Microporous and Mesoporous Materials 149, 134–141 (2012). [Link]
  3. M. Haranczyk, C. H. Rycroft, and J. A. Sethian, Empty Space and New Materials: Computational Tools for Porous Materials, SIAM News 44, Issue 8, October 2011.
  4. M. Pinheiro, R. L. Martin, C. H. Rycroft, A. Jones, E. Iglesia, and M. Haranczyk, Characterization and comparison of pore landscapes in crystalline porous materials, J. Mol. Graph. Model. 44, 208–219 (2013). [Link]
  5. M. Pinheiro, R. L. Martin, C. H. Rycroft, and M. Haranczyk, High accuracy geometric analysis of crystalline porous materials, CrystEngComm 37, 7531–7538 (2013). [Link]
  6. Computing Tools Speed Search for New Porous Materials, LBL Computational Research Division News, Novemeber 14, 2011.

Materials for carbon capture and sequestration

Overview of material screening for carbon capture applications

These computational tools led to a further collaboration with the UC Berkeley chemistry department to identify porous materials for carbon capture applications. The main challenge is to identify structures that let power plant flue gases such as N2 pass, while being capable of adsorbing CO2 the porous structure can then be heated to purge the CO2 for sequestration. A combination of screening and simulation techniques led to the identification of new materials that have the potential to be more efficient than existing technologies. In the graph shown, each material is plotted in terms of its Henry coefficient, and also the parasitic energy, measured in terms of the energy required to capture one kilogram of CO2. A number of materials in the graph are predicted to be up to 30% more efficient than existing technologies based on scrubbing with amine solutions shown by the horizontal green line.


  1. L.-C. Lin, A. H. Berger, R. L. Martin, J. Kim, J. A. Swisher, K. Jariwala, C. H. Rycroft, A. S. Bhown, M. W. Deem, M. Haranczyk, and B. Smit, In silico screening of carbon capture materials, Nature Materials 11, 633–641 (2012). [Link]
  2. Carbon Dioxide Catchers, LBL Computational Research Division News, February 29, 2012.
  3. Computer model pinpoints prime materials for efficient carbon capture, UC Berkeley News Center, May 27, 2012.
  4. New materials could slash energy costs for CO2 capture, Rice University News, May 30, 2012.
  5. Carbon Capture Materials Database.

Fluid and gas flow in shales

Schematic of a gas flow model in a shale

I have also examined material permeability from a continuum perspective, working with Grigory Isaakovich Barenblatt and Paulo Monteiro at UC Berkeley on a mathematical model of gas flow in shales. Recently, the extraction of gas for shale deposits has become a significant energy resource, although the mechanism of gas transport in these materials is not fully understood.

Shales have a different structure from conventional oil and gas deposits. Typically, a large fraction of the oil and gas is contained within small blocks of a material called kerogen, as shown by the brown regions in the diagram. These blocks have been shown to have extremely low permeability, so that conventional subterranean fluid mechanics cannot be applied. We developed a mathematical model of flow, which leads to boundary layers in the kerogen blocks that can be analyzed in terms of the coordinate x pointing normally into the block. The model makes predictions that have since been shown to be in agreement with experimental data.


  1. P. J. M. Monteiro, C. H. Rycroft, and G. I. Barenblatt, A mathematical model of fluid and gas flow in nanoporous media, Proc. Natl. Acad. Sci. 109, 20309–20313 (2012). [Link]
  2. G. I. Barenblatt, P. J. M. Monteiro, and C. H. Rycroft, On a boundary layer problem related to the gas flow in shales, J. Eng. Math. 84, 11–18 (2014). [Link]
  3. Can We Accurately Model Fluid Flow in Shale?, Berkeley Lab News Center, January 3, 2013. (Also on CRD News and ScienceWire.)