Modeling the Growth of Fractal Networks of Nanopores in Activated Carbon Mikael Wood and Peter Pfeifer Department of Physics and Astronomy, University of Missouri-Columbia Introduction: Our group is interested in several possible applications of carbon nanopore networks. Most notably we are interested in their ability to store large volumes of methane at low pressures. We hope to utilize this in the creation of an efficient fuel tank for low emissions vehicles that run on methane. We attempt to model the growth of these networks in the hopes of that the knowledge gained will allow us to optimize several of their properties. Modeling: To model the growth of nanopore networks we use a two stage probabilistic cellular automata (PCA) rule (we run two separate PCA’s in succession). The first opens up pore space from the inside out (top figure), and the second works its way in from the outside in (bottom figure). We let the first rule run until the cluster is close to percolation. The second rule opens this cluster to the outside of the lattice thereby creating a spanning cluster. This models a two stage activation process. In the bottom figure only the spanning cluster is highlighted. Fig 1: This is the lattice after the first PCA rule has run for 150 iterations. The grey sites are filled with the corrosive agent which removes carbon (the black sites) from the lattice. Fig 2: The image on the left is the lattice after both PCA rules have been run. Rule one was run for 150 iterations, and rule two has run for 120 iterations. Here the percolation cluster is colored in grey. The white sites are pore space that does not belong to the percolation cluster. The black sites represent carbon. In the image on the right the percolation cluster is colored in black. Fractal Analysis of the Percolation Cluster: We compute the fractal dimension of our percolation cluster (Fig 3) to be Ultra small angle x-ray scattering (USAXS) data,obtained from Argonne National Laboratory, of many of the carbon samples created by our group show evidence of obeying power law scaling over many different scales. If we were to create a three dimensional stack of lattices such as the ones in Fig 2 it would have a fractal dimension of The USAXS data in Fig 4 shows a that one of the samples produced by our group has a fractal dimension of approximately Conclusion: In conclusion the data produced by our model closely matches many aspects of the data produced by actual carbon nanopore networks. It is hoped that by expanding upon this basic model we can increase its accuracy and eventually use the knowledge gained from it to optimize several properties of these networks including minimizing loading times and loading heat. Acknowledgements: This research is based on work supported by the National Science Foundation, under Grant No. EEC , the University of Missouri, the Department of Education, and the Midwest Research Institute. Use of the Advanced Photon Source was supported by the U.S. Department of Energy, under Contract No. W Eng-38. Fig 3: This log-log plot show that the fractal dimension of the percolation cluster in Fig 2 is equal to Fig 4: This is a USAXS scattering intensity curve of one of the more interesting samples that we have studied. The slope of the unified fit curve is This tells us that the fractal dimension of the pore space is approximately 2.76.