Hydrocarbon Pyrolysis
Pyrolysis is the process by which materials are decomposed at high temperatures in an inert atmosphere. Hydrocarbon pyrolysis in particular is when molecules made of hydrogen and carbon undergo pyrolysis and is used to convert petroleum and natural gas into the various compounds used in industry and our every day lives. Hydrocarbon pyrolysis is also thought to produce diamonds in the interior of ice giant planets such as Jupiter.
Hydrocarbon pyrolysis is an exceedingly complicated process with a wide range of conditions under which it can occur and myriad products resulting from it. In fact, it is really many hundreds of chemical processes all occurring together. There have been attempts to model these processes with computer simulations that have had various degrees of success. For example, ab initio simulations have a relatively high degree of accuracy. However, they require extensive computational effort. Recent efforts have used force field approximations for use with MD simulations. These are less accurate than the ab initio simulations but require much less computational effort. These models provide us with a wealth of information in a much more reasonable amount of time and even more recent work is being done to realize even faster simulations.
After looking at the structure of the hydrocarbon products, my collaborators and I realized that we can model them as graphs. These are graphs of the carbon skeletons surrounded by the hydrogen atoms which we suppress in our representation. These, it turns out, have been studied by chemists before us and are called carbon graphs. Our innovation was to model the products of the hydrocarbon pyrolysis as random graphs. To generate these graphs, we need the degree distribution of the hydrocarbon molecules. We can obtain the degree distribution in two ways. First, by analyzing the results of an MD simulation. Second, by using a new model developed during the collaboration that determines the degree distribution for a system at an arbitrary temperature and initial composition that is trained on previously run MD simulations.
This new approach provides the equilibrium distribution of the molecule sizes resulting from hydrocarbon pyrolysis incredibly quickly, typically in less than a minute. It also provides a prediction for the conditions under which diamonds may form, the initial goal of the collaboration. Random graph theory provides a condition under which the carbon graph undergoes a "phase transition" where most of the carbon is in one giant molecule. e.g. diamond. It also provides a mathematical framework with which to explore the structure of individual hydrocarbon molecules.
A shortcoming of this approach is that the random graph model does not allow for loops which are present in the MD simulations. To overcome this, we recently imrpoved our original approach by incorporating graph motifs. This extension allows us to incorporate the substructures seen in simulations. Doing so increased our prediction accuracy markedly.
