Cyclic random graphs predicting giant molecules in hydrocarbon pyrolysis

Reaction models in complex chemical systems are often limited by large molecules and combinatorial complexity. We investigate equilibrium hydrocarbon pyrolysis, a system at extreme temperature and pressure conditions involving large numbers of chemical reactions and species. Atomistic simulations of hydrocarbon pyrolysis are computationally expensive and can only be run for a small number of conditions. Kinetic Monte Carlo requires the estimation of a large number of reaction rates. We pursue an alternative approach that treats the ensemble of hydrocarbons as a random graph. Our random graph model features disjoint loops and assortativity correction and a method for learning input distributions from molecular dynamics data. Only nine pairs of reaction constants must be learned and the model can be analyzed within a second with generating functions. We demonstrate that the proposed model accurately predicts the size distribution for small molecules as well as the size distribution of the largest molecule at the pressure of 40.5 GPa, temperature range of 3200K–5000K, and hydrogen carbon (H/C) ratio range of 2.25–4. This random graph model admits the formation of a giant molecule of size O(N). For carbon-rich systems with an H/C ratio of 2 and lower, loops are not disjoint and form amorphous loop clusters. Loop statistics of these clusters obtained from minimum cycle bases are not unique. We design new loop statistics to address this issue.