Application of the Monte Carlo Method to Prediction of Dispersibility of Graphene in Various Solvents

The dispersibility of graphene is modeled as a mathematical function of the molecular structure of solvent represented by simplified molecular input-line entry systems (SMILES) together with the graph of atomic orbitals (GAO). The GAO is molecular graph where atomic orbitals e.g. 1s1, 2p4, 3d7 etc., are vertexes of the graph instead of the chemical elements used as the graph vertexes in the traditionally used molecular graph (hydrogen suppressed molecular graph or hydrogen filled molecular graph). The optimal descriptors calculated with the Monte Carlo method were used to build up one variable correlations "descriptor-dispersibility". The CORAL software is used as a tool to build up the model. Based on the results of calculations the structural features which are promoters of increase or those which are promoters of decrease of the dispersibility are detected and discussed. The predictive potential of the used approach is checked up with three random and non identical splits of available data into the training, calibration, and validation (invisible during building up the model) sets. The statistics for external validation sets are the following: n=11, r2=0.6379, s=0.392 (split 1); n=8, r(2)=0.7308, s=0.378 (split 2); and n=5, r(2)=0.7797, s=0.504 (split 3).