Optimal aggregation number of reverse micelles in supercritical carbon dioxide: a theoretical perspective

The aggregation number is one of the most fundamental and important structural parameters for the micelle or reverse micelle (RM) system. In this work, a simple, reliable method for the determination of the aggregation number of RMs in supercritical CO2 (scCO2) was presented through a molecular dynamics simulation. The process of pulling surfactants out of the RMs one by one was performed to calculate the aggregation number. The free energies of RMs with different numbers of surfactants were calculated through this process. We found an RM with the lowest free energy, which was considered to have the optimal number of surfactants. Therefore, the optimal aggregation number of RMs was acquired. In order to explain the existence of an optimal aggregation number, detailed analyses of surfactant accumulation were conducted by combining molecular dynamics with quantum chemistry methods. The results indicated that in the RMs with the lowest free energy, the head-group and tail-terminal of the surfactants accumulated on an equipotential surface. In this case, the surfactant film could effectively separate water and CO2; thus, the lowest free energy was expected. This method determined the aggregation number of RMs by theoretical calculations that did not depend on experimental measurements. This presented approach facilitates the evaluation of the characteristics of RMs in scCO2 and can be further applied in the RM system of organic solvents or even in the micellar system.