“Extracting Aggregation Free Energies of Mixed Clusters from Simulations of Small Systems: Application to Ionic Surfactant Micelles” by Xiaokun Zhang, Lara Patel, Olivia Beckwith, Robert Schneider, Chris Weeden, and J.T. Kindt has been accepted for publication in the Journal of Chemical Theory and Computation.  link  This is the first publication to come out of an unusual collaboration between number theorists and computational chemists.  Xiaokun and Lara are PhD students in the Department of Chemistry while Olivia and Robert are PhD students in the Department of Mathematics and Computer Science, whose main research in number theory is supervised by Prof. Ken Ono.   Chris Weeden is a graduate of Emory College (class of 2015, double-major in chemistry and math), currently studying medicine at the University of Central Florida, whose work enabled preliminary explorations and testing of the methods.

The paper describes how tools from number theory can be used to analyze the statistics of how ionic detergent molecules aggregate with each other and their counterions to form micellar clusters of varying size and charge.  Using a very simple (coarse-grained solvent-free) model for the molecules, Xiaokun ran twelve simulations with different numbers of surfactants and concentrations, but only enough to make one or two micelles.  With software developed jointly with Lara Patel, which implemented an approach derived by Olivia and Robert that resulted in a huge leap in efficiency over the methods used in a previously study, she took the statistics from these simulations and showed that they could predict the size distributions of a much larger simulation. This is important because, if we use better models (atomistic representations of the surfactants, ions, and water), very large simulations will not be practical.  So, this work opens the door to using readily available simulation tools to make detailed predictions of how micelle size and charge distributions depend on concentration.