Mathematica code to generate mean cluster size distributions in a reversibly aggregating system with relatively few monomers, given size-dependent cluster free energies or association constants. An example free energy model for micelle formation is included.
The Mathematica notebook, initially written by Lara A. Patel and adapted by James T. Kindt, was used to generate the figures accompanying the manuscript "Theory for chemical equilibrium in small systems: General results and examination of micelle self-assembly" by Olivia Beckwith, Robert Schneider, Lara A. Patel, Xiaokun Zhang, and James T. Kindt for submission to J. Chem. Phys. in 2023.
It implements calculations described in J . Chem . Theory Comput .2017, v 13, 5195 - 5206 by Zhang et al . (referred to hereafter as Zhang 2017) eqs . 14 - 18 to calculate mean number m_j of clusters containing j monomers at a total monomer concentration Cfac as a function of the total number of monomers in the system Nsys, given a definition of the free energies or association constants of clusters as a function of integer cluster size.
The first section of the code simply defines the equilibrium constants for association of monomers, as an array called "Kactual".
Due to the figures we were generating in the paper, we wanted to track the behavior of a given size cluster j as total number of particles is increased at fixed particle concentration. Concentration is set by assigning a value to Cfac.
If you are running this for the first time, you probably just want to look at a single equilibrium cluster size distribution for a single set of equilibrium constants at a single total number of particles N and concentration. In that case, to select N=50 for instance, after the comment (loop over systems of increasing size) change the upper bound to N+1: For [Nsys = 50, Nsys < 51, Nsys++,
The first graph shown will be what you are looking for then.
Please feel free to contact James Kindt, jkindt@emory.edu , with questions.