The Voorn-Overbeek model aims to describe complex coacervation behavior, which occurs when polyelectrolyte systems phase separate into a polymer-rich phase and a dilute, supernatant phase.^{1} This model therefore is more suited towards charged polymer systems. The current version of the VO Phase Generator assumes equal concentrations of the polyanion and polycation. Similarly, the current version of the system assumes a salt-free system. Given these assumptions, the current version of the phase generator only requires the total number of monomers, N, to generate the phase diagram. The output phase diagram is plotted as a function of the charge density, sigma. The plot generates both a spinodal curve (red) and a binodal (blue) as a function of the volume fraction of the volume fraction of the 1st species.

The following code generates the free energy diagram as a function of volume fraction, including separate entropic and enthalpic contributions. In addition, a phase diagram predicting the LLE for the system is generated using a numerical root-finding algorithm to determine the binodal, while the spinodal is determined analytically. The critical values are also included, and representative values from the LLE equilibrium plot are displayed at the bottom of the page. In order to generate results, all 3 parameters: degree of polymerization for both species and a sigma value, are necessary.

1.Qin, J. Interfacial tension of polyelectrolyte complex coacervate phases. ACS Macro Lett. 2014, 3, 565–568