Hybrid Field Theory included Transfer Matrix Pairing for Complex Coacervation

Complex coacervation is a phenomenon that occurs when charged polyelectrolytes are mixed within an aqueous solution and undergo phase separation. Given the nature of polyelectrolytes, we want to understand the charge correlations and fluctuations that are necessary for these phenomena. Efforts to address these charge correlations have been made with Transfer Matrix (TM) Theory by exploiting the monomer description of the site into physical states ^[1]and this consequently allows for charge sequence effects to be considered ^[2] in predicting coacervate phase behavior. However, one of the main drawbacks of the Transfer Matrix Theory on its own is the absence of spatial information in the adsorption formalism. Alternatively, Self-Consistent Field Theory (SCFT) can provide self-assembly insight for inhomogeneous polymer systems; however, it does not account for charge correlations that have been shown to be important for predicting coacervate phase behavior. We propose a new way to investigate this system by use of a hybrid TM/SCFT method. We focus on explicitly incorporating these charge-pair correlations from the TM into the single chain partition function and therefor propagator. Using the SCFT formalism, this allows for the polymer conformations to be influenced more directly by its charge fluctuations from the local ion-pairing. We will provide a new potential methodology to incorporate charge correlations into SCFT and compare against prior work.