Phase behavior of electrostatically complexed polyelectrolyte gels using an embedded fluctuation model

Nanostructured, responsive hydrogels formed due to electrostatic interactions have promise for applications such as drug delivery and tissue mimics. These physically cross-linked hydrogels are composed of an aqueous solution of oppositely charged triblocks with charged end-blocks and neutral, hydrophilic mid-blocks. Due to their electrostatic interactions, the end-blocks microphase separate and form physical cross-links that are bridged by the mid-blocks. The structure of this system was determined using a new, efficient embedded fluctuation (EF) model in conjunction with self-consistent field theory. The calculations using the EF model were validated against unapproximated field-theoretic simulations with complex Langevin sampling and were found consistent with small angle X-ray scattering (SAXS) measurements on an experimental system. Using both the EF model and SAXS, phase diagrams were generated as a function of end-block fraction and polymer concentration. Several structures were observed including a body-centered cubic sphere phase, a hexagonally packed cylinder phase, and a lamellar phase. Finally, the EF model was used to explore how parameters that directly relate to polymer chemistry can be tuned to modify the resulting phase diagram, which is of practical interest for the development of new hydrogels.