The use of field-theoretic representations has emerged as an increasingly attractive and flexible method for describing the statistical behavior of soft materials, granting direct access to thermodynamically-derived structures and properties of interest, while avoiding the computational expense of a traditional explicit particle model. Leveraging the recently-developed complex Langevin (CL) method for full eld-theoretic simulation of exact fluctuating field theories, along with the ever-advancing capabilities of academic and industrial computing infrastructures, field-theoretic descriptions of charge-containing soft matter systems - such as polyelectrolyte solutions and polymerized ionic liquids - permit the direct simulation of inhomogeneous, strongly-fluctuating dense fluids of charged species, illuminating the collective thermal motion, and associated electrostatic correlations, of coarse-grained charge-containing molecules. Beyond the already vast materials design space available to this class of field theories, one detail that has thus far been omitted is the explicit polarizability carried by all molecular species contained in a real, charge-containing soft matter system.
This thesis describes the construction and implementation of a molecularly-informed field theory for a fluid of polarizable media, assigning "bead" molecules with a polarizability via a simple Drude oscillator model. Beads can optionally carry a net free charge or be connected in chains to produce electrolyte and polymer models, respectively. By constructing a simple fluid model of
oppositely charged, polarizable electrolyte beads, which is then solved analytically using a simple Gaussian fluctuation approximation, the model is shown to self-consistently include: short-range van der Waals (VdW) attractions between polarizable beads, short-range ion-dipole attractions between the net free charge and net dipole moment of neighboring beads, dielectric screening of electrostatic correlations due to intervening polarizable beads, and a long-range Debye-Huckel net ion-ion interaction, subject to the charge-screening and dielectric-screening effects of the bulk fluid.
Subsequently adopting a fluid model of polarizable, charge-neutral beads, the role of an applied
electric field in shifting the phase stability of a binary dielectric fluid is explored. An electric field, E0, is introduced, which interacts with polarizable beads, inducing a directional response in the average fluctuation behavior of the fluid, which is identified as its dielectric displacement, D. Linearizing D with respect to E0 leads to an explicit molecularly-based expression for the average dielectric constant of the fluid mixture. In the linear response regime, the composition dependence of the dielectric constant completely species the applied field-dependent contribution to the miscibility of the
fluid, which is cast in the form of a contribution to a Flory interaction parameter. Using a Gaussian approximation to the field theory, an analytical expression for this contribution is obtained, which illuminates the role of structural and electrostatic contrast between
dissimilar molecules on their demixing behavior in the presence of an applied field. Specifically, contrast between wavevector-dependent, single-molecule correlation functions emerges as a necessary ingredient for electric field-induced mixing, corresponding to a negative Flory contribution; the form of each correlation function is determined by the structure of its corresponding molecular species. The character of the Flory contribution is considered in three classes of binary systems: a binary simple fluid, a homopolymer blend, and a homopolymer solution. For each class of system, the predicted sign of the Flory contribution is determined by examining the asymptotic behavior of each single-molecule correlation function.
Due to their large size relative to the length-scale associated with individual monomers, microphase-forming block copolymers (BCPs) are often simulated at the mean-field level using self-consistent field theory (SCFT). To determine the dielectric behavior of a BCP melt, it is similarly appropriate to adopt a mean-field description of electrostatic behavior. With this in mind, a modified SCFT
formalism is constructed, which simulates the behavior of a BCP of dielectric monomer species, interacting with an applied electric eld; the model is subsequently used to determine the phase behavior of such a system. When different dielectric constants are assigned to each monomer type, the electric field penalizes the interfaces between species domains that are not parallel to the field.
To minimize this penalty, each BCP microphase can be expected to adopt an associated preferred orientation relative to the electric field vector. The phase diagram is therefore constructed by comparing the free energy of each competing phase at its thermodynamically-preferred orientation. The stability regions of the sphere and network phases are found to shrink with increasing field strength, in favor of the disordered, cylindrical, and lamellar phases. Additionally, the double gyroid network phase is more strongly disfavored than the orthorhombic Fddd network phase, such that the predicted region of stability for the Fddd phase is shifted to larger segregation strength (lower temperature).
