(588a) Out-of-Equilibrium Phase Behavior of Dielectric/Paramagnetic Nanoparticle Suspensions in Toggled Electric/Magnetic Fields

Structured materials self-assembled from dispersions of nanoparticles and colloids have numerous demonstrated applications including wave guides for optical computing, microlens arrays for energy harvesting, and porous electrodes for energy storage. One simple, tunable way to direct the self-assembly of these materials is by using electric and magnetic fields to induce dipole and higher order moments in dielectric or paramagnetic nanoparticles. As the particles self-assemble under a steady field, a thermodynamic constraint on the phase separation kinetics forces a tradeoff between quality of the self-assembled microstructure and its rate of formation. This is a key difficulty preventing adoption of self-assembled nanoparticle materials at scale. Dynamically self-assembling dispersions with interactions that vary in time do not have this constraint and offer a promising method to suppress kinetic arrest while accelerating growth of ordered nanostructures. In the case of dielectric/paramagnetic dispersions, varying the particle interactions in time is easily achieved by toggling the external electric/magnetic field on and off cyclically in time. Because of the cyclic driving force, materials formed by toggled self-assembly are dissipative and out-of-equilibrium, and therefore are classified as active matter, along with particles that swim, grow, or self-rotate. As toggled self-assembly cannot be understood in terms of equilibrium thermodynamics, new theories must be developed before it can be used to reliably fabricate nanomaterials, but there are several theoretical and computational challenges.

A fundamental model of these dispersions requires solving a many-bodied problem for the electric or magnetic field. Exact solutions are computationally expensive, so numerical simulations and thermodynamic calculations typically make the simplifying approximation that each particle behaves as a point dipole of fixed strength and direction. These models are inconsistent with experimental conditions, where particle moments are strong functions of configuration, and lead to phase predictions that fail to satisfy thermodynamic coexistence criteria. We have developed a new method to compute the multipole moments and forces to desired accuracy in suspensions of dielectric/paramagnetic nanoparticles. The method uses a moment expansion of the periodic, Fourier space representation of the Green’s function for Poisson’s equation. Our method is spectrally accurate, scales nearly linearly with particle number, and is parallelized on graphics processing units, allowing for rapid simulation of large dielectric/paramagnetic dispersions. We use our method to perform thermodynamic calculations predicting the equilibrium phase diagram of hard, dielectric/paramagnetic nanoparticles in steady electric/magnetic fields, which agree with results from dynamic simulations. Next, we use our simulation method to show that cyclically toggling the electric/magnetic fields on and off can avoid kinetic barriers and yield well-ordered crystalline domains in these dispersions. The rate of phase separation, local and global quality of the self-assembled structures, and range of tunable parameters leading to acceptable self-assembly are all enhanced with toggled fields compared to steady fields. The growth mechanism and terminal structure of the dispersion are easily controlled by parameters of the toggling protocol, allowing for selection of processes that yield rapidly self-assembled, low defect crystals as well as out-of-equilibrium structures that cannot be stabilized with steady fields.