Field-Directed Self-Assembly of Mutually Polarizable Nanoparticles.

Directed assembly of dielectric and paramagnetic nanoparticles can be used to synthesize diverse functional materials that polarize in response to an externally applied electric or magnetic field. However, theories capable of predicting the self-assembled states are lacking. In the proposed work, we develop a complete thermodynamic description of such assemblies for spherical nanoparticles. We show how an important physical feature of these types of particles, mutual polarization, sculpts the free energy landscape and has a remarkably strong influence on the nature of the self-assembled states. Modeling the mutual polarization among nanoparticles requires solving a many-bodied problem for the particle dipole moments. Typically, this computationally expensive task is avoided by neglecting mutual polarization and assuming that each particle in a concentrated dispersion acquires the same dipole moment as a single, isolated particle. Although valid in the limit of small dielectric or permeability contrasts between particles and solvent, this constant dipole assumption leads to qualitatively incorrect predictions for coexisting phases in equilibrium at large dielectric or permeability contrasts. Correctly accounting for mutual polarization enables a thermodynamic theory that describes the equilibrium phase diagram of polarizable dispersions in terms of experimentally controllable variables. Our theoretical predictions agree with the phase behavior we observe in dynamic simulations of these dispersions as well as that in experiments of field-directed structural transitions. In contrast to predictions of a constant dipole model, we find that dispersions of particles with different dielectric constants or magnetic permeabilities exhibit qualitatively different phase behavior. This new model also predicts the existence of a eutectic point at which two crystalline phases and a disordered phase of nanoparticles all simultaneously coexist.