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.