Dielectric Nanodroplets: Structure, Stability, Thermodynamics, Shape Transitions and Electrocrystallization in Applied Electric Fields

Abstract

The response and properties of a dielectric nanodroplet with a 10 nm diameter made of formamide placed in a uniform electric field are explored with molecular dynamics simulations and an analytic free energy formulation. Increasing fields cause the initially spherical liquid droplet to undergo gradual prolate spheroidal elongation along the field direction that culminates in a shape instability and a first-order shape transition to a slender liquid needle at a field of ∼0.50 V/nm. This transition is accompanied by enhanced reorientation of the molecular dipoles along the field direction, with the elongated droplets exhibiting a field-induced ferroelectric state, unlike the state of the droplet under field-free conditions. For larger fields, we find further gradual enhancement of the molecular dipole reorientation and the onset of a first-order electro-crystallization transition at a field of 1.4375 V/nm. This transition is portrayed by a sharp increase in the positional order parameter, a significant decrease in the molecular diffusion, and further preferential reorientation of the dipoles. Both transitions exhibit hysteresis as the change in the electric field is reversed, that is, for decreasing fields. Data from the molecular dynamics simulation were used for determination of the field-dependent dielectric permittivity of the formamide droplet. An analytic dielectric continuum model is developed, and a free energy expression which includes polarization, surface, and saturation terms is formulated, yielding results for the variation of the droplet shape as a function of the applied field, or electric Bond number, in agreement with the results obtained from the molecular dynamics simulations. Proper inclusion of dielectric saturation effects in the continuum model, expressed in terms of an electric field-dependent dielectric permittivity, is found to play an important role.