Phase Transitions of Oppositely Charged Colloidal Particles Driven by Alternating Current Electric Field

Competition between lanes and transient jammed clusters in driven binary mixtures

We consider mixtures of oppositely driven particles, showing that their nonequilibrium steady states form lanes parallel to the drive, which coexist with transient jammed clusters where particles are temporarily immobilized. We analyze the interplay between these two types of nonequilibrium pattern formation, including their implications for macroscopic demixing perpendicular to the drive. Finite-size scaling analysis indicates that there is no critical driving force associated with demixing, which appears as a crossover in finite systems. We attribute this effect to the disruption of long-ranged order by the transient jammed clusters.

Colloidal superionic conductors

Nanoparticles with highly asymmetric sizes and charges that self-assemble into crystals via electrostatics may exhibit behaviors reminiscent of those of metals or superionic materials. Here, we use coarse-grained molecular simulations with underdamped Langevin dynamics to explore how a binary charged colloidal crystal reacts to an external electric field. As the field strength increases, we find transitions from insulator (ionic state), to superionic (conductive state), to laning, to complete melting (liquid state). In the superionic state, the resistivity decreases with increasing temperature, which is contrary to metals, yet the increment decreases as the electric field becomes stronger. Additionally, we verify that the dissipation of the system and the fluctuation of charge currents obey recently developed thermodynamic uncertainty relation. Our results describe charge transport mechanisms in colloidal superionic conductors.

Field-driven cluster formation in two-dimensional colloidal binary mixtures

We study size- and charge-asymmetric oppositely charged colloids driven by an external electric field. The large particles are connected by harmonic springs, forming a hexagonal-lattice network, while the small particles are free of bonds and exhibit fluidlike motion. We show that this model exhibits a cluster formation pattern when the external driving force exceeds a critical value. The clustering is accompanied with stable wave packets in vibrational motions of the large particles.

Macroscopic charge segregation in driven polyelectrolyte solutions

Understanding the behavior of charged complex fluids is crucial for a plethora of important industrial, technological, and medical applications. Here, using coarse-grained molecular dynamics simulations, we investigate the properties of a polyelectrolyte solution with explicit counterions and implicit solvent that is driven by a steady electric field. By properly tuning the interplay between interparticle electrostatics and the applied electric field, we uncover two non-equilibrium continuous phase transitions as a function of the driving field. The first transition occurs from a homogeneous mixed phase to a macroscopic charge-segregated phase in which the polyelectrolyte solution self-organizes to form two lanes of like-charges, parallel to the applied field. We show that the fundamental underlying factor responsible for the emergence of this charge segregation in the presence of an electric field is the excluded volume interactions of the drifting polyelectrolyte chains. As the driving field is increased further, a re-entrant transition is observed from a charge-segregated phase to a homogeneous phase. The re-entrance is signaled by a decrease in the mobility of the monomers and counterions as the electric field is increased. Furthermore, with multivalent counterions, a counterintuitive regime of negative differential mobility is observed in which the charges move progressively more slowly as the driving field is increased. We show that all these features can be consistently explained using an intuitive trapping mechanism that operates between the oppositely moving charges, and present numerical evidence to support our claims. Parameter dependencies and phase diagrams are studied to better understand charge segregation in such driven polyelectrolyte solutions.

Perpendicular and parallel phase separation in two-species driven diffusive lattice gases

We study three different lattice models in which two species of diffusing particles are driven in opposite directions by an electric field. We focus on dynamical phase transitions that involve phase separation into domains that may be parallel or perpendicular to a driving field. In all cases, the perpendicular state appears for weak driving, consistent with previous work. For strong driving, we introduce two models that support the parallel state. In one model, this state occurs because of the inclusion of dynamical rules that enhance lateral diffusion during collisions; in the other, it is a result of a nearest-neighbor attractive or repulsive interaction between particles of the same or opposite species. We discuss the connections between these results and the behavior found in off-lattice systems, including laning and freezing by heating.

Electric-field-induced oscillations in ionic fluids: a unified formulation of modified Poisson-Nernst-Planck models and its relevance to correlation function analysis

We theoretically investigate an electric-field-driven system of charged spheres as a primitive model of concentrated electrolytes under an applied electric field. First, we provide a unified formulation for the stochastic charge and density dynamics of the electric-field-driven primitive model using the stochastic density functional theory (DFT). The stochastic DFT integrates the four frameworks (the equilibrium and dynamic DFTs, the liquid state theory and the field-theoretic approach), which allows us to justify in a unified manner various modifications previously made for the Poisson-Nernst-Planck model. Next, we consider stationary density-density and charge-charge correlation functions of the primitive model with a static electric field. We predict an electric-field-induced synchronization between emergences of density and charge oscillations. We are mainly concerned with the emergence of stripe states formed by segregation bands transverse to the external field, thereby demonstrating the following: (i) the electric-field-induced crossover occurs prior to the conventional Kirkwood crossover without an applied electric field, and (ii) the ion concentration dependence of the decay lengths at the onset of oscillations bears a similarity to the underscreening behavior found by recent simulation and theoretical studies on equilibrium electrolytes. Also, the 2D inverse Fourier transform of the correlation function illustrates the existence of stripe states beyond the electric-field-induced Kirkwood crossover.

Stochastic Density Functional Theory on Lane Formation in Electric-Field-Driven Ionic Mixtures: Flow-Kernel-Based Formulation

Simulation and experimental studies have demonstrated non-equilibrium ordering in driven colloidal suspensions: with increasing driving force, a uniform colloidal mixture transforms into a locally demixed state characterized by the lane formation or the emergence of strongly anisotropic stripe-like domains. Theoretically, we have found that a linear stability analysis of density dynamics can explain the non-equilibrium ordering by adding a non-trivial advection term. This advection arises from fluctuating flows due to non-Coulombic interactions associated with oppositely driven migrations. Recent studies based on the dynamical density functional theory (DFT) without multiplicative noise have introduced the flow kernel for providing a general description of the fluctuating velocity. Here, we assess and extend the above deterministic DFT by treating electric-field-driven binary ionic mixtures as the primitive model. First, we develop the stochastic DFT with multiplicative noise for the laning phenomena. The stochastic DFT considering the fluctuating flows allows us to determine correlation functions in a steady state. In particular, asymptotic analysis on the stationary charge-charge correlation function reveals that the above dispersion relation for linear stability analysis is equivalent to the pole equation for determining the oscillatory wavelength of charge–charge correlations. Next, the appearance of stripe-like domains is demonstrated not only by using the pole equation but also by performing the 2D inverse Fourier transform of the charge–charge correlation function without the premise of anisotropic homogeneity in the electric field direction.