Lane formation in oppositely charged colloids driven by an electric field: chaining and two-dimensional crystallization.

A binary mixture of oppositely charged colloids which is driven by an external electric field is studied by extensive Brownian dynamics computer simulations, ignoring hydrodynamic interactions. The particle interaction is modeled via a screened Coulomb potential together with a steric repulsion. A strong electric field leads to lane formation of oppositely driven lanes. Each lane comprises particles of the same charge. A nonequilibrium "phase diagram" classifying different steady states is obtained as a function of the colloidal volume fraction and the Coulomb coupling. Different steady states are characterized by structural correlations perpendicular and parallel to the applied field. We find a variety of different phases involving lane chains at small volume fraction and low screening, and lanes with two-dimensional crystalline order perpendicular to the field at high volume fraction. The lateral crystalline order can be a square, triangular, or rhombic lattice. In between there is a lateral network structure. These predictions can be verified in real-space experiments on oppositely charged colloids.