Arrested phase separation and amorphous patterns in charged binary fluids
Frustration generated by competing interactions can stabilise patterns with tunable lengthscales which evade indefinite coarsening and macroscopic phase separation. Here we investigate a charged binary fluid in which the tendency toward phase separation is opposed by screened electrostatic repulsion. Combining analytics and numerical simulations, we identify a regime of arrested phase separation characterised by finite-wavelength instability. The resulting states include droplet and labyrinthine phases in two dimensions, and droplets, concentric shells and tubular structures in three dimensions. Surprisingly, some of these structures are amorphous morphologies that emerge reproducibly from different initial conditions. Free-energy estimates suggest that these disordered structures may be thermodynamically stabilised by frustration, rather than being kinetically trapped. Our results identify a simple mechanism through which the competition between phase separation and screened electrostatics can generate equilibrium amorphous microphases with glassy features.