Onset of stripe order in classical fluids: Lessons from lattice-gas mixtures

When two molecular species with mutual affinity are mixed together, various self-assembled phases can arise at low temperature, depending on the shape of like and unlike interactions. Among them, stripes-where layers of one type are regularly alternated with layers of another type-hold a prominent place in materials science, occurring, for example, in the structure of superconductive doped antiferromagnets. Stripe patterns are relevant for the design of functional materials, with applications in optoelectronics, sensing, and biomedicine. In a purely classical setting, an open question pertains to the features that spherically symmetric particle interactions must have to foster stripe order. Here, we address this challenge for a lattice-gas mixture of two particle species, whose equilibrium properties are exactly determined by Monte Carlo simulations with Wang-Landau sampling, in both planar and spherical geometry and for equal chemical potentials of the species. Somewhat surprisingly, stripes can emerge from largely different off-core interactions, featuring various combinations of repulsive-like interactions with a predominantly attractive unlike interaction. In addition to stripes, our survey also unveils crystals and crystal-like structures, cluster crystals, and networks, which considerably broaden the catalog of possible patterns. Overall, our study demonstrates that stripes are more widespread than generally thought, as they can be generated by several distinct mechanisms, thereby explaining why stripe patterns are observed in systems as diverse as cuprate materials, biomaterials, and nanoparticle films.