Patterns with long and short-range order in monoloyers of binary mixtures with competing interactions

Lateral microsegregation in a monolayer of a binary mixture of particles or macromolecules is studied by molecular dynamics simulations in a generic model with the interacting potentials inspired by effective interactions in biological or soft-matter systems. In the model, the energy is minimized when like particles form small clusters, and the cross-interaction is of opposite sign. We show that the laterally microsegregated components in the dense ordered phases form alternating stripes for similar densities, or the clusters of the minority component fill the hexagonally distributed voids formed in the dense phase of the majority component. A qualitative phase diagram in the plane of densities of the two components is constructed for low temperatures. An addition of the second component significantly enlarges the temperature range of the stability of the ordered phases compared to the stability of these phases in the one-component system. At higher temperatures, the disordered phase consisting of individual particles, one-component clusters and two-component super-clusters of various sizes is stable. The product <i>kn</i>(<i>k</i>), with <i>n</i>(<i>k</i>) denoting the average number of super-clusters composed of <i>k</i> particles, decays exponentially with <i>k</i>, and the inverse decay rate depends linearly on temperature.