Two-dimensional systems with competing interactions: microphase formation under the effect of a disordered porous matrix

We have investigated the effect of a disordered porous matrix on the cluster microphase formation of a two dimensional system where fluid particles interact via competing interactions. To this end we have performed extensive Monte Carlo simulations and have systematically varied the densities of the fluid and of the matrix as well as the interaction between the matrix particles and between the matrix and fluid particles. Our results provide evidence that the matrix does have a distinct effect on the microphase formation of the fluid particles: as long as the matrix particles interact both among themselves as well as with the fluid particles via a simple hard sphere potential, they essentially reduce the available space, in which the fluid particles form a cluster microphase. On the other hand, if we turn on a long-range tail in the matrix-matrix and in the matrix-fluid interactions, the matrix particles become nucleation centers for the clusters formed by the fluid particles.