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Colloidal particles that are confined to an interface such as the air-waterinterface are an example of a two-dimensional fluid. Such dispersions have beenobserved to spontaneously form cluster and stripe morphologies in certainsystems with isotropic pair potentials between the particles, due to the factthat the pair interaction between the colloids has competing attraction andrepulsion over different length scales. Here we present a simple densityfunctional theory for a model of such a two-dimensional fluid. The theorypredicts a bulk phase diagram exhibiting cluster, stripe and bubble modulatedphases, in addition to homogeneous fluid phases. Comparing with simulationresults for this model from the literature, we find that the theory isqualitatively reliable. The model allows for a detailed investigation of thestructure of the fluid and we are able to obtain simple approximate expressionsfor the static structure factor and for the length scale characterising themodulations in the microphase separated phases. We also investigate thebehaviour of the system under confinement between two parallel hard walls. Wefind that the confined fluid phase behaviour can be rather complex.

Two-dimensional fluid with competing interactions exhibiting microphase separation: theory for bulk and interfacial properties