Exactly solvable model for self-assembly of hard core-soft shell particles at interfaces

A generic model for self-assembly of a monolayer of hybrid core-shell particles at an interface is developed. We assume that for distances larger than the size of the incompressible core a soft repulsion appears, and the repulsion is followed by an attraction at larger separations. The model is solved exactly in a one-dimensional lattice version. One, two or three periodic structures and variety of shapes of the pressure-density isotherms may occur in different versions of the model. For strong interactions the isotherm consists of nearly vertical segments at densities optimal for the periodic structures that are connected by segments with a small slope. The range of order depends very strongly on the strength of attraction and on the density. Our results agree with experimental observations.