  A lattice model with soft repulsion followed by attraction is developed for a
monolayer of hybrid core-shell particles self-assembling at an interface. The
model is solved exactly in one dimension. 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
vertical segments separated by plateaus. The range of order depends strongly on
the strength of attraction and on the density. Our results agree with
experimental observations.

Soft Condensed Matter;Statistical Mechanics