  Charged colloidal particles trapped at an air--water interface are well known
to form an ordered crystal, stabilized by a long ranged repulsion, the details
of this repulsion remain something of a mystery, but all experiments performed
to date have confirmed a dipolar-repulsion, at least at dilute concentrations.
More complex arrangements are often observed, especially at higher
concentration, and these seem to be incompatible with a purely repulsive
potential. In addition to electrostatic repulsion, interfacial particles may
also interact via deformation of the surface: so-called capillary effects.
Pair-wise capillary interactions are well understood, and are known to be too
small (for these colloidal particles) to overcome thermal effects. Here we show
that collective effects may significantly modify the simple pair-wise
interactions and become important at higher density, though we remain well
below close packing throughout. In particular, we show that the interaction of
many interfacial particles can cause much larger interfacial deformations than
do isolated particles, and show that the energy of interaction per particle due
to this "collective sinking" grows as the number of interacting particles
grows. Though some of the parameters in our simple model are unknown, the
scaling behaviour is entirely consistent with experimental data, strongly
indicating that estimating interaction energy based solely on pair-wise
potentials may be too simplistic for surface particle layers.
