  We investigate theoretically the phase diagram of an insoluble charged
surfactant monolayer in contact with a semi-dilute polyelectrolyte solution (of
opposite charge). The polyelectrolytes are assumed to have long-range and
attractive (electrostatic) interaction with the surfactant molecules. In
addition, we introduce a short-range (chemical) interaction which is either
attractive or repulsive. The surfactant monolayer can have a lateral phase
separation between dilute and condensed phases. Three different regimes of the
coupled system are investigated depending on system parameters. A regime where
the polyelectrolyte is depleted due to short range repulsion from the surface,
and two adsorption regimes, one being dominated by electrostatics, whereas the
other by short range chemical attraction (similar to neutral polymers). When
the polyelectrolyte is more attracted (or at least less repelled) by the
surfactant molecules as compared with the bare water/air interface, it will
shift upwards the surfactant critical temperature. For repulsive short-range
interactions the effect is opposite. Finally, the addition of salt to the
solution is found to increase the critical temperature for attractive surfaces,
but does not show any significant effect for repulsive surfaces.
