  Bilayers formed of two species of amphiphile of different chain lengths may
segregate into thinner and thicker domains composed predominantly of the
respective species. Using a coarse-grained mean-field model, we investigate how
mixing oil with the amphiphiles affects the structure and thickness of the
bilayer at and on either side of the boundary between two neighbouring domains.
In particular, we find that oil molecules whose chain length is close to that
of the shorter amphiphiles segregate to the thicker domain. This smooths the
surface of the hydrophobic bilayer core on this side of the boundary, reducing
its area and curvature and their associated free-energy penalties. The
smoothing effect is weaker for oil molecules that are shorter or longer than
this optimum value: short molecules spread evenly through the bilayer, while
long molecules swell the thicker domain, increasing the surface area and
curvature of the bilayer core in the interfacial region. Our results show that
adding an appropriate oil could make the formation of domain boundaries more or
less favourable, raising the possibility of controlling the domain size
distribution.
