We present a theoretical analysis of a model nucleation process
where an oil phase separates out from
a droplet microemulsion phase. We consider a homogeneous
nucleation where aggregate growth occurs
through addition of monomers. The nucleus is formed by the growth
of an already existing microemulsion
droplet. On the basis of previous equilibrium studies of the
microemulsions of the same system we can
be confident about the accuracy of the description of free energy
changes during nucleation. Using the
constraints of constant hydrocarbon volume and aggregate area, the
change in curvature free energy is
determined as an oil drop is nucleated rather than the change in
surface free energy, as in a conventional
nucleation theory. We obtain a simple analytical expression for
the barrier which has the feature that
it only exists in a finite parameter range. In the particular
system that we have studied experimentally
a two-phase system of microemulsion plus excess oil is reached through
a temperature quench and a
nucleation barrier is found for moderately deep quenches only.
Having established an expression for the
nucleation barrier, we analyze the kinetics and derive a diffusion
equation in aggregate space, which
considerably facilitates the calculation of the steady state rate for
the formation of nuclei. Experiments
confirm the existence of a nucleation barrier in the predicted range.
They also show the concentration
independence of the barrier and that experiments with different initial
radii can be put on a common scale,
as predicted. It is concluded that the system is very promising
for fundamental studies of the dynamics
of nucleation processes in liquids.