  Using a simple density functional theory (DFT) we determine the height of the
free energy barrier for forming a droplet of the liquid phase from the
metastable gas phase for a model colloidal fluid exhibiting competing
interactions. The pair potential has a hard core of diameter {\sigma}, is
attractive Yukawa at intermediate separations, and is repulsive Yukawa at large
separations. We find that even a very weak long-range repulsive tail in the
pair potential has a profound effect on nucleation: increasing the amplitude of
the repulsive Yukawa tail reduces significantly the free energy barrier height
and therefore increases the liquid droplet nucleation rate. The method we
introduce for calculating the droplet density profile and free energy employs a
fictitious external potential to stabilize a liquid droplet of the desired
size, i.e. with a given excess number of particles. For the critical droplet,
corresponding to an extremum of the grand potential, this fictitious potential
is everywhere zero. We examine the decay of the droplet density profiles into
the bulk gas. For a range of nucleation state points the DFT predicts
exponentially damped, long wavelength oscillatory decay for systems exhibiting
long-range repulsion, contrasting sharply with the monotonic decay found when
the pair potential has only an attractive Yukawa piece. The changes in
nucleation properties that we find for small amplitudes of the repulsive Yukawa
tail reflect the propensity of the fluid to form modulated structures such as
clusters or stripes.
