  Nucleation at large metastability is still largely an unsolved problem,
although is a problem of tremendous current interest, with wide practical
value. It is well-accepted that the classical nucleation theory (CNT) fails to
provide a qualitative picture and gives incorrect quantitative values for such
quantities as activation free energy barrier and supersaturation dependence of
nucleation rate, especially at large metastability. In this article, we present
a powerful alternative formalism to treat nucleation at large supersaturation.
This formalism goes over to the classical picture at small supersaturation
where CNT is expected to be valid. The new theory is based on an extended set
of order parameters in terms of k-th largest liquid-like clusters where k=1 is
the largest cluster in the system, k=2 is the second largest cluster and so on.
We derive an analytic expression for the free energy of formation of the k-th
largest cluster which shows that at large metastability the barrier of growth
for the few largest liquid-like clusters disappear, the nucleation becomes
collective and the approach to the critical size occurs by barrierless
diffusion in the cluster size space. The expression for the rate of barrier
crossing predicts a weaker supersaturation dependence than that of CNT at large
metastability. Such a cross-over behavior has indeed been observed in recent
experiments but eluded an explanation till now. In order to understand the
large numerical difference between simulation predictions and experimental
results, we carried out a study of the dependence on the range of
intermolecular interaction of both the surface tension of an equilibrium planar
gas-liquid interface and the free energy barrier of nucleation. Both are found
to depend significantly on the range of interaction for a Lennard-Jones
potential, both in two and three dimensions.
