On First-order Corrections to the LSW Theory II: Finite Systems

We consider first–order corrections to the classical theory by Lifshitz, Slyozov and Wagner (LSW) for systems with a finite number of particles. Numerical simulations in V. E Fradkov etal. Phys. Rev. E 53:3925–3932 (1996)] show a cross–over in the scaling of the correction term from ^1/3 to ^1/2 ( is the volume fraction of particles), when the system size becomes larger than the screening length. We rigorously derive this cross–over for the rate of change of the energy, starting from the monopole approximation. The proof exploits the fact that the rate of change of energy has a variational characterization.