System size dependence of the free energy surface in cluster simulation of nucleation

Recently, we presented a simulation approach to map out the free energy landscape of nucleation. One of the key ingredients of the approach was to choose a proper system volume V so that it satisfies the following two conditions due to Nishioka and Pound: (1) V is large enough so that the system can be regarded as statistically independent of its surroundings. (2) V is small enough that the probability of finding more than one uncorrelated fluctuation at any instant in the system is negligible. Insofar as nucleation is a rare event that proceeds by forming a spatially-localized high-intensity fluctuation, we expect that these conditions are satisfied simultaneously by a wide range of V . In the case of non-associative fluids, such as Lennard-Jones fluids above the triple point,the free energy determined by this method exhibits some non-trivial volume dependence. Nonetheless, if nucleation in such a system still proceeds through a spatially-localized fluctuation, the Nishioka-Pound conditions will be satisfied by a wide range of V . Since the simulation cell can be regarded as defining the field of vision involved in our observation of nucleation process, the exact choice of V should have no effect on the observed nucleation behavior. It is then natural to inquire exactly how V independent nucleation behavior arises from the apparently V dependent free energy surface. Since nucleation is a dynamical process, a part of the answer undoubtedly lies in the dynamical consideration. In what follows, however, we shall limit ourselves to the free energy consideration alone and show that, by means of an example, the free energetics relevant to the steady-state nucleation remains unchanged for a wide range of the system size.