Theory of the evaporation/condensation transition of equilibrium droplets in finite volumes
Abstract
A phenomenological theory of phase coexistence of finite systems near the coexistence curve that occurs in the thermodynamic limit is formulated for the generic case of ddimensional ferromagnetic Ising lattices of linear dimension L with magnetization m slightly less than m_{coex}. It is argued that in the limit L→∞ an unconventional firstorder transition occurs at a characteristic value m_{t}< m_{coex}, where a large equilibrium droplet ceases to exist, and the thermodynamically conjugate variable to m, the magnetic field H, exhibits a jump from H_{t}^{(1)} to H_{t}^{(2)}. It is found that H_{t}^{(1,2)} scale like L^{ d/( d+1) } their ratio being simply H_{t}^{(1)}/ H_{t}^{(2)}=( d+1)/( d1), and m_{coex} m_{t}∝ L^{ d/( d+1) } as well, while the excess thermodynamic potential (relative to its value according to the doubletangent construction) varies as g_{t}∝ L^{2 d/( d+1) }. The prefactors in all these relations are derived and it is shown that near the bulk critical point this transition shows a standard scaling behavior and the prefactors can be expressed in terms of known universal constants. Also the rounding of this transition at very large but finite L is considered and it is found that the jump in H at H_{t} is rounded over an interval ∆ m∝ L^{ d2/( d+1) }. Various simulations are interpreted in the light of these predictions, and the possibility to extract the surface free energy of liquid droplets coexisting in a finite volume with supersaturated gas is critically discussed.
 Publication:

Physica A Statistical Mechanics and its Applications
 Pub Date:
 March 2003
 DOI:
 10.1016/S03784371(02)015819
 Bibcode:
 2003PhyA..319...99B