The evaporation/condensation transition of liquid droplets.

The condensation of a supersaturated vapor enclosed in a finite system is considered. A phenomenological analysis reveals that the vapor is found to be stable at densities well above coexistence. The system size at which the supersaturated vapor condenses into a droplet is found to be governed by a typical length scale which depends on the coexistence densities, temperature and surface tension. When fluctuations are neglected, the chemical potential is seen to show a discontinuity at an effective spinodal point, where the inhomogeneous state becomes more stable than the homogeneous state. If fluctuations are taken into account, the transition is rounded, but the slope of the chemical potential versus density isotherm develops a discontinuity in the thermodynamic limit. In order to test the theoretical predictions, we perform a simulation study of droplet condensation for a Lennard-Jones fluid and obtain loops in the chemical potential versus density and pressure. By computing probability distributions for the cluster size, chemical potential, and internal energy, we confirm that the effective spinodal point may be identified with the occurrence of a first order phase transition, resulting in the condensation of a droplet. An accurate equation of state is employed in order to estimate the droplet size and the coexisting vapor density and good quantitative agreement with the simulation data is obtained. The results highlight the need of an accurate equation of state data for the Laplace equation to have predictive power.

[1]  L. G. Macdowell.  Formal study of nucleation as described by fluctuation theory , 2003 .

[2]  Kurt Binder,et al.  Theory of the evaporation/condensation transition of equilibrium droplets in finite volumes , 2003 .

[3]  M. Biskup,et al.  Comment on: “Theory of the evaporation/condensation transition of equilibrium droplets in finite volumes” , 2003, cond-mat/0302373.

[4]  A. Neimark,et al.  Bridging scales from molecular simulations to classical thermodynamics: density functional theory of capillary condensation in nanopores , 2003 .

[5]  D. Kashchiev.  Thermodynamically consistent description of the work to form a nucleus of any size , 2003 .

[6]  A. Geiger,et al.  Percolation of water in aqueous solution and liquid–liquid immiscibility , 2002 .

[7]  M. Biskup,et al.  On the formation/dissolution of equilibrium droplets , 2002, math-ph/0207012.

[8]  E. J. Smith,et al.  Dynamics of melting and stability of ice 1h: Molecular-dynamics simulations of the SPC/E model of water , 2002 .

[9]  T. Neuhaus,et al.  2D Crystal Shapes, Droplet Condensation, and Exponential Slowing Down in Simulations of First-Order Phase Transitions , 2002, cond-mat/0201324.

[10]  M. Klein,et al.  Aggregation-volume-bias Monte Carlo simulations of vapor-liquid nucleation barriers for Lennard-Jonesium , 2001 .

[11]  Yiping Tang,et al.  On the mean spherical approximation for the Lennard-Jones fluid , 2001 .

[12]  P. Debenedetti,et al.  Density-functional study of homogeneous bubble nucleation in the stretched Lennard-Jones fluid , 2001 .

[13]  D. Landau,et al.  Efficient, multiple-range random walk algorithm to calculate the density of states. , 2000, Physical review letters.

[14]  M. Pleimling,et al.  Crossing the Coexistence Line at Constant Magnetization , 2000, cond-mat/0011116.

[15]  Madrid,et al.  Equation of state and critical behavior of polymer models: A quantitative comparison between Wertheim’s thermodynamic perturbation theory and computer simulations , 2000, cond-mat/0005191.

[16]  L. G. Macdowell,et al.  Interface and Surface Properties of Short Polymers in Solution: Monte Carlo Simulations and Self-Consistent Field Theory , 2000 .

[17]  K. Gubbins,et al.  Phase separation in confined systems , 1999 .

[18]  D. Oxtoby,et al.  Identifying physical clusters in vapor phase nucleation , 1999 .

[19]  Katalin Martinás,et al.  Thermodynamics of Negative Pressures in Liquids , 1998 .

[20]  Daan Frenkel,et al.  Computer simulation study of gas–liquid nucleation in a Lennard-Jones system , 1998 .

[21]  Yiping Tang,et al.  Analytical description of the Lennard‐Jones fluid and its application , 1997 .

[22]  Vicente A Talanquer,et al.  A NEW PHENOMENOLOGICAL APPROACH TO GAS-LIQUID NUCLEATION BASED ON THE SCALING PROPERTIES OF THE CRITICAL NUCLEUS , 1997 .

[23]  A. Laaksonen,et al.  Interfacial curvature free energy, the Kelvin relation, and vapor–liquid nucleation rate , 1997 .

[24]  Percus,et al.  Stress tensor of liquid-vapor states of inhomogeneous fluids. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[25]  McGraw,et al.  Scaling properties of the critical nucleus in classical and molecular-based theories of vapor-liquid nucleation. , 1996, Physical review letters.

[26]  Borgs,et al.  Finite-size effects at asymmetric first-order phase transitions. , 1992, Physical review letters.

[27]  Daan Frenkel,et al.  COMPUTER-SIMULATION STUDY OF FREE-ENERGY BARRIERS IN CRYSTAL NUCLEATION , 1992 .

[28]  B. Berg,et al.  Multicanonical ensemble: A new approach to simulate first-order phase transitions. , 1992, Physical review letters.

[29]  R. G. Lerner,et al.  Encyclopedia of Physics , 1990 .

[30]  J. Schmelzer,et al.  Thermodynamics of finite systems and the kinetics of first-order phase transitions , 1987 .

[31]  K. Gubbins,et al.  A microscopic theory for spherical interfaces: Liquid drops in the canonical ensemble , 1986 .

[32]  R. Strey,et al.  Homogeneous nucleation rates for n‐alcohol vapors measured in a two‐piston expansion chamber. , 1986 .

[33]  A. Yang.  The thermodynamical stability of the heterogeneous system with a spherical interface , 1985 .

[34]  K. Gubbins,et al.  A molecular dynamics study of liquid drops , 1984 .

[35]  A. Yang.  Free energy for the heterogeneous systems with spherical interfaces , 1983 .

[36]  John S. Rowlinson,et al.  Molecular Theory of Capillarity , 1983 .

[37]  Kurt Binder,et al.  Monte Carlo calculation of the surface tension for two- and three-dimensional lattice-gas models , 1982 .

[38]  Kurt Binder,et al.  “Critical clusters” in a supersaturated vapor: Theory and Monte Carlo simulation , 1980 .

[39]  Bruce J. Berne,et al.  Computer simulation of the nucleation and thermodynamics of microclusters , 1978 .

[40]  A. C. Zettlemoyer,et al.  Homogeneous Nucleation Theory , 1974 .

[41]  Michael E. Fisher,et al.  The theory of condensation and the critical point , 1967 .

[42]  Frank H. Stillinger,et al.  Rigorous Basis of the Frenkel-Band Theory of Association Equilibrium , 1963 .

[43]  T. L. Hill.  Statistical Thermodynamics of the Transition Region between Two Phases. I. Thermodynamics and Quasi-thermodynamics , 1952 .

[44]  Pablo G. Debenedetti,et al.  Metastable Liquids: Concepts and Principles , 1996 .