Computer simulation study of gas–liquid nucleation in a Lennard-Jones system

We report a computer-simulation study of homogeneous gas–liquid nucleation in a Lennard-Jones system. Using umbrella sampling, we compute the free energy of a cluster as a function of its size. A thermodynamic integration scheme is employed to determine the height of the nucleation barrier as a function of supersaturation. Our simulations illustrate that the mechanical and the thermodynamical surfaces of tension and surface tension differ significantly. In particular, we show that the mechanical definition of the surface tension cannot be used to compute this barrier height. We find that the relations recently proposed by McGraw and Laaksonen [J. Chem. Phys. 106, 5284 (1997)] for the height of the barrier and for the size of the critical nucleus are obeyed.

[1]  H. Reiss.  Treatment of droplike clusters by means of the classical phase integral in nucleation theory , 1970 .

[2]  J. W. Gibbs,et al.  Scientific Papers , 2002, Molecular Imaging and Biology.

[3]  J. Kirkwood,et al.  The Statistical Mechanical Theory of Transport Processes. IV. The Equations of Hydrodynamics , 1950 .

[4]  J. Henderson,et al.  Statistical mechanics of inhomogeneous fluids , 1982, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[5]  V. Talanquer,et al.  Density functional theory of nucleation: A semiempirical approach , 1995 .

[6]  H. Reiss,et al.  Toward a molecular theory of vapor-phase nucleation. V. Self-consistency in the decoupled dimer limit , 1997 .

[7]  R. Tolman.  The Effect of Droplet Size on Surface Tension , 1949 .

[8]  V. I. Kalikmanov.  Semiphenomenological theory of the Tolman length , 1997 .

[9]  G. Saville,et al.  Computer simulation of a gas–liquid surface. Part 1 , 1977 .

[10]  M. J. Ruiz-Montero,et al.  Numerical evidence for bcc ordering at the surface of a critical fcc nucleus. , 1995, Physical review letters.

[11]  I. Hadjiagapiou.  Density functional theory for spherical drops , 1994 .

[12]  H. Reiss,et al.  Homogeneous nucleation rates for water , 1993 .

[13]  D. Kashchiev.  On the relation between nucleation work, nucleus size, and nucleation rate , 1982 .

[14]  J. Banavar,et al.  Computer Simulation of Liquids , 1988 .

[15]  A. F. Bakker,et al.  Molecular dynamics of the surface tension of a drop , 1992 .

[16]  N. García,et al.  Monte Carlo Calculation of Argon Clusters in Homogeneous Nucleation , 1981 .

[17]  J. Katz,et al.  Resolution of the Problems of Replacement Free Energy, 1/S, and Internal Consistency in Nucleation Theory by Consideration of the Length Scale for Mixing Entropy , 1997 .

[18]  D. Oxtoby,et al.  Nonclassical nucleation theory for the gas-liquid transition , 1988 .

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

[20]  Pieter Rein ten Wolde,et al.  Numerical calculation of the rate of crystal nucleation in a Lennard‐Jones system at moderate undercooling , 1996 .

[21]  H. Reiss,et al.  Toward a molecular theory of vapor‐phase nucleation. II. Fundamental treatment of the cluster distribution , 1992 .

[22]  R. Becker,et al.  Kinetische Behandlung der Keimbildung in übersättigten Dämpfen , 1935 .

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

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

[25]  Jean-Pierre Hansen,et al.  Phase Transitions of the Lennard-Jones System , 1969 .

[26]  D. Mcginty.  Molecular dynamics studies of the properties of small clusters of argon atoms , 1973 .

[27]  H. Reiss,et al.  Toward a molecular theory of vapor‐phase nucleation. III. Thermodynamic properties of argon clusters from Monte Carlo simulations and a modified liquid drop theory , 1993 .

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

[29]  D. Oxtoby,et al.  Gas–liquid nucleation in Lennard‐Jones fluids , 1991 .

[30]  A. Panagiotopoulos.  Direct determination of phase coexistence properties of fluids by Monte Carlo simulation in a new ensemble , 1987 .

[31]  Daan Frenkel,et al.  Simulation of homogeneous crystal nucleation close to coexistence , 1996 .

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

[33]  V. Talanquer,et al.  Dynamical density functional theory of gas-liquid nucleation , 1994 .

[34]  P. Clancy,et al.  A critical study of the simulation of the liquid-vapour interface of a Lennard-Jones fluid , 1993 .

[35]  Alan M. Ferrenberg,et al.  Optimized Monte Carlo data analysis. , 1989, Physical Review Letters.

[36]  G. Torrie,et al.  Monte Carlo free energy estimates using non-Boltzmann sampling: Application to the sub-critical Lennard-Jones fluid , 1974 .

[37]  I. Ford.  Thermodynamic properties of critical clusters from measurements of vapour–liquid homogeneous nucleation rates , 1996 .

[38]  J. Seinfeld,et al.  Direct evaluation of the equilibrium distribution of physical clusters by a grand canonical Monte Carlo simulation , 1998 .

[39]  J. Lothe,et al.  RECONSIDERATIONS OF NUCLEATION THEORY , 1962 .

[40]  J. A. Barker,et al.  Theory and Monte Carlo simulation of physical clusters in the imperfect vapor , 1973 .

[41]  C. Luijten,et al.  Binary nucleation rate measurements of n-nonane/methane at high pressures , 1995 .

[42]  Y. Viisanen,et al.  MEASUREMENT OF THE MOLECULAR CONTENT OF BINARY NUCLEI. III: USE OF THE NUCLEATION RATE SURFACES FOR THE WATER-N-ALCOHOL SERIES , 1995 .

[43]  H. Reiss,et al.  Molecular theory of vapor phase nucleation: The physically consistent cluster , 1990 .

[44]  D. Bedeaux,et al.  Pressure tensor of a spherical interface , 1992 .

[45]  D. J. Tildesley,et al.  The pressure tensor at the planar surface of a liquid , 1983 .

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

[47]  D. Frenkel,et al.  Enhancement of protein crystal nucleation by critical density fluctuations. , 1997, Science.

[48]  Y. Viisanen,et al.  Measurement of the molecular content of binary nuclei. II. Use of the nucleation rate surface for water–ethanol , 1994 .

[49]  A. H. Falls,et al.  Structure and stress in spherical microstructures , 1981 .

[50]  H. Reiss,et al.  Toward a molecular theory of vapor-phase nucleation. I : Identification of the average embryo , 1991 .

[51]  C. Bruin,et al.  Molecular dynamics study of the curvature correction to the surface tension , 1994 .

[52]  F. P. Buff.  Spherical Interface. II. Molecular Theory , 1955 .

[53]  V. Talanquer,et al.  Density Functional Analysis of Phenomenological Theories of Gas-Liquid Nucleation , 1995 .

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

[55]  B. Smit,et al.  Phase diagrams of Lennard‐Jones fluids , 1992 .

[56]  J. Willard Gibbs,et al.  The scientific papers of J. Willard Gibbs , 1907 .

[57]  H. Reiss,et al.  Toward a molecular theory of vapor phase nucleation. IV. Rate theory using the modified liquid drop model , 1994 .

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

[59]  Y. Viisanen,et al.  Measurement of the molecular content of binary nuclei. Use of the nucleation rate surface for ethanol–hexanol , 1993 .

[60]  G. Meier,et al.  Homogeneous nucleation of supersaturated vapors , 1989 .

[61]  A. Laaksonen,et al.  Thermodynamics, gas-liquid nucleation, and size-dependent surface tension , 1996 .

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

[63]  D. Oxtoby,et al.  A general relation between the nucleation work and the size of the nucleus in multicomponent nucleation , 1994 .