Statistical theory of nucleation, condensation and coagulation

Abstract Starting from a master-equation description of dense gases, binary mixtures, etc., we derive theories for nucleation, coagulation and droplet growth by reformulating the dynamics in terms of ‘clusters’. This treatment is shown to agree quantitatively with computer simulations of the nucleation kinetics in the lattice gas model, and also gives a much better account of recent nucleation experiments on CO2 than previous approaches. The possible definitions of clusters, the appropriate coordinates for their description and their relation to bulk equilibrium properties of the system are outlined, and the effects of fluctuations on the properties of the clusters are investigated. Near the critical point the crossover between ‘classical’ and ‘non-classical’ expressions for the droplet formation energy is described in terms of ‘scaling laws’. In contrast to the Cahn-Hilliard-Langer theories of nucleation based on the concept of a coarse-grained free energy, no significant changes of static or dynamic beh...

[1]  The self-preserving particle size distribution for coagulation by Brownian motion—III. Smoluchowski coagulation and simultaneous Maxwellian condensation☆ , 1970 .

[2]  S. Friedlander,et al.  The self-preserving particle size distribution for coagulation by brownian motion☆ , 1966 .

[3]  L. Garrido,et al.  Irreversibility in the Many-Body Problem , 1972 .

[4]  K. Binder,et al.  Calculation of dynamic critical properties from a cluster-reaction theory , 1974 .

[5]  D. Kashchiev.  Solution of the non-steady state problem in nucleation kinetics , 1969 .

[6]  R. Glauber.  Time‐Dependent Statistics of the Ising Model , 1963 .

[7]  J. Meunier,et al.  Étude spectrale de la lumière diffusée par les fluctuations thermiques de l'interface liquide vapeur de CO2 près de son point critique. mesure de la tension superficielle et de la viscosité , 1974 .

[8]  B. Widom,et al.  Structure and Free Energy of the Interface between Fluid Phases in Equilibrium near the Critical Point , 1969 .

[9]  J. Langer,et al.  Hydrodynamic Model of the Condensation of a Vapor near Its Critical Point , 1973 .

[10]  P. Hartman,et al.  Crystal growth : an introduction , 1973 .

[11]  H. Yahata.  Critical Relaxation of Stochastic lsing Model , 1971 .

[12]  K. Binder,et al.  Theory for the dynamics of clusters near the critical point. I. Relaxation of the Glauber kinetic Ising model , 1975 .

[13]  R. P. Andres,et al.  Time Lag in Multistate Kinetics: Nucleation , 1965 .

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

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

[16]  F. Abraham,et al.  Multistate Kinetics in Nonsteady‐State Nucleation: A Numerical Solution , 1969 .

[17]  D. Stauffer,et al.  Nucleation theory: Fisher's droplet picture and microscopic surface tension , 1974 .

[18]  J. E. Hilliard,et al.  Free Energy of a Nonuniform System. I. Interfacial Free Energy , 1958 .

[19]  J. A. Swanson,et al.  Frequency Factors in the Thermally Activated Process , 1961 .

[20]  J. Feder,et al.  Homogeneous nucleation and growth of droplets in vapours , 1966 .

[21]  T. Riste.  Anharmonic lattices, structural transitions and melting , 1974 .

[22]  F. Stillinger,et al.  Interfacial Density Profile for Fluids in the Critical Region , 1965 .

[23]  D. Stauffer,et al.  Droplet Model and Nucleation of Supersaturated Vapors Near the Critical Point , 1971 .

[24]  J. Cahn,et al.  Experimental test of classical nucleation theory in a liquid-liquid miscibility gap system , 1973 .

[25]  K. Binder.  Monte Carlo simulation of physical clusters of water molecules , 1975 .

[26]  J. Langer.  THEORY OF NUCLEATION RATES. , 1968 .

[27]  D. Stauffer,et al.  Application of Fisher's droplet model for the liquid-gas transition nearTc , 1970 .

[28]  W. Goldburg,et al.  Observation of Anomalously Large Supercooling in Carbon Dioxide , 1975 .

[29]  L. Hove.  The approach to equilibrium in quantum statistics: A perturbation treatment to general order , 1957 .

[30]  D. Stauffer,et al.  Heteromolecular condensation theory applied to particle growth , 1973 .

[31]  M. Fisher.  The theory of equilibrium critical phenomena , 1967 .

[32]  R. Hocken,et al.  Ising critical exponents in real fluids: An experiment , 1976 .

[33]  L. Onsager.  Crystal statistics. I. A two-dimensional model with an order-disorder transition , 1944 .

[34]  Howard Reiss,et al.  The Kinetics of Phase Transitions in Binary Systems , 1950 .

[35]  K. Kawasaki.  Growth rate of critical nuclei near the critical point of a fluid , 1975 .

[36]  John S. Huang,et al.  Homogeneous Nucleation in a Critical Binary Fluid Mixture , 1974 .

[37]  J. J. Burton.  On the validity of homogeneous nucleation theory , 1973 .

[38]  H. Müller-Krumbhaar,et al.  The droplet model in three dimensions: Monte Carlo calculation results , 1974 .

[39]  J. Katz,et al.  Nucleation in associated vapors , 1966 .

[40]  M. Hoare,et al.  Physical cluster mechanics: Statistical thermodynamics and nucleation theory for monatomic systems , 1975 .

[41]  J. R. Schrieffer,et al.  Dynamics and statistical mechanics of a one-dimensional model Hamiltonian for structural phase transitions , 1974 .

[42]  C. Mou,et al.  The kinetics of phase separation in a liquid binary mixture , 1975 .

[43]  K. Binder,et al.  Investigation of metastable states and nucleation in the kinetic Ising model , 1974 .

[44]  H. Swinney,et al.  Dynamics of Fluids near the Critical Point: Decay Rate of Order-Parameter Fluctuations , 1973 .

[45]  K. Binder,et al.  Monte Carlo study of the surface area of liquid droplets , 1972 .

[46]  O. Penrose,et al.  Rigorous treatment of metastable states in the van der Waals-Maxwell theory , 1971 .

[47]  N. E. Frankel,et al.  Nucleation Theory with a Nonclassical Free Energy , 1971 .

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

[49]  I. Lifshitz,et al.  The kinetics of precipitation from supersaturated solid solutions , 1961 .

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

[51]  N. E. Frankel,et al.  Nonclassical nucleation theory , 1975 .

[52]  J. W. Essam,et al.  Critical behaviour of the Ising model above and below the critical temperature , 1968 .

[53]  P. Hohenberg,et al.  Renormalization-Group Calculations of Divergent Transport Coefficients at Critical Points , 1974 .

[54]  John E. Hilliard,et al.  Free Energy of a Nonuniform System. III. Nucleation in a Two‐Component Incompressible Fluid , 1959 .

[55]  K. Binder,et al.  Theory for the Slowing Down of the Relaxation and Spinodal Decomposition of Binary Mixtures , 1974 .

[56]  P. C. Hohenberg,et al.  Renormalization-group methods for critical dynamics: I. Recursion relations and effects of energy conservation , 1974 .

[57]  J. Katz,et al.  Binary homogeneous nucleation as a mechanism for the formation of aerosols , 1974 .

[58]  A. Guttmann,et al.  Lattice-lattice scaling and the generalized law of corresponding states , 1971 .

[59]  Kurt Binder,et al.  Monte Carlo computer experiments on critical phenomena and metastable states , 1974 .

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