Kinetics of First-Order Phase Transitions

Phase transitions between different states of matter occur in many equilibrium and nonequilibrium systems. The kinetics of these phase changes are studied mainly in the case of condensation of a vapour in a supersaturated state via homogeneous nucleation. Based on thermodynamic investigations of heterogeneous systems, the stochastic and deterministic theory of nucleation and growth of the new phase is derived. Emphasis is put on finite-size-effects which lead to a depletion of the vapour. The results are mainly explained in terms of clusters (droplet model) and extended to the influence of external fields. Numerous computer simulations are presented.

Foreword1. Introduction1.1. Types and Classification of Phase Transitions 7 1.2. Thermodynamic and Experimental Conditions for Supersaturated Vapour States 12 1.3. Outline of Classical Nucleation Theory 19 1.3.1. The Classical Droplet Model 19 1.3.2. Kinetic Assumptions of Classical Nucleation Theory 23 1.3.3. Modifications of Classical Nucleation Theory 27 1.4. Nucleation in a Lattice Gas Model 312. Thermodynamics of Heterogeneous Systems2.1. Thermodynamic Premises of Classical Nucleation Theory 39 2.2. Gibbs' Theory of Heterogeneous Systems 40 2.3. Curvature Dependence of Surface Tension 45 2.4. Heterogeneous Systems in Non-Equilibrium States and the Principle of Inner Equilibrium 533. Thermodynamics and Nucleation in Finite Systems3.1. The Work of Formation of Clusters 58 3.2. Equilibriuni States and the Conditions for Stability of the Clusters 63 3.3. Critical Thermodynamic Parameters for Nucleation in Finite Systems 67 3.4. The Work of Formation of Critical Clusters 72 3.5. Parameters of the Critical Cluster in Dependence on the System Size 76 3.6. Formation of a Droplet Ensemble in Finite Systems 804. Kinetics of Phase Transitions in Finite Systems - A Stochastic Approach4.1. Free Energy of the Cluster Distribution 86 4.2. Kinetic Assumptions and Master Equation 92 4.3. Results of Computer Simulations 98 4.3.1. Stochastic Dynamics Technique 98 4.3.2. Evolution of a Single Cluster 100 4.3.3. Evolution of the Cluster Distribution 105 4.4. Probability Distribution and Mean First Passage Time 111 4.5. Mean Values for the Number of Clusters - Fokker-Planck Equation 1175. Kinetics of Growth of a New Phase - A Deterministic Description5.1. General Scenario of First-Order Phase Transition in Finite Systems 124 5.2. Nucleation in Finite Systems - The Quasi-Steady-State-Approximation 126 5.3. Deterministic Growth Equations 128 5.3.1. Diffusion Equation Approach 128 5.3.2. Derivation of a General Growth Equation for Clusters of a New Phase 131 5.4. Simultaneous Description of Nucleation and Growth 133 5.5. Curvature Dependence of Surface Tension and the Scenario of First-Order Phase Transitions 138 5.6. Further Applications 1406. Theory of Ostwald Ripening6.1. Basic Equations 144 6.2. The Lifshitz-Slyozov Theory 147 6.3. Thermodynamic Aspects of Ostwald Ripening in Solids and Liquid Solutions 149 6.4. A New Method of Kinetic Description of Ostwald Ripening 152 6.5. Ostwald Ripening and the Relations to the Theory of Self-Organization 1587. Growth of Bubbles in Finite Systems7.1. The Model 168 7.2. Thermodynamic Analysis 169 7.3. Kinetic Description of Nucleation and Growth of Bubbles 170 7.4. Applications to Liquid-Gas Solutions and Multicomponent Systems 1748. Nucleation and Growth in Elastic and Viscoelastic Media8.1. Derivation of a Growth Equation for Clusters in Elastic Media 176 6.2. Models for the Calculation of Elastic Strains 176 8.2.1. Elastic Strains of Nabarro Type 179 8.2.2. Elastic Strains in Segregation Processes in Elastic Media 183 8.2.3. The Influence of Viscous Properties of the Matrix on the Development of Elastic Strains 184 8.3. Formation and Growth of Single Clusters in Elastic Media 188 8.4. Ostwald Ripening in Elastic and Viscoelastic Media 190 References 195