# Homogeneous Nucleation Theory

### The Pretransition Theory of Vapor Condensation

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Homogeneous Nucleation Theory: The Pretransition Theory of Vapor Condensation discusses the influence of classical thermodynamics, statistical mechanics, and multistate kinetics on the homogeneous nucleation theory. This book is organized into 10 chapters and begins with a simple model calculation that yields an important insight into the major physical features governing supersaturated vapor condensation. The following chapters explore the development of the theory of equilibrium thermodynamics pertinent to the study of a nucleation phenomena and a postulatory formulation of statistical mechanics and its relation to the calculation of the thermodynamic potentials. The discussion then shifts to a statistical thermodynamics description of an imperfect gas assuming the droplet model of Band-Bijl-Frenkel and to the development of the multistate kinetics of cluster formation. The book also explores the development of the classical Einstein theory for crystalline solids and generalizes this theory for its applications to planar surfaces of microcrystalline clusters. It also presents a comparison of the exact free energies for the microcrystallites with the predictions of the droplet model using the capillarity approximation. Three distinct approaches for calculating the thermodynamic properties of physical clusters are covered in the concluding chapters.

## Table of Contents

Foreword

Preface

Chapter 1 The Nature of the Nucleation Process

1.1 Introduction

1.2 A Simple Droplet Model for Vapor Condensation

1.3 A Brief Historical Outline of Nucleation Theory

Bibliography

About the Appendix

Chapter 2 Thermodynamics of the Vapor-Drop System

2.1 Introduction

2.2 Postulatory Thermodynamics

2.3 The Thermodynamic System

2.4 The Equilibrium Conditions and the Generalized Laplace Equation

2.5 The Generalized Kelvin Relation

2.6 The Energy Barrier to Nucleation

2.7 An Illustration of the Working Formulas

2.8 The Curvature Dependence of the Surface Tension for the Gibbs Dividing Surface

Bibliography

Chapter 3 Statistical Mechanics of Simple Systems

3.1 Introduction

3.2 Postulatory Statistical Mechanics

3.3 The Canonical Ensemble and Independent Subsystems

3.4 The Ideal Gas

3.5 The Crystal Model with Simple Cubic Structure

3.6 The Normal Mode Model of Polymolecular Systems

3.7 The Linear Crystal

3.8 A Generalization of the Cubical Crystal Model

3.9 The Capillarity Approximation

3.10 The Replacement Free Energy

Bibliography

Chapter 4 Statistical Thermodynamics of the Imperfect Vapor

4.1 Introduction

4.2 The Model for the Vapor State

4.3 The Thermodynamic Potentials

4.4 The Law of Mass Action

4.5 The "Critical Condition" in the Equation of Mass Action

4.6 The Equation of State of the Saturated Vapor

4.7 Comparison with Frenkel's Study

Bibliography

Chapter 5 The Multistate Kinetics of Vapor Condensation

5.1 Introduction

5.2 The Kinetics Equations

5.3 The Steady-State Solutions

5.4 Comparison of Theory with Early Experiments

5.5 Transient Nucleation Kinetics: A Numerical Solution

5.6 An Equation of State for the Supersaturated Imperfect Vapor

5.7 Recent Experiments on Homogeneous Nucleation from the Vapor (by Professor G. M. Pound, Stanford University)

Bibliography

Chapter 6 Statistical Mechanics of Microcrystallites

6.1 Introduction

6.2 The Harmonic Approximation Assuming an Interatomic Potential

6.3 Comparison of Einstein Approximation with Normal Mode Analysis for the Bulk Crystal

6.4 Various Packings of Microcrystallites

6.5 Exact Excess Entropies for Certain Idealized Classical Microcrystallites

6.6 Number Dependence of the Crystallite Excess Entropy

6.7 A Generalized Einstein Model for Surface Atoms

6.8 The Replacement Free Energy

6.9 The Helmholtz Free Energy for Microcrystallites

6.10 A Comparison with the Capillarity Approximation

6.11 Multiconfigurational Free Energy Contribution for Microcrystallites

Bibliography

Chapter 7 An Empirical Theory for the Prediction of Vapor Condensation

7.1 Introduction

7.2 Model for the Imperfect Vapor

7.3 The Equation of State for a Saturated Vapor

7.4 Homogeneous Nucleation of Vapor Condensation

7.5 Predicting the Critical Supersaturation for Vapor Condensation of Water and Ammonia

7.6 Discussion

Bibliography

Chapter 8 Speculations on the Surface Structure of Embryonic Liquid Droplets

8.1 Introduction

8.2 The Structure of Water

8.3 The Liquid Surface

8.4 The Liquids of Nucleation Experiments

8.5 The Surface Free Energy of Embryonic Liquid Droplets

8.6 Disorder-Order Orientational Transition of Surface Molecules

8.7 A Further Limitation to Ascribing Liquid Water Properties to Embryonic Droplets as Suggested by Eyring's Model of Water

Bibliography

Chapter 9 A Generalized Theory and Monte Carlo Stimulation of Physical Clusters

9.1 Introduction

9.2 A Generalized Theory of Physical Clusters in an Imperfect Vapor

9.3 The Monte Carlo Procedure

9.4 The Properties of the Physical Cluster

9.5 A Comparison with the Becker-Döring and Lothe-Pound Theories Using the Capillarity Approximation

9.6 Physical Cluster Free Energy from Liquid State Perturbation Theory

Appendix 9.A

Bibliography

Appendix

Homogeneous Nucleation of Vapor Condensation I. Thermodynamic Aspects

I. Introduction

II. Free Energy of Embryo Formation

III. Critical Embryos and the Kelvin Equation

Homogeneous Nucleation of Vapor Condensation II. Kinetic Aspects

I. Introduction

II. Rates of Growth and Decay of Embryos

III. Unbalanced, Nonsteady-State Embryo Growth

IV. Balanced Steady-State Case

V. Unbalanced Steady State

VI. Summary

Subject Index

## Product details

- No. of pages: 278
- Language: English
- Copyright: © Academic Press 1974
- Published: February 28, 1974
- Imprint: Academic Press
- eBook ISBN: 9780323158046