ABSTRACT
Nucleation is the formation of a new phase from a bulk phase and is a commonly observed phenomenon in both nature and technology. It can be considered as the rst-order phase transition where a metastable phase transforms into another stable one with multiple phases. Examples of nucleation
CONTENTS
5.1 Introduction ................................................................................................ 119 5.2 Classical Nucleation Theory..................................................................... 121
5.2.1 Classical Homogeneous Nucleation ............................................ 122 5.2.2 Classical Heterogeneous Nucleation........................................... 124 5.2.3 Prediction of Nucleation Rate ...................................................... 126 5.2.4 Critical Factors ................................................................................ 127
5.2.4.1 Selection of BAs ............................................................... 127 5.2.4.2 Generation of a Uniform Polymer-Gas Mixture ........ 128 5.2.4.3 Pressure Drop Rate ......................................................... 129 5.2.4.4 Selection of Nucleating Agents ..................................... 130 5.2.4.5 Effects of Crystals ........................................................... 131
5.2.5 Effectiveness and Limitations ...................................................... 132 5.3 Pseudo-Classical Nucleation .................................................................... 135 5.4 Stress-Induced Nucleation ........................................................................ 136
5.4.1 Bubble Growth-Induced Nucleation .......................................... 141 5.4.2 Controlled Flow-Induced Bubble Nucleation ............................ 145
5.4.2.1 Extensional Strain-Induced Bubble Nucleation ......... 146 5.4.2.2 Shear Strain-Induced Bubble Nucleation .................... 150
5.5 Nucleation-Growth Relationship ............................................................ 154 5.6 Summary ..................................................................................................... 156 Nomenclature ...................................................................................................... 156
Greek Letters ............................................................................................... 157 References ............................................................................................................. 158
are formation of bubbles or crystals within a liquid and formation of liquid droplets in saturated vapor. Among these processes, an important form of nucleation is the formation of gas bubbles from a liquid phase by boiling or cavitation. The classical nucleation theory (CNT) [1] has been developed based on thermodynamics to predict the kinetic instability limit for bubble nucleation. According to the CNT, a bubble that has a radius greater than the critical radius (Rcr) grows spontaneously, while one that has a radius smaller than Rcr collapses; hence, a critical bubble (i.e., a bubble with radius equal to Rcr) is at an unstable equilibrium, where the free energy of the system is at a maximum (i.e., the free-energy barrier for nucleation). The Rcr is determined by the state of the system (e.g., temperature, pressure, gas concentration). A bubble is nucleated when it grows beyond the size of a critical bubble. For the case of plastic foaming, nucleation is typically achieved by rst dissolving a blowing agent (BA) into a polymer under high pressure and then quickly decreasing the solubility of the BA by rapid depressurization. Because of the sudden decrease in solubility, the polymer-gas solution becomes supersaturated, and the system tends to seek a lower energy and stable state by forming bubbles in the polymer-gas solution. According to the CNT, bubble nucleation occurs either within a continuous liquid phase (i.e., homogeneous nucleation) or along a liquid/liquid or liquid/solid interface (i.e., heterogeneous nucleation).
