namically favorable (Turnbull and Cormia 1961). The system is then said to exist in a metastable state. The height of the activation energy depends on the ability of crystal nuclei which are stable enough to grow into crystals to be formed in the liquid oil (see Section 184.108.40.206.). The degree of supercooling of a liquid is defined as AT = T - Tmp, where T is the temperature and Tmp is the melting point. The value of AT at which crystallization is observed depends on the chemical structure of the oil, the presence of any contaminating materials, the cooling rate, and the application of external forces (Dickinson and McClements 1995). Pure oils containing no impurities can often be supercooled by more than 10°C before any crystallization is observed (Turnbull and Cormia 1961; Dickinson et al. 1990, 1991c; McClements et al. 1993e).
Crystal growth can only occur after stable nuclei have been formed in a liquid. These nuclei are clusters of oil molecules that form small-ordered crystallites and are formed when a number of oil molecules collide and become associated with each other (Hernqvist 1984). There is a free energy change associated with the formation of one of these nuclei (Garside 1987). Below the melting point, the crystalline state is thermodynamically favorable, and so there is a decrease in free energy when some of the oil molecules in the liquid cluster together to form a nucleus. This negative free energy (AG^ change is proportional to the volume of the nucleus formed. On the other hand, the formation of a nucleus leads to the creation of a new interface between the solid and liquid phases which requires an input of energy to overcome the interfacial tension (Chapter 5). This positive free energy (AGS) change is proportional to the surface area of the nucleus formed. The total free energy change associated with the formation of a nucleus is therefore a combination of a volume and a surface term (Garside 1987):
where r is the radius of the nuclei, AHfus is the enthalpy change per unit volume associated with the liquid-solid transition (which is negative), and y, is the solid-liquid interfacial tension. The volume contribution becomes increasingly negative as the size of the nuclei increases, whereas the surface contribution becomes increasingly positive (Figure 4.5). The surface contribution dominates for small nuclei, while the volume term dominates for large r
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