Cooling rates terms

Non-isothermal crystallization kinetics can be analyzed by using the extension of the Avrami theory [68-70] and proposed by Ozawa [71, 72], This analysis accounts for the effect of cooling rate on crystallization from the melt by replacirtg the time variable in the Avrami equation with a variable cooling rate term, that is, by replacing f in the equation (3) with TIa as shown in the equation (4) ... 

Beckmann, J., Korber, C.H., Rau, G., Hubei, A., Carvalho, E.G. (1990). Redefining cooling rate in terms of ice front velocity and thermal gradient First evidence of relevance to freezing injury of lymphocytes. Cryobiol. 27,279-287. 

There is no restriction against applying polythermal models in open systems. In this case, the modeler defines mass transfer as well as the heating or cooling rate in terms of . Realistic models of this type can be hard to construct (e.g., Bowers and Taylor, 1985), however, because the heating or cooling rates need to be balanced somehow with the rates of mass transfer. 

On heating from a crystalline phase, DOBAMBC melts to form a SmC phase, which exists as the thermodynamic minimum structure between 76 and 95°C. At 95°C a thermotropic transition to the SmA phase occurs. Finally, the system clears to the isotropic liquid phase at 117°C. On cooling, the SmC phase supercools into the temperature range where the crystalline solid is more stable (a common occurrence). In fact, at 63°C a new smectic phase (the SmF) appears. This phase is metastable with respect to the crystalline solid such phases are termed monotropic, while thermodynamically stable phases are termed enantiotropic. The kinetic stability of monotropic LC phases is dependent upon purity of the sample and other conditions such as the cooling rate. However, the appearance of monotropic phases is typically reproducible and is often reported in the phase sequence on cooling. It is assumed that phases appearing on heating a sample are enantiotropic. 

Figure 4.29 Changes in volume or entropy which can occur on cooling a liquid. Crystallization may occur at Tj- or, if the liquid is supercooled below jy, a glass is formed. The temperature corresponding to the break in slopes of V(oi S) versus T is termed the glass transition temperature, T. The value of varies with the cooling rate, R(Ri > f 2)-...

The methods of freezing are expressed as cooling rates and a temperature range. Usually cooling rates that are slower than l°C/min are called slow-freezing, and rates faster than 100°C/min are called rapid freezing however, no accurate definitions exist for these terms. 

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