Supercooling degree

Fig. 15.17 Comparison of supercooling degree required for growth of Ga-bearing lanthanum silicate (LS(G)) and langasite (LGS). (Reproduced by the permission of Elsevier Ltd.)...

An interesting point is that AH itself varies with r [10].] As is the case when P is varied, the rate of nucleation increases so strongly with the degree of supercooling that a fairly sharp critical value exists for T. Analogous equations can be written for the supercooling of a melt, where the heat of fusion AH/ replaces AH . 

Another important point in connection with the rate of nuclei formation in the case of melts or of solutions is that the rate reaches a maximum with degree of supercooling. To see how this comes about, is eliminated between Eq. IX-6 and the one for liquids analogous to Eq. IX-13, giving... 

Between T j, and Tg, depending on the regularity of the polymer and on the experimental conditions, this domain may be anything from almost 100% crystalline to 100% amorphous. The amorphous fraction, whatever its abundance, behaves like a supercooled liquid in this region. The presence of a certain degree of crystallinity mimics the effect of crosslinking with respect to the mechanical behavior of a sample. 

As compared to ECC produced under equilibrium conditions, ECC formed af a considerable supercooling are at thermodynamic equilibrium only from the standpoint of thermokinetics60). Indeed, under chosen conditions (fi and crystallization temperatures), these crystals exhibit some equilibrium degree of crystallinity at which a minimum free energy of the system is attained compared to all other possible states. In this sense, the system is in a state of thermodynamic equilibrium and is stable, i.e. it will maintain this state for any period of time after the field is removed. However, with respect to crystals with completely extended chains obtained under equilibrium conditions, this system corresponds only to a relative minimum of free energy, i.e. its state is metastable from the standpoint of equilibrium thermodynamics60,61). 

To survive freezing, a cell must be cooled in such a way that it contains little or no freezable water by the time it reaches the temperature at which internal ice formation becomes possible. Above that temperature, the plasma membrane is a barrier to the movement of ice crystals into the cytoplasm. The critical factor is the cooling rate. Even in the presence of external ice, most cells remain unfrozen, and hence, supercooled, 10 to 30 degrees below their actual freezing point (-0.5 °C in mammalian cells). Supercooled cell water has a higher chemical potential than that of the water and ice in the external medium, and as a consequence, it tends to flow out of the cells osmotically and freeze externally (Figure 1). 

The view that the degree of imperfection depends on the amount of supercooling is borne out by the observations of Bekkedahl and Wood on rubber. They showed that the melting range (for fast melting) is lower the lower the temperature at which the rubber had been allowed to crystallize. Other crystalline polymers exhibit parallel behavior. 

Dried product resistance normally increases with increasing solute concentration and frequently decreases as the temperature of the frozen product approaches the eutectic temperature or T., . Production of larger ice crystals by a lower degree of water supercooling and/or an annealing process during freezing may also decrease the resistance. 

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