Supercooling, maximum

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... 

The greater the undercooling, the more rapidly the polymer crystallizes. This is due to the increased probability of nucleation the more supercooled the liquid becomes. Although the data in Fig. 4.8 are not extensive enough to show it, this trend does not continue without limit. As the crystallization temperature is lowered still further, the rate passes through a maximum and then drops off as Tg is approached. This eventual decrease in rate is due to decreasing chain mobility which offsets the nucleation effect. 

Fig. 3.2. Variation of free energy of a cluster of molecules on a surface as a function of the number of molecules, at a fixed supercooling. N is the number of molecules at which the free energy is a maximum. Any cluster larger than Ns is stable. The dashed curves show the contributions from the increase in surface area and the decrease in bulk free energy. Increasing the supercooling shifts all curves towards the origin and decreases the height of the maximum...

FIG. 5 The density of liquid and supercooled water as a function of temperature, illustrating the anomalous liquid phase density maximum of water (data from Lide, 2002-2003). 

The interphases between MDs should not be able to cause nucleation of the semicrystalline phase. If the interphase displays nucleation activity, first-order crystallization kinetics may be obtained however, the supercooling at which dynamic crystallization from the melt occurs will not be the maximum that could be possibly attained if homogeneous nucleation were in place. 

Table 15.2. Maximum allowable supercooling ATmax for aqueous salt Solutions at 298...

The rate of the supercooled liquid transition to the crystalline state at T < Tm depends on two factors the number of the crystallization centres formed per unit time in unit volume, nc, and the linear rate of the crystal growth, vc. At T < Tm, v,. at first increases as the temperature decreases. This is connected with the fact that the heat which is liberated upon formation of the crystals and retards their formation dissipates more efficiently the lower is the temperature of the solution. Then, vc reaches its maximum and,... 

Most recently, Gallagher et al.21 measured the water uptake of Nafion membrane under subfreezing temperatures, which showed a significant reduction in the maximum water content corresponding to membrane full hydration. The Nafion membrane with 1,100 equivalent weight, for example, uptakes A 8 of water at -25°C when it equilibrates with vapor over ice because of the low vapor pressure of ice compared to supercooled liquid water. They also found the electro-osmotic drag coefficient to be 1 for Nafion membrane under sub freezing temperatures. 

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