Supercooled

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... 

Still another situation is that of a supersaturated or supercooled solution, and straightforward modifications can be made in the preceding equations. Thus in Eq. IX-2, x now denotes the ratio of the actual solute activity to that of the saturated solution. In the case of a nonelectrolyte, x - S/Sq, where S denotes the concentration. Equation IX-13 now contains AH, the molar heat of solution. 

Classic nucleation theory must be modified for nucleation near a critical point. Observed supercooling and superheating far exceeds that predicted by conventional theory and McGraw and Reiss [36] pointed out that if a usually neglected excluded volume term is retained the free energy of the critical nucleus increases considerably. As noted by Derjaguin [37], a similar problem occurs in the theory of cavitation. In binary systems the composition of the nuclei will differ from that of the bulk... 

Bartell and co-workers have made significant progress by combining electron diffraction studies from beams of molecular clusters with molecular dynamics simulations [14, 51, 52]. Due to their small volumes, deep supercoolings can be attained in cluster beams however, the temperature is not easily controlled. The rapid nucleation that ensues can produce new phases not observed in the bulk [14]. Despite the concern about the appropriateness of the classic model for small clusters, its application appears to be valid in several cases [51]. 

The action of this and other anti-bumping devices e.g., minute carborundum chips) is dependent upon the fact that the transformation of a superheated liquid into the vapour will take place immediately if a vapour phase e.g., any inert gas) is introduced. The effect may be compared with that produced by the introduction of a small quantity of a solid phaM into a supercooled liquid, e.g., of ice into supercooled water. 

A liquid can sometimes be supercooled, i.e., the temperature can be reduced below the freezing point without solid separating, but as soon as solid does appear the temperature immediately rises to the true freezing point. 

It is a well-known fact that substances like water and acetic acid can be cooled below the freezing point in this condition they are said to be supercooled (compare supersaturated solution). Such supercooled substances have vapour pressures which change in a normal manner with temperature the vapour pressure curve is represented by the dotted line ML —a continuation of ML. The curve ML lies above the vapour pressure curve of the solid and it is apparent that the vapour pressure of the supersaturated liquid is greater than that of the solid. The supercooled liquid is in a condition of metastabUity. As soon as crystallisation sets in, the temperature rises to the true freezing or melting point. It will be observed that no dotted continuation of the vapour pressure curve of the solid is shown this would mean a suspended transformation in the change from the solid to the liquid state. Such a change has not been observed nor is it theoretically possible. 

The separation of the solid phase does not occur readily with some liquid mixtures and supercooling is observed. Instead of an arrest in the cooling curve at /, the cooling continues along a continuation of c/ and then rises suddenly to meet the line f g which it subsequently follows (Fig. 1,13, 1, iii). The correct freezing point may be obtained by extrapolation of the two parts of the curve (as shown by the dotted line). To avoid supercooling, a few small crystals of the substance which should separate may be added (the process is called seeding ) these act as nuclei for crystallisation. 

Commercial 2 4-dichlorophenoxyacetic acid may be recrystallised from benzene m.p. 139-140°. Reflux 10 g. of the acid with 15 ml. of thionyl chloride on a steam bath for 1 hour, distil off the excess of thionyl chloride at atmospheric pressure and the residue under reduced pressure 2 4-dichlorophenoxyacetyl chloride (8 g.) passes over at 155-157°/22-23 mm. It occasionally crystallises (m.p. 44-5-45-5°), but usually tends to remain as a supercooled liquid. 

There is a strong tendency for gallium to supercool below its freezing point. Therefore, seeding may be necessary to initiate solidification. 

As already mentioned, the choice of the supercooled liquid as reference state has been questioned by some workers who use the saturation vapour pressure of the solid, which is measured at the working temperature in the course of the isotherm determination. The effect of this alternative choice of p° on the value of a for argon adsorbed on a number of oxide samples, covering a wide range of surface areas, is clear from Table 2.11 the average value of is seen to be somewhat higher, i.e. 18 OA. ... 

The molecular area, calculated from the density of the supercooled liquid at 77 K is a ,(Kr) = 15-2 A, but Beebe found it necessary to adopt the higher value 19-5 A to bring the krypton-based area into line with the area of Harkins reference sample of anatase. ... 

It would clearly be of interest to discover how far the nonane method can be used with adsorbates other than nitrogen. A study along these lines has been carried out by Tayyab, but a discussion of his rather unexpected results is best deferred until the role of fine constrictions has been considered (p. 228). Meanwhile it may be noted that the applicability of the technique seems to be limited to adsorptives such as nitrogen or argon which have negligible solubility in solid or supercooled liquid n-nonane. 

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. 

We shall take up the kinetics of crystallization in detail in Secs. 4.5 and 4.6. For the present, our only interest is in examining what role kinetic factors play in complicating the crystal-liquid transition. In brief, the story goes like this. Polymers have a great propensity to supercool. If and when they do crystallize, it is an experimental fact that smaller crystal dimensions are obtained the lower the temperature at which the crystallization is carried out. The following considerations supply some additional details ... 

The thickness depends on the supercooling, which, in turn, is the result of kinetic considerations. Accordingly, crystal thickness is related to T, but neither have much to do with T . 

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. 

Coefficient of Linear Thermal Expansion. The coefficients of linear thermal expansion of polymers are higher than those for most rigid materials at ambient temperatures because of the supercooled-liquid nature of the polymeric state, and this applies to the cellular state as well. Variation of this property with density and temperature has been reported for polystyrene foams (202) and for foams in general (22). When cellular polymers are used as components of large stmctures, the coefficient of thermal expansion must be considered carefully because of its magnitude compared with those of most nonpolymeric stmctural materials (203). 

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