Supercooling avoidance

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. 

We now turn to obtaining estimates for the expected crystal thickness, that is the solution of Eq. (3.97), for various values of C, where C, = 0 for / < lmi and increases with l otherwise. The case C, = constant can be used to show that the finite probability of folding is sufficient to obtain a finite thickness at all supercoolings thus avoiding the SI catastrophe, which was demonstrated in Sect. 3.7.1. This case is unphysical and was only considered because of its mathematical simplicity. It leads to the prediction that the thickness, though finite, increases with AT. 

An attractive feature of K<)A is that it can replace the liquid or supercooled liquid vapor pressure in a correlation. K,-ja is an experimentally measurable or accessible quantity, whereas the supercooled liquid vapor pressure must be estimated from the solid vapor pressure, the melting point and the entropy of fusion. The use of KOA thus avoids the potentially erroneous estimation of the fugacity ratio, i.e., the ratio of solid and liquid vapor pressures. This is especially important for solutes with high melting points and, thus, low fugacity ratios. 

Usually 1-2 days (for reactors on this scale) of experimental effort are required to traverse the loop as shown in Figure 3.1b. In order to avoid obtaining an erroneous dissociation temperature and pressure, the dissociation part of the loop must be performed at a sufficiently slow heating rate (about 0.12 K/h) to allow the system to reach equilibrium (Tohidi et al., 2000 Rovetto et al., 2006). The temperature difference between the temperature at Point D to that at Point B is called the subcooling [more properly the supercooling, ArSUb, where AFsub = 7eqm(D) — T (B)]. 

Volume measurements needed to calculate the SFI are made by observing and recording the position of the dye solution meniscus in the graduated capillary tube at one temperature (typically 60°C) or two temperatures at which the sample is fully molten, and at desired measurement temperatures (which will be lower than the clear point of the sample). The sample is brought to the first measurement temperature from 0°C after a standardized tempering procedure. This and subsequent measurement temperatures must be approached from below to avoid supercooling effects. Temperature is controlled by immersing the whole dilatometer in constant temperature water baths or an ice-water bath. 

When a liquid supercools (i.e., does not crystallize when its temperature drops below the thermodynamic melting point), the liquidlike structure is frozen due to the high viscosity of the system. The supercooled liquid is in a so-called viscoelastic state. If the crystallization can be further avoided as the ten ierature continues to drop, a glass transition will happen at a certain temperature, where the frozen liquid turns into a brittle, rigid state known as a glassy state. A well-accepted definition for glass transition is that the relaxation time t of the system is 2 X10 s or the viscosity / isio Pas (an arbitrary standard, of course). 

Some indirect experimental evidence exists for the liquid-liquid critical point hypothesis from the changing slope of the melting curves, which was observed for different ice polymorphs (30, 31). A more direct route to the deeply supercooled region, by confining water in nanopores to avoid crystallization, has been used more recently by experimentalists. These researchers applied neutron-scattering, dielectric, and NMR-relaxation measurements (32-35). These studies focus on the dynamic properties and will be discussed later. They indicate a continuous transition from the high to the low-density liquid at ambient pressure. The absence of a discontinuity in this case could be explained by a shift of the second critical point to positive pressures in the confinement. This finding correlated with simulations, which yield such a shift when water is confined in a hydrophilic nanopore (36). 

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