Enthalpy of crystallization

Exothermic events, such as crystallization processes (or recrystallization processes) are characterized by their enthalpies of crystallization (AHc). This is depicted as the integrated area bounded by the interpolated baseline and the intersections with the curve. The onset is calculated as the intersection between the baseline and a tangent line drawn on the front slope of the curve. Endothermic events, such as the melting transition in Fig. 4.9, are characterized by their enthalpies of fusion (AHj), and are integrated in a similar manner as an exothermic event. The result is expressed as an enthalpy value (AH) with units of J/g and is the physical expression of the crystal lattice energy needed to break down the unit cell forming the crystal. 

Photo-oxidation leads to the formation of carbonylic products and this is classically monitored by vibrational spectroscopy. To investigate the relation between the accumulation of the oxygenated photoproducts and the change in the crystallinity of polycyclooctene, the decrease of the heat of crystallization was compared with the rise of the concentration of carbonyl function (1721 cm 1 band) as displayed in Figure 10.9. The enthalpy of crystallization falls at early stages of irradiation before significant accumulation of the carbonyl. Assuming that the decrease of the... 

The value of Xs tends to infinity as the denominator (7 0 - 7 h) -> 0 as T - Tt. Conversely, as (T 0 - T h) increases, i.e. the hexagonal phase becomes more metastable, A,s decreases as more surface contributions to the free energy, offset by the enthalpy of crystallization, are required, which according to the hypothesis must favour the hexagonal phase. 

Despite its importance, there still remain few methods to calculate log Saq. Many methods are based on the relationship between Saq and hydrophobicity (log Kow) and some measure of the enthalpy of crystallization (e.g., melting point). Other methods are based on fragment- or atom-based contributions. A full review of methods to calculate log Saq is provided by Livingstone (2003). Methods to calculate log Saq are summarized in Table 3.3. 

The solute is often an ion that is solvated by a coordination shell of solvent atoms (or other ions). At the crystal surface, desolvation of one or two of the solvent molecules in the coordination shell must occur before the solute can (1) adsorb, (2) attach to a step, and (3) integrate into the crystal at a kink. The difftision of solvent molecules (or other coordination ions) away from the crystal surface may limit the diffusion of solute toward the crystal surface and thus limit the growth rate. The solute does not become a part of the crystal until the enthalpy of crystallization has been liberated and desolvation is complete. Figure... 

An exothermic transition can sometimes be observed by DSC on crystallization of the amorphous form. This can be used to quantify the amorphous content of crystalline drugs. A calibration curve that consists of a plot of the enthalpy of crystallization as a function of crystalline content was used to determine if the lyophilized MK-0591 drug substance was... 

Bererzin et al (2) have measured the enthalpy of crystal and liquid molybdenum by levitation calorimetry in the range 1962-2869 K and 2890-2925 K, respectively. They reported Aj gH 8.741 0.314 kcal mol" at an assumed melting temperature of 2890... 

Fig. 4. Dependence of the specific enthalpy of crystallization on the heat of fusion already released (after Ref. 12).

Figure 10.6 gives a summary of data on different fillers in UHMWPE. The total degree of crystallinity, as determined by the enthalpy of crystallization, increases with filler concentrations up to 40-50% and then gradually decreases. This decrease is caused by filler aggregation which decreases its nucleation ability. 

Rajeshwar et al. (180) used DSC to determine the enthalpy of crystal structure transformations of MC104 salts, where M — Na, K, Rb, Cs, and NH4. As illustrated in Table 7.15, inconsistencies in the literature data are striking, especially with M = Na, K, Rb, and Cs. Most of the earlier studies used DTA techniques to determine the enthalpy changes. However, the literature values for NH4CI04 are in good agreement with the author s results. 

The enthalpy of crystallization, AH, equilibrium temperature, Teq, and activation energy of crystallization, Uact, values are summarized in Table 1. 

An attraction of freezing over evaporation for the removal of water from solutions is the potential for saving heat energy the enthalpy of crystallization of ice (334 kJ kg ) is only one seventh of the enthalpy of vaporization of water (2260kJkg ). In practice, however, the overall process energy consumptions, taking into account the other ancillary separation operations needed, are often comparable. 

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