Thermodynamic driving force polymorphs

Transformations between phases follow the Ostwald step rule, which states When a number of phase transformations, from a less stable state to more and more stable states are possible, usually the closest more stable modification is formed and not the most stable one corresponding to the least free energy (Ostwald 1897). The phase transition from the metastable to the lowest free-energy polymorph is unavoidable due to the thermodynamic driving force to minimize free energy. 

The three common polymorphic forms that exist in fat crystal networks are the suba, a, (), and (3 modifications. These polymorphic modifications and their characteristic crystallization patterns are shown in Figure 6. The subot and ot forms are metastable (34). Each polymorphic form yields different crystal structures dependent on the magnitude of the crystallization driving force. The polymorphic modifications also have varying thermodynamic stability, which determines their lifetime within a crystal matrix, with the tendency toward greater stability in the order a to (3 to (3 (24, 34). 

Grant has comprehensively discussed the thermodynamics of polymorphs (9). The stability of polymorphs and the driving force for polymorphic transitions is governed by the difference in Gibbs free energy, AG, between two polymorphs ... 

All SFC processes operate at above the critical temperature (Tc) of supercritical fluids. Temperature is a critical controlling variable of the SFC process based on both thermodynamic and kinetic considerations. First, solubility is a function of temperature, and this will determine the supersaturation ratio or the driving force for the crystallization of individual polymorphs. Second, the kinetics of polymorphic transformation is governed by the Arrhenius law and is also temperature dependent. The rate constant of the conversion is related to the activation energy and the mass transfer process involved (i.e., diffusion, evaporation, or mixing in supercritical fluids). 

The relative thermodynamic stability of graphite versus diamond provides a classic illustration of the interplay between thermodynamics and kinetics. Graphite and diamond are both polymorphs (same composition but different phases) of carbon. At room temperature and pressure, thermodynamics tells us that diamond is less stable than graphite—in other words, there is an energetic driving force favoring the transformation of diamond into graphite. So, are diamonds forever Thermodynamics... 

Figure 5.3 Schematic demonstrating the thermodynamic basis of the different possible nucleation modes. Here, Agpoi (c) is the driving force of the polymorphic transformation without a change of local composition c x) in a slice dx = dc/(9c/9x). Agtr c —> c")...

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