Free energy change crystallization

Proceeding as in Sec. 55, we can consider AF, the free energy change per mole accompanying the solution of this crystal in a certain solvent... 

Furthermore, even if we accept the use of A s and B s as rate constants with a ratio determined by detailed balance, there are many problems associated with evaluating the free energy changes (see e.g. Ref. [26]) and it is unlikely that they are simply related to equilibrium crystals. 

Self-organization systems under thermodynamic control (spontaneous processes with a negative free-energy change), such as supramolecular complexes, crystallization, surfactant aggregation, certain nano-structures, protein folding, protein assembly, DNA duplex. 

The defect concentration comes from thermodynamics. While we will discuss thermodynamics of solids in more detail in Chapter 2, it is useful to introduce some of the concepts here to help us determine the defect concentrations in Eq. (1.43). The free energy of the disordered crystal, AG, can be written as the free energy of the perfect crystal, AGq, plus the free energy change necessary to create n interstitials and vacancies (n, =n-o = n), Ag, less the entropy increase in creating the interstitials ASc at a temperature T ... 

The systems described above are by deLnition metastable and are affected by temperature Luctu-ations. The solubility of the solute crystals will be affected as these temperature Luctuations produce periods of undersaturation interspersed with periods of supersaturation. These Luctuations enhance the dissolution of Lne particles with concomitant growth of large particles. This crystallization process is driven by thermodynamics and can be described by an equation of the classical free energy change ... 

A second qualification is that the OSPE parameter, as well as the CFSE(crystal glass) difference parameters, eq. (8.11), are enthalpy terms and as such cannot be used to determine the affinity of a reaction. Free energy changes must be considered. However, since entropy changes are expected to be similar for all transition metal ions of the same valency, the use of an enthalpy term such as CFSE to interpret element fractionation may be a valid approximation when comparisons are made between transition metal ions of similar radius and charge. 

The quantity A/ /L does not involve the translational free energy change of a surfactant molecule since the latter was included in the mixing entropy contribution. The change from an LC crystallized solid to a disordered liquid is considered to occur in two steps the first is from the LC crystallized solid (called below LC solid) to a liquid (called LC liquid), in which the molecules become somewhat disordered but occupy the same surface area Ac and the second step is from the LC liquid to the LE liquid, in which the molecular surface area varies from Ac to Ad- The former is a kind of melting process and has a melting free energy... 

---