Melt crystallization from the bulk

In classical nucleation theory the Gibbs energy of a nucleus is considered as the sum of contributions from the bulk and the surface. Let us consider nucleation of a spherical crystal from its liquid below its melting temperature at 1 bar. The difference in Gibbs energy between a nucleus with radius r and its liquid is... 

The easiest combination of two chiral guests in the cylindrical capsule comes by the double encapsulation of racemic species with adequate size, shape and polarity to be accommodated in pairs, giving two diastereoisomeric complexes, the homochiral couple (R) - (R)/(S) - (S) and the heterochiral (R) -(S) combination. ( )-trans-1,2-Cyclohcxancdiol has all the above requisites and showed a 1.2 ratio between the two complexes in favor of the heterochiral combination [60]. This observation may be related to the preference in nature for centrosymmetric crystals or, alternatively stated, the higher melting points of racemates vs. enantiopure compounds where the resolution is driven by the less soluble pair [61,62], In the cylindrical capsule a single couple of chiral molecules is extrapolated from the bulk and the interactions between the two is governed by the shape of the cavity and their goodness of fit within the cavity. 

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