On the study of crystal growth via interfacial analysis and string optimization

Abstract

Mathematical ‘strings’ can be used with computer simulations and statistical mechanics to calculate the fraction of growth units and activation energies of flexible molecules present at the crystal–solution interface.

Prediction of the Crystal Morphology of β-HMX using a Generalized Interfacial Structure Analysis Model

“…As the desolvation corresponds to the breaking of the solvation shell on the solute, it is independent of the identity of the face, and therefore considered isotropic. The original interfacial structure analysis and further studies ,− , assumed that the value of this desolvation barrier is close to the thermal fluctuation, k B T , but this could be significantly different from the actual value. If the actual value is much larger than the assumed value as suggested by Vekilov, where the expected values are approximately 28 kJ/mol for the enthalpy part and near zero for the entropy part, the effect of reorientation barrier could be negligible.…”

“…The reason is that kinks are the only sites for the attachment and detachment of the growth units that (1) maintain the surface free energy of the edge as constant and (2) create a new kink site upon incorporation . For solution growth of small organic molecules with layered growth mechanisms, ignoring the surface diffusion and assuming the kink incorporation as the rate-determining step whose barrier corresponds to that of the desolvation of the solute molecule have become a consensus in mechanistic models. − …”

“…This desolvation barrier is usually assumed isotropic for all the faces. In the approaches referred to as the interfacial structure analysis model, ,,− two additional concepts were addressed: (1) the local concentration of the growth units at the interface and (2) the barrier related to the reorientation of the growth units at the interface, introduced as “the orientational and conformational entropy barrier” . Before desolvation for incorporation into a kink, the adsorbed growth units are assumed to go through an reorientation process with a free energy barrier between its current orientational/conformational state (called an F2-unit state) and the crystal-like orientational/conformational state (called an F1-unit state). , A generalized interfacial structure analysis model for the Kossel-like crystal systems of centrosymmetric growth units, , based on the kink rate expressions by Shim and Koo, is presented here.…”

“…Subsequently, the relative growth rate can be calculated by collecting the anisotropic factors of G hkl . where n hkl is the number of nearest neighbors in the two-dimensional lattice and α̅ hkl is the angle between the regular spiral edges. As for the values of a̅ p, hkl and a̅ e, hkl , the previously used assumptions were a̅ e, hkl ≈ a̅ p, hkl ≈ a = ( v m ) 1/3 where v m is the molecular volume. ,,− In the present work, 1 and √3/2 were assigned as the values of a̅ p, hkl / a̅ e, hkl for the cases of square and regular hexagon, respectively to account for the different polygonal spirals. Canceling of the terms results in the final expression of The average kink energy is obtained from the experimental dissolution enthalpy and other habit-controlling factors through the surface scaling factor C l( hkl ) * and molecular orientational factor t hkl , The surface anisotropy factor ξ hkl = E hkl slice / E latt and n hkl are calculated from the PBC analysis.…”

Structural Correspondence of the Oriented Attachment Growth Mechanism of Crystals of the Pharmaceutical Dirithromycin

“…The growth rate of each crystallographic surface was also evidenced by the density profile of a DIR crystalline slab (Figure S9). The corrugate peaks indicate the amount of DIR and DMF molecules at each surface, with the larger magnitude suggesting that the surface (110) grows faster than that at the surface (001) or (100). , Additional illustration of interfacial distribution of compounds along with the density profiles at each plane was clearly present side by side in Figure S10. As a result, the modified crystal habit is dominated by three surfaces, the {001}, {100}, and {110} facets.…”