Non-equilibrium Crystallization Phenomena

Occurrence of Spontaneous Crystallization of an Unseeded Enantiomer. When we consider the purity drop on the phase diagram, it is the prerequisite that the seeds added to cause the preferential resolution are completely pure. However if the seeds are contaminated by the undesired enantiomer, the phenomena could be completely different. Since in general seeds are taken from a previous batch, they are likely to have been contaminated by the adhered mother liquor due to incomplete phase separation or by some non-equilibrium crystallization phenomena such as inclusion of mother liquor or agglomeration of crystalline particles. For the case of the former, drying of the crystals generates small particles of the undesired enantiomer which will then be introduced to a racemic solution as seeds. 

Physical processes Order-disorder structures, ordered-phase transitions, symmetry breaking, spontaneous magnetization, non-equilibrium crystallization phenomena, percolation, electrodeposition, formation of dissipative structures, turbulence and instabilities in fluid dynamics, and diffusion-limited aggregation process. Biological processes Excitation in muscles, pulsation of heart, calcium waves, natural fold-up of protein molecules, deposition of lipid bilayers, auto-regulation of homeostasis morphogenesis, hyper-cycles and autocatalytic networks, etc. 

In this section, three topical non-equilibrium crystallization phenomena have been presented and briefly described, namely (1) dendritic crystal patterns, (2) growth of DLA-Iike crystal patterns, and (3) spherulitic crystal patterns. 

In examining a crystalline structure as revealed by diffraction experiments it is all too easy to view the crystal as a static entity and focus on what may be broadly termed attractive intermolecular interactions (dipole-dipole, hydrogen bonds, van der Waals etc., as detailed in Section 1.8) and neglect the actual mechanism by which a crystal is formed, i.e. the mechanism by which these interactions act to assemble the crystal from a non-equilibrium state in a super-saturated solution. However, it is very often nucleation phenomena that are ultimately responsible for the observed crystal structure and hence we were careful to draw a distinction between solution self-assembly and crystallisation at the beginning of this chapter. For example paracetamol, when crystallised from acetone solution gives the stable monoclinic crystal form I, but crystallisation from a molten sample in the absence of solvent... 

Flow imparts both extension and rotation to fluid elements. Thus, polymer molecules will be oriented and stretched under these circumstances and this may result in flow-induced phenomena observed in polymer systems which include phase-changes, crystallization, gelation or fiber formation. More generally, the Gibbs free energy of polymer blends or solutions depends under non-equilibrium conditions not only on temperature, pressure and concentration but also on the conformation of the macromolecules (as an internal variable) and hence, it is sensitive to external forces. 

We have presented a non-equilibrium molecular dynamics (MD) framework for stndying crystallization of polymer melts. By nsing cleverly constrncted simulations, we have independently observed the two phenomena responsible for melt crystallization nucleation and growth. 

Theoretical and experimental studies of surface segregation equilibrium phenomena in metallic alloys have been focused traditionally on substitutional solid solutions with elemental constituents (and non-metal impurities) assumed to be randomly distributed among the crystal lattice bulk and surface sites. Only in recent years more attention have been paid to the role of compositional order in surface segregation [1]. 

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