Crystallization driving forces

In a multicomponent fat, there is a vigorous competition between similar molecules for a vacant site in a crystal lattice. Multicomponent fats crystallize more slowly than pure TAG at the same crystallization driving force. However, crystal growth in multicomponent fats may be enhanced by the formation of compound crystals. Compound crystals usually occur in the a or p forms and rarely in the p form. 

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). 

The resistance to nucleation is associated with the surface energy of forming small clusters. Once beyond a critical size, the growth proceeds with the considerable driving force due to the supersaturation or subcooling. It is the definition of this critical nucleus size that has consumed much theoretical and experimental research. We present a brief description of the classic nucleation theory along with some examples of crystal nucleation and growth studies. 

Polymers can be crystalline, but may not be easy to crystallize. Computational studies can be used to predict whether a polymer is likely to crystallize readily. One reason polymers fail to crystallize is that there may be many conformers with similar energies and thus little thermodynamic driving force toward an ordered conformation. Calculations of possible conformations of a short oligomer can be used to determine the difference in energy between the most stable conformer and other low-energy conformers. 

Driving force for melt crystallisation is melting point (mp) difference of impurities and desired product feed must meet mp and crystal characteristics for feasibUity (see also solution crystallisation). 

The primary driving forces behind investigation of new solvents include environmental concerns and the abiUty to form Hquid crystals in the new solvent systems. By analogy with Kevlar, a synthetic aromatic polyamide fiber, spinning from a Hquid crystalline solution should yield cellulose fibers with improved strength, as has been demonstrated in laboratory experiments. 

Crystallization from Solution. Crystallization techniques are related to the methods used to iaduce a driving force for soflds formation and to the medium from which crystals are obtained. Several approaches are defined ia the foUowiag discussion. 

Crystal Formation There are obviously two steps involved in the preparation of ciystal matter from a solution. The ciystals must first Form and then grow. The formation of a new sohd phase either on an inert particle in the solution or in the solution itself is called nucle-ation. The increase in size of this nucleus with a layer-by-layer addition of solute is called growth. Both nucleation and ciystal growth have supersaturation as a common driving force. Unless a solution is supersaturated, ciystals can neither form nor grow. Supersaturation refers to the quantity of solute present in solution compared with the quantity which would be present if the solution were kept for a veiy long period of time with solid phase in contac t with the solution. The latter value is the equilibrium solubility at the temperature and pressure under consideration. The supersaturation coefficient can be expressed... 

As the stress is reduced, the rate of power-law creep (eqn. (19.1)) falls quickly (remember n is between 3 and 8). But creep does not stop instead, an alternative mechanism takes over. As Fig. 19.4 shows, a polycrystal can extend in response to the applied stress, ct, by grain elongation here, cr acts again as a mechanical driving force but, this time atoms diffuse from one set of the grain faces to the other, and dislocations are not involved. At high T/Tm, this diffusion takes place through the crystal itself, that... 

We will be looking at kinetics in Chapter 6. But before we can do this we need to know what we mean by driving forces and how we calculate them. In this chapter we show that driving forces can be expressed in terms of simple thermodynamic quantities, and we illustrate this by calculating driving forces for some typical processes like solidification, changes in crystal structure, and precipitate coarsening. 

Driving forces for solid-state phase transformations are about one-third of those for solidification. This is just what we would expect the difference in order between two crystalline phases will be less than the difference in order between a liquid and a crystal the entropy change in the solid-state transformation will be less than in solidification and AH/T will be less than AH/T . 

Compounds in which conformational, rather than configurational, equilibria are influenced by the anomeric effect are depicted in entries 4—6. Single-crystal X-ray dilfiaction studies have unambiguously established that all the chlorine atoms of trans, cis, ira j-2,3,5,6-tetrachloro-l,4-dioxane occupy axial sites in the crystal. Each chlorine in die molecule is bonded to an anomeric carbon and is subject to the anomeric effect. Equally striking is the observation that all the substituents of the tri-0-acetyl-/ -D-xylopyranosyl chloride shown in entry 5 are in the axial orientation in solution. Here, no special crystal packing forces can be invoked to rationalize the preferred conformation. The anomeric effect of a single chlorine is sufficient to drive the equilibrium in favor of the conformation that puts the three acetoxy groups in axial positions. 

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