Energy requirements for crystallization

K for PEO) in agreement with previous results (Balta Calleja Santa Cruz, 1996 Balta Calleja et al, 1994). The b/b ratio derived from the slope of the plots is around 2 for PET, 44 for PE and 95 for PEO. This result suggests that for flexible polymers the energy required for plastic deformation of the crystals is much lower than the melting enthalpy. As the chain stiffness increases, the b/b ratio seems to decrease as a consequence of a higher energy required for crystal deformation. 

The novel provision of side feeds promotes mixing between feed and crystallizing streams and increases solute concentration. This not only eliminates the need for equal volume (or residence time) of each crystallizer in the network but may also reduce the energy requirements for cooling the suspension. The magnitude of such reductions will depend, however, on the exact mixing profiles between the crystallizers. 

The practical importance of vacancies is that they are mobile and, at elevated temperatures, can move relatively easily through the crystal lattice. As illustrated in Fig. 20.21b, this is accompanied by movement of an atom in the opposite direction indeed, the existence of vacancies was originally postulated to explain solid-state diffusion in metals. In order to jump into a vacancy an adjacent atom must overcome an energy barrier. The energy required for this is supplied by thermal vibrations. Thus the diffusion rate in metals increases exponentially with temperature, not only because the vacancy concentration increases with temperature, but also because there is more thermal energy available to overcome the activation energy required for each jump in the diffusion process. 

Fig. 2b. The appearance of two crystal forms shows that the protein in the membrane exists in equilibrium between the protomeric aj8 unit and oligomeric (aj8>2 forms. The high rate of crystal formation of the protein in vanadate solution shows that transition to the E2 form reduces the difference in free energy required for self association of the protein. This vanadate-method for crystallization has been very reproducible [34-36] and it also leads to crystalline arrays of Ca-ATPase in sarcoplasmic reticulum [37] and H,K-ATPase from stomach mucosa [38]. 

In none of the above examples of organic crystals is there any evidence on whether or not there is long-range order in the proton-transferred material. It is plausible that the transfers occur initially at random sites in die crystal, which form defective sites in the parent structure. Subsequently, the energy required for further transfers may be affected by the initially formed defects, in which case clustering will occur, leading to domains of proton-transferred molecules. 

Amorphous or noncrystalline forms can exist and the energy required for a molecule of drug to escape from a crystal is much greater than that required to escape from an amorphous powder. Therefore, the amorphous form of a compound is always more soluble than a corresponding crystal form. 

The high input energies required for inversion lower the efficiency and cause severe heating problems in the crystal... 

The behavior of the fluorosulfinate as an activated alkali fluoride is readily explained in terms of a widening of the fluoride crystal lattice, and the amount of energy required for its breakdown in fluorinations is accordingly lower. 

Here, cre(oo) is the fold-surface free energy for I = 00 and S is a small constant, reflecting the fact that some finite supercooling is required for crystal growth. In the case of m > 1, S also accounts for the additional supercooling necessary for G(Fm) to overtake G(Fm i) (see Fig. 6). 

In the previous section we summarized the chemical evidence that oxide ions in a state of low coordination can act as electron donors. At the same time, spectroscopic evidence has been accumulated which shows that highly dispersed alkaline-earth oxides have optical absorption bands that are not present in the pure single crystal. This is surprising at first because the energy required for electronic excitation of bulk MgO corresponds to a frequency in the vacuum ultraviolet. In order to understand this we must look at the absorption process more closely. 

The mechanical response of composites, as shown in these exploratory studies, indicates dependence on the ease with which fracture can occur between fibers, yarns, and plies. Poorly crystallized matrices result in composites that are strong and stiff but with little yield so that failure occurs catastrophically. In contrast, more crystalline matrices seem to be not quite as strong and to have a lower effective modulus, but their increased strain capability ensures that failure is not catastrophic the composited strength decays gradually as further strain is applied. Thus, the energy required for total failure is increased, and the composite with more crystalline matrix is more tolerant of defects or stress risers. 

However, Sacconi, in his early work [90] on some nickel and zinc chelates of V-methylsalicylideneaniline, showed that compounds with different crystal structures may still form mixed crystals since conformational changes in the molecular geometry of the minor component are induced by the dominating major component. The energy required for such conformational changes is presumably small by the formation of the mixed crystal and is, in any case, very small. 

Provide the energy required for the heat of the reaction or crystallization, if applicable,... 

---