Crystallization energy requirements

Crystalhzation is important as an industrial process because of the number of materials that are and can be marketed in the form of crystals. Its wide use is probably due to the highly purified and attractive form of a chemical solid which can be obtained from relatively impure solutions in a single processing step. In terms of energy requirements, crystallization requires much less energy for separation than do distillation and other commonly used methods of purification. In addition, it can be performed at relatively low temperatures and on a scale which varies from a few grams up to thousands of tons per day. 

Initially, crystallization is a two-step process viz. nucleation and crystal growth requiring a change of free energy (Gibbs, 1928), as shown schematically in Figure 5.1. 

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. 

The charged functional groups of amino acids ensure that they are readily solvated by—and thus soluble in— polar solvents such as water and ethanol but insoluble in nonpolar solvents such as benzene, hexane, or ether. Similarly, the high amount of energy required to disrupt the ionic forces that stabilize the crystal lattice account for the high melting points of amino acids (> 200 °C). 

Because of the high electrostatic energy required to maintain them in an ionic crystal such as AgBr, we can safely ignore the following possible defects ... 

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]. 

When working with metal electrodes, the energy of the electrons in the metal is lower than the vacuum level by the work function of the metal, which tends to be 3-5 eV. Work functions of some materials relevant to LED devices are collected in Table 10.2 [11]. The work function can vary depending upon the crystal facet from which emission is measured (or if the metal is amorphous), and sample preparation details. The photoelectric (PE) effect is exploited in XPS (ESCA) or UPS to measure the work function. It is very critical to realize that, in these experiments, what is measured is the energy required to remove an electron to a point just outside the surface of the solid, not to infinity. At this range, the dipolar forces at the surface are still active, and one can learn about surface dipoles in the material. 

The theory of Benedek35) also must be regarded as semi-empirical. The authors treat the ys of alkali halide crystals as a sum of three terms, namely y+, y, and yb. The first component represents the energy required to separate the positive ions, and the second the analogous work for the anions. Both are calculated more or less ab initio. On the other hand, the expression for yb, i.e., the thermal contribution, has no theoretical foundation. It is... 

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 purpose of seeking a concentrated strip solution is to reduce the energy required to recover the product from the strip solution. In the case of metal salts, precipitation, electrolysis, direct reduction, and a host of other techniques may be used to generate the final product. In the case of the extraction of organic compounds, distillation, crystallization, or similar separation methods are used. In each case, the more concentrated the strip solution, the less energy is required to recover the desired components. 

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