Amorphous, and Crystalline States

Metastability and induction time can play an interesting role in the kinetic resolution of optical isomers, such as of resolution of ibuprofen lysinate (see Example 7.4). On the one hand in order to maintain the optical purity of the desired isomer, it is necessary to keep the (undesired) isomer in its supersaturated state for the entire crystallization period. If the undesired isomer crystallizes out from the solution, the optical purity of the desired isomer will decrease. On the other hand, it is important to release the supersaturation of the desired isomer, which starts at the same initial level of supersaturation as the undesirable isomer. These are two conflicting requirements. To overcome this dilemma, it is critical to maintain a large amount of seed bed of the desired isomer to accelerate the release of super-saturation of the desired isomer, whereas the undesired isomer remains supersaturated. As mentioned, a detailed description of the resolution process of optical isomers is given in Example 7-4. 

Upon release of supersaUiration, the initially dissolved compound will be separated from the solution and form a secondary phase, which could be either oil, amorphous solid, or crystalline solid. Crystalline materials are solids in which molecules are arranged in a periodical three-dimensional pattern. Amorphous materials are solids in which molecules do not have a periodical three-dimensional pattern. Under some circumstances with very high supersaturation, the initial secondary phase could be a liquid phase, i.e., oil, in which molecules could be randomly arranged in three-dimensional patterns and have much higher mobility than solids. Generally, the oil phase is unstable and will convert to amorphous material and/or a crystalline solid over time. At a lower degree of supersaturation, an amorphous solid can be generated. Like the oil, the amorphous solid is unstable and can transform into a crystalline solid over time. Even as a crystalline solid, there could be different solid states with different crystal structures and stability. The formation of different crystalline solid states is the key subject of polymorphism, which will be mentioned below and 

The oil, amorphous, and crystalline states of materials are phenomena frequently encountered during crystallization. In the following discussion, we will give examples of these phenomena based upon their dependence on supersaturation. 

For a less supersaturated solution, Fig. 2-12 indicates that the amorphous solid can be generated after aging of the oil droplets. An amorphous solid can also be formed by rapid cooling of a saturated solution, as in lyophilization or freeze-drying operations. Like oil droplets, amorphous solids are unstable and will transform into crystalline material upon aging under proper conditions. As shown in Example 12-5, the amorphous imipenem can be transformed into crystalline material even under freezing conditions. 

The most stable and desirable solid phase upon release of supersaturation is clearly a crystalline solid, as shown in Fig. 2-13. A crystalline solid is generally purer and more stable than an amorphous solid and oil droplets. The majority of organic chemicals, especially pharmaceuticals, are produced as crystalline solids. 

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In the broadest terms, the rate of polymer crystallization is increased by factors that increase the free energy difference between the amorphous and crystalline states and factors that favor the re-organization of amorphous chain segments. The factors that influence the crystallization rate fall into two categories molecular characteristics and external conditions. Molecular... 

The degree of crystallinity may be calculated from the density of the polymer if the density is known for the amorphous and crystalline states. Some crystallizable polymers are polymorphic, i.e., they may exist in more than one crystalline form. An unstable crystalline form may change to a more stable form, and crystalline forms may change under stress. For example, hdpe changes from an orthorhombic crystalline polymer to a monoclinic form when subjected to compressive forces. 

It can be shown that the ratio v3lvg is equal to the ratio of polymer packing densities coefficients in the amorphous and crystalline states, KJKC at Tg, because, by definition, Ka = NA V /va and Kc - NA Vi/yC)where vj is the Van der Waals volume of the chain repeat unit. The calculated values of (ATc)g correlate with the characteristic chain parameter a/o, the relationship between them being expressed by a linear equation... 

The structures of liquid crystals are intermediate between the amorphous and crystalline states. They have some short-range orientational order. Some also have positional order. Thousands of organic compounds exhibit liquid crystal structures. Most have molecules that are very long and thin, but some have molecules that are flat and pancake shaped. Many compounds may exist in more than one liquid crystalline state. Transitions from one state to another may be thermotropic (caused by temperature change) or lyotropic (caused by change of solute concentration). 

Soderholm S, Roos YH, Meinander N, HotokkaM. Raman spectra of fructose and glucose in the amorphous and crystalline states. Journal of Raman Spectroscopy 1999, 30, 1009-1018. 

Above 9 GPa the C60 molecules are pressed very close together and an increase in temperature leads to very rapid polymerization. Most samples therefore become strongly disordered and there is little consensus about the structures observed. Some of the structures identified maybe quasi-equilibrium phases, in analogy with the low-dimensional polymers already discussed, while others may be intermediate transitory states. Both amorphous and crystalline states have... 

Thus, the range of problems associated with phase transitions in polymers considerably broadens. If earlier the appearance of the liquid crystalline state for polymers was considered as an interesting exception, at the present time this phase state acquires in physics and chemistry of polymers equal rights with amorphous and crystalline states. 

Flgure 2.1 Conformational differences of polymer chains in the amorphous and crystalline states. Fringed micelle model. Parallel and coiled lines represent, respectively, portions of chains in the crystalline and the amorphous regions. 

Fig. 4 Free energy diagram for a material in the amorphous and crystalline states (Fg denotes the glass transition temperature Ff indicates the melting/fusion point).

Observations 1 and 3 indicate that the active sites of the catalysts are of similar nature but their numbers are different in the amorphous and crystalline states. The lack of chemisorption data renders it impossible to make an exact comparison of activities in terms of turnover frequencies. Nevertheless, the similarity of BET surface areas of the amorphous and crystalline samples points to the presence of more active sites per unit surface area on the amorphous catalysts than on the crystalline ones. However, as the observations cited below indicate, other factors also contribute to the activity difference between the amorphous and crystalline states. 

The SiC intensity includes curves for the amorphous and crystalline states. The SiC component is almost constant to 1200°C, beyond which it decreases before increasing abruptly at 1500°C. Carbon components with a Ce-ring structure increase with heat treatment to 1400°C and then suddenly decrease at 1500°C. These results suggest that excess carbon in SiC fibers precipitates to form carbon particles up to 1400°C, which then disappear above 1500°C. The CO gas evolution between 1400 and 1500°C may compete with the precipitation of the carbon. In the SiC fiber with the highest tensile strength (i.e., that treated at 1200°C), a small number of carbon and SiC microcrystallites (1-2 nm) are considered distributed uniformly in carbon-rich amorphous SiC [36]. 

Figure 17. The specific enthalpy curve, /i(7) the specific enthalpy curves for the fully amorphous and crystalline states and the percentage crystallinity curve, all based on the specific heat...

Amorphous and crystalline state gadolinium-iron-gold alloys... 

In line with arguments of [13], with the terms solid mesophase we identify states of matter falling in between amorphous and crystalline states, characterized by long-range order in the parallel arrangement of chain axes. 

Fig. 80. Superconducting transition tent perature of transition metals and alloys of the 4d series in the amorphous and crystalline states, as a function of electron-to-atom ratio. The result obtained on amorphous La0j0AUo2o ( ) has been included for comparison (after Johnson, 1978).

Brusf s calculations do not give correctly the experimental curves shown in Figure 4.26 and Spicer and Donovan (1970b) show that the disagreement is due to the partial conservation of the k-vector in Brust s calculation. They conclude that the photoemission data can be understood only on the basis of a non-direct model with the important consequence that the band state densities are appreciably different in the amorphous and crystalline states. 

Because the differing structures and interaction effects between the molecular chains in amorphous and crystalline states require different quantities of heat to melt, it is possible to calculate the crystallinity of a sample from the energy required to produce the melting endotherm. Thermal data from a differential scanning calorimeter (DSC) scan can be used to calculate the level of crystallinity in a p>olymer by using both the latent heat of melting obtained from the scan and the enthalpy of fusion for a 100% crystalline sample of the polymer. 

The change in free energy is regarded as a driving factor for recrystallization from the amorphous form the larger the difference in free energy between the amorphous and crystalline state, the more thermodynamically favorable is the siuiation upon recrystallization. 

Fig. 1. Relation between strength and Young s modulus for bulk alloys in amorphous and crystalline states. Reprinted from (Inoue et al., 2004b), with permission from Elsevier.

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