Crystallization supersaturation, generation

Evaporative crystalli rs generate supersaturation by removing solvent, thereby increasing solute concentration. These crystallizers may be operated under vacuum, and, ia such circumstances, it is necessary to have a vacuum pump or ejector as a part of the unit. If the boiling poiat elevation of the system is low (that is, the difference between the boiling poiat of a solution ia the crystallizer and the condensation temperature of pure solvent at the system pressure), mechanical recompression of the vapor obtained from solvent evaporation can be used to produce a heat source to drive the operation. 

It was shown in Chapter 3 that supersaturation, or concentration driving force, is essential for any crystallization. In a batch crystallizer supersaturation can be generated in several ways, either solely or in combination ... 

For solvent systems with a window of operating temperature, proper selection of the method of supersaturation generation (e.g., cooling and antisolvent addition) and mode of crystallization (e.g., batch vs. semicontinuous) can also affect the overall crystal growth rate. In many instances in which solvent or impurity rejection becomes critical, adequate mixing to avoid local high supersaturation can be critical. Examples 9-2 and 10-4 illustrate two cases of rejection of impurities and residual solvent. These examples show how various means are applied to overcome these complications. 

Lindberg, M. and A.C. Rasmuson (2000). Supersaturation generation at the feed point in reaction crystallization of a molecular compound. Chem. Eng. Sci. 55, 1735-1746. 

The removal of the metastable supersaturation is a slow process. A large amount of crystal surface is required to allow for the large number of random collisions necessary to remove the supersaturation generated during the cycle. The proper orientation of both the molecules in solution and the molecule on the crystal surface is required for deposition, and the increased complexity of the molecule increases the number of collisions required for proper orientation. 

If the supersaturation generated during the cycle is not completely removed, the level of supersaturation attained during the following cycle is increased. This increase from cycle to cycle will continue until the supersaturation level of the solution exceeds the metastable region and enters the labile region, where spontaneous nucleation occurs. The occurrence of spontaneous nucleation means loss of control of crystal size. 

Once initial nucleation has been achieved successfully, the control of secondary nucleation becomes important. Since crystal growth is a surface phenomenon, each nuclei formed is available to absorb the supersaturation generated by the cycle. This means that only one nuclei is to be formed for each single crystal removed if a constant crystal size is to be maintained. 

Due to the nature of long chain organic molecules, deposition on the crystal surface is more difficult and time consuming than for most inorganic chemicals. This must be taken into consideration and additional time allowed between cycles so that the supersaturation can be relieved. Another effective method for handling this potential problem is to limit the supersaturation generated during each cycle. 

Temperature. The process temperature of an evaporative crystallizer may be controlled by the absolute pressure in the vessel. Direct flow control of steam to an ejector, while economizing on steam utilization, is subject to pressure fluctuations due to disturbances in the steam supply pressure. Applying cascaded flow control would decrease the response time of the control loop. Flow control of a bleed gas or exhausted gas into the suction of the vacuum source is the most responsive and precise control option. Critically damped tuning of the pressure control loop should be implemented to prevent rapid temperature changes and high supersaturation generation from fast swings in pressure. 

Precipitation is an operation known for producing small crystals that are difficult to filter and dry. Batch precipitation is usually carried out in the form of a semibatch process, i.e., one or two reactants are continuously added to the reactor. The control of the particle size distribution in a precipitation process is very complicated because of the high level of supersaturation generated by the fast reaction. According to Mersmann [16], the important factors for sparingly soluble systems in isothermal precipitation are ... 

Thus, by secondary nucleation, crystals are generated at far lotver supersaturations than that via primary nucleation, both homogeneous and heterogeneous... 

If co-crystals are to solve solubility problems one must assess their true or thermodynamic solubility so that development strategies are guided by the fundamental properties of co-crystals. Measuring the solubility of co-crystals that generate supersaturation of the parent drug is often experimentally impossible due to conversion. Eutectic points, described in Section 11.4, provide a measure of co-crystal solubility under thermodynamic equilibrium conditions. The solution at the eutectic point is saturated with co-crystal and solution concentrations represent experimentally accessible thermodynamic solubility values. Once co-crystal solubility is determined at the eutectic, the solubility under different solution conditions (pH, co-former, micelle concentration) can be obtained from solubility models that consider the appropriate solution phase equilibrium expressions. 

Consider an unseeded batch crystallizer where all crystals are generated from nuclei via growth at a constant growth rate, G. The governing equation is (6.4.51), where we assume that the supersaturation level is constant with time. The size of the nuclei is Tp , the volume based shape factor for all nuclei/crystal size is and is the nuclei generation rate per unit volume. 

Primary Nucleation Homogeneous nucleation requires systems to cross a free energy barrier [34]. For example, crystal nuclei generate sporadically from a supersaturated solution which is energetically metastable and in which density fluctuations occur [35]. A similar situation occurs in the crystallization from the melt. 

Batch Crystallization. Crystal size distributions obtained from batch crystallizers are affected by the mode used to generate supersaturation and the rate at which supersaturation is generated. For example, in a cooling mode there are several avenues that can be followed in reducing the temperature of the batch system, and the same can be said for the generation of supersaturation by evaporation or by addition of a nonsolvent or precipitant. The complexity of a batch operation can be ihustrated by considering the summaries of seeded and unseeded operations shown in Figure 19. 

Crystal growth is a layer-by-layer process, and the retention time required in most commercial equipment to produce crystals of the size normally desired is on the order of 2 to 6 h. On the other hand, nucleation in a supersaturated solution can be generated in a fraction... 

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