Crystallisation from nucleation

AIChESymp. Ser. (a) 65 (1969) no. 95, Crystallization from solutions and melts (b) 67 (1971) no. 110, Factors affecting size distribution (c) 68 (1972) no. 121, Crystallization from solutions Nucleation phenomena in growing crystal systems (d) 72 (1976) no. 153, Analysis and design of crystallisation processes (e) 76 (1980) no. 193, Design, control and analysis of crystallisation processes (f) 78 (1982) no. 215, Nucleation, growth and impurity effects in crystallisation process engineering (g) 80 (1984) no. 240, Advances in crystallisation from solutions. 

In examining a crystalline structure as revealed by diffraction experiments it is all too easy to view the crystal as a static entity and focus on what may be broadly termed attractive intermolecular interactions (dipole-dipole, hydrogen bonds, van der Waals etc., as detailed in Section 1.8) and neglect the actual mechanism by which a crystal is formed, i.e. the mechanism by which these interactions act to assemble the crystal from a non-equilibrium state in a super-saturated solution. However, it is very often nucleation phenomena that are ultimately responsible for the observed crystal structure and hence we were careful to draw a distinction between solution self-assembly and crystallisation at the beginning of this chapter. For example paracetamol, when crystallised from acetone solution gives the stable monoclinic crystal form I, but crystallisation from a molten sample in the absence of solvent... 

An important feature of transient supersaturation is its duration or, in other words, the rates of solute nucleation and crystal growth. Some of the factors that influence these rates have already been discussed for the case of pure water. For crystallisation from solutions, two additional factors are the viscosity of the residual freeze-concentrated liquid phase and probably also the conflgurational complexity of the crystal structures of the solutes involved. Thus, for NaCl, a degree of supersaturation of up to 6 M, reached at ca. —25°C, seems reasonable, at which temperature the salt is likely to crystallise spontaneously. For a typical cooling rate of 10°C min the duration of supersaturation would then be ca. 5 min, with the NaCl concentration transient reaching 6 M ... 

Microporous framework solids are synthesised via solvent-mediated crystallisations from mixtures of reactive precursors. The reaction pathway is controlled by kinetic as well as thermodynamic considerations so that equilibrium phase diagrams, so relevant in the high-temperature preparation of ceramics, are not useful here. Rather, synthetic routes have been developed empirically via a major synthetic effort that continues today. The continuing industrial and academic interest in these materials provides a powerful incentive to understand the principles underlying their formation through the processes of gel formation and evolution, nucleation and crystal growth. 

The crystallisation from melt in a temperature gradient or in contact with a surface acting as a nucleating substrate may result in a transcrystalline structure with the growth a.xis of the crystals, the h-axis in the case of polyethylene, the hydrogen bonds in the case of nylon parallel to the gradient or perpendicular to the substrate. 

The crystallisation from strained melt as for instance in a blown film or in the jet during fibre spinning produces a row nucleated structure. " Linear nuclei are formed parallel to the strain direction. They contain more or less extended polymer chains. Secondary epitaxial nucleation on the surface of such linear row nuclei produces folded chain lamellae which are oriented perpendicular to the strain (Fig. 6). In such a case the sample exhibits a high uniaxial orientation of chain axes in the strain direction with random orientation of the a- and b-axes perpendicular to it. If the growing lamellae exhibit a helical twist the chain orientation in the strain direction is very soon replaced by the orientation of the axis of maximum growth rate (b-axis in the case of polyethylene) perpendicular to the strain direction and a more random orientation of the remaining two axes (a- and c-axes in the case of polyethylene) with a maximum in the strain direction. Such a row nucleated structure has parallel cylindrical spherulites (cylindrites) as its basic supercrystalline element. 

Polypropylene molecules repeatedly fold upon themselves to form lamellae, the sizes of which ate a function of the crystallisa tion conditions. Higher degrees of order are obtained upon formation of crystalline aggregates, or spheruHtes. The presence of a central crystallisation nucleus from which the lamellae radiate is clearly evident in these stmctures. Observations using cross-polarized light illustrates the characteristic Maltese cross model (Fig. 2b). The optical and mechanical properties ate a function of the size and number of spheruHtes and can be modified by nucleating agents. Crystallinity can also be inferred from thermal analysis (28) and density measurements (29). 

Apart from deliberate or accidental introduction of tiny seed crystals to the system, and productive interactions between existing crystals and quasi-crystalline embryos or clusters in solution, the most influential mode of new crystal generation in an industrial crystalliser is contact secondary nucleation between the existing crystals themselves, between crystals and the walls or other internal parts of the crystalliser, or between crystals and the mechanical agitator. Secondary nucleation rates (in m-3 s 1) are most commonly correlated by empirical relationships such as ... 

Growth and nucleation interact in a crystalliser in which both contribute to the final crystal size distribution (CSD) of the product. The importance of the population balance(37) is widely acknowledged. This is most easily appreciated by reference to the simple, idealised case of a mixed-suspension, mixed-product removal (MSMPR) crystalliser operated continuously in the steady state, where no crystals are present in the feed stream, all crystals are of the same shape, no crystals break down by attrition, and crystal growth rate is independent of crystal size. The crystal size distribution for steady state operation in terms of crystal size d and population density // (number of crystals per unit size per unit volume of the system), derived directly from the population balance over the system(37) is ... 

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