Crystallization pathways

Other factors also impact the type of crystals formed upon cooling of hot soap. Water activity or moisture content contribute to the final crystal state as a result of the different phases containing different levels of hydration. Any additive that changes the water activity changes the crystallization pathway. For example, the addition of salt reduces the water activity of the mixture and pushes the equiUbrium state toward the lower moisture crystal stmcture. Additionally, the replacement of sodium with other counter cations influences the crystallization. For example, the replacement of sodium with potassium drives toward the formation of 5-phase. 

Given the complementary nature of molecular recognition, it would appear that, when a compound crystallizes, the crystallization pathway, and hence the crystal structure obtained, should be quite specific to the molecule in question. However, the very existence of the phenomenon of polymorphism indicates that, under certain conditions, alternative crystallization pathways are feasible. In the special circumstance of concomitant polymorphism, or the simultaneous appearance of polymorphic forms in the same crystallization batch, these pathways even co-exist.1321 So, in general, the study of polymorphic systems has a bearing on a better... 

K. Seefeldt, J. Miller, F. Alvarez-Nunez, N. Rodriguez-Hornedo, Crystallization pathways and kinetics of carbamazepine-nicotinamide cocrystals from the amorphous state by in situ thermomicroscopy, spectroscopy, and calorimetry studies, J. Pharm. Sci. 96 (2007) 1147-1158. 

The solidification kinetics and compositional fluctuations in the melt will decide over the crystallization pathway which can be followed by all of the melt. If local gradients in temperature or composition exist in the system the crystallization pathway can be locally inhomogeneous and create different metastable solids at different locations in the macroscopic solidified blocks. 

Fig. 2.10 Schematic solubility diagram for a dimorphic system (polymorphs I and II) showing a hypothetical crystallization pathway (vertical arrow) at constant temperature. (Adapted from Bernstein et al. 1999, with permission.)...

From this analysis it is clear that the trade-off between kinetics and thermodynamics is not at all obvious. Consider a monotropic, dimorphic system (for simplicity) whose solubility diagram is shown schematically in Fig. 2.10. It is quite clear that for the occurrence domain given by solution compositions and temperatures that lie between the form II and I solubility curves only polymorph I can crystallize. However, the outcome of an isothermal crystallization that follows the crystallization pathway indicated by the vector in Fig. 2.10 is not so obvious since the initial solution is now supersaturated with respect to both polymorphic structures, with thermodynamics favouring form I and kinetics (i.e. supersaturation) form II. 

In this article we have discussed the significance of crystallization mechanisms and kinetics in directing crystallization pathways and have presented numerous examples that confirm the importance of controlling the crystallization events (both nucleation and growth) in the pharmaceutical industry. Advances in... 

It is imperative to know the S-L-V equilibrium compositions for the ternary (C02-solvent-solid) system, for these give the concentrations at the interface, which are needed for calculating the two-way mass transfer rates of CO2 and solvent in the antisolvent crystallization processes and for the selection of operating conditions for the desired crystallization pathways. Three kinds of data are usually generated for ternary (solute-solvent-antisolvent) systems (a) the liquid phase compositions for S-L equilibrium at a fixed... 

Stepwise or scaled lyophilization One of the solvents is more volatile than the other because of its higher vapor pressure in the frozen state and it disappears first, followed at different speeds by the others. The frozen mass, then, is earved from the inside along the crystallized pathway of the first solvent and in this open network, the islands of the second solvent are progressively extracted. This is the case for a mixed solution of cyclohexane and water. When 100 p. 100 of the cyclohexane has already been sublimated away when more than 85% of the water ice is still there. 

Figure 7 Schematic representation of classical and nonclassical crystallization. Pathway (a) the classical crystallization pathway where nucleation clusters grow to a primary nanoparticle, which is amplified to a single crystal. Pathway (b) the primary nanoparticles form an iso-oriented crystal, which can fuse to form a single crystal. Pathway (c) the primary nanoparticles can be stabilized by an additive and can form a mesocrystal. Pathway (d) amorphous particles or liquid droplets are formed, which can transform to complicated morphologies. (Reproduced from Ref. 7. John Wiley Sons, Ltd, 2008.)...

It is expected that, besides the influence of alkalinity, sodium ions [13, 22, 56-58] and duration of room-temperature gel ageing [59] also influence the crystallization pathway and properties of zeolite ZSM-5. The sodium ion is recognized as the potential template ions which make the influences on the nucleation process of MFI zeolites especially in the SDA-free system [13, 22, 57, 58]. 

The previous section highlighted the importance of the kinetic aspects since the development of co-crystals may be in competition with the crystallization of single component crystals. Knowledge of the start and end points in the phase diagram of a co-crystallization process is not sufficient in order to operate and optimize a co-crystallization pathway. Information about the kinetic pathway followed in the phase diagram during the operation remains essential. 

The properties of block copolymers are often studied in the form of solvent cast films. Depending on the preferable interaction of the solvent with each of the components, different initial states, and consequently crystallization pathways, can be established. 

This review is organized in a way that first, crystallization itself is discussed, as several non-classical and particle-based crystallization pathways... 

Driven by the intensified research on biominerahzation processes as inspiration for the synthesis of future advanced materials [30,32,51-56] and also bio-inspired mineralization [41,57], several indications were found that crystallization does not necessarily proceed along the classical textbook crystallization pathway, which is the attachment of ions/molecules to a primary particle forming a single crystal... 

Fig. 2 Crystallization pathways under thermodynamic and kinetic control Whether a system follows a one-step route to the final mineral phase (pathway A) or proceeds by sequential precipitation (pathway B), depends on the free energy of activation associated with nucleation (N), growth (g), and phase transformation (T). Amorphous phases are common under kinetic conditions. Reproduced from [40] with permission of Wiley...

Physical chemistry and physics can profit from the emerging alternative particle-mediated crystallization pathways, which have in common that they are multistep processes that follow a kinetic pathway. New physical insights into the structming of matter can be gained. For example, the reason why nanocrystals self-assemble in a three-dimensional crystaUo-graphically aligned manner in a mesocrystal is not yet revealed. 

Fig. 9 Crystallization pathways under the in-situ polymerization of acrylate...

The role of the initial domain structure in the melt and hence the crystallization pathway is illustrated by the properties of a series of diblock copolymers composed of hydrogenated poly(butadiene) and poly(3-methyl-1-butene) with varying molecular weights [53]. The change in molecular weights allows differing degrees of... 

Schlenker, J. and Martin, S. (2005). Crystallization pathways of sulfate-nilrate-ammonium aerosol particles, J. Phys. Chem. A, 199, pp. 9980-9985. 

Figure 2.8 (a) Sketch of the proposed crystallization pathway to tungstite nanoplatelets together with (b) the corresponding TEM image after 5 min, (c) overview image after... 

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