This is the sixth blog post in a special series dedicated to crystallization. In case you missed the previous posts in the series, they are available here:
- Introduction to Crystallization and Precipitation
- Common Ways to Reduce Solubility and Drive Crystallization
- Supersaturation: Driving Force For Crystal Nucleation & Growth
- Importance of Crystal Size and Shape Distribution
- Impact of Process Parameters on Supersaturation and Crystal Size and Shape
Previously, we looked at a case study that neatly illustrated the concept that slow supersaturation generation often results in a growth dominated process that is typically repeatable. As a rule of thumb, slow cooling works great – but its main drawback is the extended cycle times that often result. To overcome this problem, a common technique often used is non-linear cooling.
If we dive a little bit deeper into the governing equations of crystal growth and nucleation..
..we learn that the surface are of the crystal slurry actually plays a very important role. In fact, the surface area (A) is contained in the growth constants kg and kb meaning the rate of crystal growth and nucleation depends on the surface area of the crystals in the slurry. Further investigation of the derivation of these equations shows growth rates are highly dependent on surface area, far more than nucleation rates. To look at this in more detail I suggest reading Nyvlt’s seminal paper – Kinetics of Nucleation in Solutions Journal of Crystal Growth Volumes 3-4, 1968, Pages 377-383
Surface area has important implications for the design of a crystallization process. At the start of crystallization, the surface area of crystals present in the slurry is very small – meaning nucleation is likely to dominate growth. As the crystallization proceeds, the surface are increases and growth begins to dominate.
With this in mind, it becomes clear that a clever technique for enhancing growth would be to cool very slowly at first, when surface area is small. This would keep supersaturation low and would allow growth to dominate. After some time, when surface area has increased, the cooling rate could be increased, reducing batch time, while still favoring growth (because of all that surface area!). This technique strikes the right balance between controlling supersaturation and excessive nucleation and avoiding very long batch times. The figure below compares linear, optimized cooling rates. It should be noted that ambient cooling (simply leaving the material to cool down to a fixed temperature) is the worst possible scenario with a fast cooling rate at first and then slow at the end! For more information and to look at the graphs shown below in more detail check out this paper – A Review of the Use of Process Analytical Technology for the Understanding and Optimization of Production Batch Crystallization Processes – Organic Process Research & Development 2005, 9, 348-355
A Review of the Use of Process Analytical Technology for the Understanding and Optimization of Production Batch Crystallization Processes – Organic Process Research & Development 2005, 9, 348-355
Kinetics of Nucleation in Solutions Journal of Crystal Growth Volumes 3-4, 1968, Pages 377-383
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