Supersaturation: Driving Force For Crystal Nucleation & Growth

This is the third blog post in a series dedicated to crystallization.  In case you missed the first and second in the series, they are available here: Introduction to Crystallization and Precipitation and Common Ways to Reduce Solubility and Drive Crystallization.

Supersaturation is the driving force for all solution crystallization processes. Crystallization scientists gain control over crystallization process and product quality by carefully controlling the prevailing level of supersaturation during the process.

Supersaturation: The difference between the actual concentration and the solubility concentration at a given temperature is defined as the supersaturation (Note: Here we are referring to solution crystallization only. This definition does not necessarily apply to melt or vapor crystallization processes).

The figure below illustrates the concept of supersaturation and introduces the metastable zone width (MSZW), the kinetic boundary at which crystallization occurs.

crystallization supersaturation kinetic boundary

Supersaturation is critical because it is the driving force for crystal nucleation and growth. Nucleation is the birth of new crystal nuclei – either spontaneously from solution (primary nucleation) or in the presence of existing crystals (secondary nucleation). Crystal growth is the increase in size of crystals as solute is deposited from solution. These often competing mechanisms ultimately determine the final crystal size distribution – an important product attribute. The relationship between supersaturation and nucleation and growth is defined by the following (somewhat simplified) equations.

supersaturation nucleation growth

G = Growth Rate

kg = growth constant

g = growth order

B = Nucleation Rate

kb = nucleation constant

b = nucleation order

ΔC = supersaturation

For organic crystallization systems, the value of the growth order is typically between 1 and 2 and the value of the nucleation order is typically between 5 and 10. When we plot what this looks like in theory it becomes clear why controlling supersaturation is so important. At low supersaturation, crystals can grow faster than they nucleate resulting in a larger crystal size distribution. However, at higher supersaturation, crystal nucleation dominates crystal growth, ultimately resulting in smaller crystals. This diagram, relating supersaturation to nucleation, growth and crystal size clearly illustrates how controlling supersaturation is vitally important when it comes to creating crystals of the desired size and specification.

supersaturation dictates crystal size

Having learned how supersaturation dictates crystal size, in the next blog post in this series, we will look at why crystal size is important. In the mean time, the crystallization treasure map illustrates once more the importance of understanding solubility, the metastable zone width and most important of all supersaturation.

For something a little more formal, the following books are great places to start:

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