The metastable zone width is an important parameter in crystallisation and crystal growth with many factors that can affect its size. Each of these factors requires strict control, in order to obtain the desired crystal size and quality, especially for crystallizers used in the pharmaceutical industry, writes Emma Guinane.

Ketoprofen (KTP) is a nonsteroidal anti-inflammatory drug (NSAID), that contains both analgesic and antipyretic properties to reduce the feeling of pain and inflammation. It is also associated with the ability to decrease fever and prevent blood clots.

The metastable zone width (MSZW) can be defined as the width, in units of temperature, as the difference between the saturation temperature and the temperature at which the first crystal appears at a constant cooling rate (Egku et al 2019), as shown in Figure 1.

For industrial crystallisers, in order to obtain the desired product quality with respect to median particle size, crystal size distribution, shape and purity, they must be operated at the optimum supersaturation.

Additionally, knowledge on the MSZW is of great importance for setting the experimental conditions for nucleation and crystal growth experiments. Inside the MSZW, crystal  growth will occur without spontaneous nucleation. This allows the size of the particles to grow without the number of particles increasing. 

Figure 1: Ostwald-Miers diagram: General scheme of the different scenarios and processes in a cooling crystallisation experiment (Billot et al 2010)

Project overview

Using the polythermal method, as described below, the MSZW of KTP was investigated using four organic solvents: ethyl acetate, acetonitrile, butanol and toluene.

The study shows the effect experimental conditions, stated below, have on the MSZW, namely saturation temperature, stirring speed and cooling rate. Using Nŷvlt’s equation, the nucleation kinetics from the MSZW determined at different cooling rates were investigated and finally, characterisation of the solids formed from the crystallisation process was performed to examine the most relevant features on the crystal’s morphology.  

Polythermal Method: The polythermal method is the most widely used method of obtaining the MSZW (Barret et al 2019). This method involves gradually cooling the crystals, at a constant cooling rate, which contains a fixed amount of solute (Ansari et al 2018).

The solution is cooled from above saturation temperature, to a temperature where the first nuclei can be detected (Shiau. L 2019). The difference in these two temperatures is the MSZW.

Experimental conditions:

Saturation temperature: 303K, 298K, 293K, 288K, 283K at 1K/min and 450 rpm

Cooling rate: 1, 1.5 and 2K/min at 303K and 450 rpm

Stirring rate: 200, 450 and 700 rpm at 303K and 1K/min

Results

The results below, illustrate how saturation temperature, cooling rate, stirring rate and choice of solvent will have an effect on the MSZW of KTP.

• Comparison of solvents and saturation temperatures on MSZW of ketoprofen

In theory, the MSZW will increase as the saturation is increasing. Figure 3 illustrates how the MSZW changed with saturation temperature and choice of solvent.

In all the cases the MSZW increased with increasing saturation temperature except in acetonitrile, where the MSZW was found to be almost independent of the saturation temperature with an approximated constant value MSZW of 18 °C.

In the case of the solvent change, we can see that acetonitrile, had the smallest metastable zone at each saturation temperature. While, ethyl acetate had the largest at the majority of the saturation temperatures but was closely followed by butanol and toluene.

Figure 3: Saturation temperature vs the metastable zone width

• SEM images of ketoprofen crystals in different solvents

Using scanning electron microscopy (SEM), the crystal morphology of KTP in each solvent was investigated. As shown below in figure 4, it is clear to see how each solvent has an effect on the characteristics of the crystal formed. The morphology of each crystal is different in each solvent.

Due to the low melting point of KTP (94°C), a max voltage of 5kV was used when conducting SEM, as any voltage higher would cause the crystals to melt as the image was being captured.

Figure 4 SEM images of KTP in different solvents: (A) Acetonitrile, (B) Butanol, (C) Toluene, (D) Ethyl Acetate.

• Effect of cooling rate on the MSZW of ketoprofen

In theory, the metastable zone width should increase as the cooling rate increases. This is due to the solution having less time for solute collisions and accumulation to occur and therefore, less time for nucleation to occur.

When the cooling rate is increased, the temperature drops at a faster rate causing the MSZW to be larger as the crystallisation temperature will be lower.

The experiments to examine the effect of cooling rate on the MSZW of ketoprofen were performed under a saturation temperature of 303 K and a stirring speed of 450 rpm. The two solvents used to examine the effect of the cooling rate were butanol and ethyl acetate.

As seen in Figure 5, the cooling rate had a similar effect on the MSZW of both solvent-systems. An overall increase of the MSZW is observed in both solvents.

Figure 5:The effect of cooling rate on the metastable zone width of ketoprofen

• Effect of stirring speed on the MSZW of ketoprofen

In theory, the metastable zone width should decrease as the stirring speed is increased. This is due to the increase in the nucleation rate as the number of molecule collisions occurring as the stirring speed is increased. This leads to the temperature at which the solution crystallises to increase resulting in a smaller MSZW.

The experiments to examine the effect of stirring speed on the MSZW of ketoprofen were performed at a saturation temperature of 303 K and a cooling rate of 1°C/min. Butanol, ethyl acetate and toluene were used as the solvents to examine the effect of stirring speed.

It can be seen in Figure 6, that the overall change of the MSZW in all of the solvents decreased. However, there was an increase in the MSZW observed in butanol between 200 rpm and 450 rpm, this may be due to the presence of an impurity found in the reactor that makes the data at 450 rpm as non-reliable. However, the overall examination of the stirring speed still showed a decrease as the stirring speed increased which agrees with the theory.

Figure 6. The effect of stirring speed on the metastable zone width of ketoprofen

• Modelling of the nucleation kinetics

When the polythermal method is used to determine the metastable zone width (MSZW) of a system, the Nŷvlt’s equation can be used to estimate the nucleation order and the mass nucleation rate.

where, n is the cooling rate, m is the nucleation order, k_n is the nucleation rate constant and ∆T_max is the metastable zone width at the saturation temperature (T).

Comparison of nucleation order and rate constants for both solvents

From table 1 below, we can see that the onset of nucleation for ketoprofen crystals should occur faster in butanol than in ethyl acetate as the reaction constant is higher, which expresses faster nucleation kinetics in butanol. Therefore, the MSZW of butanol will smaller than that of ethyl acetate, which is in good agreement with the experimental observations.

Conclusion

Through the experiments performed in this project, the MSZW of ketoprofen was determined with the effects of saturation temperature, stirring speed and cooling rate examined.

It was found that the MSZW decreased as the saturation temperature decreased in three of the four solvents, with acetonitrile showing variations as the saturation temperature changed.

It is interesting to note that at 298K, for all polar solvents, the MSZW decreased but increased again at 293K. However, this trend was not observed for the non-polar solvent, toluene.

For the solvents used to assess the effect of stirring speed, the MSZW decreased as the stirring speed increased. It was also determined that the MSZW would increase as the cooling rate increased. From all theses, we can see how these factors have an impact on the size of the MSZW.

The choice of solvent is expected to have an effect on the MSZW as each solvent will interact differently with ketoprofen, forming weak and strong bonds and interactions that will make it easier or harder to nucleate the ketoprofen crystals out of the solution.

References

1.) Ansari, Z., Zeng, Y., Demopoulos, G. and Li, Z. (2018). Nucleation kinetics of MgCl 2 –ethanol adducts for the supported Ziegler–Natta catalysts with a thermodynamic approach. Journal of Crystal Growth, 494, pp.44-52. [Accessed 29 Nov 19]

2.) Barret, P. and Glennon, B. (2019). [online] Pdfs.semanticscholar.org. Available at: https://pdfs.semanticscholar.org/3dec/0f1ed334db14b248d598fff71b827bb15063.pdf [Accessed 18 Nov. 2019].

3.) Billot, P., Couty, M. and Hosek, P. (2010). Application of ATR-UV Spectroscopy for Monitoring the Crystallisation of UV Absorbing and Nonabsorbing Molecules. Organic Process Research & Development, 14(3), pp.511-523. [Accessed 29 Nov 19]

4.) Egku. N.E.M.N, Fatinah A.R., Syarifah A.R, Raihane Z.E, Nornizer A., (2019). Preliminary Study on Operating Parameters toward the Metastable Zone-Width of Carbamazepine Co-Crystal - UMP Institutional Repository. [online] Available at: http://umpir.ump.edu.my/17467/ [Accessed 18 Nov. 2019].

5.) Shiau, L. (2016). Comparison of the interfacial energy and pre-exponential factor calculated from the induction time and metastable zone width data based on classical nucleation theory. Journal of Crystal Growth, 450, pp.50-55. [Accessed 29 Nov 19]

Author

Emma Guinane, chemical and biochemical engineering student, University of Limerick