Controlling Crystal Growth Department Editor: Rita L. D’Aquino Chemical Engineering Magazine

The formation of crystals requires the birth of new particles, also called nucleation, and the growth of these particles to the final product size. The driving force for both rates is the degree of supersaturation, or the numerical difference between the concentration of solute in the supersaturated solution in which nucleation and growth occurs vs. concentration of solute in a solution that is theoretically in equilibrium with the crystals.

In a batch crystallizer, the crystal size distribution (CSD) is controlled by first seeding the initially supersaturated batch with a known number and size distribution of crystals, and then controlling the rate of evaporation or cooling (i.e., rate of energy transfer) so as to achieve a level of supersaturation that supports adequate crystal growth and an acceptable rate of nucleation.

The relationship between supersaturation and growth is linear, but that between nucleation and growth is raised to a power that is usually greater than one, making it difficult to grow large crystals when nucleation is occurring.

The following procedure describes how to achieve the optimal growth rate:

1. Screen the seeds at the beginning of the experiment to determine the cumulative number of crystals that are greater than a given size N’. Estimate N_Li, the number of crystals of a given size (L_av) obtained from the screening:

(1)

The parameters are defined in the table of nomenclature. To convert from μm to ft, multiply by 3.28 x 10–6.

2. Continue to measure the number and size of crystals as the cooling or evaporation program is in progress. Prepare an inverse cumulative plot of the number of crystals greater than a given size vs. size of the crystal (Figure 1). The crystal growth rate depends on the energy transfer rate, so modify the rate of energy transfer until a desirable product is obtained.

3. Repeat the first two steps at intervals throughout the batch cycle and plot the results as shown in Figure 1. The family of curves resulting from data plotted under the selected conditions indicates that the number of crystals is not increasing with time. Thus, no additional nucleation is occurring yet.

4. Proceed to collect crystal samples, anticipating the onset of nucleation. Figure 2 indicates that the number of crystals is significantly increasing with time. In this figure, t1 (not to be confused with t1 in Figure 1) represents the start of this new set of batch dynamics. It is safe to assume that significant nucleation is now occurring and that the rate of energy transfer is too high.

5. By taking the slope of the curve representing the estimated number of nuclei present at the measured point in time (Nti) vs. time (ti), one can determine the nucleation rate.

Using your representation of Figure 3, create a dashed, horizontal line across the lower portion of the graph depicting the selected, cumulative number of crystals (Ni’), and their sizes (L1–L4) over time (t1–t4).

6. For a selected cumulative number of crystals (Ni’), plot the crystal size (L) vs. time (t), as demonstrated in Figure 3. The slopes represent the crystal growth rate (G). If the level of supersaturation changes during the run, the growth rate also changes. Non-parallel lines would indicate that the larger crystals are growing at a faster rate, due to a reduced diffusional resistance [layer] at the crystal surface. With larger particles, the resistance layer may be smaller, allowing the solute to more readily reach the crystal surface and incorporate itself into the lattice. These factors collectively contribute to the accelerated growth rate of the larger particles. Parallel lines indicate that the growth rate is not dependent on crystal size.

7. Increase the rate of cooling or evaporation until additional nucleation occurs, upon which you can safely assume that the growth rate is too high.

8. Develop a seeding and evaporation profile that will yield a growth rate that is lower than the value found in Step 6. When determining the growth rate, keep in mind the difference in mixing characteristics between a laboratory-scale vessel and a commercial configuration. A small tank generally offers a higher relative pumping capacity, shorter blend time, and higher average shear rates within a narrower range.

Useful observations

• Most processors will agree that when it comes to crystals, the larger, the better. Large crystals are easier to handle in downstream operations, such as washing, centrifugation and drying.

• As previously mentioned, it is desirable for the seeds’ size distribution to reflect a narrow cut of particles. In this cut, the weight of crystals with sizes finer than Ls should be minimal because these tiny particles add enormously to the number of crystals that compete for supersaturation and growth.

• Studies show that milled seeds may not grow as well as unmilled seeds. Furthermore, not all crystals of a given size grow at the same constant rate. This is sometimes attributed to the differences in the surface characteristics of particles that have equal dimensions.

• Fines destruction in a batch system can greatly reduce the effects of secondary nucleation on the CSD, and significantly increase crystal size while narrowing the CSD.

• In practice, not all additional nucleation can be suppressed. Crystallizations carried out at low levels of supersaturation near the metastable zone (i.e., the conditions under which crystals grow, but do not typically nucleate) will display some secondary nucleation, due to crystal-crystal interactions and contact between the crystals and the impeller.

Nevertheless, the mean crystal size, shape and distribution are dramatically improved when seeding is followed by a programmed rate of energy transfer.

Reference: Genck, W., Better Growth in Batch Crystallizers, Chem. Eng., Vol. 106, No. 8, pp. 90–95, Aug. 2000. E-mail: genckintl@aol.com