Discover Our New Population Balance Modelling Feature

Automated secondary nucleation and crystal growth constant screening at small scale

We are very proud to introduce our new Population Balance Modelling (PBM) feature on the Crystalline instrument. Now you can calculate secondary nucleation and crystal growth constants on ml scale and rapidly screen solvents and conditions to better understand your process earlier in development and select conditions or solvent to optimize for growth or nucleation. 

Introduction

Crystallization is a commonly used process in a wide range of industries including pharmaceuticals, agrochemicals and cosmetics. Despite this, it still remains a complex and challenging process with multiple competing factors such as agglomeration, growth and nucleation. There are several strategies and technologies that allow for better understanding and increasing control of a crystallization process. Population balance modeling is one of the strategies used, as it models the change in size and number of crystals at any point in the crystallization process, which can then be optimized to give the desired size distribution. From these models, secondary nucleation and growth constants can be calculated, providing deeper insight into a molecule’s crystallization behavior and enabling more effective process optimization.

The new Population Balance Modeling (PBM) feature available on Crystalline is based on the methodology developed by Capellades et al [1]. Crystalline offers a versatile platform for collecting high resolution images of particles to calculate PSD throughout crystallization. Now with the new population balance modelling feature you can calculate secondary nucleation and crystal growth constants on ml scale and rapidly screen solvents and conditions to better understand your process earlier in development and select conditions or solvent to optimize for growth or nucleation.

Population Balance Modelling

Using population balance modelling to calculate the nucleation and growth constants of crystallization is a powerful way to understand how to achieve the required particle size distribution. Traditionally, population balance models are employed in the later stages of crystallization process development due to their scale dependency and high material and time requirements. As a result, critical process parameters, such as solvent composition, are often already established before kinetic modeling begins. The Crystalline platform overcomes these limitations by enabling the calculation of nucleation and crystal growth kinetics at the milliliter scale, using a methodology based on the work of Capellades et al. [1]. Utilizing the standardized high-resolution cameras, particle detection and size analysis, a simplified population balance model can be applied to calculate nucleation and growth constants from as few as 3 experiments and a few 100 mg of material.

The approach allows you to screen solvents to give preferred nucleation and growth behavior. This new standardized approach facilitates generating kinetic trends to better understand the crystallization process, enabling faster decisions earlier in development on important process inputs whilst removing false leads. Additionally, these values can be used to test robustness of a crystallization through understanding the effect changes such as impurities have on the nucleation and growth behavior. Furthermore, understanding the nucleation and kinetics of a molecule can be used to identify behavioral analogues which could be used for troubleshooting when material is scarce.

Case study 1: Solvent selection for faster nucleation rate

The new population balance analysis function on the Crystalline instrument enables the calculation of nucleation and growth constantans using data collected on the Crystalline. This analysis involves conducting isothermal nucleation experiments, where a sample is dissolved by heating then cooled rapidly (5-10 ˚C/min) to generate supersaturation; the sample is then held at this temperature to measure the change in the size and number of crystals when nucleation starts. This is repeated at different concentrations to provide the data needed for the modeling. (Figure 1).

The software requires a predicted solubility curve which uses compound and solvent properties as well as user generated solubility data points. The inputs needed are the melting point & enthalpy, molecular weight and density of the compound, as well as the molar mass, density and volume % of the solvents used. Using this information the software estimates solution activities and supersaturation. Next the particle detection data needs to be cropped to find the window where the particles are detected clearly with no substantial overlap, and to remove outlier images where the impeller is in frame. To aid this it is recommended to use AI hybrid particle detection and shape filtering in the experiment. This is done using a calculated rolling average which automatically crops the data, with the option for manual fine tuning. Finally, the calculated nucleation and growth rate constants are used to fit model curves to the particle count, length, area, and volume data (assuming a cubic particle), as shown in Figure 2.

To demonstrate the capability of deriving nucleation and growth rate constants from milligram-scale experiments, the effect of solvent composition on the crystallization behavior of paracetamol was investigated. This solvent combination presents negligible differences in refractive index between solvent and antisolvent, thus providing the most accurate representation of solvent effects on kinetics. The results of these experiments and analysis are shown in Figure 3.[2]. The results show that crystallization from pure EtOH had much lower growth and nucleation constants than any EtOH/water mixtures tested, both being ~10X lower. Additionally, these results show that increasing alcohol percentage decreases both nucleation and kinetic behavior. These results show that for the same supersaturation, higher levels of water promotes kinetics. Therefore, nucleation and growth can be optimized through controlling the amounts of water used.

Case Study 2: Solvent selection for desired particle size

The second case study investigates the effect solvent composition has on the crystallization of potassium sulfate. Two samples were studied in pure solvent (water) and a mixture with 25% antisolvent (EtOH). These results are shown in Figure 4.[3].

Analysis of the nucleation and growth constants for potassium sulfate showed that the nucleation behavior was unaffected by the change in solvent composition. However, the growth constant in pure solvent was 2X higher than the antisolvent mixture showing a suppression of crystal growth. This can be used to optimize the final particle size distribution of a crystallization, where if larger particles are required then a crystallization from water would be used, however if smaller particle size was needed then crystallization with an antisolvent mixture should be selected.

Conclusions

The Crystalline instrument is a powerful tool in crystallization development, allowing for particle size, number and shape analysis in real-time at mL scale. This enables critical process decisions to be made earlier in a molecule’s development cycle, accelerating initial process development. The new population balance analysis feature on the Crystalline allows the use of the data generated to calculate scale-dependent growth rate (Kg) and nucleation rate (Kb) constants, values that are typically only available in later stages of development.

The use and application of the population balance feature has been demonstrated on the crystallization of two compounds to understand the effect solvent composition has on the nucleating and growth behavior. The results for paracetamol showed that any mixture of solvent antisolvent tested gave greater nucleation and growth behavior by ~10X compared to pure solvent. Additionally, the study of potassium sulfate showed that whilst nucleation behavior was unaffected by the change in solvent composition the growth constant was 2X higher in the pure solvent, allowing for solvent selection for larger or smaller particles respectively.

This new methodology to reveal the crystallization behavior of a molecule in different solvents can empower scientists to identify potential challenges earlier, screen solvents to optimize growthand nucleation as well as make informed decisions on crucial process parameters.

References

1 Automated and Material-Sparing Workflow for the Measurement of Crystal Nucleation and Growth Kinetics; Ryan J. Arruda, Paul A.J. Cally, Anthony Wylie, Nisha Shah, Ibrahim Joel, Zachary A. Leff, Alexander Clark, Griffin Fountain, Layane Neves, Joseph Kratz, Alpana A. Thorat, Ivan Marziano, Peter R. Rose, Kevin P. Girard, and Gerard Capellades; Crystal Growth & Design 2023, 23, (5), 3845-3861; DOI: 10.1021/acs.cgd.3c00252

2 Solvent Effects on Crystallization Kinetics: Investigating Trends across Scales; Ibrahim Joel, Alpana A. Thorat, Kevin P. Girard, Gerard Capellades, Methods, and Process Analytical Technologies. Org. Process Res. Dev. 21 November 2025; 29 (11): 2834–2845. https://doi.org/10.1021/acs.oprd.5c00282

3 Automated and standardizable approach to quantify crystal nucleation and growth kinetics: Extension to inorganic salts; Parul Sahu, Joshua Zaharof, Kennedy Tomlinson, Gerard Capellades, Chemical Engineering Research and Design, 2025, 222, 532-54 https://doi.org/10.1016/j.cherd.2025.09.029.