Thermodynamics and crystallization kinetics

Thermodynamics and crystallization kinetics

Goals within this topic are to gain a deeper understanding of the complex phase behavior of substances and substance/solvent systems, the related crystallization kinetics and its consequences on separation process design. In this connection also development of improved measurement techniques and rationalization of process design is considered as important.

Solubilities, phase diagrams and solid phase behavior

Solid-liquid equilibria (SLE), i.e. equilibria between solid and liquid phases, are the thermodynamic foundation of crystallization processes and therefore their knowledge of essential importance for crystallization process design. Based on the solubility data and thermal analysis, we construct the phase diagrams as initial point for separation process design. Thermodynamic models and experimental tools are combined to have a fundamental understanding of the complex systems. Examples investigated in the last years originate from pharmaceutical, food and agrochemical sectors, and relate to, for example, the resolution of chiral systems, modeling of solid solution forming systems or the isolation of certain target compounds from multi-component mixtures based on plant extracts.

Figure 1 illustrates the solubility behavior of guaifenesin in several solvents alongside with the thermodynamic modeling using PC_SAFT. Guaifenesin is an anti-cough medication, which also has other therapeutic effects when it is combined with other drugs. In this figure, guaifenesin shows a peculiar solubility behavior in water that is correctly captured using the model.

Figure 2 shows the phase diagram of the ˪‑valine/˪‑leucine/water mixture at 298.15 K. In this system ˪‑valine and ˪‑leucine form solid solutions. This phase diagram and the related tie lines are modeled using the PC-SAFT model. Thermodynamic modeling is successful except some extreme points near the alyotropic point.

Solid-state forms of Active Pharmaceutical Ingredients (APIs) comprise polymorphs, solvates, salts, co-crystals (binary compounds), solid solutions and amorphous forms (Scheme 1). These different phases show diverse properties, such as solubility, dissolution rate and bioavailability. New solid-state forms can thus significantly improve the chemical and physical properties of APIs. Moreover, screening for solid forms is important to find the optimum form and to minimize unexpected form conversion in the process.

The application of a mechanochemical approach to reveal new polymorphs of the drug praziquantel and the potential of variable amounts of solvent in liquid-assisted grinding for solid form screening has been demonstrated recently. Praziquantel is a chiral prescribed drug for the treatment of schistosomiasis worms. Without solvent usage and by varying the amount of solvent added, we found two new polymorphs and an amorphous form of drug praziquantel, which were not reported previously (Scheme 2). The finding portrays the advantage of the mechanochemical approach as a means of the polymorph screening strategy.

In close collaboration with Prof. E. Kotelnikovas group at St. Petersburg University further projects are concerned with studying the formation and occurrence of solid solutions and non-stoichiometric binary compounds in chiral systems aimed at a deeper understanding of its origins and potential future applications.

Crystallization kinetics

Thermodynamics define the final state of a certain system, while the kinetics provide the pathway to this state, which is essential for process design. In crystallization, mostly growth, nucleation and dissolution kinetics are of interest, which can be measured with various methods, e.g. in single crystal growth cells or directly in the reactor of interest. Observing one crystal surrounded by supersaturated mother liquor with a microscope gives two-dimensional information on the evolution of the crystal shape. Hence, the effect of different additives on the specific face-related growth rates can be evaluated efficiently and fast in a qualitative way. However, a certain number of individuals have to be observed to achieve statistical significance of the measures if the extracted growth kinetics shall be used afterward for process predictions.

Thus, it can be beneficial to investigate a collective of crystals directly under process conditions to decrease the necessary time of kinetic measurements. A measurement technique applicable for this purpose is online microscopy. Suspension is withdrawn from the crystallizer for its application and fed continuously, unclassified, to a flow-through cell where it is observed with appropriate optics, light sources and a camera (Figure 3). Exemplarily, Figure 4 shows growth rates determined for L-asparagine monohydrate crystals from racemic and pure L-asparagine solutions. Together with information on the mother liquor, i.e. temperature, composition and/or concentration, kinetic parameters of appropriate mathematical approaches are estimated, which can subsequently be applied with more detailed population balance equations to design, visualize or optimize crystallization processes.

For example, a preliminary step to relatively quickly access the key performance indicators of the batch Preferential Crystallization process for racemate resolution is introduced using a shortcut model (SCM). It quantifies the process with the help of only five ODEs and a polarimeter for measurements.
The liquid phase mass balance for preferred and counter enantiomers (index 1 and 2, respectively) and solvent (index 3):

The equations comprise of three parts, where keff, is the effective crystallization rate constant, 4πNR2, is the total surface area of all the crystals and S-1neff , is the driving force for the crystallization process. The three essential free parameters for shortcut model that are required to be estimated using PC experiments are stop time (tstop), effective crystallization rate constant (keff) and order of crystallization (neff). Figure 5 shows an illustrative result of the shortcut model.


Sadeghi, M., Cascella, F., Tenberg, V., Seidel-Morgenstern, A., Lorenz, H. (2021). ‘Solubility analysis of pharmaceuticals guaifenesin, ketoprofen and artemisinin in different solvents’  J. Mol. Liq. 343 (2021) 117503.

Sadeghi, M., Tenberg, V., Münzberg, S., Lorenz, H., Seidel-Morgenstern, A. (2021). ‘Phase equilibria of l–valine/l–leucine solid solutions’  J. Mol. Liq. 340 (2021) 117315.

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Saikia, B., Seidel-Morgenstern, A., Lorenz, H. (2021). Role of Mechanochemistry in Solid Form Selection and Identification of the Drug Praziquantel. Cryst. Growth Des. 21 (2021) 5854.

Wünsche, S., Yuan, L., Seidel-Morgenstern, A., & Lorenz, H. (2021). A Contribution to the Solid-State Forms of is(demethoxy) curcumin: Co-Crystal Screening and Characterization. Molecules, 26, 720.

Lorenz, H., Temmel, E., & Seidel-Morgenstern, A. (2020). Continuous Enantioselective Crystallization of Chiral Compounds. In [R5]: N. Yazdanpanah, & Z. K. Nima (Eds.), The Handbook of Continuous Crystallization (pp. 422-468). Royal Society of Chemistry

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Isakov, A. I., Lorenz, H., Zolotarev, A. A. & Kotelnikova, E. N. (2020). Heteromolecular compounds in binary systems of amino acids with opposite and same chiralities, CrystEngComm, 22, 986–997.

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Kotelnikova, E., Sadovnichii, R., Kryuchkova, L. & Lorenz, H. (2020). Limits of Solid Solutions and Thermal Deformations in the L-Alanine–L-Serine Amino Acid System, Crystals, 10, 618.

Henniges, M., Lorenz, H., & Seidel-Morgenstern, A. (2020). Influence of an additive on growth and solubility behavior of chiral 2-chloromandelic acid. Journal of Crystal Growth, 547, 125798.

Isakov, A. I., Lorenz, H., Zolotarev Jr.,A. A., Kotelnikova, E. N. (2019). Crystal chemistry of heteromolecular compounds of amino acids. Organic Mineralogy. In V. Russian Conference with international participation, Pushchino (Russia), 43-44.

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Elena N. Kotelnikova, Anton I. Isakov & Heike Lorenz (2018). Thermal deformations of crystal structures formed in the systems of malic acid enantiomers and L-valine–L-isoleucine enantiomers, CrystEngComm, 20, 2562-2527.

Bhandari, S., Temmel, E., Carneiro, T., Qamar, S., Lorenz, H., & Seidel-Morgenstern, A. (2018). Modeling Batch Preferential Crystallization for Conglomerates and Racemic Compounds. In BIWIC2018 - 25th International Workshop on Industrial crystallization. Rouen, France, 121-125.

Henniges, M., Seidel-Morgenstern, A., & Lorenz, H. (2018). Crystal Growth Rate Studies in the Chiral 2-Chloromandelic Acid/Water System. In BIWIC2018 - 25th International Workshop on Industrial crystallization. Rouen, France, 219-224.

Kryuchkova, L. Yu., Lorenz, H., Zolotarev Jr, A.A., Bocharov, S.N., Kotelnikova, E.N. (2018). Solid phases in the chiral phenylglycine system according to PXRD and SCXRD data. In BIWIC2018 - 25th International Workshop on Industrial crystallization. Rouen, France, 226–231.

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