# Item

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Poster

#### Investigation the influence of the presence of counter-enantiomers on the growth rate of enantiomers

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Seidel-Morgenstern, A., Perlberg, A., Elsner, M. P., Lorenz, H., Grandeury, A., Warnecke, G., et al. (2007).
*Investigation the influence of the presence of counter-enantiomers on the growth rate of enantiomers*.
Poster presented at PBM 2007: 3rd International Conference on Population Balance Modelling, Québec City, Canada.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-973D-8

##### Abstract

_{2}O and (b) compound forming system mandelic acid-H

_{2}O. Two different observations were made. In system (a) no significant interdependence between the target and the counter-enantiomer on crystallization kinetics has been observed, i.e. the growth rates of the two enantiomers are independent. In contrast a strong influence of the presence of the counter-enantiomer on the growth rate could be observed in case of system (b). Moreover, it can be shown that the mandelic acid counter-enantiomer may even change the specific rates of growth for particular crystal faces which results in different crystal shapes (hexagonal for pure enantiomer in solution, rhombic for mixture of enantiomers). In theoretical investigations usually (effective) growth rates are considered to be proportional to the power of supersaturation of the crystallising compound: eq. 1 (attachment) Such an approach is not capable to describe the observations made for mandelic acid, where a modified growth rate law in which the dependence of the influence of both enantiomers on growth is needed: eq. 2 (attachment) In a theoretical study possible models are tested in order to describe the experimentally determined crystal growth rates for the mandelic acid enantiomers adequately. At first a one-dimensional population balance model (eq. 3) is applied capturing the interaction of both enantiomers: eq. 3 (attachment) where F

_{N}

^{(k)}denotes the particle size distribution with z being an effective length coordinate. To simulate a different evolution of the crystal faces a multidimensional treatment of this population problem has to be done. E. g. for the two-dimensional case with the two length coordinates y and z the following population balance equations must be solved in conjunction with the corresponding mass balances of the liquid phase: eq. 4 (attachment) To solve the problem stated numerically, newly developed high resolution adaptive discretisation methods are applied [4, 5] which will be also presented. [1] LORENZ, H.; PERLBERG, A.; SAPOUNDJIEV, D.; ELSNER, M.P.; SEIDEL-MORGENSTERN, A. (2006): Crystallization of enantiomers, 45(10), 863-873 [2] PERLBERG, A. (2006): Zur enantioselektiven Kristallisation aus Lösungen. Dissertation, Otto-von-Guericke-Universität Magdeburg [3] GRANDEURY, A.; LORENZ, H.; SEIDEL-MORGENSTERN, A. (2007): Impact of Heterochiral Interactions during the Growth of Enantiopure Materials: Example of Mandelic Acid (in preparation) [4] QAMAR, S.; ELSNER, M.P.; ANGELOV, I.; WARNECKE, G.; SEIDEL-MORGENSTERN, A. (2006): A Comparative Study of High Resolution Schemes for Solving Population Balances in Crystallization. Comp. Chem. Eng. 30(6-7), 1119-1131 [5] QAMAR, S.; ASHFAQ, A.; WARNECKE, G.; ANGELOV, I.; ELSNER, M.P.; SEIDEL-MORGENSTERN, A. (2006): Adaptive High Resolution Schemes for Multidimensional Population Balances in Crystallization Processes. Comp. & Chem. Eng. (in press), doi: 10.1016/j.compchemeng.2006.10.014