Controlling the shape of crystals is of great practical relevance in fields like pharmacology and fine chemistry. Here we examine the paradigmatic case of urea which is known to crystallize from water with a needle-like morphology. To prevent this undesired effect, inhibitors that selectively favor or discourage the growth of specific crystal faces can be used. In urea the most relevant faces are the {001} and the {110} which are known to grow fast and slow, respectively. The relevant growth speed difference between these two crystal faces is responsible for the needle-like structure of crystals grown in water solution. To prevent this effect, additives are used to slow down the growth of one face relative to another, thus controlling the shape of the crystal. We study the growth of fast {001} and slow {110} faces in water solution and the effect of shape controlling inhibitors like biuret. Extensive sampling through molecular dynamics simulations provides a microscopic picture of the growth mechanism and of the role of the additives. We find a continuous growth mechanism on the {001} face, while the slow growing {110} face evolves through a birth and spread process, in which the rate-determining step is the formation on the surface of a two-dimensional crystalline nucleus. On the {001} face, growth inhibitors like biuret compete with urea for the adsorption on surface lattice sites; on the {110} face instead additives cannot interact specifically with surface sites and play a marginal sterical hindrance of the crystal growth. The free energies of adsorption of additives and urea are evaluated with advanced simulation methods (well-tempered metadynamics) allowing a microscopic understanding of the selective effect of additives. Based on this case study, general principles for the understanding of the anisotropic growth of molecular crystals from solutions are laid out. Our work is a step toward a rational development of novel shape-affecting additives.

Process alternatives for continuous crystallization, i.e., cascades of mixed suspension, mixed product removal crystallizers (MSMPRCs) and plug flow crystallizers (PFCs), as well as batch crystallizers are discussed and modeled using population balance equations. The attainable region approach that has previously been used in the design of chemical reactor networks and separation systems is applied to the above-mentioned alternatives for crystallization processes in order to identify attainable regions in a diagram of mean product particle size vs. total process residence time. It is demonstrated that the boundaries of these attainable regions can be found numerically by solving appropriate optimization problems and that the region enclosed by these boundaries is fully accessible. Knowing the attainable region of particle sizes, it is possible to generate feasible process alternatives that allow specific particle sizes to be obtained in a given process configuration. The attainable regions presented in this article are useful to determine whether a desired mean particle size can be achieved in a specific crystallizer type. The concept of the attainable region is illustrated on three case studies: the cooling crystallization of paracetamol grown from ethanol, the anti-solvent crystallization of L-asparagine monohydrate from water using isopropanol as the anti-solvent and the combined cooling/anti-solvent crystallization of aspirin from ethanol using water as the anti-solvent.

Understanding crystal growth from solution is crucial to control the evolution of crystal morphologies. Experiments, molecular simulations, and theory were combined to examine the morphology of urea crystals grown in different solutions. To get a rational representation of all the possible habits a shape diagram (see picture) is introduced in which the habit dependence on the relative growth rates is illustrated.

In this work, we investigate a comprehensive model describing nucleation, growth and Ostwald ripening based on the kinetic rate equation and compare it to commonly used population balance equation models that either describe nucleation and crystal growth or crystal growth and Ostwald ripening. The kinetic rate equation gives a microscopic description of crystallization, i.e., the process is seen as an attachment

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Crystal nucleation from solution is of central importance in the chemical and biological sciences. Linking nucleation kinetics to the properties of solutes and solvents remains a grand-challenge in physical chemistry. Through a unique dataset of compounds able to self-assemble via both hydrogen-bonds and aromatic stacking, we are able to compare the importance of these two types of interaction in driving the nucleation process. Contrary to previous reports in which solution chemistry and hydrogen bonding have been seen as controlling factors, we are now able to show that cluster growth via aromatic stacking holds the key.

Unravelling the molecular complexities of crystal nucleation from solutions is predicated on our ability to measure and interpret high quality kinetic data. This allows us to link nucleation rates to supersaturation, as well as to kinetic rate expressions and their parameters, arising from mechanistic considerations. In this context it is vital to be able to assess the reliability of measured nucleation rate data. Accordingly this contribution details a statistical approach that aims at quantifying the inherent uncertainty associated with nucleation rates obtained from induction time measurements carried out in small volumes. We investigate how uncertainties attached to nucleation rates propagate to mechanistic parameters derived from them and make recommendations for experimental protocols as well as data analysis strategies that minimize said uncertainty. The approach is applied to induction time measurements obtained for benzoic acid/toluene solutions in a wide range of supersaturations.