Controlling and Predicting Crystal Shapes: The Case of Urea

Abstract

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.

Molecular-dynamics simulations of urea nucleation from aqueous solution

“…In this derivation, we proceed following an approach similar to that used to derive a free-energy profile associated with crystal growth from solution in a confined system reported in the supplementary material of ref. 26. Our final expression is in agreement with those derived by Veesler and coworker (27) for the nucleation of proteins in a droplet as well as with other theoretical results obtained for the description of first-order phase transitions in confined volumes (28)(29)(30).…”

“…The metadynamics production runs were carried out for 0.26, 0.34, and 0.35 μs, respectively. Consistently with our previous works (9,26,38), generalized Amber force field (GAFF) (39,40) was chosen for urea together with the TIP3P water model. Each system was at first minimized with the conjugate gradient algorithm with a tolerance on the maximum force of 200 kJ·mol −1 ·nm −1 , and then a 100-ps NVT equilibration with a time step of 0.5 fs was performed to relax the system at the temperature assigned.…”

“…Such CVs can be decomposed in single-molecule contributions that account for the density of the local molecular environment surrounding each solute molecule, as well as the degree of orientation order of the molecules belonging to the coordination sphere of that solute molecule. The orientation order is defined with respect to an intramolecular vector (26,38,45). In the following, we shall define Γ CO , the molecular degree of order associated to the relative orientation of urea molecules with respect to the CO axis, and Γ NN , the degree of order associated to the relative orientation with respect to the NN axis.…”

In Silico Prediction of Growth and Dissolution Rates for Organic Molecular Crystals: A Multiscale Approach

“…However, MD can, at most, only probe behavior on the nanometer and nanosecond scale. Thus, most investigations of growth and dissolution processes using MD are reported for relatively small and simple molecules like, e.g., urea [11][12][13] and glycine [14][15][16][17], or even for simple model systems, such as hard spheres and Lennard-Jones particles [18][19][20][21], whereas most organic molecules, especially those used as active pharmaceutical ingredients (APIs), form more complex crystal structures, and it is extremely challenging to capture their crystal growth using fully-atomistic simulations [22]. Replacing atomistic details with lower resolution, coarse-grained (CG) beads, in which groups of co-localized atoms are treated as a single interaction site, allows one to overcome the complexity of molecules and the long time scale associated with the crystallization [22,23].…”

“…Moreover, upon introduction of an extra term into the system Hamiltonian, the actual dynamics of the system is to some extent hampered [28]. Recently, Salvalaglio et al [13] demonstrated that using well-tempered metadynamics, applied within MD, one can quantitatively estimate the ratio between growth rates and thus predict the crystal habits and their dependence on additive concentration and supersaturation. However, the authors stressed that the approach does not allow computing absolute growth rates.…”