(189f) Examination of Crystal Nucleation and Polymorph Transitions through Molecular Dynamics Simulations of Hard-Core Screened Coulomb Particles

Organic crystals are found in many products and serve countless purposes. To create the functionality of these products, the properties of the crystal form must be taken into account. Since the crystal structure greatly affects the chemical and physical properties of the final product, it is important to know what crystal structure will be formed. Most molecules can form two or more crystal structures (polymorphs) (Bernstein 2002). At present little is known about why a certain polymorph forms under given conditions and which polymorphs will be found in experiments (Blagden & Davey, 2003). In order to predict polymorph formation, and control polymorph selection, knowledge of the governing principles of nucleation and morphological progression during crystallization are necessary. Understanding crystal growth and final crystal shape prediction improved tremendously in the last decade, but solid nucleation science is just beginning to take strides forward. Nucleation is an extremely important area for polymorph prediction since recent experiments suggest crystal structure and therefore polymorph is set at this stage (Yau & Vekilov, 2001; Sato 1993). Insight into the effect of structure in nucleation was gained in this study by utilizing molecular dynamics simulations of hard-core screened Coulomb spherical particles.

While the need for greater understanding of nucleation has been recognized since studies of crystallization began, the necessary tools have only now reached the level where detailed molecular information about this phenomenon can be gained. Overall computing power has increased to the point that large numbers of particles can be simulated for longer time scales. Of the available simulation techniques, molecular dynamics was chosen so that the development of the nucleus could be observed and a kinetic description of the nucleation phenomenon could be gained. To study the development of the nucleus under widely varying conditions, the hard-core screened Coulomb (repulsive Yukawa) pair potential with its adjustable parameters and phase space regions of body-centered-cubic (BCC) and face-centered-cubic (FCC) structures was utilized (Hynninen & Dijkstra, 2003). With parameters corresponding to a highly screened potential (hard-core limit), FCC is the stable structure. In the limit of low screening (Coulomb limit), BCC is the stable structure. The size of the stable solid area depends on temperature, particularly the BCC stable area. To examine the nucleation phenomenon inside this phase space, simulations were performed with initial conditions containing nuclei of set size, shape, and structure. This method of preset nuclei allowed for observation of the minimum size of growth, time of growth, and the preferred shape of a nucleus. The affect of structure can also be monitored by comparing the minimum size of growth and the final crystal structure, for nuclei of different initial structures.

To explore the effect of structure on nucleation, nuclei of BCC and FCC structure were grown with parameters corresponding to several points inside the phase space. At higher temperatures (where the BCC region of stability is small) when the potential was near the hard-core limit, nuclei with BCC structure transformed to FCC structure upon further growth. As the potential approached the Coulomb limit, the BCC nuclei no longer transformed to FCC, but grew into BCC crystals. Nuclei with FCC initial structure always yielded FCC crystals even in the area of BCC stability. This polymorph conversion of BCC to FCC indicates that BCC structure can precede FCC in the nucleation process as indicated by Monte Carlo simulations of hard-core screened Coulomb particles (Auer & Frenkel, 2002), molecular dynamics simulations of Lennard-Jones particles (Anwar & Boateng, 1998) and Landau theory (Alexander & McTague, 1978). This is in contrast to a strictly applied Ostwald's Rule of Stages (Ostwald 1897) where the metastable form is expected to precede the stable form (FCC converts to BCC in BCC region of stability and BCC converts to FCC in FCC region of stability). Also observed with the development of structure, was the development of the nuclei shape. Sphere shaped nuclei were found to remain nearly spherical as they grew, but the surface roughened as found in colloidal experiments (Gasser et. al. 2001). The ability of this simulation method to observe the influence of structure, shape, and size indicate the usefulness of molecular dynamics simulations with pre-constructed nuclei in studying nucleation and polymorph prediction.

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