Morphology Calculation

Elucidating crystal structures paves the way to understanding and controlling all properties of high-performance pigments. This involves the control of particle morphology and the tailoring of the interfacial properties of the pigment particles.

Crystal morphology has a crucial influence on the properties of most crystalline products. It determines handling, mechanical, optical, and even chemical proper­ties of the crystals.

Because of their insolubility, pigments are used in the form of dispersed submi­cron particles. Interfacial and scattering properties of the pigment particles deter­mine their in-use and optical properties. As a consequence, the optical properties of pigments can be controlled by the size and the shape of their particles.

Crystal morphology describes both the size and the shape (habit) of a crystal. Crystal polyhedra develop according to the growth rates of their surfaces. Crystal growth is controlled by kinetic effects such as diffusion and heat transfer in crystallizing solu­tions or melts as well as by supramolecular recognition processes at crystal sur­faces.

Ever since three-dimensional crystal structures have been known, researchers have been searching for a relationship between morphology and crystal structure. From a purely thermodynamic perspective, this relationship can be elucidated by measuring or calculating the surface energy of the individual crystal faces. The thermodynamically most stable crystal polyhedron is the one possessing the low­est overall surface energy.

Knowing the crystal structure also enables one to calculate the surface energies of organic molecular crystals using force field methods [58]. Thus the thermody­namically most stable morphology can be calculated rapidly and easily by deter­mining the attachment energies of the various crystal faces. The attachment ener­gy of a crystal face corresponds to the energy which is gained if two parts of a crys­tal which were cleaved parallel to this face are brought together from infinite sepa­ration (Figure 8.11). Attachment energies give access to “equilibrium morpholo­gies” which are formed if the crystallization process is carried out close to equilib­rium conditions without the influence of perturbing factors such as during slow sublimation or ripening (e. g., during a pigment finishing procedure).

Computational methods are particularly valuable in determining the morphol­ogy of pigments since it is difficult, timeconsuming and often impossible to deter-

growth units slice crystal

Figure8.11 Calculation of the attachment energy Eatt. Building a slice from growth units (molecules or dimers) yields the slice energy Esl. Attachment of stable slices to growth faces yields the attachment energy Eatt, which is proportional to the surface energy and may be used to derive the crystal habit.

mine crystal habit using electron microscopy. In contrast, the calculations yield reliable and comprehensive information about both observed and potential growth faces.

8.4.5

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