The implication of the connected net topology on the morphology of β-monoacid triacylglycerol crystals

The crystal morphology of beta n.n.n TAGs, still the only triacylglycerol series of which the crystallographic structures have been elucidated, is predicted using a revised version of the Hartman-Perdok theory. In an earlier publication by Bennema et al.(1) the morphology was predicted on the basis of attachment energy. The platelike shape of the crystals was predicted well, but the indices for the top faces failed. Second, the experimentally observed crystals are much more elongated. In the present approach, the morphology is not only predicted using the attachment energy but also use is made of roughening: temperatures. For faces that grow below the roughening temperature at low supersaturation, the rate-limiting step is the formation of steps on the surface. Therefore, under these growth conditions, the roughening temperatures of the faces determine the morphology rather than the attachment of new growth units to the surfaces. The roughening temperature of a flat face {hkl} can be estimated by the Ising temperatures, which are calculated from substitute nets constructed from all possible step energies found from the connected nets. In some cases, depending on the topology of the connected net, exceptionally low Ising temperatures can be found. In these cases, it is shown that the roughening temperature is not directly determined by the slice energy. If this concept is used for the prediction of the morphology of TAG crystals, a good agreement with the experimentally observed faces is obtained. Moreover, the dependence of the morphology for the various TAGs on the chain length n is explained. Using this concept, however, the presence of the {31l} faces on the morphology cannot be explained. It is shown that this face is probably an F-face that is stabilized by solvent molecules.