(437f) Molecular Conformation and Crystal Structure of N-Alkanes Using Multi-Scale Terrain/Funneling Optimization

Waxing of petroleum or hydrocarbon fuels such as home heating and diesel fuels is a nagging and costly problem in the petroleum industry. Billions of dollars are spent annually on additives to these fuels to prevent waxing or crystal formation and on production, operational, and transportation difficulties that arise due to wax formation. This problem is further exacerbated by the fact that there are a large number of phase transitions that, in turn, can lead to a variety of crystal structures. The early literature on the structure of n-alkanes describes the molecular conformation of n-alkanes up to about C50 as a zigzag structure with planar chains of methylene (or CH2) units terminated by methyl groups (CH3), where the orientation between the methyl end (or side) groups and the planar chain is either perpendicular or tilted. Crystal lattice structures correspond to low energy configurations of horizontal and vertical arrangements of these zigzag molecules. However, more recent studies using molecular dynamics show that even single crystal structures of large n-alkanes are not planar zigzag structures but show considerable wrapping at the ends of the molecule. In this work, the molecular conformation of n-alkanes and the interplay between molecular conformation and crystal structure in the waxing of petroleum fuels are studied. Typical fuel oils are modeled as pure n-alkanes while fractional coordinates are used to describe crystal structure. A multi-scale global optimization methodology based on the combined use of a terrain method and funneling algorithm is used to find minimum energy molecular conformations of diesel, home heating, and residual fuel oils as well as low energy crystal structures. The terrain method is used to gather average gradient and average Hessian matrix information at the small length scale while funneling is used to generate structural changes at the large length scale that drive iterates to a global minimum on the potential energy surface. In addition, the funneling method uses a mixture of average and point-wise derivative information to produce a monotonically decreasing sequence of objective function values and to avoid getting trapped at local minima on the potential energy surface. Computational results clearly show that the calculated molecular conformations are comprised of zigzag structure with considerable wrapping at the ends of the molecule and that planar zigzag conformations usually correspond to saddle points. Moreover, it is shown that these minimum energy molecular conformations undergo rearrangement as molecules pack in either rotator (R) or low temperature ordered (LO) solid phases. Numerical results also clearly demonstrate that our terrain/funneling approach is robust and fast.