Ornstein-Zernike equation and Percus-Yevick theory for molecular crystals

Abstract

We derive the Ornstein-Zernike equation for molecular crystals of axially symmetric particles and apply the Percus-Yevick approximation to this system. The one-particle orientational distribution function has a nontrivial dependence on the orientation and is needed as an input. Despite some differences, the Ornstein-Zernike equation for molecular crystals has a similar structure as for liquids. We solve both equations for hard ellipsoids on a sc lattice. Compared to molecular liquids, the tensorial orientational correlators exhibit less structure. However, depending on the lengths a and b of the rotation axis and the perpendicular axes of the ellipsoids, different behavior is found. For oblate and prolate ellipsoids with b >= 0.35 (units of the lattice constant), damped oscillations in distinct directions of direct space occur for some correlators. They manifest themselves in some correlators in reciprocal space as a maximum at the Brillouin zone edge, accompanied by maxima at the zone center for other correlators. The oscillations indicate alternating orientational fluctuations, while the maxima at the zone center originate from nematic-like orientational fluctuations. For a <= 2.5 and b <= 0.35, the oscillations are weaker. For a >= 3.0 and b <= 0.35, no oscillations occur any longer. For many of the correlators in reciprocal space, an increase of a at fixed b leads to a divergence at the zone center q = 0, consistent with nematic-like long range fluctuations, and for some oblate and prolate systems with b ~< 1.0 a simultaneous tendency to divergence of few other correlators at the zone edge is observed. Comparison with correlators from MC simulations shows satisfactory agreement. We also obtain a phase boundary for order-disorder transitions.