Geometric Frustration in Molecular Crystals

Abstract

Unlike Lego bricks that perfectly assemble next to one another, solid assemblies of organic compounds often include some inevitable misfit between constituents, giving rise to geometric frustration. In order to fit into the assembly the molecular building blocks must distort, at some finite energetic cost. In cases where this distortion at the ground state is uniform across all the units in the assembly, the associated geometric frustration is said to be locally resolved. Such locally resolved frustration carries little implications on the morphology and response properties of the assembled structure. However, in many cases, for small enough assemblies there are non-local compromises that are more energetically favorable. These conformations are associated with non-uniform distortions and highly cooperative response between the molecular constituents. The cooperative nature of frustrated assemblies may result in growth arrest, tendency to form filaments, exotic response properties and large morphological variations during the growth of the assembly.Almost a century ago German mineralogist Ferdinand Bernauer discovered that a large fraction of small organic compounds could form twisted molecular crystals. These are straight and narrow needle-like structures with mesoscopic pitch, a crystalographically impossible structure. Recent revived interest in twisted molecular crystals discovered even more compounds that form these exotic assemblies and led to their study by modern means. Electron microscopy revealed straight faceted structures with sharp diffraction peaks in selected area electron diffraction, much like regular crystals. Moreover, the pitch of the molecular crystals varied with size, with thicker crystals exhibiting less twist. In this work we review twisted molecular crystals as frustrated assemblies. In this approach twist emerges from the preferred morphology at the constituent scale, and gets attenuated with size by the incompatibility of twist and largescale crystalline order. We discuss two distinct mechanisms that produce twisted molecular crystals, and provide a prediction for the twist decay as a function of the crystals' spatial dimensions.

Existence of twisting in dislocation-free protein single crystals

“…Furthermore, it is presumed that the handedness of twisting can be attributed to the anisotropic interaction of chiral protein molecules associated with asymmetric units in the crystal forms. These results may correspond to experimental evidence for the geometric frustration mechanism proposed with molecular dynamics simulation as a primary mechanism of twisting in molecular crystals ( 18 , 22 – 24 ). This suggests that many other faceted protein crystals that look like perfect crystals also may include slight twisting.…”

Formation and Growth Mechanism of Ceftezole Sodium Monohydrate Ring-Banded Spherulites

“…The formation of defects is naturally accompanied by the arrival of the stress field, and the lamellae will deform to release the stress driven by this environment. Moreover, the third source is the relative shear stress in adjacent lamellae . When the interface between the lamellae is squeezed, they will compete for space and hinder each other’s growth, resulting in shear stress in the crystals.…”

“…Moreover, the third source is the relative shear stress in adjacent lamellae. 36 When the interface between the lamellae is squeezed, they will compete for space and hinder each other's growth, resulting in shear stress in the crystals. Finally, some lamellae will compromise to release the stress by twisting, and this twisting effect will be magnified to form a macroscopically visible deformation when there is a multilayer structure or multiple shear interfaces in the lamellae.…”

Transport in Twisted Crystalline Charge Transfer Complexes

“…However, when crystals are at the nanoscale, they need not conform to a lattice, they need not have long range translational symmetry. Simulations and mechanical considerations , suggest that crystals may accommodate some frustration to continue to grow, thereby approximating a familiar crystal. Only molecules that conform to a lattice can be assembled from a semi-infinite number of molecules.…”