Density of mechanisms within the flexibility window of zeolites.

By treating idealized zeolite frameworks as periodic mechanical trusses, we show that the number of flexible folding mechanisms in zeolite frameworks is strongly peaked at the minimum density end of their flexibility window. 25 of the 197 known zeolite frameworks exhibit an extensive flexibility, where the number of unique mechanisms increases linearly with the volume when long wavelength mechanisms are included. Extensively flexible frameworks therefore have a maximum in configurational entropy, as large crystals, at their lowest density. Most real zeolites do not exhibit extensive flexibility, suggesting that surface and edge mechanisms are important, likely during the nucleation and growth stage. The prevalence of flexibility in real zeolites suggests that, in addition to low framework energy, it is an important criterion when searching large databases of hypothetical zeolites for potentially useful realizable structures.

Flexibility of ideal zeolite frameworks.

We explore the flexibility windows of the 194 presently-known zeolite frameworks. The flexibility window represents a range of densities within which an ideal zeolite framework is stress-free. Here, we consider the ideal zeolite to be an assembly of rigid corner-sharing perfect tetrahedra. The corner linkages between tetrahedra are hard-sphere oxygen atoms, which are presumed to act as freely-rotating, force-free, spherical joints. All other inter-tetrahedral forces, such as coulomb interactions, are ignored. Thus, the flexibility window represents the null-space of the kinematic matrix that governs the allowable internal motions of the ideal zeolite framework. We show that almost all of the known aluminosilicate or aluminophosphate zeolites exhibit a flexibility window. Consequently, the presence of flexibility in a hypothetical framework topology promises to be a valuable indicator of synthetic feasibility. We describe computational methods for exploring the flexibility window, and discuss some of the exceptions to this flexibility rule.

Flexibility mechanisms in ideal zeolite frameworks.

Zeolites are microporous crystalline aluminosilicate materials whose atomic structures can be usefully modelled in purely mechanical terms as stress-free periodic trusses constructed from rigid corner-connected SiO4 and AlO4 tetrahedra. When modelled this way, all of the known synthesized zeolite frameworks exhibit a range of densities, known as the flexibility window, over which they satisfy the framework mechanical constraints. Within the flexibility window internal stresses are accommodated by force-free coordinated rotations of the tetrahedra about their apices (oxygen atoms). We use rigidity theory to explore the folding mechanisms within the flexibility window, and derive an expression for the configurational entropic density throughout the flexibility window. By comparison with the structures of pure silica zeolite materials, we conclude that configurational entropy associated with the flexibility modes is not a dominant thermodynamic term in most bulk zeolite crystals. Nevertheless, the presence of a flexibility window in an idealized hypothetical tetrahedral framework may be thermodynamically important at the nucleation stage of zeolite formation, suggesting that flexibility is a strong indicator that the topology is realizable as a zeolite. Only a small fraction of the vast number of hypothetical zeolites that are known exhibit flexibility. The absence of a flexibility window may explain why so few hypothetical frameworks are realized in nature.

Polar solvation dynamics in supercritical fluids: a mode-coupling treatment.

A mode-coupling treatment of polar solvation dynamics in supercritical fluids is presented. The equilibrium solvation time correlation function for the solute fluctuating transition frequency is obtained from the mode-coupling theory method and from molecular-dynamics simulations. The theory is shown to be in good agreement with the simulation. The solvation time correlation function exhibits three distinct time scales, with rapid initial decay, followed by a recurrence at intermediate times, and a slowly decaying long-time tail. Our theoretical analysis shows that the short-time decay arises from the coupling of the solute energy gap to the solvent polarization modes, the recurrence at intermediate times is due to the energy modes, while the slow long-time decay reflects the coupling to the number density modes.