Density of frameworks

Another important factor influencing the produet in clathrasil synthesis is the active concentration of the SDA. For some SDA, high concentrations lead to frameworks with higher densities of framework-speeifie eages. Pyrrolidine, for example, gives siliea sodalite (2.9 eages per 1000 A) at high concentrations of SDA. whereas RUB-10 (2.0 per 1000 A ) and dodecasil 3C (1.1 per 1000 A ) form at lower eoncentrations. 

The electronic properties of single-walled carbon nanotubes have been studied theoretically using different methods[4-12. It is found that if n — wr is a multiple of 3, the nanotube will be metallic otherwise, it wiU exhibit a semiconducting behavior. Calculations on a 2D array of identical armchair nanotubes with parallel tube axes within the local density approximation framework indicate that a crystal with a hexagonal packing of the tubes is most stable, and that intertubule interactions render the system semiconducting with a zero energy gap[35]. 

Tlie suffices i and J refer to individual atoms and S and Sj to the species of the atoms involved. The summation over j extends over those neighbors of the atom i for which ry, the separation of atoms i and J, is within the cutoff radii of these potentials. The second term in Equation (la) is the attractive many-body term and both V and are empirically fitted pair potentials. A Justification for the square root form of the many-body function is provided in the framework of a second moment approximation of the density of states to the tight-binding theory incorporating local charge conservation in this framework the potentials represent squares of the hopping integrals (Ackland, et al. 1988). 

Ni [182], V [183], and A1 [184]. SU-M [185] is a mesoporous germanium oxide with crystalline pore walls, possessing one of the largest primitive cells and the lowest framework density of any inorganic material. The channels are defined by 30-rings. Structural and thermal information show that there exists a mismatch between framework stability and template decomposition. The latter requires temperatures higher than 450 °C, while the structure is preserved only until 300 °C. 

In more recent years, additional progress and new computational methodologies in macromolecular quantum chemistry have placed further emphasis on studies in transferability. Motivated by studies on molecular similarity [69-115] and electron density representations of molecular shapes [116-130], the transferability, adjustability, and additivity of local density fragments have been analyzed within the framework of an Additive Fuzzy Density Fragmentation (AFDF) approach [114, 131, 132], This AFDF approach, motivated by the early charge assignment approach of Mulliken [1, 2], is the basis of the first technique for the computation of ab initio quality electron densities of macromolecules such as proteins [133-141],... 

The importance of framework density and molar volume is evident also for large pore, mesoporous silica [33] and for AIPO4 polymorphs [34], Data for the latter are included in Figure 7.19. For mesoporous silica a transition from a regime where cages and pores affects the energetics to one in which the large pores act as inert diluent is reported. A further increase in pore diameter does not appear to increase the enthalpy of the compound [33], The similarity in enthalpy of many different structures shows that the synthesis of metastable microporous framework... 

---