Inverse molecular lattices

The borides of this type can be considered as sort of inverse molecular lattices. In molecular compounds the bonding between the molecules is weaker than between the atoms in the molecule. An external force will strain the intermolecular distances more than the molecular configuration. In these borides, on the other hand, the bonds between the icosahedra are stronger than the ones with them, which explains their remarkable combination of physical properties. Their lattice stiffness and high sound propagation rate are inconsistent with their very low heat conductivity. 

A more direct link with molecular volumes holds for alkali halides, because the lattice energy (IT) is inversely proportional to interatomic distance or the cube root of molecular volume (MV). The latter has been approximated by a logarithmic function which gives a superior data fit. Plots of AH against log(MV) are linear for alkali halides 37a). Presumably, U and AH can be equated because AH M, ) is a constant in a series, and AH (halide )) is approximately constant when the anion is referred to the dihalogen as the standard state. 

However, the obscure choice of frequencies in the visible and UV regions in the original calculations may have been guided by a desire to fit experimental heats. In fact, the Debye rotational and translational crystal frequencies relate to sublimation energies of the lattice, and, together with internal molecular vibrations, can be used to calculate thermodynamic functions (16). An indirect connection between maximum lattice frequencies (vm) and heats of formation may hold because the former is inversely related to interatomic dimensions (see Section IV,D,1) ... 

While the nuclei 3H and 13C relax predominantly by the DD mechanism, relaxation of a quadrupole nucleus such as deuterium essentially involves fluctuating fields arising from interaction between the quadrupole moment and the electrical field gradient at the quadrupole nucleus [16]. If the molecular motion is sufficiently fast (decreasing branch of the correlation function, Fig. 3.20), the 2H spin-lattice relaxation time is inversely proportional to the square of the quadrupole coupling constant e2q Q/H of deuterium and the effective correlation time [16] ... 

Fig. 4.15. Inversion-recovery experiment for carbon-13 7, determination or2,2 -bipyridine (400 mg in 1 mL hexadeuteriobenzene, 30 °C 15.08 MHz 16 scans for a single experiment [73 i]). The principal axis of (the fastest) molecular rotation passes C-2 (2 ) and C-5 (5 ). This rotation is too fast for optimum dipolar relaxation of C-3, C-4, and C-6 but does not influence the C-5-H bond which is affected by rotation about other axes. These rotations are slower and more effectively contribute to dipolar spin-lattice relaxation of C-5 (5 ) according to Section 3.3.3.3. To conclude, C-5 (5 ) relaxes faster (3 s) than all other CH carbons (6 s) and can be clearly distinguished from C-3 (3 ) with similar shift.

Relaxation parameters provide valuable information about molecular motions. The spin-lattice relaxation time T is usually determined by the so-called inversion recovery pulse sequence (65). The experiment comprises a set of spectra with different interpulse delays, and Tx is determined by fitting the signal intensities for a given nucleus to Eq. 2, where A and B are constants, x is the respective interpulse delay, and /,is the intensity measured at that delay ... 

The model simulates an experimentally observed trend (25) that the solubility of chains in a SCF shows a strong inverse dependence on the molecular mass of the polymer. Figure 5 shows that changing the molecular weight of the chain molecule from 100 to 700 causes a reduction in solubility of nearly 6 orders of magnitude. The model also shows that all the solubility plots tend to flatten out around 300 bar, as observed in experiments (25). Classical EOS like a modified cubic EOS (2JD > when applied to such systems, produce solubility curves which tend to show a sharp maximum around 200 bar. For polymer-SCF systems, therefore, the lattice EOS is believed to be superior to modified cubic EOS. 

Muller and co-workers (02JPC(B)7781) investigated the molecular behavior of perdeuterated 1,3,5-trioxane in a cyclophosphazene inclusion compound by dynamic 2D NMR spectroscopy. The experimental data revealed a relatively complex motional behavior (rotational motion around the C3 axis of the molecule and around the channel long axis) in the phosphazene host channels the ring inversion process was almost uneffected by the host lattice and activation barriers, as reported from solution NMR studies (90JPC8845), were derived. 

Theoretical expressions for spin-lattice relaxation of 2H nuclei (determined by locally axially symmetric quadrupolar interactions modulated by molecular motions) can be derived for specific dynamic processes, allowing the correct dynamic model to be established by comparison of theoretical and experimental results [34,35]. In addition, T, anisotropy effects, which can be revealed using a modified inversion recovery experiment, can also be informative with regard to establishing the dynamic model [34,35]. 

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