Anisotropic molecular shape

Another important application of perturbation theory is to molecules with anisotropic interactions. Examples are dipolar hard spheres, in which the anisotropy is due to the polarity of tlie molecule, and liquid crystals in which the anisotropy is due also to the shape of the molecules. The use of an anisotropic reference system is more natural in accounting for molecular shape, but presents difficulties. Hence, we will consider only... 

As has been noticed by Gelbart and Gelbart [7], the predominant orientational interaction in nematics results from the isotropic dispersion attraction modulated by the anisotropic molecular hard-core. The anisotropy of this effective potential comes from that of the asymmetric molecular shape. The coupling between the isotropic attraction and the anisotropic hard-core repulsion is represented by the effective potential... 

Time Resolved Fluorescence Depolarization. In Equation 3, it is assumed that the polarization decays to zero as a single exponential function, which is equivalent to assuming that the molecular shape is spherical with isotropic rotational motion. Multiexponential decays arise from anisotropic rotational motion, which might indicate a nonspherical molecule, a molecule rotating in a nonuniform environment, a fluorophore bound to tbe molecule in a manner that binders its motion, or a mixture of fluorophores with different rotational rates. 

Almond and Axelson have introduced an approach of some resemblance to TRAMITE, but based on the molecule s gyration tensor, which more closely reflects molecular shape and thus provides higher accuracy for molecules of highly anisotropic shape.104 They propose that the eigenvalues of the order tensor can be predicted to an accuracy which nearly matches SSIA, according to the simple relationship,... 

A pseudo solid-like behavior of the T2 relaxation is also observed in i) high Mn fractionated linear polydimethylsiloxanes (PDMS), ii) crosslinked PDMS networks, with a single FID and the line shape follows the Weibull function (p = 1.5)88> and iii) in uncrosslinked c/.s-polyisoprenes with Mn > 30000, when the presence of entanglements produces a transient network structure. Irradiation crosslinking of polyisoprenes having smaller Mn leads to a similar effect91 . The non-Lorentzian free-induction decay can be a consequence of a) anisotropic molecular motion or b) residual dipolar interactions in the viscoelastic state. 

Fig. 4.—Molecular shapes and correlation times for isotropic and anisotropic motion, (a) Spherical molecule (b) axially symmetric molecule (c) asymmetric molecule.

Atomic and molecular displacement under constraint. Thermal expansion and compressibility are large and anisotropic. Sometimes structural data have been extrapolated from the room temperature (RT) down to low temperature (LT) simply by considering changes in lattice dimensions. This has led to disappointing results since, even in the absence of a phase transition, molecular shapes and orientations may change substantially. Similarly, if we find an isostatic pressure at room temperature whose effect is equivalent to a given temperature decrease at ambient pressure for, say, the chain contraction, the equivalence will not usually match for, say, the... 

In quantitative modeling of PESs the description of the molecular shape as a superposition of atomic components remains an attractive approach, but it is clear from the earlier discussion that it must be extended to accommodate two important factors. The atomic shape is not a rigid, but rather a soft, exponentially decaying electronic charge cloud. In addition, it should be anisotropic with the anisotropy depending not only on the atom itself, but also on its partner in the chemical bond. 

As to infrared spectroscopy - and the same holds good for other spectral ranges -the orientational order is readily observable in form of dichroism Being related to the molecular shape, the molecular polarizability is anisotropic as well. By the alignment of the molecules this anisotropy is transferred to the sample, however damped due to the imperfect order as described by the order parameters. As a consequence, the dielectric function and furthermore the (complex) refractive index are anisotropic, so that eventually (linear) dichroism and birefringence occur. 

Both theoretical approaches qualitatively describe the "thermotropic" and "lyotropic" liquid crystalline state of rod-like molecules ( see also D.B. DuPre, R. Parthasarathy, this book). Combination of both theories (Flory, Ronca)(7) slightly improves the predictions compared to the experimental findings. Anisotropic dispersion interactions and/or anisometric molecular shape can thus be the basis for explaining theoretically the appearance of "lyotropic" and "thermotropic" liquid crystalline phases. 

If the orientation of the principal optical directions can be found with respect to the unit cell vectors of the crystal, the orientations of the molecules in the unit cell, especially those with very anisotropic shapes and considerable unsaturation, may be found. This information was useful in the determination of the shape and size of the steroid nucleus (see Figure 1.11, Chapter 1). The relationship of molecular shape to refractive index is listed in Table 5.2, and the different refractive indices of naphthalene are shown in Figure 5.11. 

A number of different types of molecules form liquid-crystalline phases. What most of them have in common is that their physical properties are anisotropic. Either the molecular shape is such that the length of... 

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