Anisotropy of diamagnetic susceptibility

Magnetic properties. Anisotropy of diamagnetic susceptibility has been used, in much the same way as optical anisotropy, as evidence of molecular orientation in crystals. 

Figure 9, A 76.8-MHz resolution-enhanced deuterium NMR spectrum of neat nitrobenzene showing quadrupole splittings due to partial alignment resulting from anisotropy of diamagnetic susceptibility, (Reproduced, with permission, from Ref, 11. Copyright 1981, Academic Press,)...

The threshold magnetic field, Bth> for Freedericksz transitions has a similar form to Eq. (5.25), but involves the permeability of free space, 1 0, and the anisotropy of diamagnetic susceptibility. A/. Obtain the appropriate equation and check it by dimensional analysis. Use it to calculate the splay elastic constant for 5CB (Fig. 5.1), given that the threshold magnetic field for a pure planar-homeotropic deformation was measured to be 0.54 T in a cell of thickness 10 qm. Use values for 5CB as follows mass diamagnetic susceptibility Ax = 2.14 x 10 m kg and density p = 1.008 g cm . ... 

Your work on conjugated circuits reminds me of a paper that I wrote on the diamagnetic anisotropy of aromatic molecules. Journal of Chemical Physics 4, 673 (1936). You might want to look at this paper, which was the first theoretical discussion of anisotropy of diamagnetic susceptibility of aromatic molecules. 

Closely related to anisotropy, the concept of diamagnetic susceptibility exaltation was discussed early on by Craig and Dauben et al. These groups suggested that the difference, the exaltation, between the observed molar magnetic susceptibility Xm and that calculated from atomic and bond contribution xm provides a useful criterion for assessing aromaticity. Dauben et al. ° have provided a survey, authoritative at the time, of the subject and a comprehensive compilation of exaltation values for benzenoid, nonbenzenoid, and pseudo-aromatics, aromatic cations, keto aromatics, and heteroaromatics. Some uncertainties arise in the calculations of xm for five-membered heteroaromatics. 

Values of the diamagnetic anisotropy of benzene and other aromatic hydrocarbon molecules are calculated on the basis of the assumption that the p, electrons (one per aromatic carbon atom) are free to move from carbon atom to adjacent carbon atom under the influence of the impressed fields. When combined with the assumed values for the contributions of the other electrons (-2.0X 10-6 for hydrogen, —4.5 X10 c for aromatic carbon, — 6.0XlO-6 for aliphatic carbon) these lead to principal diamagnetic susceptibilities of molecules in approximate agreement with the available experimental data. The diamagnetic anisotropy of graphite is also discussed. 

With respect to the physical properties mentioned, band-structure calculations have attracted considerable interest, e.g., for SbSBr, SbSI, and SbSel (234). For the compounds having reference 22i in column 4 of Table XXIX, a temperature-independent diamagnetism has been found, with values of about 10 cm" g between 77 and 340 K. A small temperature-dependence is exhibited by BiTel, a narrow-gap semiconductor (41). The anisotropy of the magnetic susceptibility has been studied for SbSI, BiSel, and BiTel (41, 420). 

Some diamagnetic crystals (graphite, bismuth, naphthalene and other aromatic substances) show prohounced diamagnetic anisotropy. The observed anisotropy of crystals of benzene derivatives correspond to the molar diamagnetic susceptibility —54 X 10 with the field direction perpendicular to the plane of the benzene ring and —37 X lO"6 with it in the plane. This molecular anisotropy has been found to be of some use in determining the orientation of the planes of aromatic molecules in crystals.1... 

From the lJ residual dipolar coupling the molecular magnetic anisotropy tensor is obtained, which differs from the metal contribution by an extent which depends on the magnetic anisotropy of the diamagnetic part. For example, in cytochrome b the diamagnetic, the paramagnetic and the total susceptibility anisotropy values are A Xax = —0.8, 2.8, 2.20 x 10 32 m3, respectively, and Axrh = 0.1, —1.1, — 1.34 x 10-32 m3, respectively [60]. The corresponding tensors sum up as expected. 

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