With tetrahedral rotation

Figure 3-18 c-axis projection of a calculated phlogopite structure with tetrahedral rotation of a = 20. ... 

Chiral separations are concerned with separating molecules that can exist as nonsupetimposable mirror images. Examples of these types of molecules, called enantiomers or optical isomers are illustrated in Figure 1. Although chirahty is often associated with compounds containing a tetrahedral carbon with four different substituents, other atoms, such as phosphoms or sulfur, may also be chiral. In addition, molecules containing a center of asymmetry, such as hexahehcene, tetrasubstituted adamantanes, and substituted aHenes or molecules with hindered rotation, such as some 2,2 disubstituted binaphthyls, may also be chiral. Compounds exhibiting a center of asymmetry are called atropisomers. An extensive review of stereochemistry may be found under Pharmaceuticals, Chiral. 

Figure 5,44 Sketch of tetrahedral rotational angle a, for two limiting conditions, = 0° and = 12°. From Hazen and Wones (1972). Reprinted with permission of The Mineral-ogical Society of America.

It is quite surprising that the dipole moments in theTi(ORD)4 series - from trimeric butoxide to monomeric nonanoxide — are practically the same (1.60 to 1.68 D) and do not differ from the theoretical values calculated for a tetrahedral monomer with freely rotating OR- groups [61]. 

Molecular models show that during the course of the acylation reaction, the bound substrate is pulled partially out of the cyclodextrin cavity in forming the tetrahedral reaction intermediate. In other words, the model enzyme is not exhibiting the required transition state selectivity. Furthermore, excessively rigid substrates experience difficulty in rotating while bound in order to accommodate the need of the cyclodextrin hydroxyl group to attach perpendicular to the substrate ester plane, and subsequently rotate to become incorporated into the plane of the new ester product (Scheme 12.1). These problems were addressed by examination of substrates, such as p-nitro derivatives in which the ester protrudes further from the cavity, and substrates with more rotational flexibility such as alkyne 12.3. In these refined systems, much more enzyme-like rate accelerations of factors of up to 5 900 000-fold were observed for 12.4, for example. 

The data for the expanded and contracted minerals plot as two separate linear relations with contracted clays having larger tetrahedral rotation values for given oct.Atet. values than the expanded clays. This is presumably due to the K which aids the tetrahedral rotation in the contracted clays. 

Using the structural formulas that were used to plot Fig.29, the oct./ tet. ratio was calculated for a number of clays and the amount of tetrahedral rotation estimated from the graphs in Fig.32. Some of these values are shown in Fig.31. The montmoril-lonites with a low tetrahedral A1 and low octahedral R3+ have high ratio values and presumably a low degree of tetrahedral rotation (0° —1.5°). As the amount of octahedral R3+ increases, Mg decreases, the octahedral sheet becomes smaller, and the amount of tetrahedral rotation increases (6.5°). 

The amount of rotation systematically increases (attaining a maximum value of approximately 10°) concomitantly with an increase in the amount of tetrahedral A1 and an increase in size by the tetrahedral sheet. When much of the octahedral A1 is replaced by the larger Fe3+ (nontronite), the amount of rotation decreases. As the amount of tetrahedral A1 increases, the amount of octahedral R3+ remains relatively constant and the tetrahedral rotation increases from 0°—3° to 7.5°. 

Present data indicate that Fe3+-rich low-charge clays increase their layer charge by increasing the Mg and Fe2+ content of the octahedral sheet at the expense of Fe3 + more so than of Al. The average Al content of glauconite and celadonite is similar to that of nontronite, but the Fe3+ values are lower. With increased octahedral charge there is an increase anion-anion repulsion and the octahedral sheet increases relatively more in the c direction than the 6 direction, which also favors the large cations. Thus, relatively less tetrahedral Al is required to afford the sheet size differential to allow sufficient tetrahedral rotation to lock the K into place. 

The calculated tetrahedral rotation for glauconites with high octahedral R3 + values ranges from 8 to 10°. There appears to be no overlap of the illite values (12°—13.5°). As the amount of octahedral R3+ decreases, the octahedral sheet increases in size and charge and rotation values decrease. As the amount of tetrahedral Al decreases, the sheets become similar in size and the amount of rotation approaches zero (K cannot be locked in position to provide sufficient layer separation). As octa-... 

The compressibility of the octahedra is greater than that of the tetrahedra. This results in an increased dimensional misfit between tetrahedral and octahedral sheets, so that there is an increase in the tetrahedral rotation angle, a, with P (from 16.0 to 18.4° at 41 kbar for paragonite, and from 11.5 to 12.7° at 28 kbar for muscovite). 

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