Equatorial

A monosubstituted cyclohexane, e.g. methylcyclohexane, exists theoretically in two isomeric forms with a chair-form ring, and the methyl substituent either axial or equatorial. Since these rapidly interconverl through a CH3... 

An alternative to obtaining 0 directly involves defining some more convenient shape-dependent function, and an early but still very practical method is the following. We define a shape-dependent quantity as S = dsldg, as indicated in Fig. 11-16, de is the equatorial diameter and ds is the diameter measured at a distance de up from the bottom of the drop. The hard-to-measure size parameter h in Eq. 11-17 is combined with 0 by defining the quantity H = -0(defb). Thus... 

Since h denotes the distance from the apex to the equatorial plane, then aty - h, p , and Eq. 11-33 becomes... 

This very simple result is independent of the value of the contact angle because the configuration involved is only that between the equatorial plane and the apex. 

This equation is the Porod law for the large-angle tail of the scattering curve along the equatorial direction, which indicates that the equatorial scattered intensity I q is proportional to in the Porod... 

As the spins precess in the equatorial plane, they also undergo random relaxation processes that disturb their movement and prevent them from coming together fiilly realigned. The longer the time i between the pulses the more spins lose coherence and consequently the weaker the echo. The decay rate of the two-pulse echo amplitude is described by the phase memory time, which is the time span during which a spin can remember its position in the dephased pattern after the first MW pulse. Tyy is related to the homogeneous linewidth of the individual spin packets and is usually only a few microseconds, even at low temperatures. 

In order to account for axial and equatorial positions of protons bonded to cyclo-hcxanc-likc rings, Eq, (19) was used, where 1 is an atom three non-rotatablc bonds (totally atoms) away from the proton and belonging to a six-membered ring, and is a dihedral angle in radians (Figure 10.2-6c). 

In this case, the transition structure must have symmetry, with the two F atoms arranged axially and the H atoms being equatorial. In fact, the transition structure is the lowest energy compound that satisfies this symmetry criteria. 

An interesting aspect of this reaction is the contrasting stereoselective behaviour of the dimethyisulfonium and dimethyloxosuifonium methylides in reactions with cyclic ketones (E.J. Corey, 1963 B, 1965 A C.E. Cook, 1968). The small, reactive dimethyisulfonium ylide prefers axial attack, but with the larger, less reactive oxosulfonium ylide only the thermodynamically favored equatorial addition is observed. 

The addition of large enolate synthons to cyclohexenone derivatives via Michael addition leads to equatorial substitution. If the cyclohexenone conformation is fixed, e.g. as in decalones or steroids, the addition is highly stereoselective. This is also the case with the S-addition to conjugated dienones (Y. Abe, 1956). Large substituents at C-4 of cyclic a -synthons direct incoming carbanions to the /rans-position at C-3 (A.R. Battersby, 1960). The thermodynamically most stable products are formed in these cases, because the addition of 1,3-dioxo compounds to activated double bonds is essentially reversible. 

We shall describe a specific synthetic example for each protective group given above. Regiosdective proteaion is generally only possible if there are hydroxyl groups of different sterical hindrance (prim < sec < tert equatorial < axial). Acetylation has usually been effected with acetic anhydride. The acetylation of less reactive hydroxyl groups is catalyzed by DMAP (see p.l44f.). Acetates are stable toward oxidation with chromium trioxide in pyridine and have been used, for example, for protection of steroids (H.J.E. Loewenthal, 1959), carbohydrates (M.L. Wolfrom, 1963 J.M. Williams, 1967), and nucleosides (A.M. Micbelson, 1963). The most common deacetylation procedures are ammonolysis with NH in CH OH and methanolysis with KjCO, or sodium methoxide. 

An unactivated methyl group can be functionalized by the cyclopalladation of oximes. The equatorial methyl of geminal methyls in steroids or hexapyr-anosides is selectively aceto.xylated by the reaction of the palladation complex 523 of the 3-oxime with lead tetraacetate[467,468]. 

The conformational features of six membered rings are fundamental to organic chemistry so it is essential that you have a clear understanding of the directional prop erties of axial and equatorial bonds and be able to represent them accurately Figure 3 17 offers some guidance on the drawing of chair cyclohexane rings... 

Draw the axial bonds before the equatorial ones alternating their direction on adjacent atoms Always start by placing an axial bond up on the uppermost carbon or down on the lowest carbon... 

Place the equatorial bonds so as to approximate a tetrahedral arrangement of the bonds to each carbon The equatorial bond of each carbon should be parallel to the ring bonds of its two nearest neighbor carbons... 

Following this pattern gives the complete set of equatorial bonds... 

The most important result of ring inversion is that any substituent that is axial in the original chair conformation becomes equatorial in the ring flipped form and vice versa... 

Ring inversion in methylcyclohexane differs from that of cyclohexane m that the two chair conformations are not equivalent In one chair the methyl group is axial m the other It IS equatorial At room temperature approximately 95% of the molecules of methylcyclohexane are m the chair conformation that has an equatorial methyl group whereas only 5% of the molecules have an axial methyl group... 

When two conformations of a molecule are m equilibrium with each other the one with the lower free energy predominates Why is equatorial methylcyclohexane more sta ble than axial methylcyclohexane ... 

The greater stability of an equatorial methyl group compared with an axial one IS another example of a steric effect (Section 3 2) An axial substituent is said to be crowded because of 1,3 diaxial repulsions between itself and the other two axial sub stituents located on the same side of the ring... 

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