General
The carbon-carbon bonds along the cyclohexane ring are sp³ hybrid orbitals, which have tetrahedral symmetry. Therefore, the angles between bonds of a tetravalent carbon atom have a preferred value θ ≈ 109.5°. The bonds also have a fairly fixed bond length λ. On the other hand, adjacent carbon atoms are free to rotate about the axis of the bond. Therefore, a ring that is warped so that the bond lengths and angles are close to those ideal values will have less strain energy than a flat ring with 120° angles.
For each particular conformation of the carbon ring, the directions of the 12 carbon-hydrogen bonds (and therefore the positions of the hydrogen atoms) are fixed.
There are exactly eight warped polygons with six distinguished corners that have all internal angles equal to θ and all sides equal to λ. They comprise two ideal chair conformations, where the carbons alternately lie above and below the mean ring plane; and six ideal boat conformations, where two opposite carbons lie above the mean plane, and the other four lie below it. In theory, a molecule with any of those ring conformations would be free of angle strain. However, due to interactions between the hydrogen atoms, the angles and bond lengths of the actual chair forms are slightly different from the nominal values. For the same reasons, the actual boat forms have slightly higher energy than the chair forms. Indeed, the boat forms are unstable, and deform spontaneously to twist-boat conformations that are local minima of the total energy, and therefore stable.
Each of the stable ring conformations can be transformed into any other without breaking the ring. However, such transformations must go through other states with stressed rings. In particular, they must go through unstable states where four successive carbon atoms lie on the same plane. These shapes are called half-chair conformations.
Read more about this topic: Cyclohexane Conformation
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