Theory of the Change in Cholesteric Pitch Near Cholesteric-Smectic Phase Transitions

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Abstract
The large change in pitch of cholesterics in the vicinity of a transition to a smectic phase is argued to be governed entirely by the behavior of the twist elastic constant, K 22. The twist constant increases rapidly near a smectic phase transition because of the coupling of the director n(r) with local smectic-like positional correlations. This coupling gives a rapidly increasing term in the energy of the form (n.δ × n)2. The other important energy term is of the form n. δ × n and comes from chiral intermolecular interactions. We derive a mean field theory of a typical such interaction and obtain a contribution to the energy which is relatively insensitive to smectic-like order. We thus predict that, although both K 22 and the pitch increase rapidly, the ratio of K 22 to pitch should be constant near the transition to the smectic phase.