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ID: past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2020/paper-2/section-b/22/i/b/solution

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Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2020 / Paper 2 / Section B / 22 / i / b / Solution by

Codex  0 2026-10-20

A cholesteric liquid crystal is locally nematic but its nematic director rotates helically, for example

n (z) = (cos q_{0} z, sin q_{0} z, 0), p = 2 π /∣ q_{0} ∣.

(1)

The sign of

q_{0}

specifies handedness and

p

is the full-turn pitch. The sketch shows rods rotating through transverse planes. This is helical orientational order, not a smectic density-layer lattice. Although an apolar director repeats physically after a half-turn, the conventional pitch denotes a full

2 π

turn. A pitch comparable to visible wavelengths can give selective reflection.

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