Quasicrystallinity in twist-grain-boundary phases

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Abstract
We present a simplified polymer model for twist-boundary phases in liquid crystals. The thermodynamic phases of this model are characterized by an angle 2πα̃. There are incommensurate phases with α̃ an irrational number and commensurate phases with α̃=P/Q, with P and Q relatively prime integers. The latter have quasicrystalline symmetry for Q=5 or Q>6. Equilibrium phases with all values of α̃ can be produced by varying a control parameter α. The curve α̃(α) is an incomplete devil’s staircase with finite locking intervals about every rational α̃.