A nematic film shows a bend distortion: the director rotates through over a distance of

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Soft condensed matter · Soft condensed matter

Soft Matter at the Thermal Scale, Ch Frank elasticity, defects and smectic layers

Problem

A nematic film shows a bend distortion: the director rotates through

45^\circ

over a distance of

3\,\mu\mathrm{m}

, and the bend constant is

K_3 = 10\,\mathrm{pN}

. ((a)) Estimate the Frank elastic energy density stored in this distortion, treating the rotation rate as uniform over the

3\,\mu\mathrm{m}

. ((b)) A different smectic has

K_1 = 5\,\mathrm{pN}

and compression modulus

B = 8\times10^6\,\mathrm{Pa}

. Estimate its smectic penetration length.