Near an edge

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

Near an edge, a nematic director splays through

45^\circ

over a distance of

5\,\mu\mathrm{m}

, with splay constant

K_1 = 6\,\mathrm{pN}

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

5\,\mu\mathrm{m}

. ((b)) A smectic has

K_1 = 9\,\mathrm{pN}

and compression modulus

B = 3\times10^6\,\mathrm{Pa}

. Estimate its smectic penetration length.