A strength disclination sits in a nematic film with Frank constant (one-constant…

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Order, broken symmetry and collective behaviour · Soft condensed matter

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

Problem

A strength

s = +1

disclination sits in a nematic film with Frank constant

K = 8.0\,\mathrm{pN}

(one-constant approximation). The defect core has radius

r_c = 5.0\,\mathrm{nm}

and the sample extends to

R = 2.0\,\mu\mathrm{m}

from the core. ((a)) Calculate the line energy per unit length

E/L = \pi Ks^2\ln(R/r_c)

. ((b)) Express this as an energy per micrometre of line, in multiples of

k_BT

T = 298\,\mathrm{K}

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