In a small nematic domain

PHYSICS · Subjective · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Soft condensed matter · Soft condensed matter

Soft Matter at the Thermal Scale, Ch Nematic order and the isotropic-nematic transition

Problem

In a small nematic domain, orientational scattering data show that

70\%

of the rod-like molecules make an angle of

15^\circ

with the local director and the remaining

30\%

make an angle of

75^\circ

with it (the director has no head, so only

\cos^2\theta

matters). Calculate the nematic order parameter

S_{\rm n} = \langle P_2(\cos\theta)\rangle

of this domain, where

P_2(x) = \tfrac12(3x^2-1)