Rigid, uncharged, rod-shaped colloidal particles of length and diameter are suspended…

PHYSICS · Multi-part · 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

Rigid, uncharged, rod-shaped colloidal particles of length L=1.2 μmL = 1.2\,\mu\mathrm{m} and diameter D=20 nmD = 20\,\mathrm{nm} are suspended in water. The particle material has density ρ=1.30 g cm−3\rho = 1.30\,\mathrm{g\,cm^{-3}}. ((a)) Estimate the volume fraction ϕI\phi_{\rm I} at which the suspension begins to order into a nematic phase, using ϕI=3.29 D/L\phi_{\rm I} = 3.29\,D/L. ((b)) Estimate the corresponding mass concentration cIc_{\rm I} in mg mL−1\mathrm{mg\,mL^{-1}}, taking the suspension's mass concentration to be c=ϕρc = \phi\rho.

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