Tobacco mosaic virus (TMV) forms rigid rods of length and diameter

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

Tobacco mosaic virus (TMV) forms rigid rods of length

L = 300\,\mathrm{nm}

and diameter

D = 18\,\mathrm{nm}

. A thermotropic nematic made of similarly rod-shaped molecules has Landau-de Gennes coefficients (in the magnitude normalisation used for the invariants of

Q_{ij}

)

a = 0.15\,\mathrm{MJ\,m^{-3}\,K^{-1}}

B = 1.5\,\mathrm{MJ\,m^{-3}}

and

C = 4.0\,\mathrm{MJ\,m^{-3}}

. ((a)) Using the numerically exact solution of Onsager's equation,

\phi_{\rm I} = 3.29\,D/L

and

\phi_{\rm N} = 4.19\,D/L

, compute the coexistence concentrations at which the TMV suspension separates into isotropic and nematic phases. ((b)) Using

T_{\rm NI} - T^* = 2B^2/9aC

and

S_{\rm n}(T_{\rm NI}) = 2B/3C

, compute the supercooling range and the order-parameter jump of the thermotropic nematic.

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