The fd virus is a rigid rod with and bare diameter

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Condensed Matter, Materials & Soft Matter · Interacting systems, real gases and phase equilibria

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

Problem

The fd virus is a rigid rod with

L = 880\,\mathrm{nm}

and bare diameter

D = 6.6\,\mathrm{nm}

. The numerically exact solution of Onsager's equation places the isotropic-nematic coexistence at

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

and

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

: between these two volume fractions the sample separates into coexisting isotropic and nematic phases, exactly as a mixture between two free-energy branches separates into two coexisting phases at fixed overall composition. ((a)) Compute

\phi_{\rm I}

and

\phi_{\rm N}

for fd virus. ((b)) Express the width of this biphasic gap,

\Delta\phi = \phi_{\rm N} - \phi_{\rm I}

, as a fraction of

\phi_{\rm I}

. ((c)) The hard-sphere fluid freezes at

\phi_{\rm f} = 0.494

and its coexisting crystal melts at

\phi_{\rm m} = 0.545

. Compute the same fractional gap width,

(\phi_{\rm m}-\phi_{\rm f})/\phi_{\rm f}

, for hard spheres. ((d)) Give the ratio of the fd virus's fractional gap to the hard sphere's fractional gap.

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