Hard spheres have diameter (radius ).

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 Brownian particles, sedimentation and the hard-sphere fluid

Problem

Hard spheres have diameter σ=200 nm\sigma = 200\,\mathrm{nm} (radius a=100 nma = 100\,\mathrm{nm}). ((a)) Write the Mayer function f(r)f(r) for hard spheres and evaluate B2=−2π∫0∞f(r) r2 drB_2 = -2\pi\int_0^\infty f(r)\,r^2\,\mathrm{d}r to obtain B2HSB_2^{\rm HS} in terms of σ\sigma. ((b)) Compute B2HSB_2^{\rm HS} in m3\mathrm{m^3}. ((c)) Compute the particle volume vp=43πa3v_p = \tfrac43\pi a^3 and confirm that B2HS=4vpB_2^{\rm HS} = 4v_p.

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