Iron has a cohesive energy of per atom and a nearest-neighbour spacing of ; its…

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Condensed Matter, Materials & Soft Matter · Solid continuum mechanics and complex fluids

Condensed Matter Physics, Ch Soft matter: when entropy, not bonding, sets the structure

Problem

Iron has a cohesive energy of

4.28\,\mathrm{eV}

per atom and a nearest-neighbour spacing of

2.48\,\mathrm{\mathring{A}}

; its measured shear modulus is about

82\,\mathrm{GPa}

. A soft hydrogel is organised at the thermal energy scale, with a structural length of about

50\,\mathrm{nm}

. ((a)) Estimate iron's shear modulus from

G\sim\varepsilon_{\rm b}/d_{\rm b}^3

and compare it with the measured value. ((b)) Estimate the gel's modulus with the same formula, using

k_BT

300\,\mathrm{K}

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