A biochemist estimates the aggregate shape of a single-chain surfactant with…

PHYSICS · Subjective · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Soft condensed matter · Soft condensed matter

Forces, Machines and Signals, Ch Charges in salt water and the assembly of amphiphiles

Problem

A biochemist estimates the aggregate shape of a single-chain surfactant with hydrocarbon tail volume v=0.35 nm3v=0.35\,\mathrm{nm^3}, extended chain length ℓc=1.70 nm\ell_c=1.70\,\mathrm{nm}, and a head-group area measured by X-ray scattering as a0=50 A˚2a_0=50\,\mathring{\mathrm{A}}^2 per molecule. Their working: p=va0ℓc=0.35 nm350×1.70=0.3585=4.1×10−3p=\frac{v}{a_0\ell_c}=\frac{0.35\,\mathrm{nm^3}}{50\times1.70}=\frac{0.35}{85}=4.1\times10^{-3} They conclude that, because p≪1/3p\ll1/3, the surfactant packs into small spherical micelles. Find the error in this working, and give the packing parameter and the aggregate shape it correctly predicts.

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