Small-angle X-ray scattering from a lyotropic surfactant solution shows three peaks at

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Crystal structure, bonding and diffraction · Soft condensed matter

Soft Matter at the Thermal Scale, Ch Amphiphiles and self-assembly

Problem

Small-angle X-ray scattering from a lyotropic surfactant solution shows three peaks at q1=1.45 nm−1q_1 = 1.45\,\mathrm{nm^{-1}}, q2=2.51 nm−1q_2 = 2.51\,\mathrm{nm^{-1}} and q3=2.90 nm−1q_3 = 2.90\,\mathrm{nm^{-1}}. ((a)) Identify the lyotropic phase from the ratios q1:q2:q3q_1:q_2:q_3. ((b)) Using Bragg's law q1=2π/d10q_1 = 2\pi/d_{10}, find the spacing d10d_{10} associated with the first peak, and hence the centre-to-centre distance aa between neighbouring cylinders (for a hexagonal lattice, a=2d10/3a = 2d_{10}/\sqrt3).

Browse the problem library