A lamellar phase of a phospholipid in water shows a first-order X-ray peak 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

A lamellar phase of a phospholipid in water shows a first-order X-ray peak at wavevector q1=1.25 nm−1q_1 = 1.25\,\mathrm{nm^{-1}} when the lipid volume fraction is ϕ=0.60\phi = 0.60. Assume the repeat distance dd obeys Bragg's law q1=2π/dq_1 = 2\pi/d, that the bilayer thickness δ\delta stays fixed as water is added, and that the layers swell ideally so that ϕ=δ/d\phi = \delta/d at every water content. ((a)) Find the bilayer thickness δ\delta. ((b)) Water is added until the lipid volume fraction falls to ϕ=0.30\phi = 0.30. Estimate the new repeat distance dd and the new position q1q_1 of the first peak.

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