Simulation Project SANS-2: A full virtual experiment - Liposome sample

The component Sans_liposomes uses the formfactor for a spherical shell

$F_{\rm {shell}}(q)={\dfrac {{\frac {4\pi }{3}}R_{\rm {out}}^{3}f(qR_{\rm {out}})-{\frac {4\pi }{3}}R_{\rm {in}}^{3}f(qR_{\rm {in}})}{{\frac {4\pi }{3}}(R_{\rm {out}}^{3}-R_{\rm {in}}^{3})}},$

where \(f(x)\) is the formfactor of a sphere as found in the previous problem. The intensity from diluted monodisperse liposomes is given by

$I(q)=\phi V(\Delta \rho )^{2}F^{2}(q),\,$

where \(V=V_{\rm out}-V_{\rm in}\) is the volume of the liposome and \(\Delta \rho\) is the excess scattering length density in the shell.

Use the average \(\Delta \rho\) that you calculated for the phospholipid bilayer liposomes (\(\Delta \rho \approx -0.6\) fm\(/\)Å\(^3\), include your derivation in the report), and the volumefraction \(\phi=0.01\). Each unit of the phospholipid bilayer consists of two DMPC groups with the hydrofobic chains facing each other. Calculate the thickness of the phospholipid bilayer by assuming an area of 59 Å\(^2\) of each DMPC headgroup and a cylindrical shape of the DMPC bilayer unit. The volume of a DMPC headgroup is 319 Å\(^3\) and 808 Å\(^3\) for the tails.Use the liposome bilayer thickness in the Sans_liposomes component and simulate the total scattering intensity for \(R_{\rm out}=100\) Å and \(R_{\rm out}=400\) Å. Plot also the theoretical total scattering intensity for \(R_{\rm out}=100\) Å and \(R_{\rm out}=400\) Å.