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Small-angle scattering model for multilamellar vesicles.

A small-angle neutron-x-ray-light-scattering model for multilamellar vesicles is developed on the basis of a simple geometry. N spherical shells with radii of an arithmetic series are allowed for displacements DeltaR which are limited by DeltaR<R/N due to sterical reasons, with R being the radius of the vesicle. The model shows many properties over a large Q range which include a Guinier region, a first power law, a correlation peak, and a second power law connected to the surface properties of the bilayer. The first power law is related to the compactness of the vesicle and lies between Q(-2) for surfaces and Q(-4) for compact volumes (Porod law). The exact exponent is related to the number of shells N. The correlation peak has a maximum sharpness for rather small displacements DeltaR, but no second order peak is predicted. Only for rather large displacements the correlation peak widens up and shifts to smaller scattering angles. Then the important bilayer spacing is larger. The predictive power of the model lies in the connection of the compactness with N and in the maximum correlation peak sharpness. This model considers many length scales at a time while existing theories focus on length scales of the bilayer spacing and the bilayer itself.