Structure of Particles Contrast Variation

We consider a system of monodisperse particles of number density N which are oriented at random. The scattering intensity I(q) as function of q, the magnitude of the scattering vector is given by [1-5] 

For a particle of arbitrary shape immersed in a solvent of scattering length density p j, Io(q) can in general be calculated through resort to the Debye-equa- 

It is expedient to render p(r) as the product of a shape function T(F) and the local electron density Pp(r) inside the particle. For objects with sharp siufaces r may assume only the value 1 or 0 depending on whether T(F) is a point inside or outside of the particle. This condition may also be relaxed and T(F) is allowed to vary continuously between 0 and 1 [56,57,60]. Thus we have 

Given this definition of the shape function, the volume Vp of the particle follows as 

In the following, the difference p - Pm will be designated as contrast. The local excess electron density may be spHt into a part depending on the contrast P Pm function Ap(F) independent of contrast  

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