Form factors and scattering laws

Form factors for scattering particles or molecules with a regular morphology (spheres, cylinders, hollow spheres, lamellae) are available in the literature 

In the most general case, that of a deuterium-labelled polymer (subscripts D) together with its hydrogenous equivalent (//) dissolved in a solvent (5), eqn (8.3) can be expanded to  

The system is assumed to be incompressible, i.e. density fluctuations of H, D and S components are self-cancelling, so that the overall fluctuation in density is zero, in which case  

Averaging the coherent scattering lengths over the volume of the solvent molecule or segment volume (assumed to be equal), then this equation can be written in terms of the scattering length density  

If the total number of polymer molecules is N, then let NdIN = x and Nh/N=( -x). The scattering laws Sxy(Q) in eqn (8.10) have intra- and inter-molecular contributions  

---