Neutron Scattering

length density of a sample against vacuum occurs in the 1/cm Q region and is usually
subtracted from the cross-section. So, one gets the expression for the cross-section according
to :
z
LLQ) = V
~,d,r (p(r)- _ P)e'2' (14 .3)
This form of the scattering cross-section £i . is the starting equation for the analysis of
micellar structures, which we will not discuss in this lecture .
14.3 . Theory of Small Angle Scattering from linear Polymers
We now consider the main features of diffraction from linear polymer chains .
14.3 .1 Diffraction from a linear homo polymer
As a model of a linear chain one considers a polygon of z vectors r,, whose directions are
statistically independent. Such a polygon of a freely joint chain is depicted in Figure 14 .2 .
Figure 14.2 : Model ofafreely joint linear chain
Each vector r, represerts a moromer, which the chemical unit of a polymer of segment length
b . Such a chair can also be represented by another polygon with larger vectors r ; representing
several monomers . Both polygons correctly represent the global properties of the chain as the
end-to-end vector R, which is evaluated from the sum of all vectors according to
14-3