Neutron Scattering - JUWEL - Forschungszentrum Jülich

8 H. Frielinghaus, M.-S. Appavou
molecule is 14307g/mol. What is the connection between the chemical concentration and
the number density?
3. The correlation peak appears at a scattering vector Qmax. How would it relate to the unit
cell parameter of a simple cubic lattice? What is the dependence of Qmax as a function of
the chemical concentration c?
4. If the packing of the globules was fcc (face centered cubic) or hexagonal (with arbitrary
layer order) the system is more dense by a factor of 6√ 2. What would be the function
Qmax(c)?
(II) Cylindrical Micelles in D2O
The Q-dependence of the scattering curve will be evaluated in two different ways to obtain the
diameter of the cylinders.
1. The Taylor expansion for small scattering vectors Q yields the following functional form
I(Q) ∝ Q−1 · exp(− 1
4R2Q2 ). What would you plot in a simple graph to obtain a linear
dependence? Which role does the radius R play in this graph?
2. Knowing that the formula occurs from a Taylor expansion with the parameter x = QR
around the point x =0, what would be criterion for a good approximation? (Don’t argue
too mathematically!)
3. As for many compact (and monodisperse) bodies the scattering curve shows oscillations.
The first minimum of such a curve also indicates the radius of the cylindrical micelle.
Mathematical calculations yield Qmin =3.832/R. This is another example for connections
in real space to reciprocal space. Where does the name reciprocal space come from?
4. The mathematical form of an ideal, infinitely long cylinder with a radius R would predict
a zero intensity for the Qmin-value. Why would we observe a finite intensity nonetheless?