Neutron Scattering - JUWEL - Forschungszentrum Jülich

KWS-3 5
2. The standard Q-range of KWS-3 is from 10 -4 to 3·10 -3 Å -1 . What the size of particles
could be investigated in this Q-range? What are the form factor P(Q) and structure
factor S(Q)? In which case the scattering intensity d�/d�(Q) could be represented as a
product of the structure factor and form factor d�/d�(Q)= d�/d�(0)�P(Q)�S(Q)? What
is the physical “content” of the forward scattering d�/d�(0) [I(0)]?
3. The standard wavelength at KWS-3 is 12.5Å. What are disadvantages of this
wavelength? What should we correctly select before sample preparation?
4. What is the difference between pine-hole SANS and focused SANS? Why the beam
size at KWS-3 is 20cm 2 ?
4 Experiment Procedure
Within the frame of this practicum we will explore aquaeous solution of monodisperse
polystyrene (PS) microspheres with diameter 8000Å and the initial concentration 1% of
particles in H2O. In future, this sample will be used at KWS-3 as “a standard sample” to check
the performance of instrument, absolute calibration, instrument resolution.
In Table 1 there is collected information about PS microspheres obtained from the
producer; additionally all necessary information about H2O and D2O is listed there.
Table 1. Parameters of used components
Polystyrene Spheres H2O D2O
Scattering Length Density [Å -2 ] 1.41·10 -6 -0.56·10 -6 6.50·10 -6
Density, 20°C [g/cm 3 ] 1.05 1.0 1.05
Radius [Å] 4000±45
The contrast variation is proposed to proceed simply by step-by-step adding of D2O to the
initial H2O solution of spheres. To estimate how much of D2O we should add, the simulation
of the forward scattering should be done as function of D2O concentration:
d�
d� 0 ����SpheresV 2
Spheres��Spheres � �Water�, where VSpheres is volume of PS spheres, �Spheres SLD of PS spheres, �Water SLD of D2O/H2O
mixture, �Spheres volume fraction of PS spheres in D2O/H2O mixture. We could rewrite the
above-mentioned equation in terms of �0 and �D2O, the volume fraction of PS spheres in the
initial H2O solution and volume fraction of D2O in D2O/H2O mixture respectively:
d�
d� 0
��� �0 (1 ��D2O )
VSpheres �Spheres � � H 2O ��D2O (�D2O � � H 2O )
1 �� 0� D2O
� � 2
In Figure 3 the forward scattering d� d� 0
�� as a function of �D2O and � is plotted. At the
starting point of the experiment (�D2O=0) we have PS spheres in pure H2O and maximal
volume fraction of spheres �Spheres = �0 = 1%. Minimum of the plotted curve corresponds to
the matching point of PS spheres in water. In Table 2 seven points around matching
concentration are labeled with “CV” mark. In case of CV, from the scattering curves of
above-mentioned samples we need to extract only “integral” parameter forward scattering to
.