Neutron Scattering

14 . Soft Matter : Structure
Dietmar Schwahn
14.1 . Introduction
The methods of small angle scattering (SAS) wich neutrons and X-rays are broadly used for
investigations ofmesoscopic structures in condensed materials . Whenever, atomic density or
chemical composition inhomogeneities of mesoscopic length scale exist in a sample, this
method can in principle be applied . SAS is a complimentary method to transmission electron
microscopy (TEM) ; TEM makes visible the microstructure in real space while the SAS
methods measure in reciprocal space and give quantitative data averaged over macroscopic
large volumes .
In this lecture the theoretical basis of small angle scattering with neutrons (SANS)
should be developed for the topic of the physics of polymers or, as it is said today, of "soft"
matter und should be clarified with simple experimental examples. Since the end of 1939 the
method of SAS was mainly developed by Guinier and Kratky and applied for questions in
metal physics . In one of Guinier's first experiments scattering from copper precipitates in
aluminum was correctly interpreted and the precipitates were identified as the origin of
hardening in so-called Duralumin . This type of precipitation are so-called Guinier-Preston
zones ; they are still subject of active research. Today, neutron small angle scattering
technique is mainly used for soft matter; the main reason might be the relatively simple
possibilities of contrast variation using hydrogen and deuterium, which scatter neutrons quite
differently but do not change the chemistry ofthe polymer .
14.2 . Diffraction ofNeutrons at 3-Dimensional Particles
In this part the basic equations of small angle scattering are discussed . For qualitatively
understanding in Figure 14 .1 two neutron pencils of rays are depicted in two spheres of
différent size. From this figure it becomes clear that diffraction from thé langer sphere occurs
into smaller angles and therefore smaller scattering vectors Q . The basic equation of small
angle scattering is given in Eq .(14 .1) .
dY- (Q) -
1
L~ bi ez
V-~,
dS2 -
(14 .1)
14-1