Techniques for the characterization of physical gels - Physical Gels from Biological and Synthetic Polymers - page 19

neutron scattering have developed rapidly over the last two decades because of the
availability and performance of large-scale facilities accessible to the whole scienti

c
community. However, it is outside the scope of this topic to treat the theoretical back-
ground of scattering techniques in detail, and the reader is referred to specialist mono-
graphs (Glatter and Kratky, 1982 ; Roe, 2000 ). Instead we wish to stress the type of
information on the structure of physical gels that can be obtained by these techniques.
The junction zones in physical gels are somewhat analogous to a crystalline structure
(for example, the multi-stranded helices in some biopolymer gels), so X-ray diffraction
techniques (wide-angle X-ray scattering or WAXS) should be able to elucidate the
periodicity of the crystals. However, the proportion of crystalline structure is very
small and the scattering by the solvent, which is a major component, is superposed on
the diffraction patterns of the crystals, and resolution is often poor.
When diffraction techniques are to be used, the gel can be conditioned as an oriented

fibre, and allowed to dry slowly in order to eliminate the scattering due to the solvent. In
turn, to observe a good diffraction pattern it is often necessary to create preferential chain
orientation by withdrawing a liquid drop of a concentrated solution and stretching it
between two tips, when the gel starts to form (for cold-set gels, for instance). The
microcrystals in gels are normally randomly oriented, but when a gelling drop is pulled,
the junctions (crystals) orient along the fibre is allowed to dry under

tension, more crystals can be nucleated and, eventually, in the totally dried state the

fibre axis. When the

bre
has an oriented semi-crystalline structure. Such a stretching and drying procedure is not
especially natural: chain conformations different from the junctions developed at rest
may be adopted during the preparation step (Paul, 1967 ; Arnott et al., 1974 ; Lemstra and
Keller, 1978 ; Foord and Atkins, 1989 ), so the method must be used with caution.

2.2.1 Principles of scattering

Scattering techniques are based on the interaction of radiation with matter. X-rays and
light (photons) are electromagnetic waves characterized by very different wavelengths,
close to 0.1 nm for X-rays and about 600 nm for visible light. Neutrons are moving
particles having a wavelength of several nanometres. X-rays interact with the electrons in
atoms, while neutrons interact with the atomic nuclei. When light passes through a
transparent medium, it creates a dipole and radiates an electromagnetic field proportional

to the polarizability of the medium.
When X-rays strike an object, every electron becomes the source of a scattered wave
and the scattered waves are coherent (incoherent scattering is neglected). Coherence
means that the amplitudes scattered by different electrons are added. The amplitudes are
of equal magnitudes and they differ only in their phase, , which depends on the position

of the electron in space. The principle of a scattering experiment is to measure the spatial
repartition of the scattered radiation. The secondary wave can be written in the complex
form eiϕ. i ϕ . The calculation of

ϕ

ϕ

is illustrated in Figure 2.1 .

Let us denote by k i ( |k i | =2 π / λ ) the wave vector of the incident beam along u i , and by k s

the wave vector of the scattered wave in the direction u s . (By convention, the angle

between u s and u i is denoted θ in light scattering experiments, and 2 θ in X-ray scattering.)