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small chop

Small-angle neutron scattering

Small angle neutron scattering (SANS) is a laboratory technique, similar to the often complementary techniques of small angle X-ray scattering (SAXS) and light scattering. These are particularly useful because of the dramatic increase in forward scattering that occurs at phase transitions, known as critical opalescence, and because many materials, substances and biological systems possess interesting and complex features in their structure, which match the useful length scale ranges that these techniques probe. The technique provides valuable information over a wide variety of scientific and technological applications including chemical aggregation, defects in materials, surfactants, colloids, ferromagnetic correlations in magnetism, alloy segregation, polymers, proteins, biological membranes, viruses, ribosome and macromolecules. While analysis of the data can give information on size, shape, etc., without making any model assumptions a preliminary analysis of the data can only give information on the radius of gyration for a particle using Guinier's equation.

Technique

During a SANS experiment a beam of neutrons is directed at a sample, which can be an aqueous solution, a solid, a powder, or a crystal. The neutrons are elastically scattered by changes of refractive index on a nanometer scale inside the sample which is the interaction with the nuclei of the atoms present in the sample. Because the nuclei of all atoms are compact and of comparable size neutrons are capable of interacting strongly with all atoms. This is in contrast to X-ray techniques where the X-rays interact weakly with hydrogen, the most abundant element.

In zero order dynamical theory of diffraction the refractive index is directly related to the scattering length density and is a measure of the strength of the interaction of a neutron wave with a given nucleus. The following table shows the scattering lengths for various elements (in 10-12 cm).

H D C N O P S
-0.3742 0.6671 0.6651 0.940 0.5804 0.517 0.2847
Note that the relative scale of the scattering lengths is the same. Another important point is that the scattering from hydrogen is distinct from that of deuterium. Also, hydrogen is one of the few elements that has a negative scatter, which means that neutrons deflected from hydrogen are 180° out of phase relative to those deflected by the other elements. These features are important for the technique of contrast variation (see below).

SANS usually uses collimation of the neutron beam to determine the scattering angle of a neutron, which results in an ever lower signal-to-noise ratio for data that contains information on the properties of a sample at relatively long length scales, beyond ~1 μm. The traditional solution is to increase the brightness of the source, as in Ultra Small Angle Neutron Scattering (USANS). As an alternative Spin-echo Small-angle Neutron Scattering (SESANS) was introduced, using neutron spin echo to track the scattering angle, and expanding the range of length scales which can be studied by neutron scattering to well beyond 10 μm.

SANS in biology

A crucial feature of SANS that makes it particularly useful for the biological sciences is the special behavior of hydrogen, especially compared to deuterium. In biological systems hydrogen can be exchanged with deuterium which usually has minimal effect on the sample but has dramatic effects on the scattering.

The technique of contrast variation (or contrast matching) relies on the differential scatter of hydrogen vs. deuterium. Figure 1 shows the scattering length density for water and various biological macromolecules as a function of the deuterium concentration. (Adapted from .) Biological samples are usually dissolved in water, so their hydrogens are able to exchange with any deuteriums in the solvent. Since the overall scatter of a molecule depends on the scatter of all its components, this will depend on the ratio of hydrogen to deuterium in the molecule. At certain ratios of H2O to D2O, called match points, the scatter from the molecule will equal that of the solvent, and thus be eliminated when the scatter from the buffer is subtracted from the data. For instance the match point for proteins is typically around 40-45% D2O, and at that concentration the scatter from the protein will be indistinguishable from that of the buffer.

To use contrast variation, different components of a system must scatter differently. This can be based on inherent scattering differences, e.g. DNA vs. protein, or arise from differentially labeled components, e.g. having one protein in a complex deuterated while the rest are protonated. (For some examples of this method see .)

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