Small-angle neutron scattering
Encyclopedia
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
, used for investigations of structure of various substances, with spatial sensitivity of about 1 - 1000 nm. 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, surfactant
s, colloids, ferromagnetic correlations in magnetism, alloy
segregation, polymer
s, protein
s, biological membranes, virus
es, ribosome
and macromolecule
s. There are numerous SANS instruments available worldwide. 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.
, 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).
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.
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.
)
Small-angle X-ray scattering
Small-angle X-ray scattering is a small-angle scattering technique where the elastic scattering of X-rays by a sample which has inhomogeneities in the nm-range, is recorded at very low angles...
(SAXS) and light scattering
Light scattering
Light scattering is a form of scattering in which light is the form of propagating energy which is scattered. Light scattering can be thought of as the deflection of a ray from a straight path, for example by irregularities in the propagation medium, particles, or in the interface between two media...
, used for investigations of structure of various substances, with spatial sensitivity of about 1 - 1000 nm. These are particularly useful because of the dramatic increase in forward scattering that occurs at phase transitions, known as critical opalescence
Critical opalescence
Critical opalescence is a phenomenon which arises in the region of a continuous, or second-order, phase transition. Originally reported by Thomas Andrews in 1869 for the liquid-gas transition in carbon dioxide, many other examples have been discovered since. The phenomenon is most commonly...
, 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, surfactant
Surfactant
Surfactants are compounds that lower the surface tension of a liquid, the interfacial tension between two liquids, or that between a liquid and a solid...
s, colloids, ferromagnetic correlations in magnetism, alloy
Alloy
An alloy is a mixture or metallic solid solution composed of two or more elements. Complete solid solution alloys give single solid phase microstructure, while partial solutions give two or more phases that may or may not be homogeneous in distribution, depending on thermal history...
segregation, polymer
Polymer
A polymer is a large molecule composed of repeating structural units. These subunits are typically connected by covalent chemical bonds...
s, protein
Protein
Proteins are biochemical compounds consisting of one or more polypeptides typically folded into a globular or fibrous form, facilitating a biological function. A polypeptide is a single linear polymer chain of amino acids bonded together by peptide bonds between the carboxyl and amino groups of...
s, biological membranes, virus
Virus
A virus is a small infectious agent that can replicate only inside the living cells of organisms. Viruses infect all types of organisms, from animals and plants to bacteria and archaea...
es, ribosome
Ribosome
A ribosome is a component of cells that assembles the twenty specific amino acid molecules to form the particular protein molecule determined by the nucleotide sequence of an RNA molecule....
and macromolecule
Macromolecule
A macromolecule is a very large molecule commonly created by some form of polymerization. In biochemistry, the term is applied to the four conventional biopolymers , as well as non-polymeric molecules with large molecular mass such as macrocycles...
s. There are numerous SANS instruments available worldwide. 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
Radius of gyration
Radius of gyration or gyradius is the name of several related measures of the size of an object, a surface, or an ensemble of points. It is calculated as the root mean square distance of the objects' parts from either its center of gravity or an axis....
for a particle using Guinier
André Guinier
André Guinier was a French physicist who did important work in the field of X-ray diffraction and solid-state physics. He worked at the Conservatoire National des Arts et Métiers, then taught at the University of Paris and later at the University of Paris-Sud in Orsay...
'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 powderPowder diffraction
Powder diffraction is a scientific technique using X-ray, neutron, or electron diffraction on powder or microcrystalline samples for structural characterization of materials.-Explanation:...
, 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
Atomic nucleus
The nucleus is the very dense region consisting of protons and neutrons at the center of an atom. It was discovered in 1911, as a result of Ernest Rutherford's interpretation of the famous 1909 Rutherford experiment performed by Hans Geiger and Ernest Marsden, under the direction of Rutherford. The...
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
Hydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...
, the most abundant element.
In zero order dynamical theory of diffraction the refractive index
Refractive index
In optics the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium....
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
Deuterium
Deuterium, also called heavy hydrogen, is one of two stable isotopes of hydrogen. It has a natural abundance in Earth's oceans of about one atom in of hydrogen . Deuterium accounts for approximately 0.0156% of all naturally occurring hydrogen in Earth's oceans, while the most common isotope ...
. 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
Neutron spin echo
Neutron spin echo spectroscopy is an inelastic neutron scattering technique invented by Ferenc Mezei in the 1970's, and developed in collaboration with John Hayter.In recognition of his work and in other areas, Mezei was awarded the first in 1999....
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
Water
Water is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a...
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
Hydrogen-deuterium exchange
Hydrogen–deuterium exchange is a chemical reaction in which a covalently bonded hydrogen atom is replaced by a deuterium atom, or vice versa. Usually the examined protons are the amides in the backbone of a protein. The method gives information about the solvent accessibility of various parts of...
with any deuteriums in the solvent
Solvent
A solvent is a liquid, solid, or gas that dissolves another solid, liquid, or gaseous solute, resulting in a solution that is soluble in a certain volume of solvent at a specified temperature...
. 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.
)
See also
- Neutron scatteringNeutron scatteringNeutron scattering,the scattering of free neutrons by matter,is a physical processand an experimental technique using this processfor the investigation of materials.Neutron scattering as a physical process is of primordial importance...
- Small angle scattering
- Small angle X-ray scattering (SAXS)Small-angle X-ray scatteringSmall-angle X-ray scattering is a small-angle scattering technique where the elastic scattering of X-rays by a sample which has inhomogeneities in the nm-range, is recorded at very low angles...