Small Angle Neutron Scattering (SANS)

The small angle neutron scattering (SANS) technique allows for the

characterization of structures such as particles in solution, clusters, or precipitates on the nanometer scale [11]. The technique yields information on the number, size and shape of aggregates within the sample, phase transitions, and the location of different molecules or molecular components [11, 17]. In particular, the SANS technique can be a useful tool for studying the micellar structures and inter-micellar interactions in ionic liquid samples. It is a particularly attractive investigative technique because it is noninvasive [17, 18].

Neutron scattering measures the deflection of neutrons in a collimated incident beam by a target. To achieve useful resolution, the technique uses cold (low thermal

temperature = low translational energy or velocity, ‘slow’) neutrons that have a de Broglie wavelength () that is comparable with the size range of the particles/structures of interest in a given scattering experiment.

In neutron scattering experiments the scattered neutrons are collected and

analyzed as a function of the momentum transfer to the neutrons by the scattering events. This can be defined using Bragg wave vectors,

(3.12)

where q is momentum transfer, ki is the incident wave vector, and ks is the scattered wave

vector. The primary type of scattering of interest is elastic scattering, where

| | | | , where n is the index of refraction. The magnitude of q is then given by

( ₎

(3.13)

where θsa is the scattering angle. Schematically this type of neutron scattering is

illustrated in Figure 3.4 [19].

Figure 3.4 The partially transmitted and partially reflected neutron beam resulting from a beam incident on the interface between any two media (A and B).

The refractive index of a medium depends on its scattering length density (SLD). This is a product of the density of atoms per unit volume (ρ) in the medium and their coherent scattering length (b), where the coherent scattering length is a property

characteristic to the atomic nuclei [19]. It is the distinctive coherent scattering length that makes neutron scattering especially beneficial for the purpose of examining micelles in solution. The scattering of hydrogen varies greatly from the scattering of heavier deuterium, resulting in very different SLD values for these isotopes. Thus, neutron scattering can be especially beneficial for the purpose of studying micelles and their surrounding aqueous solution in contrast matching experiments in which normal water or deuterated water is used.

Small angle neutron scattering instruments use small angles or long wavelengths (and sometimes both) to realize a low value for q. Long neutron flight paths before and after the sample allow for good collimation of the neutrons and precise scattering angle measurements. There are two varieties of SANS instrument neutron selectors to narrow the neutron beam energy distributions. Time-of-flight (TOF) instruments use choppers at the source and a detector to select neutron wavelengths, while utilizing a wide range of the available neutron beam spectral distribution. Alternatively, instruments with broad spectrum neutron sources use velocity detectors to choose a portion of the neutron spectrum.

The SANS analyses described in this work were performed at the National Research Universal (NRU) reactor at Atomic Energy of Canada Limited (AECL), Chalk River Laboratories using the N5 triple axis neutron spectrometer that is operated by the Canadian Neutron Beam Centre (CNBC). The NRU reactor does not have a cold neutron

source and for SANS studies a confocal Soller collimator (CSC) has been designed and implemented. This collimator allows the neutron flux at the sample to increase by a factor of 20, and gives the N5 spectrometer the capability to perform as a SANS instrument.

The NRU instrument is configured according to Figure 3.5 [20]. An extended q range is achieved by using a variety of different neutron wavelengths. Using either a sapphire or beryllium filter before the pyrolytic graphite (PG) monochromator aids in filtering unwanted neutrons. The desired neutron beam is sent through the collimator and the resultant beam converges at a point on the sample. Depending on the experiment, either a pyrolytic graphite filter or a horizontal Soller collimator (HSC) is used to reduce vertical divergence in the beam. The scattered neutrons are filtered through a horizontal Soller collimator before reaching a 32-wire 3He position sensitive neutron detector.

Accumulated neutron scattering intensities are measured and analysis is performed. The raw scattered intensity (Iraw (q)) is given by

(3.14)

where Io is the incident neutron intensity, ΔΩ is the sample-to-detector solid angle, ηe is

the detector efficiency, Tsam(λ) is the transmission of a sample, V is the sample scattering

volume, and Ibgd(q) is the background neutron flux [20]. The term

refers to the

differential scattering cross section per unit volume. Ultimately, the goal of a SANS experiment is to obtain the of a sample as a function of q. This is related to the size and morphology of the sample. In order to obtain this information, the appropriate data reduction must be performed to yield a SANS curve. This is achieved by

normalizing the collected scattered data to the scattered neutron intensity of an empty cell (Iemt(q)) (the background intensity). This is used to express the reduced intensity [20],

[ ]

[ ]

(3.15)

where Iemp(q) is the empty cell scattering, and Temp(λ) is the transmitted intensity of the

empty cell. By putting the reduced intensity (Ired(q)) on an absolute scale, the reduced

intensities merge to result in a single SANS curve from which one can perform data analysis and obtain the system information. A program for data analysis is available at NRU that has been specifically written for this purpose by the research scientists there.