Scattering, neutrons

Neutron scattering offers a valuable technique for determining the dimensions and structure of microemulsion droplets. The scattering intensity I(Q) is given by 

The Q values at the maximum can be used to calculate the lattice spacing using Bragg s equation. Alternatively, one can use a hard-sphere model to calculate S Q) and then fit the data of f(Q) versus Qto obtain the droplet radius R. 

Small angle neutron scattering (SANS) has been employed in investigation of chain conformation in ultrathin polymer films [ 144,498]. 

The theory of neutron scattering (Marshall and Lovesey, 1971) is very closely related to that of light scattering. Neutrons are scattered by the nuclei of atoms and molecules 

Some Experimental Probes of Time Correation Functions 

Experiment Dynamical Quantity Time-Correlation Function 

Raman scattering depolarization of fluorescence u, unit vector along molecular transition dipole E2(u(o) u(0  

The wave mechanical description of a moving neutron implies an associated wavelength as given by the de Broglie relation  

There are two kinds of scattering processes during the interaction between neutrons and a material elastic neutron scattering and Inelastic neutron scattering. The former is also called neutron diffraction and is similar to X-ray diffraction, but due to the different scatter ng properties of neutrons compared to X-rays, complementary Information can be obtained. The latter is used for the study of atomic vibrations and other excitations, and the results are often compared 

Neutron diffraction experiments have provided very similar structural information on chalcogenide glasses to X-ray measurements. For example, Rao et al. investigated GexSei xglasses with 0.1 

Data on neutron diffraction in GejfASj,Sei jf j, glasses are so far unavailable, and this might be due to the difficulties in interpreting the experimental results. 

The VIR and not the SRO has been ascribed to an expression of network connectivity [64]. This appears to imply that although 

GVDOS for Ge-As-Se glasses with the same MCN but different compositions. Reprinted with permission from Effey B. and Cappelletti, R. L., Neutron inelastic scattering study of Se-As-Ge glasses a test of the vibrational isocoordinate rule, Phys. Rev. B, 59, 4119-4124 (1999). Copyright (1999] by the American Physical Society. 

It should, of course, be possible to perform elastic neutron scattering experiments in a very similar way to X-ray ones indeed, when studying low-atomic-number samples this may be advantageous. However, the difficulty in getting regular access to neutron sources has meant that little progress has been made in this direction with electrochemical systems. The only such study appears to be that of Bomchil and Rekel on nickel oxide formation. Since the availability of sources is unlikely to improve significantly, it is unlikely that this will ever become a widely applied technique. 

The size of w/c microemulsion droplets has been measured by neutron scattering for a di-chain hybrid surfactant (C7Hi5)-(C7Fi5)CHS04 Na [32], 667 g/mol PFPE-C00 NH4 [33], and for a partially fluorinated di-chain sodium sulfo-succinate surfactant [34]. For the PFPE-COO NH4 surfactant, the droplet radius increases from 20 A to 36 A for W o values of 14 and 35, respectively. For the di-chain sodium sulfosuccinate surfactant, droplet radius varied linearly from 12 to 36 A as Wo increased from 5 to 30. This linear relationship has also been shown for AOT reverse micelles in organic solvents [7]. In each of these studies for a one-phase microemulsion, droplet size and Wq were found to be only a weak function of pressure, unless the pressure is reduced to the phase boundary where droplets aggregate. This trend was calculated theoretically [6,23] and has been measured in AOT w/o microemulsions in supercritical propane [35,36]. 

Use of the above expression is described as static approximation because all neutrons are detected irrespective of elastic or inelastic scattering. This is avoided by using an additional monochromator in a triple axes spectrometer in which only the elastically scattered neutrons are detected. 

Inelastic neutron scattering (Sinclair, 1985 Leadbetter, 1973) can be used to investigate vibrational spectra of glasses. Thermalized neutrons have energies under 50 meV (roughly 400 cm ). Therefore, during the 

Here the term (pp — pnl)2 replaces the refractive index term in equation (7.3) pp and pm are, respectively, the neutron scattering-length densities of the particle and the medium. A is a constant incorporating the other factors in equation (7.3) and is a characteristic of the apparatus, i.e. the. wavelength of the neutrons, the distance from target to detector. In this case the simple equation for P(Q) given in equation (7.13) no longer applies. For spheres it now has the form 

This technique, although not superior to ordinary light scattering for the determination of particle size, has a number of important advantages over light scattering when applied to more complex problems. Two examples may be mentioned briefly. 

The first arises from the fact that the neutron scattering-length densities of different atoms vary widely in particular those for hydrogen and deuterium differ considerably so that by mixing H2O and D20 in varying proportions media of widely different values of p can be prepared. Equation (7.18) shows that if Pp = Pm there is no scattering, i.e. neutrons do not see the particles. This principle can be exploited in the study of compo- 

A second important application of neutron scattering is to concentrated dispersions which cannot be studied by light scattering because of their opacity. The method has close analogies with the use of low-angle X-ray scattering to study the structure of liquids, and its main application so far has been to investigate the radial distribution function for colloid particles in concentrated dispersions. 

Rheology is concerned with the flow and/or deformation of matter under the influence of externally imposed mechanical forces. Two limiting types of behaviour arc possible. The deformation may reverse spontaneously (relax) when the external force is removed this is called elastic behaviour and is exhibited by rigid solids. The energy used in causing the deformation is stored, and then recovered when the solid relaxes. At the other extreme, matter flows and the flow ceases (but is not reversed) when the force is removed this is called viscous behaviour and is characteristic of simple liquids. The energy needed to maintain the flow is dissipated as heat. Between the two extremes arc systems whose response to an applied force depends on the lime-scale involved. Thus pitch behaves as an elastic solid if struck but flows if left for years on a slope. Similarly, a ball of Funny Putty , a form of silicone rubber, bounces when dropped on a hard surface, when the contact time is a few milliseconds, but flows if deformed slowly on a time-scale of seconds or minutes. Systems of this kind are said to be visco-elastic. The precise nature of the observable phenomena depends on the ratio of the time it takes for the system to relax to the time taken to make an observation. This ratio is called the Deborah number (De)  

One of the most powerful techniques by which protein-protein neighborhoods within the ribosomal particles can be elucidated is neutron scattering. When using this method to determine the relative positions of proteins in the 30 S subunit, the pardcle is reconstituted with two specific proteins that are deuterated whereas all other ribosomal components are in the protonated form (Moore, 1980). The subunits containing the two deuterated proteins give additional contributions to the scattering curves which provide information on the lengths of the vectors between the two deuterated proteins. 

The length-distribution studies were recently extended to include an estimate of the radii of gyration of the protein in situ (Ramakrishnan et ai, 1981). The constraint used was that the proteins must have a radius of gyration greater than that of an anhydrous sphere. From their results Ramakrishnan to/. (1981) conclude that only SI and S4 show signs of an extended conformation in situ, whereas 12 proteins (S3, S5, S6, S7, S8, S9, SIO, Sll, S12, S14, S15, and S18) appear quite compact and globular. However, the experimental errors of these estimations are very large. 

Using 59 data pairs sufficient data exist to rather accurately position the 14 proteins relative to each other (Fig. 11). It is gratifying that there is very good agreement between these results and those from lEM. 

Singlet-Singlet Fhunrescent Energy Transfer between Proteins 

Fundamentals. Neutrons can interact with matter in several ways. Depending on the neutron-nucleus interaction, they can be scattered coherently or incoherently and both processes can occur elastically or inelastically. For structural studies in electrochemical systems, diffraction, i.e. elastic coherent scattering, is of particular interest. Fundamentals of these modes of interaction, including spectroscopic aspects relevant for mobility studies, have been reviewed [989]. 

Instrumentation. The basic setup of a neutron scattering experiment is depicted in Fig. 5.157. 

Sheppard, H.A. Willis, J.C. Rigg, Pure Appl. Chem. 57,105 (1985) 

Electrochemistry of Silicon and its Oxide (Kluwer/Plenum, New York, 

Wagner Ir., in Techniques for Characterization of Electrodes and Electrochemical Processes, ed. by R. Vatma, J.R. Selman (WUey, New York, 1991), p. 3 

spez specific volume of the polymer (more exact,, the partial specific volume at infinite dilution) 

In most cases the ground-state rotational tunnel splitting, as well as the two transitions to the split excited librational state, are observed. Because the tunnel splittings (typically 1-10 cm-1) can be measured with much better accuracy than the librational transitions, the value for the barrier height V2 is usually extracted from the former. Higher terms in the expansion of the potential are introduced only if the librational transitions derived do not agree well with other observations. For 

Luminescence spectroscopy provides simple access to the splitting of the ground multiplet but this technique is not always accessible due to nonradiative decay and strong ligand absorptions as encountered, for example, in the [Ln(Pc)]-/0 systems. For these reasons, alternative spectroscopic tools should be available for magnetochemists. The use of INS as a spectroscopic probe for molecular magnetic systems has recently been reviewed by Guidi [36], Amoretti et al. [37] 

SMM with = 2.2 A at T = 1.5 and 50 K. PhBG refers to the phonon background extracted from downscaling the 

Er(trensal) molecular structure with two sub- and peripherally substituted analogues (2 stituted analogues Er(3-l,5-Me-trensal) (2), and 3). (Reprinted with permission from Er(5-Cltrensal) (3). (b) Comparison of the [13]. Copyright 2014, Royal Chemical Society.) 

— second, third. osmotic virial coefficients M2 molar mass of the polynaer 

Z(9) differential scattering cross section per volume unit K contrast factor for neutron scattering 

The Flory-Huggins interaction parameter, xu is determined from SANS experiments with the following expression  

SANS measurements on blends of PVME/PS have been reported in a number of studies [187-192]. PS/PVME is a widely studied blend, at least partly due to the lest behavior well-documented by various characterization methods. The results show miscibility in the region classified as single phase by more conventional methods. The difference in the lest temperature ( 40 °C) of deuterated PS/PVME versus PS/PVME blends was noted, yielding a relatively small effect, thus justifying the use of deuterated polymers to model hydrogenated polymer blends [187,192]. Additional SANS studies include PMMA/PVF2 [187], PS/P(nBMA) [189], PB(different vinyl contents)/PS [193],polyaniline/PA6 [194] and chlorinated PE/PMMA [195] blends as well as citations noted in Table 5.1. 

PS PoCS Polystyrene/poly(o-chlorostyrene) blends exhibit lest and ucst behavior. SANS results show the interaction function was independent of composition and temperature 197 

PI dPB lest behavior observed good agreement of SANS with SALS measurements 199 

Poly (methyl Poly(ethyl SANS employed to measure yn over a 201, 

The positions of the secondary maxima in hexagonally packed cylinders, relative to the principal peak, follow the scaling 1, 7, ... [210,211]. The most 

Scattering by neutrons can be exploited for obtaining precious structural and morphological information on polymeric materials. An excellent textbook covering all the aspects of neutron scattering, from instrumentation to theory to data interpretation, has recently been written by Hammouda, and is freely available on the World Wide Web [212]. 

Neutron scattering is a very flexible technique, which allows to probe stmctures with sizes from the near atomic to the near micrometer scale. This made SANS a method of choice when the hierarchical structure of complex materials must be elucidated, especially in conjunction with other techniques such as WAXD, SAXS, or light scattering [213-222]. 

The scattering objects can be either polymer chains, or dispersed particles, such as fillers for example. 

Analogous to other scattering methods, SANS yields a picture of the sample in the reciprocal space. SANS data must therefore be interpreted basically with one of the following four approaches, which are very similar to those enumerated for SAXS [212]  

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Another statistical mechanical approach makes use of the radial distribution function g(r), which gives the probability of finding a molecule at a distance r from a given one. This function may be obtained experimentally from x-ray or neutron scattering on a liquid or from computer simulation or statistical mechanical theories for model potential energies [56]. Kirkwood and Buff [38] showed that for a given potential function, U(r)... 

SANS Small-angle neutron scattering [175, 176] Thermal or cold neutrons are scattered elastically or inelastically Incident-Beam Spectroscopy Surface vibrational states, pore size distribution suspension structure... 

The polymer concentration profile has been measured by small-angle neutron scattering from polymers adsorbed onto colloidal particles [70,71] or porous media [72] and from flat surfaces with neutron reflectivity [73] and optical reflectometry [74]. The fraction of segments bound to the solid surface is nicely revealed in NMR studies [75], infrared spectroscopy [76], and electron spin resonance [77]. An example of the concentration profile obtained by inverting neutron scattering measurements appears in Fig. XI-7, showing a typical surface volume fraction of 0.25 and layer thickness of 10-15 nm. The profile decays rapidly and monotonically but does not exhibit power-law scaling [70]. 

The structure of microemulsions have been studied by a variety of experimental means. Scattering experiments yield the droplet size or persistence length (3-6 nm) for nonspherical phases. Small-angle neutron scattering (SANS) [123] and x-ray scattering [124] experiments are appropriate however, the isotopic substitution of D2O for H2O... 

The equilibrium properties of a fluid are related to the correlation fimctions which can also be detemrined experimentally from x-ray and neutron scattering experiments. Exact solutions or approximations to these correlation fiinctions would complete the theory. Exact solutions, however, are usually confined to simple systems in one dimension. We discuss a few of the approximations currently used for 3D fluids. 

Vibrational spectroscopy provides detailed infonnation on both structure and dynamics of molecular species. Infrared (IR) and Raman spectroscopy are the most connnonly used methods, and will be covered in detail in this chapter. There exist other methods to obtain vibrational spectra, but those are somewhat more specialized and used less often. They are discussed in other chapters, and include inelastic neutron scattering (INS), helium atom scattering, electron energy loss spectroscopy (EELS), photoelectron spectroscopy, among others. 

Figure Bl.9.1. Diagrams showing that x-ray and light scattering involve extra-nuclear electrons, while neutron scattering depends on the nature of the atomic nucleus.

Neutron scattering depends upon nuclear properties, which are related to fluctuations in the neutron scattering cross section a between the scatterer and the surroundings. The scattered amplitude from a collection of scatterers can thus be written as (similar to (B 1.9.29)) ... 

Two of the most important functions in the application of neutron scattering are the use of deuterium labelling for the study of molecular confomiation in the bulk state and the use of deuterium solvent in polymer solutions. In the following, we will consider several different applications of die general fomuda to deuteration. 

There are many different data analysis schemes to estimate the structure and molecular parameters of polymers from the neutron scattering data. Herein, we will present several connnon methods for characterizing the scattering profiles, depending only on the applicable q range. These methods, which were derived based on different assumptions, have... 

In polymer solutions or blends, one of the most important thennodynamic parameters that can be calculated from the (neutron) scattering data is the enthalpic interaction parameter x between the components. Based on the Flory-Huggins theory [4T, 42], the scattering intensity from a polymer in a solution can be expressed as... 

Lovesey S W 1984 Theory of Neutron Scattering from Condensed Matter vo 1 (Oxford Oxford University Press)... 

Higgins J S and Beno i t H C 1994 Poiymers and Neutron Scattering (Oxford Oxford Science)... 

Kjems J K, Passell L, Taub H, Dash J G and Novaco A D 1976 Neutron scattering study of nitrogen adsorbed on basal plane-oriented graphite Rhys. Rev. B 13 1446-62... 

McTague J P, Nielsen M and Passell L 1979 Neutron scattering by adsorbed monolayers Crit. Rev. Solid State Sc/8 125-56... 

Hamley I W, Garnett S, Luckhurst G R, Roskilly S J, Pedersen J S, Richardson R M and Seddon J M 1996 Orientational ordering in the nematic phase of a thermotropic liquid crystal A small angle neutron scattering study J. Chem. Phys. 104 10 046-54... 

Richardson R M 1998 Neutron scattering Handbook of Liquid Crystais Voi 1. Fundamentais ed D Demus, J Goodby, G W Gray, H-W Spiess and V Vill (New York Wiley-VCH)... 

The early Hartley model [2, 3] of a spherical micellar stmcture resulted, in later years, in some considerable debate. The self-consistency (inconsistency) of spherical symmetry witli molecular packing constraints was subsequently noted [4, 5 and 6]. There is now no serious question of tlie tenet tliat unswollen micelles may readily deviate from spherical geometry, and ellipsoidal geometries are now commonly reported. Many micelles are essentially spherical, however, as deduced from many light and neutron scattering studies. Even ellipsoidal objects will appear... 

Figure C2.3.12. Two-dimensional neutron scattering by EOggPO gEOgg (Pluronic F88) micellar solution under shear witli (a) tlie sample shear axis parallel to tlie beam, and (b) tlie sample rotated 35° around tlie vertical axis. Reflections for several of tlie Miller indices expected for a bee lattice are annotated. Reproduced by pennission from figure 4 of [84]-...

Mortensen K 1996 Structural studies of PEO-PPO-PEO triblock copolymers, their micellar aggregates and mesophases a small-angle neutron scattering study J. Phys. Condens Matters A103-A104... 

Stassis C 19. Lattice Dynamics. In Skald and D L Price (Editors) Methods of Experimental Physics Volume 23 Neutron Scattering Part A. Orlando, Academic Press, pp. 369-440. 

Recently, this observation has been confirmed experimentally through neutron scattering studies, making use of isotopic substitution . These studies have revealed that the water molecules in the... 

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