This paper provides a brief introduction to the subject of off-specular neutron scattering by rough interfaces. Such scattering can be calculated using the distorted-wave Born approximation (DWBA) in which the neutron wavefunctions for a system with smooth interfaces are used as the basis for perturbation theory. Although it has been applied successfully to model the scattering from rough surfaces, the DWBA has several quantitative and qualitative limitations, some of which are described in this paper. When it is applied to multilayer systems, the DWBA correctly predicts a number of qualitative features of the diffuse scattering, including fringes of scattering that result from correlations between the roughnesses of neighbouring interfaces. A remarkable feature of diffuse neutron reflection is the range of length scales within a surface or interface that is probed. This is illustrated here by data obtained with a self-assembled multilayer of organic molecules where distances between 500 Å and 3 μm parallel to the layers are probed.

The use of neutron scattering as a tool for exploring surfaces and interfaces has become more prevalent over the last several years, mainly due to the increasing popularity of reflectivity techniques, which study specular reflection from single surfaces or multilayers. Due to intensity limitations, the use of off-specular or grazing-incidence neutron scattering techniques has been much less prevalent. In this paper we shall discuss the origins of magnetic off-specular scattering (e.g., as observed in magnetic multilayers) and the origins of anomalies seen in the X-ray or neutron diffuse scattering from multilayers near Bragg reflections in terms of the Dynamical Theory of Scattering.

A method of using parametric B-spline curves to interpret neutron and x-ray specular reflectivity spectra is described. The introduction of parametric curves for scattering length density profiles greatly expands the function space accessible to low-dimensional representations but also requires means to restrict the space to physically acceptable functions. A practical fitting procedure is outlined, and two examples are shown.

This paper presents an analysis of the relationship between Parratt's recurrence formula and several existing analytical formulations for the neutron and x-ray reflectance of a surface film. In particular, it was shown that the Born approximation and the weighted-superposition approximation (WSA) for the neutron and x-ray reflectance can both be derived directly from Parratt's recurrence formula. It was also shown that the well-known nonlinear differential equation for the reflectance at an arbitrary point inside a film can be obtained from Parratt's recurrence formula and the WSA was an approximate solution to this equation. Finally, the nonlinearity in the WSA was discussed through a comparison between the Born approximation and the WSA. It was pointed out that the exponential factor in the WSA correctly accounted for both the phase shift effect due to the scattering length density of the film and the amplitude attenuation effect due to evanescence.

Specular and off-specular neutron intensities were measured at grazing incidence from an optical grating. The periodicity of the grating was determined from the locations of the intensity peaks in the off-specular data. An analysis of the widths of the off-specular intensity peaks showed that the effect of the coherence length of the neutron beam on the determination of a surface length scale of approximately 30 μm was negligible when compared to that of the instrument resolution.

The technique of neutron reflection has been developed by us to investigate a variety of thin film electrochemical systems, including polymer bilayers, matrix-trapped active biological molecules and inorganic oxides. Measurements have been made with the electrodes in contact with the electrolyte, allowing studies of structural rearrangements after polymerisation, redox cycling and solvent exchange have taken place. In this paper we demonstrate these possibilities for the technique by concentrating on thin layers of an electrochemically produced polymer. polybithiophene.

Neutron reflectometry (NR) studies1 of thin films of amorphous 11B/l0B on silicon indicate that a non-standard form of Fickian diffusion occurs across the boron interface upon annealing. In order to verify this observation, the samples were examined by neutron depth profiling (NDP). Comparison of the results from models of a step function, standard Fickian diffusion and Fickian diffusion with a fixed composition at the interface were made and compared to the previous NR results. The diffusion constant resulting from the non-standard Fickian model for the NDP data differs slightly from that obtained from the commonly used Fickian diffusion model and is not inconsistent with the NR results. This finding suggests that more information regarding diffusion at interfaces can be gained from these higher resolution neutron scattering techniques.

The interfacial characteristics of an oil-water-surfactant sample were studied using the thermal neutron reflectometer at the Rhode Island Nuclear Science Center (RINSC). The sample was a mixture of deuterated octane with H2O and non-ionic surfactant (C10E4), spread onto an H2O substrate. A mixture of low surfactant concentration was used so that it could demix into a lamellar oil-water structure, stabilized by a monolayer of surfactant intervening at each oil-water interface. The reflectivity data showed a clearly visible difference between 25.2° C and 30.2°C, indicating that the significant increase of interfacial tension between these two temperatures induced a structural transition.

We report neutron reflectivity data on (poly)styrene-(poly)ethylene oxide (PS-PEO) diblock copolymers adsorbed onto quartz from the selective solvent deuterated cyclohexane (a non-solvent for PEO and a poor solvent for PS). The PEO "anchor block" adsorbs strongly to form a thin layer on the quartz substrate, while the PS chains dangle into the solvent. We find that under static conditions the density profile of the PS block in a poor solvent can be well described by a Schultz function which is indicative of a polymer "mushroom." Furthermore, we have studied the same system under shear at shear rates from 0-400s-l. We find that there is a dramatic increase in the thickness of the PS layer under shear in cyclohexane and that the relaxation time from the shear-on profile back to the static profile is on the order of several days.

Neutron reflection is used to compare the swelling of two chemically end-grafted polystyrene brushes having different grafting densities exposed to a theta solvent cyclohexane and to a good solvent toluene. The relative swelling of tie brushes with a variation of solvent quality becomes smaller and the temperature dependence becomes weaker with an increase of grafting density. This type of swelling is very similar to polymer networks where an increase of cross-linking density leads to a decreased range of swelling and diminished dependence of the swelling. Our model density profile fits to the body of both brushes is parabolic in a good solvent so that some fluctuation effects, as found generally in lower density brushes, are obtained as the brush expands.

The coverage and structure of the monododecyl ethers of oligoethylene glycols, C12Em where m = 2, 4, 6 and 8, adsorbed at the air-water interface have been studied by neutron reflection. At their c.m.c.s, the area per molecule is 33 ± 3 Å2 for C12E2, 44 ± 3 Å2 for C12E4 55 ± 3 Å2 for C12E6 and 62 ± 3 Å2 for C12E8. In terms of the width of a Gaussian distribution at 1/e of its height the thicknesses of the dodecyl chains are found to be constant at 16 ± 2 Å and those of the heads to vary from 11 to 19±2Å from m = 2 to 8. There is also found to be some overlap between the two chains at the interface.

Microemulsions are isotropic mixtures of water, oil, and surfactant which self-assemble to form interfacial monolayers with a characteristic length scale on the order of hundreds of Angstroms. Small angle neutron scattering was used to determine the bulk structure of a wateroctane-C10E4 bicontinuous microemulsion. The mean curvature of the surfactant film was verified to be near zero by independently measuring the scattering contributions from the water-surfactant and oil-surfactant interfaces through hydrogen-deuterium contrast variation. The exponentially damped, oscillatory scattering length density profile of the microemulsion near a hydrophobic silicon surface was also observed with neutron reflectivity. The surface reflectivity results as well as the bulk small angle scattering measurements are explained using a simple Ginzburg-Landau theory.

The structure and morphology of titanium thin film electrodes have been investigated by neutron reflectometry. This technique yields a detailed depth profile of the scattering density, which is used to determine hydrogen and oxygen concentration profiles within the electrode. By depositing the electrode on a thick silicon crystal window, we are able to monitor the growth and dissolution of the protective oxide film covering the titanium as a function of time, electrode potential, and electrolyte composition. We find that, in 0.1 N sulfuric acid, the oxide dissolves at 0.7 A/h and is self-healing, meaning that as the oxide dissolves the metal underneath is oxidized to maintain a protective barrier. In contrast, when a -2 V cathodic bias is applied to a passive film, the oxide thins with no compensating oxide growth underneath, and the film undergoes electrochemical breakdown.

Simultaneous measurements of neutron reflectivity and prompt gamma ray emission, from samples with buried Gd layers, are shown to be of significant aid in determining the depth profile of the entire sample. Because of resonant enhancement of the neutron standing waves in the sample, the gamma ray signals are considerably enhanced making these experiments possible. A possible application of this technique to study grazing angle neutron diffraction is also mentioned.

In this study we use small angle neutron scattering to investigate the conformation of linear deuterated polystyrene chains trapped in a crosslinked protonated polystyrene matrix. The second virial coefficient was obtained as a function of crosslink density for a wide range of crosslink density. It is shown that the second virial coefficient decreases with increasing crosslink density. By extrapolating the scattering to zero concentration of the linear chain at all values of q, the single chain scattering was obtained and radius of gyration was measured the function of network density. It was found that when the network density is low (NI < Nc where NI and Nc are the number of monomer units in the linear chain and the monomer units between crosslinks, respectively) the radius of gyration does not change. As the network density increases (NI > Nc ) radius of gyration decreases. In this region the inverse of the radius of gyration varies linearly with the inverse of Nc. When the crosslink density is very high (NI » Nc ), segregation of linear polymer chains occurs. These results are in agreement with prediction and computer simulation results of polymer chain conformation in a field of random obstacles where the crosslink junctions act as the effective obstacles.

The solid-state morphology and liquid-state homogeneity of blends of high-density polyethylene (HDPE) and low-density polyethylene (LDPE) were investigated by small-angle neutron and x-ray scattering (SANS and SAXS). The solid state morphology was investigated as a function of composition and cooling rate from the melt. After slow cooling, the evidence indicated that the mixtures were either completely (HDPE-rich blends) or almost completely (LDPE-rich blends) phase separated into separate HDPE and LDPE lamellae over the whole compositional range. In contrast, for rapidly quenched blends the components are extensively co-crystallized for all concentrations, though the SANS data indicated that the branched component had a tendency to be preferentially located in the inter-lamellar regions. In the liquid state, the blends were homogenous at all compositions, showing that the solid state morphology is not determined by the melt structure, but is a function of the crystallization kinetics. Further evidence for blend homogeneity in the liquid is presented. In particular we examine the hypothesis that a phase separated mixture might give a scattering pattern similar to a homogenous blend if the domain sizes were larger that the maximum spatial resolution of the SANS experiment (D > 2π/Qmin ~ 2000Å). In this scenario, the differential scattering cross section dΣ/dΩ(Q) ~ Q-2, though phase separation decreases the cross section in this Q-range with respect to the homogenous blend. For HDPE/LDPE blends in the melt, this decrease in intensity was not observed, thus ruling out the possibility of phase separation.

Small-angle neutron scattering is used to investigate swelling effects of polystyrene in carbon tetrachloride and cis-decalin in the semidilute regime. The observed scaling exponent m where Rg2 ~ ф-m was m=0.15±0.01 both in carbon tetrachloride and in cis-decalin at T=180 C, which is much weaker than the theoretical prediction m=0.25. A review of the literature has found the scaling exponent to vary from 0.1 to 0.25. Possible causes for this variation in the observed scaling exponent are discussed.

Using neutron diffraction we studied the incorporation of small hydrophobic compounds into bilayers consisting of phosphatidylcholine (PC) and cholesterol. They were found to be localized in a narrow band at the center of the hydrocarbon region, between the two halves of the bilayer. The structures formed by introduction of the compounds are therefore intercalated structures with the long axis of the intercalated molecules lying in the plane of the bilayer. We worked with several bilayers which differed by the length of the hydrocarbon chain of the PC. The quality of the localization depended on the presence of cholesterol, the water content and the PC chain length.

As part of our work on the structure of composite materials we have been exploring the use of small-angle neutron scattering using the method of contrast variation to dissect the component form, structure and distribution. This approach has resulted in a new look at very old problemreinforcement of elastomers by carbon black.

Using this approach we studied an experimental high surface area (HSA) carbon black and a gel of "HSA-bound" rubber in cyclohexane/deuterocyclohexane mixtures. HSA in cyclohexane is found to be short rodlike particle aggregates. The aggregates have a shell-core structure with a high density graphitic outer shell and an inner core of lower density amorphous carbon. The core is continuous throughout the carbon black aggregate, making the aggregate a stiff, integral unit. Contrast variation of swollen composite gels shows that there are two length scales in the gel structure. Above 10 Å, scattering from carbon black predominates, and below 10 Å the scattering is from both carbon black and the elastomer. The HSA in the composite is completely embedded in polyisoprene. An estimate of the carbon black structure factor shows strong exclusion of neighboring aggregates, probably from excluded volume effects. The surface structure of the carbon black is unaltered by the interactions with elastomer and appears smooth over length scales above about 10 Å. These results show that contrast variation can provide information on composite structure that is not available by other means. This information relates to the reinforcement mechanism of elastomers by carbon blacks.

Using small-angle neutron scattering (SANS), we have investigated the transient alignment and relaxation under Couette shear of viscoelastic aqueous micellar solutions of cetyltrimethylarmmonium 3,5-dichlorobenzoate (CTA3,5C1) and CTA3,5C1/CTAB mixtures at concentrations well above ф* (but below 1.0 wt. %). Time constants of the order of ten's of minutes are reported for alignment and relaxation, orders of magnitude slower than any previously observed in similar micellar systems. The collective properties of the network of entangled, threadlike micelles, rather than the individual micellar segments, dominate the alignment and relaxation behavior. At low micellar surface charge density (σ) (e.g., in pure CTA3,5C1), the first observation of alignment proceeding in two stages has been made. Increasing a decreases by an order of magnitude the shear rate required to reach full alignment and provides a comparable decrease in the rate constant for relaxation after cessation of shear.