The development of neutron reflectometry as a probe of the nanoscale structure of polymer thin film systems - founded on the pioneering work of Professor Thomas P. Russell.

Among Professor Russell's numerous, original, and significant contributions to polymer science are those in which he helped pioneer the application of neutron reflectometry to the study of thin film systems. For this groundbreaking work, along with his support of neutron scattering methods in general, he was awarded the 2020 Clifford G. Shull Prize by the Neutron Scattering Society of America, named after and in honor of the Nobel Prize laureate. This article highlights some of the first applications of neutron reflectometry to probe the nanoscale structure of polymer thin film systems that Professor Russell and his colleagues pioneered. A concise account of the subsequent evolution of even more powerful phase-sensitive reflectometry techniques, following the success of their early work, is then presented. In addition to a general description of this current methodology, several particularly relevant and illustrative examples are given.

The effect of transverse wavefront width on specular neutron reflection.

In the analysis of neutron scattering measurements of condensed matter structure, it normally suffices to treat the incident and scattered neutron beams as if composed of incoherent distributions of plane waves with wavevectors of different magnitudes and directions that are taken to define an instrumental resolution. However, despite the wide-ranging applicability of this conventional treatment, there are cases, such as specular neutron reflectometry, in which the structural length scales of the scattering object require that the wavefunction of an individual neutron in the beam be described by a spatially localized packet - in particular with respect to the transverse extent of its wavefronts (i.e. normal to the packet's mean direction of propagation). It is shown in the present work that neutron diffraction patterns observed for periodic transmission phase gratings, as well as specular reflection measurements from patterned thin films with repeat units of the order of micrometres, can be accurately described by associating an individual neutron with a wave packet and treating a beam as a collection of independent packets. In these cases, accurate analysis requires that the transverse spatial extent of a neutron packet wavefront be accounted for in addition to the angular divergence of the beam that is characterized by a distribution of packet mean wavevector directions. It is shown how a measure of the effective transverse spatial extent of the neutron packet - over which its wavefronts are of sufficient uniformity to produce coherent scattering - can be determined by employing reference diffraction gratings and patterned thin films of known structure and composition.

A large beam high efficiency radio frequency neutron spin flipper.

A design for a radio frequency (RF) neutron spin flipper obtained from magneto-static and neutron spin transport simulations is presented. The RF flipper constructed from this design provides a flipping probability of 0.999 or better for a beam size 6 cm wide and 15 cm high and a wavelength band between 0.4 and 0.6 nm. Three permanent magnet guide field sections with air gaps provide a linear field gradient along the beam propagation direction over a large cross-sectional area. An RF oscillator based on coupling the resonant coil of a Hartley oscillator to the excitation coil was developed, which provides a higher current and, thereby, a larger RF amplitude, as compared to a conventional RF power amplifier. Two opaque He3 neutron spin filters were employed to measure the flipping probability of the flipper with very high precision. A spatially uniform flipping probability of 0.9995(2) or higher was measured over the large cross-sectional area neutron guide. This RF neutron spin flipper will be employed in a polychromatic beam reflectometer at the National Institute of Standards and Technology Center for Neutron Research. This design can be applied to other polarized neutron instruments or applications requiring a very high continuous flipping probability of the neutron spin for a large cross-sectional area beam.

6LiF:ZnS(Ag) Neutron Detector Performance Optimized Using Waveform Recordings and ROC Curves.

We used Gaussian separation and receiver operating characteristic (ROC) curves to optimize the neutron sensitivity and gamma rejection of an ultra-thin 6LiF:ZnS(Ag)-scintillator-based neutron detector paired with a silicon photomultiplier (SiPM). We recorded the waveforms while operating the detector in a monochromatic cold neutron beam and in the presence of isotopic 137Cs and 60Co gamma sources. We used a two-window charge comparison (CC) pulse-shape discrimination (PSD) technique to distinguish the neutron capture events from other types of signals. By feeding the recorded waveforms through variants of this algorithm, it was possible to optimize the duration of the integration windows [(0-100 ns) for the prompt window and (100-2300 ns)] for the delayed window. We then computed the detector's ROC curve from waveform recordings and compared that with the experimental performance. We also used this procedure to compare a series of detector configurations to select the optimal bias voltage for the SiPM photosensor.

Phase-sensitive neutron reflectometry measurements applied in the study of photovoltaic films.

Due to low charge carrier mobilities in polymer-based solar cells, device performance is dictated by the nanoscale morphology of the active layer components. However, their morphological details are notoriously difficult to distinguish due to the low electron contrast difference between the components. Phase-sensitive neutron reflectivity (PSNR) is uniquely suited to characterize these systems due to the large, natural scattering length density difference between two common device materials, poly(3-hexylthiophene) and [6,6]-phenyl-C61-butyric acid methyl ester (PCBM). Using PSNR we find a high concentration of PCBM at the substrate and near but not at the air interface. Herein we discuss the method of applying PSNR to polymer-based solar cells, the results obtained, and an evaluation of its effectiveness.

Analysis of multibeam data for neutron reflectivity.

We offer mathematical proof that multiple-beam neutron reflectivity, corresponding to simultaneous collection of data at multiple angles (wavevector transfers) does not perform better, errorwise for counting noise, than single-beam data collection for the same total number of reflected neutrons-and may perform much worse, depending on the beam modulation strategy used. The basic idea is that the nominal statistical benefit of summing data at, say, N different wavevector transfers is undone by needing to collect N differently modulated (i.e., weighted) sums in order to extract the reflectivities. To our knowledge, a general proof of this behavior for arbitrary strategies has been lacking. The formal result can be summarized by saying that the best nondiagonal matrix modulation strategies are orthogonal (unitary) matrices, or constant multiples thereof, and that these can do no better than diagonal--i.e., single-beam--strategies.

Statistical analysis of phase-inversion neutron specular reflectivity.

The phase-inversion approach to neutron specular reflection is elucidated in a formal setting, in order to emphasize its conceptual coherence and to facilitate study of some of its statistical properties in the context of real data. An operational notion of data degradation is introduced and illustrated with the randomizing effects of shot noise ("counting" noise) and the systematic "bias" induced by data truncation. Some basic statistical effects of phase-inversion are worked out in the new formalism and illustrated by simulated examples. A principal is advanced that phase-inversion sets the limit of available information from specular reflection.

Progress in the development of phase-sensitive neutron reflectometry methods.

It has been a number of years since phase-sensitive specular neutron reflectometry (PSNR) methods employing reference layers were first introduced to help remove the ambiguity inherent in the reconstruction of scattering length density (SLD) depth profiles (Majkrzak, C. F.; Berk, N. F. Physica B 2003, 336, 27) from specular reflectivity measurements. Although a number of scientific applications of PSNR techniques have now been successfully realized (Majkrzak, C. F.; Berk, N. F.; Perez-Salas, U. A. Langmuir 2003, 19, 7796 and references therein), in certain cases practical difficulties remain. In this article, we describe possible solutions to two specific problems: (1) the need for explicit, detailed knowledge of the SLD profile of a given reference layer of finite thickness; and (2) for a reference layer of finite thickness in which only two density variations are possible, how to identify which of two mathematical solutions corresponds to the true physical structure.

Interlayer coupling in EuS/SrS, EuS/PbSe and EuS/PbTe magnetic semiconductor superlattices.

Neutron reflectivity studies of EuS/SrS, EuS/PbSe and EuS/PbTe all-semiconductor superlattices were carried out in a search for exchange interlayer coupling. A relatively weak antiferromagnetic coupling was found in EuS/SrS and EuS/PbSe systems but no interlayer coupling was detected in EuS/PbTe superlattices. In EuS/SrS, where the SrS spacer is an insulator (E(g)≈4 eV), a very weak and short range interlayer coupling is in agreement with the earlier theoretical predictions that the interlayer coupling strength in EuS-based magnetic semiconductor superlattices depends strongly on the energy gap of the nonmagnetic layer and should decrease with an increase of the energy gap of the spacer material. A weak coupling in EuS/PbSe and no coupling in EuS/PbTe, where both PbSe and PbTe are narrow-gap semiconductors (E(g)≈0.3 eV), is in disagreement not only with the theoretical expectations but also in stark contrast with earlier results for another narrow-gap spacer system, EuS/PbS, where pronounced antiferromagnetic coupling persists even in samples with PbS layer thicknesses as large as 200 Å. A possible influence of the increasing lattice mismatch between EuS and the spacer materials (0.5%, 0.8%, 2.5% and 8.2% for PbS, SrS, PbSe and PbTe, respectively) on the magnetic ordering of the EuS layer near the interfaces and, consequently, on the interlayer coupling is discussed.

The use of symmetry to correct Larmor phase aberrations in spin echo scattering angle measurement.

Spin echo scattering angle measurement (SESAME) is a sensitive interference technique for measuring neutron diffraction. The method uses waveplates or birefringent prisms to produce a phase separation (the Larmor phase) between the "up" and "down" spin components of a neutron wavefunction that is initially prepared in a state that is a linear combination of in-phase up and down components. For neutrons, uniformly birefringent optical elements can be constructed from closed solenoids with appropriately shaped cross sections. Such elements are inconvenient in practice, however, both because of the precision they demand in the control of magnetic fields outside the elements and because of the amount of material required in the neutron beam. In this paper, we explore a different option in which triangular-cross-section solenoids used to create magnetic fields for SESAME have gaps in one face, allowing the lines of magnetic flux to "leak out" of the solenoid. Although the resulting field inhomogeneity produces aberrations in the Larmor phase, the symmetry of the solenoid gaps causes the aberrations produced by neighboring pairs of triangular solenoids to cancel to a significant extent. The overall symmetry of the SESAME apparatus leads to further cancellations of aberrations, providing an architecture that is easy to construct and robust in performance.

Pinpointing chiral structures with front-back polarized neutron reflectometry.

A new development in spin-polarized neutron reflectometry enables us to more fully characterize the nucleation and growth of buried domain walls in layered magnetic materials. We applied this technique to a thin-film exchange-spring magnet. After first measuring the reflectivity with the neutrons striking the front, we measure with the neutrons striking the back. Simultaneous fits are sensitive to the presence of spiral spin structures. The technique reveals previously unresolved features of field-dependent domain walls in exchange-spring systems and has sufficient generality to apply to a variety of magnetic systems.

Two-stage magnetization reversal in exchange biased bilayers.

MnF(2)/Fe bilayers exhibit asymmetric magnetization reversal that occurs by coherent rotation on one side of the loop and by nucleation and propagation of domain walls on the other side of the loop. Here, we show by polarized neutron reflectometry, magnetization, and magnetotransport measurements that for samples with good crystalline "quality" the rotation is a two-stage process, due to coherent rotation to a stable state perpendicular to the cooling field direction. The result is remarkably asymmetrically shaped hysteresis loops.

Hydration state of single cytochrome c monolayers on soft interfaces via neutron interferometry.

Yeast cytochrome c (YCC) can be covalently tethered to, and thereby vectorially oriented on, the soft surface of a mixed endgroup (e.g., -CH3/-SH = 6:1, or -OH/-SH = 6:1) organic self-assembled monolayer (SAM) chemisorbed on the surface of a silicon substrate utilizing a disulfide linkage between its unique surface cysteine residue and a thiol endgroup. Neutron reflectivities from such monolayers of YCC on Fe/Si or Fe/Au/Si multilayer substrates with H2O versus D2O hydrating the protein monolayer at 88% relative humidity for the nonpolar SAM (-CH3/-SH = 6:1 mixed endgroups) surface and 81% for the uncharged-polar SAM (-OH/-SH = 6:1mixed endgroups) surface were collected on the NG1 reflectometer at NIST. These data were analyzed using a new interferometric phasing method employing the neutron scattering contrast between the Si and Fe layers in a single reference multilayer structure and a constrained refinement approach utilizing the finite extent of the gradient of the profile structures for the systems. This provided the water distribution profiles for the two tethered protein monolayers consistent with their electron density profile determined previously via x-ray interferometry (Chupa et al., 1994).

First-principles determination of hybrid bilayer membrane structure by phase-sensitive neutron reflectometry.

The application of a new, phase-sensitive neutron reflectometry method to reveal the compositional depth profiles of biomimetic membranes is reported. Determination of the complex reflection amplitude allows the related scattering length density (SLD) profile to be obtained by a first-principles inversion without the need for fitting or adjustable parameters. The SLD profile so obtained is unique for most membranes and can therefore be directly compared with the SLD profile corresponding to the chemical compositional profile of the film, as predicted, for example, by a molecular dynamics simulation. Knowledge of the real part of the reflection amplitude, in addition to enabling the inversion, makes it possible to assign a spatial resolution to the profile for a given range of wavevector transfer over which the reflectivity data are collected. Furthermore, the imaginary part of the reflection amplitude can be used as a sensitive diagnostic tool for recognizing the existence of certain in-plane inhomogeneities in the sample. Measurements demonstrating the practical realization of this phase-sensitive technique were performed on a hybrid bilayer membrane (self-assembled monolayer of thiahexa (ethylene oxide) alkane on gold and a phospholipid layer) in intimate contact with an aqueous reservoir. Analysis of the experimental results shows that accurate compositional depth profiles can now be obtained with a spatial resolution in the subnanometer range, primarily limited by the background originating from the reservoir and the roughness of the film's supporting substrate.

Hybrid bilayer membranes in air and water: infrared spectroscopy and neutron reflectivity studies.

In this report we describe the fabrication and characterization of a phospholipid/alkanethiol hybrid bilayer membrane in air. The bilayer is formed by the interaction of phospholipid with the hydrophobic surface of a self-assembled alkanethiol monolayer on gold. We have characterized the resulting hybrid bilayer membrane in air using atomic force microscopy, spectroscopic ellipsometry, and reflection-absorption infrared spectroscopy. These analyses indicate that the phospholipid added is one monolayer thick, is continuous, and exhibits molecular order which is similar to that observed for phospholipid/phospholipid model membranes. The hybrid bilayer prepared in air has also been re-introduced to water and characterized using neutron reflectivity and impedance spectroscopy. Impedance data indicate that when moved from air to water, hybrid bilayers exhibit a dielectric constant and thickness that is essentially equivalent to hybrid bilayers prepared in situ by adding phospholipid vesicles to alkanethiol monolayers in water. Neutron scattering from these samples was collected out to a wave vector transfer of 0.25 A(-1), and provided a sensitivity to changes in total layer thickness on the order of 1-2 A. The data confirm that the acyl chain region of the phospholipid layer is consistent with that observed for phospholipid-phospholipid bilayers, but suggest greater hydration of the phospholipid headgroups of HBMs than has been reported in studies of lipid multilayers.

Neutron and X-ray reflectivity studies of human serum albumin adsorption onto functionalized surfaces of self-assembled monolayers.

Neutron and X-ray reflectivity (NR and XR) have been widely used for the investigation of the structure of thin organic films. Here we demonstrate how these sensitive techniques may be applied to the study of protein adsorption to well-characterized self-assembled monolayers (SAMs) with different chemical functionalities. NR can be used for in situ study, while XR provides complementary information on the initial surfaces and dried layers measured in air after protein has been adsorbed. In situ measurements of adsorption of human serum albumin onto a hydrophilic NH2-terminated monolayer clearly show the presence of a thin layer of adsorbed protein next to the SAM. Adsorption of albumin onto a hydrophobic, deuterated, CD3-terminated SAM causes even bigger changes in the NR. Upon replacing the protein solution with protein-free buffer solution, the reflectivities from both kinds of monolayers do not change, demonstrating that the albumin adsorption is irreversible after several hours of contact with the protein solution. X-ray reflectivity measurements of dried substrates performed ex situ in air provide a lower bound estimate of the amount of protein which must be at the interface in situ. This combination of techniques provides a uniquely sensitive approach for studying changes that occur upon protein adsorption at an interface.

Neutron reflectivity studies of single lipid bilayers supported on planar substrates.

Neutron reflectivity was used to probe the structure of single phosphatidylcholine (PC) lipid bilayers adsorbed onto a planar silicon surface in an aqueous environment. Fluctuations in the neutron scattering length density profiles perpendicular to the silicon/water interface were determined for different lipids as a function of the hydrocarbon chain length. The lipids were studied in both the gel and liquid crystalline phases by monitoring changes in the specularly-reflected neutron intensity as a function of temperature. Contrast variation of the neutron scattering length density was applied to both the lipid and the solvent. Scattering length density profiles were determined using both model-independent and model-dependent fitting methods. During the reflectivity measurements, a novel experimental set-up was implemented to decrease the incoherent background scattering due to the solvent. Thus, the reflectivity was measured to Q approximately 0.3 A-1, covering up to seven orders of magnitude in reflected intensity, for PC bilayers in D2O and silicon-matched (38% D2O/62% H2O) water. The kinetics of lipid adsorption at the silicon/water interface were also explored by observing changes in the reflectivity at low Q values under silicon-matched water conditions.

Neutron Reflectivity and Grazing Angle Diffraction.

Over the last 10 years, neutron reflectivity has emerged as a powerful technique for the investigation of surface and interfacial phenomena in many different fields. In this paper, a short review of some of the work on neutron reflectivity and grazing-angle diffraction as well as a description of the current and planned neutron rcflectometers at NIST is presented. Specific examples of the characterization of magnetic, superconducting, and polymeric surfaces and interfaces are included.