Norman F. Berk

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 films supporting substrate.

Phase determination and inversion in specular neutron reflectometry

Abstract We present results testing the experimental feasibility of recently discovered solutions of the dynamical phase problem for specular reflection. Using layers of Cu, Ni, and Mo as references, the real and imaginary parts of the complex reflection amplitude were measured from neutron reflectivities for an asymmetric composite film consisting of deuterated polystyrene and Si. The reflection amplitude was also measured from neutron reflectivity without references for a symmetric deuterated polystyrene film. These amplitudes were inverted using the Gel’fand–Levitan–Marchenko equation to produce scattering length density profiles for the films studied. The inverted profiles compared reasonably well to the expected potentials. We conclude that such methods are practical with current instrumentation.

Determination of the Effective Transverse Coherence of the Neutron Wave Packet as Employed in Reflectivity Investigations of Condensed-Matter Structures. I. Measurements

The primary purpose of this investigation is to determine the effective coherent extent of the neutron wave packet transverse to its mean propagation vector k, when it is prepared in a typical instrument used to study the structure of materials in thin film form via specular reflection. There are two principal reasons for doing so. One has to do with the fundamental physical interest in the characteristics of a free neutron as a quantum object while the other is of a more practical nature, relating to the understanding of how to interpret elastic scattering data when the neutron is employed as a probe of condensed matter structure on an atomic or nanometer scale. Knowing such a basic physical characteristic as the neutrons effective transverse coherence can dictate how to properly analyze specular reflectivity data obtained for material film structures possessing some amount of in-plane inhomogeneity. In this study we describe a means of measuring the effective transverse coherence length of the neutron wave packet by specular reflection from a series of diffraction gratings of different spacings. Complementary non-specular measurements of the widths of grating reflections were also performed which corroborate the specular results. (Part I principally describes measurements interpreted according to the theoretical picture presented in Part II.) Each grating was fabricated by lift-off photo-lithography patterning of a nickel film (approximately 1000 Angstroms thick) formed by physical vapor deposition on a flat silicon crystal surface. The grating periods ranged from 10 microns (5 microns Ni stripe, 5 microns intervening space) to several hundred microns. The transverse coherence length, modeled as the width of the wave packet, was determined from an analysis of the specular reflectivity curves of the set of gratings.

Experimental demonstration of phase determination in neutron reflectometry by variation of the surrounding media

Abstract We have recently shown that it is possible to unambiguously determine the real part of the complex reflection coefficient for a thin film structure by measuring the neutron specular reflectivities for the film in contact with two different backing or two different fronting media, thus simplifying the reference methodology of phase determination and making it more practical. Here we demonstrate the technique in two different experiments. In the first, one backing medium is air, the other, heavy water. In the second, sapphire and silicon serve as two different fronting (incident) media. In addition, we show how the two possible branches of the imaginary part of the reflection coefficient inferred by the real part, while not required for inverting the data to find the film structure, can be a sensitive diagnostic for indicating whether the film of interest is inhomogeneous on a transverse scale comparable to the neutron coherence length. This is especially important in avoiding misinterpretation of data which result from the incoherent average of reflectivities from large-scale heterogeneities.

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).

USING POLARIZED NEUTRONS TO DETERMINE THE PHASE OF REFLECTION FROM THIN FILM STRUCTURES

Abstract It is now known that the phase of neutron specular reflection from a flat film structure can be determined exactly using reference layers, even in the dynamical regime at small wavevector transfer where the Born approximation is not valid. By employing a single buried ferromagnetic layer and polarized beams, two complex reflection amplitudes for the unknown part of the film can be algebraically extracted, only one of which is physical. We describe here a means of identifying the physical branch for actual polymer film data which fits the true reflection amplitude and produces the films scattering length density profile directly and unambiguously.

Neutron reflectometry at the NCNR

Abstract For more than a decade, neutron reflectometry has been an active part of the research program at NIST and, over the years, a broad range of experiments have been performed on polymeric, magnetic, superconducting, and biomimetic thin film systems. Some examples include studies of diblock copolymer lamellar ordering [1], the magnetic coupling in “Giant Magneto-Resistance” and other multilayers [2,3], the structure of Langmuir-Blodgett films [4], the corrosion of electrode surfaces [5], the oxide layers of semiconductor surfaces, the absorption of macromolecules by biomimetic bilayers, and grazing angle diffraction experiments with polarized neutrons [6].

Inverting neutron reflectivity from layered film structures using polarized beams

Abstract It has recently been discovered that the phase of neutrons specularly reflected from a film structure can be determined exactly, even in the dynamical scattering region at small wave vector transfer, by using polarized beams and a buried magnetic reference layer. This is possible for both magnetic and nonmagnetic material films of interest. Given the reflection amplitude as a function of wave vector transfer, the scattering potential can be uniquely obtained by direct inversion, without resort to fitting. A review of some of the theory is presented, and new experimental results are reported.

When beauty is only skin deep; optimizing the sensitivity of specular neutron reflectivity for probing structure beneath the surface of thin films

Specular neutron reflectometry has become an established probe of the nanometer scale structure of materials in thin film and multilayered form. It has contributed especially to our understanding of soft condensed matter of interest in polymer science, organic chemistry, and biology and of magnetic hard condensed matter systems. In this paper we examine a number of key factors which have emerged that can limit the sensitivity of neutron reflection as such a probe. Among these is loss of phase information, and we discuss how knowledge about material surrounding a film of interest can be applied to help resolve the problem. In this context we also consider what role the quantum phenomenon of interaction-free measurement might play in enhancing the statistical efficiency for obtaining reflectivity or transmission data.

Phase sensitive reflectometry and the unambiguous determination of scattering length density profiles

Exact methods for determining the complex neutron reflection amplitude for a thin film, which make use of multiple measurements of the specularly reflected intensities of composite systems, composed of the film adjacent to a reference layer and/or surrounding media, have been developed over the past several years. These techniques are valid even where the Born or distorted wave Born approximations break down. Thus, given both the modulus and phase of the specular reflection, a first-principles inversion can be performed which yields the scattering length density (SLD) depth profile of the film directly. Ideally, if the reflection amplitude is known for all wave vector transfers Q, the associated SLD profile is unique. Applying the aforementioned methods to a purely real SLD profile, which, effectively, is almost always that encountered in neutron reflection, at least two distinct reflectivity curves, corresponding to two different composite film systems, are required to determine the phase by direct algebraic computation, independently at each value of Q. Each of the composite systems consists of the common unknown part of the film plus a different reference layer segment and/or surrounding medium (e.g., the backing). Recently, investigations of certain classes of SLD profiles have been reported in the literature which examine whether a single X-ray reflectivity curve, given certain a priori knowledge about the system, i.e., about known parts of the film SLD and/or substrate, suffices to reconstruct the phase. Employing the exact formulation of phase sensitive reflectometry, we consider several illustrative and realistic cases in which a minimum of two reflectivity curves are required to distinguish the true SLD profile.