Structural evidence of charge renormalization in semi-dilute solutions of highly charged polyelectrolytes

We show experimentally that Manning counterion condensation also leads to a renormalization of the charge density at high concentrations of highly charged, flexible, hydrophilic polyelectrolytes. Investigations by small angle neutron and X-ray scattering of semi-dilute solutions of poly(acrylamide-co-sodium-2-acrylamido-2-methylpropane sulfonate) at different charge densities above the condensation threshold, show that the scattering function is invariant with the charge density. Received 16 June 1998     

Structure of polymer micelles close to the solid interface

Block copolymers are widely used in industry. For scientific interests their aqueous solutions offer a model system for the investigation of crystallisation as the macromolecules agglomerate for elevated concentrations into micelles, which crystallise when a critical volume fraction is reached. We report on grazing incidence small angle neutron scattering (GISANS) or near surface small angle neutron scattering (NS-SANS) as an experimental tool to investigate the micelle crystallisation close to interfaces with different chemical termination. We find that in general crystallization is suppressed at a repulsive surface and favoured at an attractive one. Furthermore we show that the crystallization close the interface can be controlled by the micelle stability, resulting from the different composition and length of the monomers. The effect of the interface is found more important for a high micelle stability, whereas for a low stability it is shadowed by adsorbed monomers.     

Small angle neutron scattering at very high time resolution: Principle and simulations of ‘TISANE’

The time resolution of SANS experiments is generally limited by frame overlap to some ms. We report on a new time-resolved stroboscopic SANS method, called TISANE, offering μs time resolution without a major sacrifice in intensity by making use of very large frame overlap. We may explore a new field in neutron scattering and complement the emerging field of time resolved small angle X-ray scattering. Here we discuss the principle of TISANE, its mathematical treatment and its limitations.     

Effective long-range attraction between protein molecules in solutions studied by small angle neutron scattering

Small angle neutron scattering intensity distributions taken from cytochrome C and lysozyme protein solutions show a rising intensity at a very small wave vector Q, which can be interpreted in terms of the presence of a weak long-range attraction between protein molecules. This interaction has a range several times that of the diameter of the protein molecule, much greater than the range of the screened electrostatic repulsion. We show evidence that this long-range attraction is closely related to the type of anion present and ion concentration in the solution.     

Optimum and standard beam widths for numerical modeling of interface scattering problems

Gaussian beams provide a useful insonifying field for surface or interface scattering problems such as encountered in electromagnetics, acoustics and seismology. Gaussian beams have these advantages: (i) They give a finite size for the scattering region on the interface. (ii) The incident energy is restricted to a small range of grazing angles. (iii) They do not have side lobes. (iv) They have a convenient mathematical expression. The major disadvantages are: (i) Insonification of an interface is nonuniform. The scattered field will depend on the location of the scatterers within the beam. (ii) The beams spread, so that propagation becomes an integral component of the scattering problem. A standard beam parameterization is proposed which keeps propagation effects uniform among various models so that the effects of scattering only can be compared. In continuous wave problems, for a given angle of incidence and incident amplitude threshold, there will be an optimum Gaussian beam which keeps the insonified area as small as possible. For numerical solutions of pulse beams, these standard parameters provide an estimate of the smallest truncated domain necessary for a physically meaningful result.     

Development of a tuneable channel cut crystal

We have developed the first tuneable channel cut crystal for ultra small angle neutron scattering and neutron optical experiments. The Darwin range of a perfect crystal can be reduced down to a fraction of its natural width. This “Darwin reduction” was realised without any change of the beam geometry which yields an intensity gain relative to conventional asymmetric Bragg diffraction. With such tuneable channel cut crystal peaks nearly δ-peaks can experimentally be realised.     

Probing How Counterion Structure and Dynamics Determine Polyelectrolyte Solutions Using EPR Spectroscopy

In this review article, we describe how methods of electron paramagnetic resonance (EPR) spectroscopy were used to investigate polyion–counterion interactions in polyelectrolyte solutions. This subject is usually treated experimentally by light, X-ray, or neutron scattering techniques. It is shown that a large arsenal of EPR spectroscopic methods–from various sophisticated methods of line shape analysis of continuous-wave EPR, via electron spin echo envelope modulation, nanoscale distance measurements through double electron–electron resonance to high-field pulse EPR–can be used to characterize the intrinsically complicated structures formed in polyelectrolyte solutions. We show that even polymer physical models such as scaling relations can be tested in this way. The distinguishing feature with respect to the numerous scattering studies in this area is that EPR techniques are local methods, and by employing spin-carrying (i.e., EPR-active) probe ions, it is possible to examine polyelectrolytes from the counterions’ point of view.     

The SSA+ for scattering from dielectric surfaces at very low grazing angles

Previously we developed a practical model for scattering from randomly-rough surfaces at very low grazing angles for the Dirichlet problem which was found to give good numerical results. In this paper, we derive the expression for the bistatic scattering cross-section for the non-local small slope approximation for dielectric interfaces. We then extend our practical model to dielectric surfaces based on this result. We discuss numerical results for scattering at low forward grazing angles for a Gaussian roughness spectrum with an angle of incidence of 80^○.     

Structural properties of charged diblock copolymer solutions

Aqueous micellar solutions of ionic/neutral block copolymers have been studied by light scattering, small angle neutron scattering and small angle X-ray scattering. We made use of a polymer comprised of a short hydrophobic block (polyethylene-propylene) PEP and of a long polyelectrolytic block (polystyrene-sulfonate) PSSNa which has been shown previously to micellize in water. The apparent polydispersity of these micelles is studied in detail, showing the existence of a few large aggregates coexisting with the population of micelles. Solutions of micelles are found to order above some threshold in polymer concentration. The order is liquid-like, as demonstrated by the evolution with concentration of the peak observed in the structure factor (), and the degree of order is found to be identical over a large range of concentrations (up to 20 wt%). Consistent values of the aggregation number of the micelles are found by independent methods. The effect of salt addition on the order is found to be weak. Received: 19 June 1997 / Received in final form: 4 September 1997 / Accepted: 9 October 1997     

Form-factors for different aggregation models of micelles

Spherical micelles in ionic micellar solutions, often aggregate to form spherical, cylindrical or chain-like aggregates on addition of salt to the solution. It is known that the technique of small angle neutron scattering (SANS) can be used to distinguish spherical and cylindrical aggregates. To examine if SANS can be used to distinguish the latter two aggregation processes, we have calculated the angular distribution of scattered neutrons from 0.002 M CTAB solutions. These calculations show that aggregation of CTAB micelles results in large changes in SANS spectra. The shapes of SANS spectra are different for the above three types of aggregates, suggesting that technique of SANS can indeed be used to distinguish the three aggregation processes. The size of the aggregate can also be obtained from such studies.     

Polarized He neutron spin filter program at the JCNS

Polarized neutron instruments will occupy about 80% of the Jülich Centre for Neutron Science (JCNS) instrument park. A successful polarized ³He program will be integral to many of these instruments. We have been focusing the developments on spin-exchange optical pumping (SEOP) to polarize the ³He gas in situ. Where possible, in situ polarization using the SEOP method will provide higher time averaged performance of the instruments. Further this allows a custom-built and independent source of polarized ³He to be developed optimized for each instruments demands. In this paper we will: present an argument for the advantages of in situ polarization; describe an in situ polarizer we have constructed, and initial tests of its performance; describe testing of polarization analysis for small angle neutron scattering on biological samples, and our plans for an in situ polarizer for this application.     

A model of magnetic inhomogeneous structure for Fe-Ni invar alloys

The magnetic inhomogeneous structure revealed by neutron small angle scattering for Fe-Ni Invar alloys can be interpreted in terms of a model in which an effective local concentration of Fe for each atom within a sphere is taken into account in order to determine the magnetic moment of the atom.     

On the influence of anisotropy on the magnetic small-angle neutron scattering of superparamagnetic particles

This paper presents a calculation of the magnetic small-angle neutron scattering cross-section resulting from a dilute ensemble of superparamagnetic particles exhibiting uniaxial magnetic anisotropy. We focus on the two experimentally relevant scattering geometries in which the incident neutron beam is perpendicular or parallel to an applied magnetic field, and we discuss several orientations of the anisotropy axes with respect to the field. Magnetic anisotropy has no influence on the magnetic small-angle neutron scattering when the particles are mobile, as is the case e.g. in ferrofluids, but, when the particles are embedded in a rigid non-magnetic matrix and the orientations of the anisotropy axes are fixed, significant deviations compared to the case of negligible anisotropy are expected. For the particluar situation in which the anisotropy axes are parallel to the applied field, closed-form expressions suggest that an effective anisotropy energy or anisotropy-energy distribution can be determined from experimental scattering data. Received 8 November 2001     

Homogeneous and inhomogenous polyacrylamide gels as observed by small angle neutron scattering: A connection with elastic properties

Small angle neutron scattering of polyacrylamide solutions and gels is presented for different polymer and cross link concentrations. The gels are analyzed in connection with their elastic properties. For less than 11% of polymer concentration and for small cross link contents , it was found that the gels are no more heterogeneous than the solutions. This corresponds to the range of where the elastic modulus increases with . For larger cross link contents when the elastic modulus decreases if increases, the sample appears to be strongly heterogeneous with a large size distribution of the inhomogeneities. The results are compared with the recent model of Oshmyan and Benguigui of the elastic properties of the polyacrylamide gels. Thus a relation can be proposed between the observation of the inhomogeneities by scattering and the mechanical properties Received 30 December 1997 and Received in final form 26 June 1998     

Region of validity of perturbation theory for dielectrics and finite conductors

We present a study of region of validity of first-order perturbation theory applied to rough surface scattering. The scattering problem is solved numerically for the case of periodic surface or gratings varying in one dimension. Scattering of electromagnetic waves from an ensemble of gratings of sufficiently long period will give a good approximation to the case of an infinite rough surface. We use this to test the validity of the first-order perturbation theory. Use of an infinite periodic surface allows us to give results for a range of angle of incidence covering those representing a low grazing angle, near 90° from the mean surface normal. We consider the case for perfect dielectrics and finite conductors. The real and imaginary parts of the refractive index used were limited to less than three due to the numerical instability of the numerical calculation method involved. We find that for perfect dielectrics the first-order small perturbation theory remains for TE polarization valid for all incidence angles, while for TM polarization it seems to fail if the incidence angle approaches the Brewster angle.     

Dynamics of water in real space and time

Owing to marked advances in instrumentation in X-ray and neutron scattering the time-dependent pair correlation function, the Van Hove function, can now be determined by inelastic X-ray and neutron scattering measurements. The local dynamics of water in real space and time is visualised by this approach. We discuss how the dynamic properties, such as viscosity and diffusion, can be elucidated through the Van Hove function of water.     

Magnetic filaments in resistive manganites

The magnetic phase separation in single crystals of the Pr0.67Ca0.33MnO3 manganites is studied using polarized small angle neutron scattering. The measured spectra give a fractal dimension consistent with a configuration in ferromagnetic filaments of nanometric diameter. We argue here that localized charge carriers hop in a random walk fashion mediating a ferromagnetic "hopping exchange" which coexists with superexchange to create the filamentary phase separation. The arguments for this physical picture are validated by Monte Carlo simulations, where magnetism and transport are treated in a self-consistent manner.     

A neutron resonance spin echo spectrometer for quasi-elastic and inelastic scattering

We propose a modified neutron spin echo (NSE) spectrometer using high frequency spin flippers to replace the static spin flipper and the long magnetic precession field in each arm of the classicalspin echo setup. The spectrometer is suitable for quasi-elastic as well as inelastic scattering and can work with an arbitrary magnetic field on the sample. The restrictions on sample size and scattering angle can be relaxed, in comparison with the classical NSE method.     

The application of quasi-elastic neutron scattering techniques (QENS) in surface diffusion studies

Neutron scattering techniques such as quasi-elastic neutron scattering, QENS, have proven to be well-suited tools for studying structure and dynamics of surface adsorbed molecules. In contrast to many more widely used surface science techniques neutron scattering allows the microscopic characterization of samples under a wide range of thermodynamic conditions, as the samples are not constrained to ultra high vacuum environment. Moreover, neutron scattering allows the separation of coherent and incoherent scattering, giving access to different diffusive mechanisms such as single particle diffusion, mass transport, rotations, or vibrations. In this paper we will review recent progress and the state-of-the-art in neutron scattering experiments on surface adsorbed molecules in the sub-monolayer coverage range with a specific emphasis on studies of carbon and other high surface density substrates. We will also cover recent progress in theoretical modeling, since the usefulness of neutron scattering data on surface dynamics can be strongly enhanced by computational modeling, such as molecular dynamics (MD) simulations and the development of analytical models.