Spin-echo Small-angle Neutron Scattering Research Articles

Milk Gelation Studied with Small Angle Neutron Scattering Techniques and Monte Carlo Simulations

The sol-gel transition of fat-free milk by acidification was studied with neutron scattering experiments and Monte Carlo simulations. Spin-echo small angle neutron scattering (SESANS) and ultrasmall angle neutron scattering (USANS) experiments were performed to measure the static structure of milk and yogurt, as well as the aggregation kinetics. Colloidal gelation was simulated from a reaction limited domain (RLCA) to the diffusion limited regime (DLCA) as cluster-cluster aggregation of adhesive, hard spheres on a three-dimensional lattice. Comparisons were drawn between experimental and numerical correlation functions. Milk was modeled as a suspension of casein micelles in water, and its structure was described with a dilute system of solid spheres with a log-normal distribution of sizes. The structure and formation of yogurt were described with a self-affine model, used for systems containing heterogeneities with a wide range of sizes. Simulation speed was increased by 1 order-of-magnitude using a new algorithm to eliminate dead time. Observations by SESANS and USANS of milk particle sizes and yogurt length scales were consistent and agreed well with literature. Kinetic USANS data yielded reliable information about the growth of typical length scale during aggregation. The simulation model predicted the measurement data qualitatively best staying close to the RLCA regime until large structures had formed. Correlation lengths were in good quantitative agreement, but longest simulated length scales were a of factor 2(1)/(2) below experimental findings. We conclude that small, mobile aggregates are formed during the first 3 h, mostly influencing the dimensionality of the system and that large, inert structures are formed from 2 up to 8 h, which determine the typical length scale.

A Monte Carlo algorithm for computing spin echo small angle neutron scattering correlation functions in real space: Hard sphere liquids

A Monte Carlo algorithm is developed to compute the autocorrelation function of liquids and the corresponding spatial correlation function from spin echo small angle neutron scattering (SESANS) spectra. The accuracy of the simulation algorithm is tested with isolated hard spheres and single dumbbells consisting of two hard spheres separated by a given distance. The simulation results accurately reproduce the exact expressions of these two models. To further test the algorithm for many-body systems, two liquid models are considered including hard sphere fluids and hard spheres with an attractive tail. The many-particle Monte Carlo simulation is carried out to obtain the ensemble average of these correlation functions. Meanwhile, the Percus-Yevic (PY) integral equation theory is resorted to compute the autocorrelation function and SESANS spatial correlation function for a density that the PY theory is reasonably applicable. The agreement between simulation and theory indicates that the algorithm is quite robust and can be extended to more complex fluids in the future. Furthermore, we find that the SESANS spatial correlation function is highly sensitive to the interaction potential between particles, which may serve as a useful tool to explore particle interactions in a liquid.

Spatial modulation of a neutron beam by Larmor precession

Abstract We modulated the intensity of a neutron beam using Larmor precession techniques. We simulated triangular coils by using magnetised foils in electromagnets with rectangular pole shoes. Reversing the orientation of two of the magnetised foils in the spin-echo small-angle neutron scattering (SESANS)-instrument in Delft and changing the field settings was sufficient to obtain a modulation with a period in the order of 1 mm. We expect to be able to go to a modulation with a period of 20 μ m . This technique can be used to measure small-angle neutron scattering, analogous to the method used in SESANS, but with the advantage that all the manipulation of the neutron spin occurs before the sample. This means that the technique is insensitive to magnetic perturbations at the sample position. By positioning several of these devices after each other it will be possible to obtain a sharper modulation, or a modulation in two directions.

Real-Space Neutron Scattering without Collimation: SESANS at the Delft University of Technology

Spin-echo small-angle neutron scattering (SESANS) is a real-space [1] scattering technique that does not need any collimation to obtain high resolution. In this article, we present the SESANS instrument at the Delft University of Technology [2], which measures microstructures on length scales between 20 nm and 20 μm. In order to discuss the technical issues with the choice of precession devices, we will present the principle in this article in reciprocal space. We have applied the technique to a wide variety of samples, amongst which are colloidal phase transitions [3] and aggregation processes in dairy products [4]. In this article we show two other examples: artificial lattices [5] and cream cheese [6].

Analysis of spin-echo small-angle neutron scattering measurements

Spin-echo small-angle neutron scattering (SESANS) is, in contrast to conventional small-angle neutron scattering (SANS), a real-space technique. SESANS measures the projection of the density–density correlation function of a sample, rather than, as in SANS, its Fourier transform. This paper introduces a toolkit for interpretion and analysis of a SESANS measurement. Models that are used in SANS are discussed and translated into a SESANS formalism. These models can be used to analyse and fit the data obtained by SESANS. Dilute, concentrated, random, fractal and anisotropic density distributions are considered. Numerical methods used to calculate the projection from numerical data are presented, either by using Fourier transformation orviathe real-space pair correlation function.

Structure in cohesive powders studied with spin-echo small angle neutron scattering

Extracting structure and ordering information from the bulk of granular materials is a challenging task. Here we present Spin-Echo Small Angle Neutron Scattering Measurements in combination with computer simulations on a fine powder of silica, before and after uniaxial compression. The cohesive powder packing is modeled by using molecular dynamics simulations and the structure, in terms of the density–density correlation function, is calculated from the simulation and compared with experiment. In the dense case, both quantitative and qualitative agreement between measurement and simulations is observed, thus creating the desired link between experiment and computer simulation. Further simulations with appropriate attractive potentials and adequate preparation procedures are needed in order to capture the very loose-packed cohesive powders.

Structure, anisotropy and fractals in compressed cohesive powders

Correlation functions are commonly used to characterise the microstructure of materials. The correlation function is then related to other properties or phenomenology connected to the investigated material. In this paper, we investigate the bulk microstructure in two cohesive powders — a silica powder containing spherical grains and a carbon nanotube powder, by means of Spin-echo Small-angle Neutron Scattering technique. We show that, for the silica powder, the typical size of the heterogeneities decreases with increasing strain, thus linking microscopic deformations with the macroscopic ones. Measurements also show that the compressed silica powder is isotropic in terms of its density distribution. On the compressed nanotube powder we are able to conclude that the applied uniaxial stress induces anisotropy in the density distribution. We are able to link the compressive strain with the measured anisotropy, thus creating the link between macroscopic and microscopic behaviours. Both powders are shown to have a fractal structure, and are characterised in terms of a fractal dimension.

Microfabricated silicon gratings as neutron-optical components

Microfabricated silicon gratings provide unique test procedures for instruments in neutron scattering and the interpretation of experimental data. Ultra-Small Angle Neutron Scattering (USANS) is currently becoming an effective technique for the analysis of structures in the micrometer range. A series of one-dimensional silicon gratings was fabricated using a highly anisotropic ion etching technique (RIE) and measured at the USANS instrument S18 at ILL, Grenoble. The scattering patterns show up to 17 orders of diffraction, grating parameters derived from these data are in good agreement with the nominal values. Scattering length density correlation functions calculated from the USANS data are compared to Spin Echo SANS (SESANS) correlation functions measured at the Delft University of Technology, demonstrating the complementarity of the two scattering methods.

Analysis of artificial silicon microstructures by ultra-small-angle and spin-echo small-angle neutron scattering

Ultra-Small-Angle Neutron Scattering (USANS) is currently becoming an effective technique for the analysis of structures in the micrometer range. The new Spin-Echo SANS (SESANS) method measures a signal in real space. In both cases microfabricated silicon gratings provide unique test procedures for the related devices and interpretations of the experimental data. A series of one-dimensional gratings was fabricated using a highly anisotropic ion etching technique (RIE) and measured at the USANS instrument S18 at ILL, Grenoble. Grating parameters derived from the experimental data are in agreement with the nominal values. Scattering length density correlation functions calculated from the USANS data are compared to SESANS correlation functions measured at the Delft University of Technology, demonstrating the reciprocity of the two scattering methods. Reconstruction techniques for one-dimensional scattering length density distributions are applied to the USANS data. The results are in good agreement with SEM micrographs of the samples.

Probing the droplet cluster structure in acidified temperature‐cycled o/w emulsion gels by means of SESANS†

SummaryThe structure of the emulsion droplet aggregates in whey‐protein‐stabilised oil‐in‐water (o/w) model emulsion gels was investigated using the novel spin‐echo small‐angle neutron scattering (SESANS) technique. This technique allows the assessment of the droplet cluster structure in an emulsion gel in terms of a density correlation function at relatively long length scales (∼100 nm–10 µm) compared with regular SANS. As an example, the effect of one/two homogenisation stages on emulsion droplet cluster structure was studied in relation to acidification and temperature cycling. It is found that temperature cycling and acidification induce bigger changes in emulsion droplet cluster structure than the application of one or two homogenisation stages, and the results are compared with droplet size measurements (by pfg‐NMR), firmness measurements and confocal microscopic images.

Spin-echo small-angle neutron scattering study of the domain structure of an Ni layer on a Cu substrate

Spin-echo small-angle neutron scattering (SESANS) is used to study the magnetic domain structure of an Ni layer electrodeposited onto a Cu substrate. The domain structure of the sample corresponds to the hard-plane model, where the magnetization in the domains is directed perpendicular to the layer; the domain length coincides with the thickness of the layer of the order of 10 µm and its width is of the order of 1 µm. The pair correlation function of the magnetization has been directly measured. It is established that the width of the domain depends linearly on its thickness. The domain structure does not depend on heating at temperatures below T_{\rm C} of nickel. Annealing at T\, \gt\, T_{\rm C} results in a reconstruction of the domain structure with a tendency to the easy-plane model, i.e. with domain magnetization in the plane. The multiple scattering effect is studied and may be taken into account. This experiment demonstrates the possibilities of magnetic SESANS. Some aspects of this novel technique are pointed out.

Multiple scattering in magnetic SESANS

Magnetic spin-echo SANS (SESANS) gives real-space information about correlations in a ferromagnetic material on a length scale 10–10 000 nm, inaccessible in conventional SANS. In non-magnetic SESANS correction for multiple scattering is done analytically. For magnetic SESANS we propose a modified formula and verify it by magnetic-SESANS measurements in stacks of copper plates with electro-deposited Ni. Such Ni film consists of domains magnetized perpendicular to the plane and length equal to its thickness. Perspectives of the technique are mentioned.

Neutron refraction by cylindrical metal wires

Undesired Small-Angle Neutron Scattering (SANS) from interior features of an object can be minimised by reducing the sample thickness. However, refraction effects produced by the exterior shape of the object depend upon the scattering cross-section and not on the thickness of the object. In the field of polarised neutrons a wire coil is often used to manipulate the polarisation vector of the neutron. In this paper, we show that the cylindrical shape of the wire together with the refractive index introduces an angular distribution in the neutron beam. This can be observed in instrumentation sensitive to SANS. We show results measured on three different SANS instruments: Ultra Small-Angle Neutrons Scattering (USANS), Spin-Echo Small-Angle Neutron Scattering (SESANS) and a Time-of-Flight (TOF) SESANS. These results are all in good agreement with the theory of refraction.

Phase-object approximation in small-angle neutron scattering experiments on silicon gratings

The phase-object approximation for neutron scattering based on a one-dimensional dynamic forward scattering theory is discussed and used to calculate the differential cross section of an object. It is shown that this approximation is valid in ultra-small-angle neutron scattering (USANS) and spin-echo small-angle neutron scattering (SESANS) experiments on silicon gratings. In the weak scattering limit, the phase-object approximation reduces to the kinematic or first Born approximation. The spatial coherence function is used to describe instrumental resolution effects. Measurements on three different instruments are in good agreement with calculation results. In the experiment with a time-of-flight SESANS instrument, the effect ofPendellösungwith object size is observed.

Effect of processing on droplet cluster structure in emulsion gels

The fat droplet cluster structure in acidified and neutral emulsion gels is investigated after storage at fixed temperature or after temperature cycling. Amongst other techniques, the novel non-invasive Spin-echo Small-angle Neutron Scattering (SESANS) technique is applied to probe the structure of emulsion droplet aggregates up to a length scale of ∼10 μm. The SESANS data show that fat droplet clusters in non-cycled emulsions become smaller with increasing homogenisation pressure (next to the droplets themselves getting smaller as well), and that the emulsion gel becomes more homogeneous as a result. Upon temperature-cycling, it is found that the fat droplet clusters increase in size (next to the droplets themselves getting larger as well). The presence of these more lumpy aggregates is not the direct cause of the higher firmness of the emulsion gels, but the rearrangement process itself may promote the partial coalescence that causes an increase in firmness of these emulsion gels upon temperature-cycling.

Three-dimensional magnetic spin-echo small-angle neutron scattering and neutron depolarization: A comparison

The recently developed magnetic spin-echo small-angle neutron scattering (SANS) technique provides unique information about the distance correlation of the local vector magnetization as a function of the spin-echo length within a magnetic material. The technique probes the magnetic correlations on a length scale from 10nm up to 10μm within the bulk of a magnetic material by evaluating the Larmor precession of a polarized neutron beam in a spin-echo setup. The characteristics of the spin-echo SANS technique are discussed and compared to those of the more conventional neutron depolarization technique. Both of these techniques probe the average size of the magnetic inhomogeneities and the local magnetic texture. The magnetic spin-echo SANS technique gives information on the size distribution of these magnetic inhomogeneities perpendicular to the beam and, in principle, independent on the local magnetic induction. This information is not accessible by the neutron depolarization technique that gives the average size parallel to the beam multiplied with the square of the local magnetic induction. The basic possibilities of the magnetic spin-echo SANS technique are demonstrated by experiments on samples with a strong magnetic texture.

A novel application of neutron scattering on dairy products

The successful application of spin echo small angle neutron scattering (SESANS) has been demonstrated for studying concentrated, turbid colloid suspensions with respect to their structure without dilution. The structure could be studied in a distance range between 50 nm and 3 μm. Data on the size distribution of casein micelles in non-diluted fat-free milk was obtained. This distribution is similar to earlier observations. The structure of casein gels resulting from processes aimed to simulate curdling (early stage of cheese making) and yoghurt production (acidification) was investigated and found to be not very different, the yoghurt gel being somewhat less dense.

On the Guinier law for spin-echo small-angle neutron scattering

It is shown that Guinier analysis of spin-echo small-angle neutron scattering (SESANS) data is dependent on the instrumental setup, in particular the range of scattering vectors accessible by the detector. In the case that Guinier analysis is permissible, the length scale obtained is proportional to the average width of the density autocorrelation function of the scattering particle, and not its radius of gyration.

Structure of hard-sphere colloid observed in real space by spin-echo small-angle neutron scattering

Spin-echo small-angle neutron scattering (SESANS) opens a wide range of potential applications. One of them is the study of colloids. Using SESANS we measured the structure of hard-sphere colloidal suspensions at two concentrations. We show that SESANS measures real-space correlations due to the particle shape as well as interactions between them. The dilute suspension showed no correlations exceeding the particle diameter. For a concentrated colloid the effect of the excluded volume is observed as a minimum in correlation function. Experimental correlation functions are compared with theoretical ones for noninteracting spheres and a hard-sphere liquid. The scattering density, volume fraction and the radius of particles are also determined from SESANS correlation function.

SESANS with a monochromatic beam or with time-of-flight applied on colloidal systems

Spin-echo small-angle neutron scattering (SESANS) is an efficient method to measure particle sizes in real-space, because it eliminates the need for strong collimation of the beam. The fact that the information is in real-space gives some interesting differences with conventional SANS, which is discussed with measurements of the phase transition in a colloidal system from gas via liquid to solid. Structures can be determined over three orders of magnitude in length scale, from 10 nm to 10 μm . We show the results with two different methods to realise SESANS: with π-flipping foils for a steady source with a monochromatised beam and with the neutron spin resonance echo method for a white pulsed source.