Chord length distributions and small-angle scattering

Chord length distributions describe size, shape and spatial arrangement of geometrical objects (particles). The chord length distribution is in principle proportional to the second derivative of the correlation function of small-angle scattering. It is calculable from a relative measurement of the scattering intensity I(h). In structure research, the characterization of numerous particle systems can be achieved by comparing experimental chord distributions with theoretical ones, provided the latter are available with sufficiently high precision for a lot of fundamental, universal shapes. Both sides of this concept are exemplified: – the step from a relative measurement of the scattering intensity of an isotropic two-phase sample to the chord length distribution (errors in and in , limited h-interval, corresponding to the region (1-2) nm < r in real space, must be observed); as well as the geometric matter of calculation of chord distributions as fingerprints for basic geometric figures, including the non-convex case. Received 15 March 1999 and Received in final form 26 April 2000     

Study of silica templates in the rice husk and the carbon–silica nanocomposites produced from rice husk

Carbon–silica nanocomposites obtained by rice husk carbonization in a fluidized-bed reactor using a deep oxidation copper–chromium catalyst were studied. Dispersion characteristics of the silica phase in these systems were determined by small-angle X-ray scattering (SAXS) using the full contrast technique. SiO₂ was found in the initial rice husk as compact nanoparticles having a wide size distribution. This distribution consists of a narrow fraction with particle sizes from 1 to 7 nm and a wider fraction with particle sizes from 8 to 22 nm. Oxidative heat treatment of rice husk in a fluidized bed in the presence of the catalyst decreased the fraction of small SiO₂ particles and increased the fraction of large ones. It was demonstrated that the particle size of silica in the carbon matrix can be determined selectively for deliberate design of porous carbon materials with desired properties.     

Application of small-angle scattering for the identification of small amounts of platinum supported on porous silica

Pt-porous glass catalysts have been studied by small-angle X-ray scattering. The catalysts have been prepared by impregnating two micro- or mesoporous glasses with 0.1 wt% of Pt. Two different pore systems of the catalyst supports have been generated and investigated: on the one hand, the mesoporous structure is formed by finely dispersed colloidal silica inside a macroporous glass. On the other hand, micropores are given by the porous glass itself. The pure supports and the supported catalysts have been investigated via chord length analysis for a selected range order, based on the analysis of the scattering intensity for relatively large scattering vectors (up to the upper limit of SAS). The obtained specific structure parameters of both supported catalysts like dispersion, specific metal surface areas, basic arrangement, size distribution and volume fraction of the metal particles basically differ with both pore systems.     

Small-angle neutron and dynamic light scattering study of gelatin coacervates

The state of intermolecular aggregates and that of folded gelatin molecules could be characterized by dynamic laser light and small-angle neutron scattering experiments, which implied spontaneous segregation of particle sizes preceding coacervation, which is a liquid-liquid phase transition phenomenon. Dynamic light scattering (DLS) data analysis revealed two particle sizes until precipitation was reached. The smaller particles having a diameter of ～50 nm (stable nanoparticles prepared by coacervation method) were detected in the supernatant, whereas the inter-molecular aggregates having a diameter of ～400 nm gave rise to coacervation. Small-angle neutron scattering (SANS) experiments revealed that typical mesh size of the networks exist in polymer dense phase (coacervates) [1]. Analysis of the SANS structure factor showed the presence of two length scales associated with this system that were identified as the correlation length or mesh size, ξ = 10.6 Å of the network and the other is the size of inhomogeneities = 21.4 Å. Observations were discussed based on the results obtained from SANS experiments performed in 5% (w/v) gelatin solution at 60°C (ξ = 50 Å, ζ = 113 Å) and 5% (w/v) gel at 28°C (ξ = 47 Å, ζ = 115 Å) in aqueous phase [2] indicating smaller length scales in coacervate as compared to sol and gel.     

A small-angle X-ray scattering study of the isotropic and nematic phases of V2O5 suspensions

We report small-angle X-ray scattering experiments performed in both the isotropic and nematic phases of aqueous V₂O₅ suspensions. We show that the scattering in the isotropic phase can be well described in the whole accessible q-range by only considering the form factor of non-interacting ribbons. We investigate the influence of concentration and pH on the dimensions of V₂O₅ ribbons and show that these parameters do not have any significant effect, as long as the system stays well within the chemical stability domain of the ribbons. We then show that nematic single domains display an anisotropic small-angle scattering pattern, even at scattering vectors small compared to that at which a characteristic correlation peak is observed. This feature is expected for a nematic phase, but was rarely observed. We finally try to describe this scattering within the framework of theories developed for the structure factor of a nematic polymer, and we reach the conclusion that chain ends are certainly important to understand this pattern. Received 21 July 1999 and Received in final form 17 December 1999     

Structure of gels and aggregates of disk-like colloids

The static structure factor (S(q)) of dispersions and gels of disk-like mineral colloids (Laponite) was investigated using time- and ensemble-averaged light scattering. The evolution of S(q) in time after increasing the ionic strength of well-dispersed Laponite suspensions shows that Laponite aggregates and forms fractal clusters. The structure of the aggregates does not depend on the ionic strength, but the rate of growth increases very strongly with the ionic strength. At concentrations below about 3 g/l (0.12% v/v) the aggregates sediment while at higher concentrations space-filling gels are formed. The gels are homogeneous on length scales larger than the correlation length which decreases strongly with decreasing ionic strength and increasing concentration. However, the local structure is the same, independent of the concentration and the ionic strength. Received 6 August 2000 and Received in final form 16 March 2001     

Copper and copper oxide nanoparticles in a cellulose support studied using anomalous small-angle X-ray scattering

Microcrystalline cellulose is a porous natural material which can be used both as a support for nanoparticles and as a reducer of metal ions. Cellulose supported nanoparticles can act as catalysts in many reactions. Cu, CuO, and Cu₂O particles were prepared in microcrystalline cellulose by adding a solution of copper salt to the insoluble cellulose matrix and by reducing the copper ions with several reducers. The porous nanocomposites were studied using anomalous small angle X-ray scattering (ASAXS), X-ray absorption spectroscopy, and X-ray diffraction. Reduction of Cu²⁺ with cellulose in ammonium hydrate medium yielded crystalline CuO nanoparticles and the crystallite size was about 6–20 nm irrespective of the copper concentration. The size distribution of the CuO particles was determined with ASAXS measurements and coincided with the crystallite sizes. Using sodium borohydrate or hydrazine sulfate as a reducer both metallic Cu and Cu₂O nanoparticles were obtained and the crystallite size and the oxidation state depended on the amount of reducer.     

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     

Pore size distribution in porous glass: fractal dimension obtained by calorimetry

By differential Scanning Calorimetry (DSC), at low heating rate and using a technique of fractionation, we have measured the equilibrium DSC signal (heat flow) J _q ⁰ of two families of porous glass saturated with water. The shape of the DSC peak obtained by these techniques is dependent on the sizes distribution of the pores. For porous glass with large pore size distribution, obtained by sol-gel technology, we show that in the domain of ice melting, the heat flow J_q is related to the melting temperature depression of the solvent, ΔT _m , by the scaling law: J _q ⁰∼ΔT _m ^{- (1 + D)}. We suggest that the exponent D is of the order of the fractal dimension of the backbone of the pore network and we discuss the influence of the variation of the melting enthalpy with the temperature on the value of this exponent. Similar D values were obtained from small angle neutron scattering and electronic energy transfer measurements on similar porous glass. The proposed scaling law is explained if one assumes that the pore size distribution is self similar. In porous glass obtained from mesomorphic copolymers, the pore size distribution is very sharp and therefore this law is not observed. One concludes that DSC, at low heating rate ( q? 2^°C/min) is the most rapid and less expensive method for determining the pore distribution and the fractal exponent of a porous material. Received 23 July 1999 and Received in final form 16 February 2001     

The microstructure of hydrogen- and deuterium-doped nanocrystalline palladium studied by small-angle neutron scattering

By means of small-angle neutron scattering the microstructure of two nanocrystalline Pd samples (prepared by inert gas condensation) has been studied at room temperature in a Q-range from [0pt] to [0pt] . An additional subsequent doping of the two samples with H as well as with D (concentrations < 4 at%) caused contrast variations that provided more detailed structural information. The measured scattering intensity was modeled by a Porod contribution from large heterogenities (e.g. pores) and a contribution from spherical grains with a log-normal distribution of their radii. To account for the presence of grain boundaries, the grains were considered to be surrounded by a shell with a reduced Pd density and a thickness half as large as the thickness of the grain boundaries. For the above model, the data of the H-doped, D-doped and undoped sample were simultaneously fitted with one single set of adjustable parameters. The fits yielded for the two samples volume-weighted mean grain radii of 10 nm and 13 nm. The values for the grain boundary thickness lie between 0.2 and 0.8 nm. Almost all of the H- and D-atoms are, at low hydrogen concentrations, located in the grain boundaries. Received 1 May 2000     

Synthesis of core–shell nanoparticles with a Pt nanoparticle core and a silica shell

A method to prepare a core–shell structure consisting of a Pt metal core coated with a silica shell (Pt(in)SiO₂) is described herein. A silica shell was grown on poly(vinylpyrrolidone) (PVP)-stabilized Pt nanoparticles 2–3 nm in size through hydrolysis and condensation reactions of tetraethyl orthosilicate (TEOS) in a water/ethanol mixture with ammonia as a catalyst. This process requires precise control of the reaction conditions to avoid the formation of silica particles containing multiple Pt cores and core-free silica. The length of PVP molecules, water content, concentration of ammonia and Pt nanoparticles in solution were found to significantly influence the core–shell structure. By optimizing these parameters, it was possible to prepare core–shell particles each containing a single Pt nanoparticle with a silica layer coating approximately 10 nm thick.     

Electron relaxation and transport in nanostructured and bulk silica

Processes of ballistic and hot electron relaxation in extended bulk as well as nanostructured silica have been analyzed by means of a phonon-based scattering model and respective Monte-Carlo computer simulation. Optical as well as acoustic phonons are taken into account. Trajectories of electrons and their energy attenuation in nanostructured silica are additionally affected by scattering processes at the grain boundaries between the nanoparticles, i.e. by surface phonon as well as potential scattering. Moreover, a flatter conduction band and a higher effective electron mass have been taken into account too. According to these calculations, electrons with an initial energy of several eV, but still below the valence band ionization threshold, were thermalized in 50–300 fs increasing with the silica grain size from 1 nm up to bulk material. The electron emission probabilities over the surface barrier into vacuum are extended up to depths of 60–100 nm, respectively, increasing with enhancement by an electric field.     

浓悬浮液中纳米SiO_2团聚体的渗透率

本文基于悬浮液中渗透性颗粒的短时扩散动力学理论,采用低相干光纤动态光散射方法,测量了相同粒径的纳米SiO_2团聚体在不同体积分数时的扩散系数,利用扩散系数随渗透率的变化关系得到纳米SiO_2团聚体的渗透率.结果表明:恒温条件下,具有一定渗透率的团聚体颗粒扩散得比硬球颗粒快.实验测量得到的团聚体渗透率与采用photoshop CS6对团聚体SEM图像进行处理计算得到的渗透率符合较好.     

A high-speed particle-detection in a large area using line-laser light scattering

We study the optical characteristics of a home-built line-laser surface light scattering system that detects sub-micron scale irregularities on a large area in high speeds. The sensitivity of the detection system, i.e. signal to noise (STN) ratio, is found to depend strongly on the detection angle. We find an optimal detection angle at 30°, at which STN ratio is maximized for 2500 nm silica particles on wafer surface. Experimental results of scattering intensity measurements from a smooth surface and from surfaces with spherical irregularities are in excellent agreement with corresponding theoretical model calculations. The line scan speed can be as high as ∼17 mm/s, while identifying the presence of a particle as small as 700 nm in a pixel area (∼15 μm × ∼17 μm). The presence of irregularities found by the line scan system is confirmed by confocal laser-scanning microscopy imaging. Due to unique advantages such as non-disruptiveness, high-speed over large area, and high sensitivity, this line scan system may be used as a surface inspection system that meets the requirements of recent flat panel display manufacturing environments.     

Percolation in two-scale porous media

Two-scale porous media are generated by filtering a Gaussian random correlated field with a random correlated threshold field. The percolation threshold and the critical exponent ν are derived with the help of a finite-size scaling method. The percolation threshold for the three-dimensional media is a decreasing function of the variance and correlation length of the threshold field. A simplified model predicts these trends in 3d; moreover, it suggested some effects in 2d which were all numerically verified. Received 17 August 2000     

Trends in anomalous small-angle X-ray scattering in grazing incidence for supported nanoalloyed and core-shell metallic nanoparticles

As atomic structure and morphology of particles are directly correlated to their functional properties, experimental methods probing local and average features of particles at the nanoscale elicit a growing interest. Anomalous small-angle X-ray scattering (ASAXS) is a very attractive technique to investigate the size, shape and spatial distribution of nanoobjects embedded in a homogeneous matrix or in porous media. The anomalous variation of the scattering factor close to an absorption edge enables element specific investigations. In the case of supported nano-objects, the use of grazing incidence is necessary to limit the probed depth. The combination of grazing incidence with the anomalous technique provides a powerful new method, anomalous grazing incidence small-angle X-ray scattering (AGISAXS), to disentangle complex chemical patterns in supported multi-component nano-structures. Nevertheless, a proper data analysis requires accurate quantitative measurements associated to an adapted theoretical framework. This paper presents anomalous methods applied to nanoalloys phase separation in the 1–10 nm size range, and focuses on the application of AGISAXS in bimetallic systems: nanocomposite films and core-shell supported nanoparticles.     

Aggregating block copolymers as model systems to study polymer brush dynamics

Summary A-B block copolymers in a selective solvent—good for the B-species and bad for the A-species—form micellar aggregates with a compact A-core with a corona (brush) of B ?hairs? reaching into the solvent. Whereas polystyrene(PS)-polyisoprene(PI) in decane forms spherical micelles with a PS core of about 10 nm radius, polyethylene(PE)-polyethylenepropylene(PEP) forms micellar platelets, the shape of which is goverend by the habitus of PE crystallites forming the core. These planar aggregates have large (several hundred nanometers) lateral extension and a core thickness in the range of 10 nm. Both systems are model systems for polymer brushes, either on a spherical surface or planar. Neutron spin-echo experiments allow for the investigation of the dynamics of the brushes which reflects their viscoelastic properties. Results of neutron small-angle and spin-echo investigations are reported. The brush dynamics is explained using a model based on an idea of de Gennes describing the brush properties in terms of scaling relations for osmotic pressure and viscosity of a semi-dilute solution with inhomogeneous density. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Counterion distribution in a spherical charged sparse brush

The counterion distribution within a spherical polyelectrolyte sparse brush was measured by small-angle X-ray scattering using contrast variation with different counterions by means of ion dialysis. The brush was made by self-association of charged diblock copolymers. Thanks to the contrast variation method, we were able to separate the signal due to the monomers and the signal due to the counterions. At a small length scale, it is demonstrated that the system behaves as independent charged rods whose counterion distribution follows the Poisson-Boltzmann model. Received 14 February 2001 and Received in final form 2 May 2001     

Detection of submicron-sized raft-like domains in membranes by small-angle neutron scattering

Using coarse grained models of heterogeneous vesicles we demonstrate the potential for small-angle neutron scattering (SANS) to detect and distinguish between two different categories of lateral segregation: 1) unilamellar vesicles (ULV) containing a single domain and 2) the formation of several small domains or “clusters” (~10 nm in radius) on a ULV. Exploiting the unique sensitivity of neutron scattering to differences between hydrogen and deuterium, we show that the liquid ordered (lo) DPPC-rich phase can be selectively labeled using chain deuterated dipalymitoyl phosphatidylcholine (dDPPC), which greatly facilitates the use of SANS to detect membrane domains. SANS experiments are then performed in order to detect and characterize, on nanometer length scales, lateral heterogeneities, or so-called “rafts”, in ~30 nm radius low polydispersity ULV made up of ternary mixtures of phospholipids and cholesterol. For 1:1:1 DOPC:DPPC:cholesterol (DDC) ULV we find evidence for the formation of lateral heterogeneities on cooling below 30 °C. These heterogeneities do not appear when DOPC is replaced by SOPC. Fits to the experimental data using coarse grained models show that, at room temperature, DDC ULV each exhibit approximately 30 domains with average radii of ~10 nm.     

Chain length dependence of anomalous swelling in multilamellar lipid vesicles

Using small-angle X-ray scattering, the repeat distance vs. temperature is measured for a homologous series of multilamellar vesicles of lecithins with varying acyl chain length in excess water condition around the lipid main transition. A systematic chain length dependence is found which is in accordance with a bending rigidity renormalization and critical unbinding of the lamellae close to the transition, as previously suggested in H?nger et al. [Phys. Rev. Lett. 72, 3911 (1994)]. Received 13 January 1999 and Received in final form 6 September 1999