Scattering Wave Vector Research Articles

Dynamic Light-Scattering Study of Aggregating and Gelling Colloidal Disks

We have studied the relaxation of the concentration fluctuations of gelling disk-like clay particles (Laponite) in water containing 5 mM NaCl. At a Laponite concentration of 10 g/l a gel is formed that does not flow when tilted. The comparison of dynamic light scattering and dynamic mechanical measurements shows that the terminal relaxation time of concentration fluctuations diverges not at the gel point, but only when the gel is sufficiently dense to inhibit motion over the length scale on the order of the inverse scattering wave vector. The initial decay of the concentration fluctuations is due to cooperative diffusion and is insensitive to the gel formation. At a concentration of 1 g/L, large aggregates that slowly precipitate are formed. The scattering wave vector dependence of the decay of the concentration fluctuations shows that the aggregates are semi-flexible.

Aggregation Kinetics and Fractal Structure of γ-Alumina Assemblages

Suspensions of a variety of different aluminum oxides have previously been shown to require very high concentrations of chloride and nitrate anions (>0.5 M) to induce rapid aggregation. This high stability has been accredited to the presence of surface forces considered to be due to the formation of highly charged Al13 polymeric species at slightly acidic pH's and aluminum oxyhydroxide gel formation under alkaline conditions. The effect of this stability on the structure of the resulting aggregates is investigated here using well-established static light-scattering techniques. Power law behavior of scattered light intensity as a function of scattering wave vector is observed in all cases and is suggestive of fractal structure. The fractal dimensions obtained fall within the expected range of 1.8 to 2.3 observed for colloidal aggregates but do not appear to follow the typical observations for colloids destabilized by indifferent electrolytes where lower fractal dimensions are associated with rapid (diffusion-limited) aggregation and higher fractal dimensions with slower (reaction-limited) aggregation. Indeed, relatively constant fractal dimensions (2.10 to 2.25) are observed over the range of salt concentrations at which the slow to rapid aggregation rate transformation occurs with, if anything, a slightly higher fractal dimension observed for higher aggregation rates. The presence of specifically binding sulfate anions appears to negate the strong near-distance repulsive forces leading to rapid aggregation at low (1 to 2 mM) sulfate concentrations. Significantly lower fractal dimensions (1.85 to 1.91) are observed for aggregates formed by destabilization using sulfate ions than obtained when chloride or nitrate are used with, again, an apparent slight increase in fractal dimension upon increasing aggregation rate.

Experimental study on the fluctuations of dipolar chains.

Dynamic light scattering is used to study experimentally the dynamics of dipolar chains consisting of ferrofluid particles subjected to a magnetic field (H0). The effective diffusion coefficient shows a pronounced dependence on the scattering wave vector q, reflecting two modes of motion: translational diffusion of the whole chain, and fluctuations of particles within a chain. The characteristic probed frequency of particle displacements is inversely proportional to H0, and exhibits a q(3) dependency. Based on the striking analogy to polymer chain dynamics, we attribute these behaviors to the contribution of hydrodynamic interactions (HI's) that couples particles motion within a chain. This work suggests that chain fluctuations cannot be ignored even for the very strong magnetic field applied (coupling constant<10(6)). HI's can still be important, even at an extremely low particle volume fraction of 10(-5).

LIGHT SCATTERING STUDY OF PARTICLE DYNAMICS IN DIPOLAR MAGNETIC FLUIDS

Halsey and Toor theoretical model (HT) predicts that a thermally induced long-range chain-chain interaction might be responsible for chain-chain lateral aggregation in dipolar fluids. However, this model fails with experiments. To characterize thermally induced chain vibrations, we measured the dynamics of particles in a chain configuration in a very dilute ferrofluid emulsion using Dynamic Light Scattering (DLS). The transverse particle diffusion coefficient at short times is studied as a function of the scattering wave vector, q, and the coupling constant, λ. By varying q, transverse motions of the whole chain can be well separated from transverse motions of the chain components (particles). The results show that the characteristic frequency of particle position fluctuations scales as [Formula: see text], where a is the particle radius. This is interpreted using a polymer analogy including Hydrodynamic Interactions (HI) known as Rouse-Zimm model. Since HI are not included in HT model, HI could be responsible for the discrepancy with experiments. When the volume fraction increases, chains gather and DLS is inappropriate to study the system. A more recently developed technique, known as Diffusing Wave Spectroscopy (DWS) is used to obtain the mean square displacement of particle within columns. Since the particle dynamics is closely related to the viscoelastic properties of the system, studying particle dynamics may help us to understand better the rheological properties of MR fluids.

Light Scattering Study of the Dispersion of Laponite

The dispersion process of laponite clay powder in water was investigated using light scattering. The complete dispersion process takes about 12 h. Laponite solutions were characterized in salt-free water and in 10-3 M NaCl using static and dynamic light scattering, which shows that laponite has a large size polydispersity if it is assumed that it disperses into individual particles. Alternatively, if it is assumed that laponite particles are monodisperse, the results imply that it disperses into a distribution of individual particles and small oligomers. Laponite solutions also contain a small fraction of very large aggregates which dominate the scattering at small scattering wave vectors, but which can be removed by filtration. If the ionic strength is increased, the clay particles aggregate with a rate that strongly increases with increasing ionic strength. At ionic strength above 2 × 10-3 M the aggregation may interfere with the dispersion process.

Topological lifshitz line, off-specular scattering, and mesoporous materials

Ordered phases formed by surfactants in water solutions, and used in technological processes as templates for the synthesis of mesoporous materials, exhibit topological fluctuations. From the results of the Monte Carlo simulations of the lamellar phase we have established a relation between topological fluctuations and the behavior of the off-specular scattering intensity. We have defined the topological Lifshitz line. At this line the peak position in the off-specular scattering intensity moves from the zero (lamellar phase with fixed topology) to the nonzero value of the scattering wave vector (lamellar phase with fluctuating topology).

Structural and Dynamical Properties of Semirigid Polyelectrolyte Solutions: A Light-Scattering Study

Dynamic and static light-scattering experiments were performed on aqueous solutions of the highly charged semiflexible polyelectrolyte chitosan in the dilute and the semidilute regime. In the dilute regime, typical good solvent behavior is found. However, in the overlapped regime the time autocorrelation function of the scattered electric field is found to be bimodal. The short time relaxation has a typical q2 dependence, characteristic of diffusion, and the long time relaxation an approximately q2 dependence, where q is the scattering wave vector. Static and dynamic light-scattering experiments were carried out to analyze the two modes. The fast mode is attributed to the relaxation of concentration fluctuations characterized by a cooperative diffusion mechanism of the polymer network meshes. The slow relaxation time appears to be related to the diffusion of polymer associations. The effect of the excess of salt concentration and polymer concentration was investigated.

Stimulated Brillouin scattering in a plasma with ion-acoustic turbulence

A theory of stimulated Brillouin scattering (STBS) in a plasma with ion-acoustic turbulence is developed using concepts of parametric instability under conditions when equations of two-temperature hydrodynamics can be used to describe ion-acoustic perturbations of the electron density. The temporal growth rate of the absolute instability and the spatial gain of the scattered wave are determined. The dependence of the threshold density of the radiation flux on the angle between the scattering wave vector and the direction of anisotropy of the turbulent noise is described. A new effect of STBS forbiddenness caused by anomalous turbulent heating of the ions is predicted for a plasma with a high level of turbulent noise.

Size distribution effect on the power law regime of the structure factor of fractal aggregates.

We consider the large qR(g), where q is the magnitude of the scattering wave vector and R(g) is the aggregate radius of gyration, part of the structure factor of fractal aggregates, and quantify the coefficient C of the power law, S(q) approximately C(qR(g))(-D), where D is the fractal dimension, for various structure factors proposed in the literature. With the aid of earlier work, we conclude the most accurate structure factors have C=1.0. We then calculate the effects of polydispersity on this coefficient, and show the effects are significant, enough so to allow a measurement of the distribution width. These concepts are accurately supported with scattering data from a diffusion limited aerosol and a reaction limited colloid.

Quasielastic light scattering from rutile

Quasielastic light scattering consisting of two components has been observed in single crystals of rutile $({\mathrm{TiO}}_{2}).$ The broad component with a linewidth of 330 GHz at 297 K becomes narrower with decreasing temperature. In contrast, the narrow component, which has a linewidth of 1.1 GHz at 297 K, broadens as the temperature decreases. We present a unified explanation for both components, which is based on two-phonon difference Raman scattering. For the narrow component, it will be shown that two-phonon difference processes from a single acoustic phonon branch explain the temperature dependence of the intensity and the wave vector dependence of the linewidth at low temperatures. The conventional explanation in terms of entropy-fluctuation scattering is also attempted for temperatures above 200 K where phonon collisions occur more frequently than at lower temperatures and the phonon system may be considered hydrodynamically. For the broad component, two-phonon difference scattering from different phonon branches will be shown to provide a good explanation for the temperature dependent intensity. Furthermore, temperature dependence of the linewidth and its insensitivity to changes in scattering wave vector are also explained with this model.

Anharmonic phonon-polariton excitation through impulsive stimulated Raman scattering and detection through wave vector overtone spectroscopy: Theory and comparison to experiments on lithium tantalate

We study theoretically the generation of coherent, anharmonic phonon-polariton responses through impulsive stimulated Raman scattering with intense, crossed ultrafast excitation pulses. We find that the refractive index appears modulated at the stimulated scattering wave vector and the corresponding phonon-polariton frequency, and, due to anharmonicity, at stimulated scattering wave vector overtones and their corresponding frequencies. A realistic model of the soft lattice vibrational mode of the ferroelectric crystal lithium tantalate is considered in detail. Specific predictions for the magnitudes of different wave vector overtone contributions to the lattice displacement are made compared to experimental observations of anharmonic lattice responses.

Coherent Soft-X-Ray Dynamic Light Scattering from Smectic-AFilms

We have used coherent soft-x-ray dynamic light scattering at the Bragg peak to measure the thermally driven layer fluctuations in freely suspended films of five different smectic- $A$ liquid crystals: 4O.8, 7O.7, 8CB, 8OCB, and 10OCB. The measured relaxation times at a scattering wave vector corresponding to the interlayer spacing ( $2\ensuremath{\pi}{q}^{\ensuremath{-}1}\ensuremath{\approx}30\AA{}$) ranged from 2 to $60\ensuremath{\mu}\mathrm{s}$ for films from 4 to $50\ensuremath{\mu}\mathrm{m}$ thick. Thus, we have achieved the same time resolution as conventional laser dynamic light scattering, but with 100 times higher spatial resolution.

Scaling Approach for the Structure Factor of a Generalized System of Scatterers

A scaling approach for understanding the broad, general features of scattering of waves from nanoscale systems is presented. The approach uses the concept of a system of scatterers with arbitrary length scales, mass and surface fractal dimensions, and correlations between scatterers. It is based on comparing q−1, where q is the magnitude of the scattering wave vector, to the various length scales of the system of scatterers to determine whether the waves are scattered in phase or not. This comparison along with the fact that only fluctuations in the density of the scatterers scatter waves, yields power laws and cross over points which make up the structure factor. The system of scatterers can represent single spheres, fractal aggregates, or ensembles of such entities in a scattering volume. Hence a large range of experimental situations can be described and are unified under this comprehensive description.

Scaling description of the structure factor of fractal soot composites

This paper studies the static structure factor of a system of fractal aggregates at various degrees of densification. The system we use for this study is carbonaceous soot, which is composed of diffusion limited cluster aggregates with a fractal dimension of 1.8. The range of density is great, from the aerosol to a system of lightly touching clusters and then to ground and compressed samples. The data involve a combination of light scattering and small-angle x-ray scattering over a q range of $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}&lt;~q&lt;~6{\mathrm{nm}}^{\mathrm{\ensuremath{-}}1}.$ We are able to explain all the features of the data with scaling arguments based on comparisons of the scattering length scale ${q}^{\ensuremath{-}1},$ where q is the magnitude of the scattering wave vector, and the various length scales of the system that are density dependent.

Velocity difference measurement with a fiber-optic coupler.

Two single-mode fibers collect light with the same scattered wave vector from two spatially separated regions in a sample. These regions are illuminated by a single coherent laser beam, so that the collected signals interfere when combined by means of a fiber-optic coupler, before they are directed to a photomultiplier tube. The fibers and the coupler are polarization preserving to guarantee a high signal-to-noise ratio. The measured intensity fluctuations are used to determine the velocity difference omega v(L) for spatial separations L in the sample. Specifically, an intensity autocorrelation function is calculated theoretically for rigid body rotation and is tested experimentally. Experimental results span two orders of magnitude in L and agree with theoretical predictions with an error of less than 5%. This new technique will be very useful in the study of turbulent flow and particle settling dynamics.

Magnetically scattered polarized neutrons: static and dynamic features of the sample

An investigation of the cross-section for polarized neutrons scattered by a magnetic material is reported. Included in the investigation are the cross-sections for elastic (Bragg), total, and inelastic scattering processes. Special attention is paid to the information available on the chiral character of magnetic states. It is possible that the magnetic response function (also known as the spin van Hove function) is spatially anisotropic, in which case the observed signals are different for the scattering wave vectors k and . This situation can arise with materials in which the magnetic ions are not at centres of inversion symmetry, and when the magnetic order is not collinear, e.g. a helimagnet.

Light scattering by collective excitations in the fractional quantum hall regime

Resonant inelastic scattering methods give access to measurements of low-lying collective excitations of the 2D electron gas at Landau level filling ν= 1 3 . In experiments at finite light scattering wave vectors | k|=k⩽0.15 l 0 −1 , where l 0 is the magnetic length, we find strong light scattering by the collective gap mode of the fractional quantum Hall liquid. Long wavelength spin waves also become allowed in the tilted-field configuration of the present experiments. Such measurements enable the exploration of dispersive charge- and spin-excitations. The energies of the long wavelength collective gap mode at ν= 1 3 display a square-root dependence on perpendicular magnetic field in agreement with current theories of the incompressible quantum fluid. We also consider weaker spectra assigned to light scattering by large wave vector spin wave and collective gap excitation modes. These features are associated with breakdown of wave vector conservation in resonant inelastic light scattering.

Analysis of a simple method for the reduction of phonon peak broadening in surface Brillouin Light Scattering

We present an investigation of the effect of the collecting lens aperture on the line shape of phonon peaks observed in surface Brillouin light scattering (SBLS) from surfaces of opaque materials and transparent thin films. In general, the broadening that is due to the aperture is asymmetric and can be as large as 60% of the peak frequency shift in the case of a f/1.4 aperture with an angle of incidence theta(i) = 30 degrees. We calculated SBLS spectra accounting for the spread in scattering wave vectors across the collecting lens aperture, the polarization and angular dependence of the scattering, and the spectrometer instrumental function. By performing a detailed comparison between measured and calculated SBLS spectra for Si(001), we identified a set of simple rules for the placement of a rectangular slit in the collecting lens aperture to reduce the effects of aperture broadening. By use of a slit, the peak linewidths can be reduced substantially, without reducing the peak heights significantly, while eliminating false shifts in the measured frequency values.

A core-shell model of calcium phosphate nanoclusters stabilized by beta-casein phosphopeptides, derived from sedimentation equilibrium and small-angle X-ray and neutron-scattering measurements.

Calcium phosphate nanoclusters were prepared under standardised conditions using 10 mg ml(-1) of the 25-amino-acid N-terminal tryptic phosphopeptide of bovine beta-casein as a stabilising agent. The Mr determined by sedimentation equilibrium was 197,600+/-13,700 and the apparent radius of gyration determined by X-ray scattering was 2.80+/-0.05 nm. A small-angle neutron scattering contrast variation study in 1H2O/2H2O mixtures was performed and gave radii of gyration at the calculated match points for the calcium phosphate (88.2% 2H2O) and phosphopeptide (41.3% 2H2O) of 3.39+/-0.08 nm and 1.85+/-0.05 nm, respectively. Measurements at larger scattering wave vector showed a subsidiary maximum at about Q = 1.6 nm(-1). The results are consistent with a model of the nanoclusters comprising a spherical core of 355+/-20 CaHPO4 x 2 H2O units, density 2.31 g ml(-1) and radius 2.30+/-0.05 nm surrounded by 49+/-4 peptide chains with a partial specific volume of 0.7 cm3 g(-1), forming a tightly packed shell with an outer radius of 4.04+/-0.15 nm. This model suggests that the phosphopeptide is able to arrest the process of growth of the precipitating phase of calcium phosphate at its earliest stages. A similar role for whole casein could be vital to the normal functioning of the mammary gland during milk secretion.

Internal Dynamics and Elasticity of Fractal Colloidal Gels

The dynamic structure factor of fractal colloidal gels is shown to exhibit a stretched exponential decay to a finite plateau with an exponent of about 0.7. The value of the plateau depends on both initial particle volume fraction ${\ensuremath{\varphi}}_{0}$ and scattering wave vector. We show that this behavior results from the contribution of internal elastic modes of many length scales, and present a model which accounts for the data. From the observed plateau we determine that the very small elastic modulus scales as $G\ensuremath{\sim}{\ensuremath{\varphi}}_{0}^{3.9}$, in agreement with predictions, and with direct mechanical measurements.