Small-angle polarized light scattering by spherulites

The light-scattering matrix for a three-dimensional spherulite is derived within the Ray-leigh-Gans-Debye light-scattering approximation. New expressions for the polarized, small-angle light-scattering intensities I_VV and I_VH are derived from the scattering matrix. These expressions are compared with the I_VV and I_VH expressions derived for a spherulite by Stein and Rhodes. For the case of a weakly anisotropic spherulite having an average refractive index mismatch with its surroundings, the two sets of expressions predict different I_VV and I_VH intensities. In particular, our expressions show that the I_VVand I_VH patterns usually attributed to the spherulitic anisotropy and crystallinity are also predicted for an isotropic sphere. This is in accord with recent experiments.     

In situ measurements of nanotube dimensions in suspensions by depolarized dynamic light scattering

We show that the dimensions of carbon nanotubes (CNTs) in suspension can be characterized by depolarized dynamic light scattering. Taking advantages of this in situ technique, we investigate in detail the influence of sonication procedures on the length and diameter of CNTs in surfactant solutions. Sonication power is shown to be particularly efficient at unbundling nanotubes, whereas a long sonication time at low power can be sufficient to cut the bundles with limited unbundling. We finally demonstrate the influence of CNT dimensions on the electrical properties of CNT fibers. Slightly varying the sonication conditions, and thereby the suspended nanotube dimensions, can affect the fibers conductivity by almost 2 orders of magnitude.     

Small-angle polarized light scattering from amorphous spheres

Small-angle light-scattering measurements have been made using micron-diameter isotropic and spherical polymer latex particles placed between crossed polarizers. Four-leaf clover patterns are obtained, reminiscent of those commonly found for spherical birefringent scatterers. The experimental results compare closely with predictions of Mie scattering theory for isotropic spheres.     

Determination of static microstructure of dilute and concentrated suspensions of anisotropic particles by ultra-small-angle X-ray scattering

Ultra-small-angle X-ray scattering was performed on suspensions of anisotropic polystyrene particles of varying degrees of anisotropy. The wave vector dependence of particle form factors is well described by a model developed by Debye for the scattering from fused spheres. As volume fraction is raised, all suspensions undergo a disorder/order phase transition. The scattering from disordered and ordered suspensions of anisotropic particles is the same as that of spheres up to volume fractions of 0.45, suggesting that, in the dilute crystalline phase, the anisotropic particles order into a rotator or plastic crystal phase, where the particle centers of mass are ordered, but the particle directors are randomly distributed. Further increase in particle volume fraction leads to differences in scattering between homonuclear dicolloids and spheres, implying that the homonuclear dicolloids form a body-centered tetragonal phase with both positional and directional order. This conclusion is supported by real-space imaging of dried films of the particles.     

Small-angle neutron scattering of colloidal silica dispersions in a non-polar solvent

Small-angle neutron scattering studies were performed on dilute dispersions of colloidal silica spheres in mixtures of h₁₂- and d₁₂-cyclohexane. The particles consisted of a SiO₂-core and a layer of stearyl alcohol molecules terminally attached with a chemical bond (Si-O) to the particle surface. The contrast variation method was applied to reveal the internal structure of the particles. The matchpoints determined with this method were in accordance with those calculated from the mass density of the particles and the atomic composition, as determined with elemental analysis.For a detailed interpretation of the scattering curves, we assumed that the particles were spherosymmetrical and consisted of two concentric layers. With the relation we derived between the radius of gyration and the reciprocal contrast for such a model, it was possible to determine all the parameters characterizing the particle in terms of this model. The model calculations performed using these parameters fitted very well to the experimental intensities for high contrasts. For lower contrasts, the fit was somewhat less good. This is probably due to random fluctuations in the scattering length density within the particle core.The different radii as found by neutron scattering, agreed very well with those determined using other techniques, such as light scattering (static and dynamic) and electron microscopy.     

Model interpretation in static light scattering

For sufficiently large species, the fit of the experimentally obtained scattering curve with theoretically calculated ones for different basic structure types (sphere, random coil, rod, wormlike chain and others) gives information about the structure type, the polydispersity, the structure density, the molecular parameters M_w and s_z, and a characteristic size parameter a_m, the definition of which depends on the used structure model type. An iterative algorithm is offered to separate bimodal scattering curves into the curves of the components and to characterize the single ones. The theoretical background of such procedures and a corresponding software system will be presented. Application examples demonstrate the efficiency of the procedures.     

Small-angle light scattering from a distribution of spherulite sizes

Depolarized small-angle light scattering from spherulites in semicrystalline polymers gives rise to a characteristic cloverleaf pattern. For scattering from a single spherulite, the position of the maximum in scattered intensity is readily related to the spherulite radius. For a distribution of spherulites, the maximum should be related to some characteristic measure of the distribution. It is shown for a wide variety of distributions that this characteristic radius is a ratio of high moments of the size distribution, specifically R* ≈ 〈R⁷〉/〈R⁶〉. The shape of the light-scattering profile should in principal be related to the nature of the spherulite distribution. Calculations of scattering profiles from a variety of distributions fail to demonstrate this, owing to the strong dependence of scattering power on spherulite size. Exceptions are noted for the case of certain bimodal distributions.     

Small-angle light scattering and crystallization processes in solid polymer films

Information, not previously measurable, about the internal crystallization processes occurring within spherulitic films can now be obtained by combining refractive index, birefringence, and small-angle light-scattering measurements. The surroundings of a spherulite in a solid film are composed of both the adjacent spherulites and their interstices (boundaries), and it is shown that different crystallization processes can occur in each of these regions. Upon annealing a quenched isotactic polypropylene film, the rate of crystallization within the interstices of the space-filling spherulites is observed to be greater than the rate of crystallization within the spherulites themselves.     

Effective static and high-frequency viscosities of concentrated suspensions of soft particles

We obtain an analytic expression that allows to determine the static η and high-frequency η(∞) viscosities as function of the volume fraction φ of a concentrated suspension of soft spherical particles in a liquid of viscosity η(0). The particles consist of a hard core of radius a covered by a porous layer of thickness d. Suspensions of hard spheres and homogeneous porous particles are limiting cases of the model. The proposed expression incorporates the results for the intrinsic viscosity obtained on the basis of a cell model [H. Ohshima, Langmuir 26, 6287 (2010)] into a recently obtained relation for the effective viscosity of concentrated colloidal suspensions [C. I. Mendoza and I. Santamari?a-Holek, J. Chem. Phys. 130, 044904 (2009); J. Colloid. Interface Sci. 346, 118 (2010)]. In this model, the correlations between the particles due to crowding effects are introduced through an effective volume fraction φ(eff) which is then used as integration variable in a differential effective medium procedure. The final expression is simple, accurate, and allows to collapse all the data in a universal master curve that is independent of the parameters characterizing the system. The only difference between the static and high-frequency cases is that in the later case φ(eff) also incorporates hydrodynamic interactions arising from the so-called relaxation term. We have tested the accuracy of our model comparing with experimental results for spherical polymeric brushes and simulations for the high-frequency viscosity of homogeneous porous particles. In all cases the agreement with the data is extremely good.     

Small-angle X-ray scattering and light scattering on lysozyme and sodium glycocholate micelles

Small-angle X-ray scattering (SAXS) together with static (SLS) and dynamic light scattering (DLS) measurements were carried out on aqueous solutions of lysozyme (LY) and of the ionic biological detergent sodium glycocholate (NaGC). Apparent diffusion coefficients (D app), excess Rayleigh ratio, and SAXS spectra were measured for 0.1 M NaGC solutions at different ionic strengths (0.05-0.30 M NaCl). The same data were collected for LY in sodium acetate buffer 50 mM without and with 92 mM NaCl as a function of protein concentration (10-80 g L(-1)). A correlated analysis of SLS data and SAXS spectra was first tested on the LY samples and then extended to the interpretation of the NaGC data to infer information on particle structure and interaction potential. A hard-core (HC) interaction shell of uniform thickness, a screened Coulomb potential of the electric double layer (EDL) or the complete DLVO potential were alternatively used to represent the long-range tail of the interaction potential. Whenever an essentially repulsive tail is expected, all the representations give reasonable results, but the data analysis does not allow the discrimination between the oblate and the prolate symmetries of the NaGC aggregates. The DLVO model allows the interpretation of the data even when the attractive component determines the tail character. With this model an overall fit of the micelle data at all the NaCl concentrations was successfully performed by assuming a simple spherical symmetry of the micelles and invariant values of their ionization degree and Hamaker constant, thus considering just the screening effect of the added electrolyte. Whatever model is used, the results point out that the aggregates are quite hydrated (26-38 water molecules per monomer) and very slightly grow by increasing the NaCl concentration. When spherical symmetry is assumed the aggregate radii for all the samples fall in the range 15-16 A. From the SAXS and SLS, best fitting geometrical parameters, and interparticle structure factor, a D app value was calculated for each sample. An excellent consistence is achieved for LY results. On the contrary, calculated D app values systematically lower than the experimental values are always obtained for the NaGC micelles. Micelle polydispersity and internal dynamics seem to be the most probable reasons of the bad agreement.     

Supramolecular crystal growth in concentrated suspensions of charged monodisperse spherical silica particles

Concentrated suspensions of charged monodisperse spherical silica particles (MSSP) stabilized by alkalis or ammonia are able to crystallize at a certain destabilization. Crystal structures with the particles fixed at certain distances from each other show an isotropic normal mechanism of continuous growth with a rough phase boundary. The crystallization is determined by three parameters,víz. the concentration of particles, temperature, the thickness of the ion atmosphere around the particles and the concentration of counterions. The crystallization of MSSP suspensions is considered as a model of the supramolecular crystallization in the field of synthesis of mesoporous structures.     

Small-angle scattering of polarized light. VI. Sphere doublets at rest and during shear

The polarized or depolarized light scattering by well-defined monodispersed sphere doublets is investigated. Two configurations of doublets are studied. In the first (at rest) the doublets are randomly oriented in a plane, in the second the doublets are oriented in a preferred direction. This is achieved by submitting a suspension of doublets to a shear flow. The scattering patterns are compared to two theoretical predictions based on simplified geometries. In the first approach, the doublet is approximated by two interpenetrating spheres scattering independently, whereas in the second, an ellipsoid geometry is used. A good qualitative comparison is obtained. However, the HV and VH patterns of a randomly dispersed suspension are not similar. The observation of the flow of a doublet suspension in shear shows that the doublets are spiraling around the vorticity axis. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 2005–2013, 1998     

Static and dynamic light scattering in turbid suspensions

The application of static and dynamic light scattering to many colloidal systems of practical interest has often been considered too complicated due to strong multiple scattering. There are two new approaches to overcome this problem. One of them aims at suppressing contributions from multiple scattering using novel cross‐correlation schemes. While this relies on the suppression of multiple scattering, the so‐called diffusing wave spectroscopy (DWS) works in the limit of very strong multiple scattering. DWS can be used for the characterization of dynamic and static properties of colloidal systems on a large range of time and length scales ranging from a few Ångstroms to hundreds of nanometers. We demonstrate that a wealth of information can be obtained from these methods on the structure, dynamics, interaction effects, stability, aggregation, and sol‐gel transition in colloidal dispersions.     

Small-angle light scattering study of quasi-two-dimensional structures of magnetic particles

We studied quasi-two-dimensional magnetic domain structures using a small-angle light scattering technique. The structures are formed when magnetic particles in an aqueous suspension between two parallel glass plates are assembled and oriented in a magnetic field H perpendicular to the plates. Three different structure regions can be identified, and they are bounded by two critical field lines H_c1 (φ) and H_c2(φ). Below H_c1 (φ) the system consists of single particles; between H_c1 (φ) and H_C2 (φ), the particles assemble into elongated disordered domains; and above H_c2 (φ), the domains develop a strong in-plane correlation. In the strong field limit H H_c2, the structure factor of the magnetic fluid resembles that of a two-dimensional liquid. However, long lasting metastability and hysteresis observed in the experiment suggest that the system is essentially locked in a glassy state.     

Ion-specific effect on the gelation kinetics of concentrated colloidal silica suspensions

The comparative gelation kinetics of concentrated colloidal silica suspensions at pH 9.8 has been studied in the presence of two different counterions, ammonium as a representative structure-breaker ion and sodium as a representative structure-maker ion. For the same ionic strength of 0.45 M, the experimental results have indicated a pronounced effect of the ion-specificity on the aggregation kinetics and on the microstructure of the gelified networks at the sol-gel transition. This was ascribed to the significant difference of the critical coagulation concentration value in the presence of the two electrolytes.     

Dynamic light scattering from concentrated colloidal dispersions

From the scattered intensity as a function of scattering wave number, local ordering in concentrated latex dispersions in benzene is found. From the combination of intensity and photon correlation experiments follows the existence of strong hydrodynamic interactions between the dispersed particles.     

Small-angle scattering of circularly polarized light from an anisotropic sphere

A theory of the small-angle scattering of circularly polarized light from an anisotropic sphere has been derived. The validity of the theory has been verified, and a relationship between the structural information thus obtained and the structural information obtained with linearly polarized light has been demonstrated.     

Energy dissipation in concentrated monodisperse colloidal suspensions of silica particles in polyethylene glycol

Highly concentrated colloidal suspensions exhibit a discontinuous shear-thickening behaviour. The transition from a low to a high viscosity state is associated to a large energy dissipation. This effect could find applications in structural damping while the viscosity increase brings added stiffness. In the present work, highly concentrated suspensions of monodisperse spherical silica particles in polyethylene glycol were selected for their strong thickening at low critical shear rates. Their damping properties were characterized by measuring the energy dissipated per cycle at low frequency (below 2 Hz) during oscillatory tests using a rheometer. The influence of parameters such as particle concentration, size and frequency was investigated. Damping was found to overcome that of benchmark elastomeric materials only in high frequencies and high strain domains.