Small-angle light scattering from thin polymer films: Multiple scattering from Debye–Bueche scatterers

An extension of Hartel's theory for multiple scattering has been applied to the case of small-angle light scattering from polymer films with random two-phase morphology. The scattering is treated in terms of Debye–Bueche theory from which values of the correlation length, an average phase size, and mean-square fluctuation in polarizability are determined. It is shown that multiple scattering leads to a reduction in the angular dependence of scattering due to an enhancement of scattering at high angles. This leads to an underestimate of the correlation length and an overestimate of the magnitude of the mean-square polarizability fluctuation.     

Scattering of light from thin polymer films. I. Multiple scattering

A general method is described to take into account the multiple scattering effect in a small-angle light scattering from thin polymer films. It is seen that multiple scattering tends to make the scattering envelope more diffuse, reducing the intensity in the high intensity regions and increasing it in the low intensity regions. The method is applied here to a spherulitic system, but it is valid for any other system where the principal scattering is in the forward direction.     

Study of dynamic light scattering in nematic liquid crystal and its optical,electrical and switching characteristics

In the present study, the polarisation-independent dynamic light scattering (DLS) in a nematic liquid crystal (LC) with a negative dielectric anisotropy has been compared in two operating modes by applying DC voltage or AC voltage to LC cells with a vertical and hybrid alignment. The attenuation of light transmittance and the DLS optical threshold without polarizers as well as a phase retardation of LC bend–splay deformation and a Fredericks threshold voltage with polarizers have been determined. Diffuse scattering of a light beam and broadband transmittance spectra of LC cells have been examined using the DC voltage in the interval of 0–40 V. Multi-domain structures and turbulent flows in the LC cells have been observed by polarisation optical microscope. The results show that the enhancement of the diffuse scattering of light in the LC cells correlate with ion density increase. The largest attenuation of the light intensity in the LC cells with a vertical alignment was 16.4 dB at a wavelength of 650 nm with a minimum decay time equal to 2.5 ms at DC voltage of 60 V. Our study has been shown that switching from a diffuse light scattering state to a transparent state can be twice accelerated by applying AC voltage with high frequency to LC cells.     

具有高散射能力的聚碳酸酯复合材料的制备与性能研究

以双酚A型聚碳酸酯(PC)为基体、苯乙烯-丙烯腈共聚物(SAN)为散射体,通过熔融共混方法制备了同时具备高透光率和高雾度的高散射聚碳酸酯光散射片,研究了SAN含量对光散射片微观结构和光散射性能的影响,发现透光率和雾度同时随着散射体含量增加而提高的现象.研究结果表明,当SAN含量低于30%时,分散相为球形颗粒,颗粒的平均粒径随着SAN含量的增加而增加,而颗粒的数量浓度则随之减小,这使得其透光率和雾度均随着SAN含量的增加而增加,当SAN含量为30%时,透光率和雾度达到最大值,分别为89.1%和91.7%.并结合Mie散射理论解释说明了透光率和雾度同时随着散射体含量的增加而提高的现象.但当SAN含量的进一步增加,分散相颗粒尺寸已远大于光波的波长,不再适用于Mie散射理论,且部分不再呈球形颗粒,使得PC片的透光率和雾度略有降低.     

Dynamic small-angle x-ray scattering from crystalline polymers

The variation in small-angle x-ray scattering (SAXS) for samples of crystalline polymers subjected to oscillatory strains has been observed employing the 10-m SAXS apparatus with a two-dimensional position-sensitive detector at the National Center for Small-Angle Scattering Research at Oak Ridge National Laboratory. Signal averaging has been carried out in accordance with the π/2-sector technique by gating the detection of scattered intensity in synchronism with the sample strain. In-phase and out-of-phase intensity changes have been observed for a high-density polyethylene at various frequencies (0.05–3.2 Hz) and temperatures (0–70°C). Changes are greatest at small scattering angles. Frequency dependence is greatest at lower temperatures, indicating a time-dependent response of the structural changes leading to scattering at these temperatures. The behavior is not pronounced at elevated temperatures. The similarity of the scattering at both azimuthal angles of 0° and 90° suggests the existence of an additional mechanism, perhaps microvoid formation. To evaluate void contribution, the dynamic invariant function is determined as a function of frequency and temperature. It appears that the microvoid formation lags behind the applied strain. The static and swelling SAXS studies present further evidence of void generation during elongation.     

Multiple scattering of light from polymer dispersed liquid crystal material

Light scattering from polymer dispersed liquid crystal (PDLC) material has been studied experimentally and by Monte Carlo simulation. Light scattering was measured as a function of both scattering angle and cell thickness. The cell thicknesses of practical interest are in an intermediate regime where neither single scattering nor light diffusion applies. Both the angular and the thickness dependence of the scattering intensity can be described accurately by a Monte Carlo simulation of multiple scattering from a homogeneous distribution of independent scatterers. The model smoothly interpolates between the single scattering limit for thin cells and the diffusion limit for thick cells. It can easily be extended to include any specific feature of a scattering display system.     

High-performance liquid chromatography applications of optical rotation detection with compensation for scattering and absorbance at the laser wavelength.

Use of instrumentation developed to enable simultaneous monitoring of optical rotation (OR) and transmittance allows OR measurements to be made in the presence of high levels of absorbance, scattering or other effects that change the intensity of the plane-polarised light at the photodiode detector. This extends the application of OR detection to areas where it was previously difficult. Examples of the application of high-performance liquid chromatography (HPLC) with the improved OR detector include (i) the analytical scale separation of fructose and sucrose and (ii) the semi-preparative separation of enantiomers of warfarin and Tr?gers base. A signal-to-noise improvement of up to 150% is found when comparing signals with and without correction for transmittance changes. The improved OR detector has been used in series with a UV detector and the system shown to be suitable for on-line measurement of peak purity in separations using a chiral column under overload conditions.     

Multiple collisions in molecular beam scattering experiments

Due to the forward peaked differential cross section for elastic atom—atom scattering the effect of multiple collisions has to be considered in the analysis of crossed beam measurements of the total cross section and especially of the small angle differential cross section at large values of the beam attenuation. At angles θ ≈ θ₀, with θ₀ the quantum mechanical scaling angle of the elastic differential cross section, the correction for the latter case amounts to 20% at beam attenuations I/I₀ = exp(?1). Firstly, a careful analysis of the probabilities for single and multiple scattering is given, resulting in an expression for the measured beam signals which is correct for all values of the beam attenuation. The probability for multiple scattering is then calculated for an inverse power potential V(r) = ?C_sr^?s, with s = 4 through s = 7, which include both the case of ion—atom scattering (s = 4) and atom—atom scattering (s = 6). The results are given as effective differential cross sections σ_n(θ) for n-fold scattering. They are described by a single, simple analytical function with four free parameters that have been determined for n = 2, 3 and 4 by a least squares method. The σ_n(θ) are normalised to the total cross section Q.     

A simple representation of small-angle light scattering from an anisotropic sphere

An explicit form of Mueller's phenomenological matrix has been derived which characterizes the small-angle light scattering from an anisotropic sphere when the requirements of the Rayleigh-Gans approximation are fulfilled.     

Light scattering from swollen textured polymer network composites

Light scattering from a swollen textured heterogeneous polymer network is discussed using example of a network composite filled by spherical inclusions anisotropically distributed in the matrix. The dependence of the scattering intensity on the Fourier transform of the correlation function dry-state shear moduli fluctuations has been established. H_v scattering patterns from uniaxial textures and their ratio with the composite anisotropy parameter are analyzed. The sensitivity of the H_v scattering pattern on restrictions during the swelling is emphasized. © 1993 John Wiley & Sons, Inc.     

Brillouin scattering from polymers and gels

We report results from Brillouin scattering on highly swollen and crosslinked polymeric gels, i.e. methyl methacrylate (MMA) gels crosslinked with ethylene dimethacrylate (EDMA). The study is performed varying the crosslink amount of the gels from 0 to 6%. The Brillouin spectra are measured at different scattering wavevectors in the angular ranges 90°–150°. Ve also measured the spectra at constant wavevector (90°) changing the scattering volume, in particular we select the size and the positions of the sample scattering volume. The wavevector dependence of the measured quantities confirms that in our system a micro—phase separation phenomenon takes place. In particular, for samples with crosslink contents higher than 3%, Brillouin data (studied in terms of the group velocity) give information about the existence of well defined solid- and liquid-like islands (heterogeneities in the gel structure) with an extent of several hundred Angstroms (as confirmed by elastic scattering data). Furthermore, selecting different spatial positions of the scattering volume (of micrometric sizes) and the overall sizes of the same, and performing the measurements at different times, we are able to observe (for the first time with Brillouin scattering) the non–ergodic behavior typical of this system. We report here preliminary results of such a study.     

In situ small-angle neutron scattering and rheological measurements of shear-induced gelation

The microscopic structure of shear-induced gels for a mixed solution of 2-hydroxyethyl cellulose and nanometer-size spherical droplets has been investigated by in situ small-angle neutron scattering (SANS) with a Couette geometry as a function of shear rate gamma. With increasing gamma, the viscosity increased rapidly at gamma approximately 4.0 s(-1), followed by a shear thinning. After cessation of shear, the system exhibited an extraordinarily large steady viscosity. This phenomenon was observed as a shear-induced sol-gel transition. Real-time SANS measurements showed an increase in the scattering intensity exclusively at low scattering angle region. However, neither orientation of polymer chains nor droplet deformation was detected and the SANS patterns remained isotropic irrespective of gamma. It took about a few days for the gel to recover its original sol state. A possible mechanism of gelation is proposed from the viewpoint of shear-induced percolation transition.     

Transient light scattering in helix ferroelectric liquid crystal cells

The static model to describe coherent (regular) transmittance in helix ferroelectric liquid crystal cells under the transient light scattering mode is proposed. It can be used to develop three-dimensional volumetric and two-dimensional liquid crystal displays. The dependence of coherent transmittance on cell parameters and the amplitude of the applied electric field is analysed. Conditions for increasing scattering efficiency and contrast ratio enhancement through an interference quenching effect of the coherent transmittance are indicated.     

Light scattering from assemblies of spherulites

A general equation describing the small-angle H_v light-scattering intensity for a system of N undeformed spherulites located at random within the sample and taking into account the truncation and interference effects is given. Scattering contour plots or radial scans are reported for various arrangements of the N spherulites. The results show that the interference effect may explain the speckled appearance of the experimental patterns. Moreover, the interference and truncation effects (for the special cases where truncation is considered here) do not seem to shift the position of the maximum scattering angle of the cloverleaf pattern as calculated from the single spherulite theory. Finally, the calculations show that the truncation effect increases the relative intensity of the pattern at large and low scattering angles and at azimuthal angles 0 and 90°C, as compared with the intensity at the position of maximum scattering angle.     

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.     

Assessment of branching in polymers from small-angle x-ray scattering (SAXS)

Small-angle x-ray scattering from solutions was applied in assessing branching using well-characterized dextran hydrolyzates. It was found that the longitudinal and cross-sectional properties of the polysaccharides vary in a manner predictable by the molecular topology of the chains. A hydrodynamically equivalent linear model for dextran is proposed and it has been shown that this model correctly predicts values of Φ and K, Flory's universal hydrodynamic constant and the Flory–Fox–Schaefgen parameter, respectively.     

A close look at silver oxide colloid for surface-enhanced Raman scattering

A silver oxide hydrosol has been prepared by reacting silver nitrate with sodium hydroxide in an aqueous solution. The colloidal particle composition and particle size have been characterized by X-ray diffractometry and transmittance electron microscopy. We have demonstrated that the sol is surface-enhanced Raman scattering active. One major advantage of this sol is the absence of the spectral interference arising from reaction products of the sol formation process. The mechanism of surface-enhanced Raman scattering activity is essentially contributed by the silver particles generated from the photochemical process during the laser excitation.     

Analysis of the structure of very large bacterial aggregates by small-angle multiple light scattering and confocal image analysis

This work aims at developing a more accurate measurement of the physical parameters of fractal dimension and the size distribution of large fractal aggregates by small-angle light scattering. The theory of multiple scattering has been of particular interest in the case of fractal aggregates for which Rayleigh theory is no longer valid. The introduction of multiple scattering theory into the interpretation of scattering by large bacterial aggregates has been used to calculate the fractal dimension and size distribution. The fractal dimension is calculated from the form factor F(q) at large scattering angles. At large angles the fractal dimension can also be computed by considering only the influence of the very local environment on the optical contrast around a subunit. The fractal dimensions of E. coli strains flocculated with two different cationic polymers have been computed by two techniques: static light scattering and confocal image analysis. The fractal dimensions calculated with both techniques at different flocculation times are very similar: between 1.90 and 2.19. The comparison between two completely independent techniques confirms the theoretical approach of multiple scattering of large flocs using the Mie theory. Size distributions have been calculated from light-scattering data taking into account the linear independence of the structure factor S(q) relative to each size class and using the fractal dimension measured from F(q) in the large-angle range or from confocal image analysis. The results are very different from calculations made using hard-sphere particle models. The size distribution is displaced toward the larger sizes when multiple scattering is considered. Using this new approach to the analysis of very large fractal aggregates by static light multiple scattering, the fractal dimension and size distribution can be calculated using two independent parts of the scattering curve.     

Laser light scattering study of polyacrylamide gels

Laser light scattering experiments with polyacrylamide gels containing diffusing bovine plasma albumin are described. Complete heterodyne beating has not been assumed, and an account is given of a novel method for finding the degree of spectral broadening by scanning angles of scatter while measuring the temporal autocorrelation function. Results obtained by this method for polyacrylamide gels and un-cross-linked solutions in the absence of diffusing protein, are compared with those of other authors. In the presence of the protein there is a complex interaction between the diffusion coefficient of the protein and the coefficient associated with the diffusing fluctuations in segment density of polyacrylamide. The diffusing protein dominates at low gel concentrations, and the gel density fluctuations dominates at high gel concentrations. It is proposed that the protein preferentially occupies the less dense regions of the gel, so that at low gel concentrations, where it diffuses faster than the gel fluctuations, it tends to cancel them out, whereas at high gel concentrations where the protein is highly impeded by the gel structure, it tends to be carried along by the gel density fluctuations.