Light scattering from tilted two-dimensional spherulites

The theory of small-angle light scattering was developed for oblique incidence of the light beam on the surface of a two-dimensional spherulite. Results of the theory were compared with previously reported results of light scattering from two-dimensional and three-dimensional spherulites for normal incidence, and with some experimental patterns. The comparisons suggest that the scattering intensity distributions of two-dimensional spherulites deviate from those of three-dimensional spherulites when the sample surface is tilted with respect to the propagation direction of the incident beam, although they are almost identical when the sample surface is normal to the incident beam. Observation of the change of scattered intensity distributions upon tilting the samples thus provides a method of distinguishing between two-dimensional and three-dimensional spherulites. Moreover, this observation makes it possible to determine the degree of planar orientation of the optic axes of optically anisotropic scattering elements within two-dimensional spherulites. The calculations were carried out for special cases of two-dimensional spherulites with the optic axis orientation confined to the two-dimensional plane and randomly or helicoidally rotated around the spherulite radii.     

Small-angle light scattering by random assemblies of incomplete spherulites. II. Truncated spherulites

Previous theoretical calculations of the scattering from spherulites are for isolated complete spheres, whereas most spherulitic polymer samples contain truncated spherulites as a result of impingement by other spherulites. The effect of such truncations on the scattering patterns for two-dimensional spherulites is explored as a function of the size, number and location of the truncations. The scattering of severely truncated spherulites is modified, particularly with regard to the enhancement of the H_V scattering at small angles. However, reasonable amounts of truncation corresponding to experimentally observed structures do not produce appreciable modification of the pattern so that the neglect of truncation will not lead to appreciable error in the estimated spherulite size from light scattering.     

Multiple-order light scattering from ringed spherulites

Light scattering from polymer films containing ringed spherulites may show multiple-order intensity maxima directly related to the period of the banded structure. Calculations based on spherulite models where the angle of twist of lamellae ω varies linearly with radial distance predict only first-order peaks. If the variation of ω is nonlinear, even though the ring spacing remains constant, higher-order intensity maxima will result. Other sources of multiple-order scattering are considered. It is concluded that for polyethylene the presence of multiple-order scattering is due to non-uniform twisting of the lamellae.     

Small-angle light scattering by random assemblies of incomplete spherulites. I. Sheaflike textures

The calculation of the scattering from a sheaflike sector of a two-dimensional spherulite has been carried out as a function of the apex angle of the sector. It is found that while for a complete spherulite the H_v scattered intensity is zero at zero scattering angle, there is an increasing intensity of scattering at 0° as the sector angle narrows. For very small values of the sector angle, the scattering becomes similar to that of a rod, with the exception that a scattering maximum is still seen at an angle close to that at which the spherulite scattering maximum occurs. The predictions of the model compare favorably with the scattering patterns observed for polymers in early stages of spherulitic growth.     

A lattice theory of light scattering from disordered spherulites

A lattice theory of orientational disorder in two-dimensional spherulites is developed in which the orientation direction of the optic axis in lattice cells is allowed statistically to deviate from its mean value in a manner correlated with the orientation in neighboring cells. The H_v light scattering patterns arising from such disordered spherulites deviate from the patterns for perfect spherulites in that there is excess intensity at both small and large scattering angles and the intensity at the maximum is lower. A comparison of the calculated scattering angular dependence with that which is experimentally measured permits assignment of values of correlation parameters. A consequence of this disorder is that the spherulite birefringence is reduced below that calculated on the basis of perfect crystalline orientation in agreement with experiment.     

Small-angle light scattering by random assemblies of incomplete spherulites. Systems with partial degree of volume filling

A theory is presented to account for the effect of the impingement of growing spherulites on their H_v small-angle light scattering patterns. The theory is developed on the basis of results of computer-simulated two-dimensional spherulite growth and calculated scattered intensities. The impingement produces a lowering of the intensity of the scattering maximum and the diminishing of the overall sharpness of the scattering peak. The extent of these effects increases with area fraction of spherulites. A procedure is suggested for determining correction factors that may be applied to intensity data obtained during the course of spherulite crystallization. An interpretation is made of the type of average spherulite size determined from the scattering angle of maximum intensity.     

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.     

Surface-enhanced Raman scattering from magneto-metal nanoparticle assemblies

Binary nanoparticles composed of a superparamagnetic Fe₃O₄ core and an Au nanoshell (Fe₃O₄@Au) were prepared via a simple co-precipitation method followed by seed-mediated growth process. The nanoparticles exhibited functions of both fast magnetic response and local surface plasmon resonance. The Fe₃O₄@Au nanoparticles were used as probes for surface-enhanced Raman scattering (SERS) using p-thiocresol (p-TC) as reporter molecule. With the ability of analyte capture and concentration magnetically, the Fe₃O₄@Au nanoparticles showed significant SERS properties with excellent reproducibility. Under non-optimized conditions, detection limit as low as 4.55 pM of analyte can be reached using Fe₃O₄@Au nanoparticle assemblies, which excel remarkably the cases with traditional Au nanoprobes.     

Light scattering from albumins

In light scattering data of albumins, one distinguishes a large broad band from the normal Raman lines. That broad band in ovuline albumin is shown to have a pseudo-Raman behavior.     

Light scattering from spherulitic materials

The azimuthal angular dependence of the depolarized component of the light scattered from spherulitic materials is derived by an algebraic method that avoids the difficult angular integrations of the usual approach. The result appears as a sum of products of two factors, a molecular factor, that depends only on the structure and the scattering angle θ, and a geometrical factor that depends only on the azimuthal angle ? and the scattering angle θ. The molecular factors are evaluated for models of spherulitic structure that assume a constant tilt of the optical polarizability tensor. The radial distribution, in principle, is arbitrary, and an evaluation for the layered spherulite is made. If the tilt angle is ω when the azimuthal patterns depend only on a linear combination of P₂(cos ω) and P₄(cos ω), where P_n(x) is the Legendre polynomial of order n. In our theory the V_H scattering pattern is a four-leaf clover whose axes are restricted by the theory to be at either 0 or 45° to the polarization directions.     

Small-angle Hv light scattering from deformed spherulites with orientational fluctuation of optical axes

Mathematical evaluation was done for small-angle light scattering from disordered spherulites under Hv polarization conditions. The calculation was carried out for a two-dimensional deformed spherulite whose major optical axes are oriented at 0 or 45° with respect to the radial direction. The calculated results were compared with the scattering patterns observed for polypropylene (PP) spherulites, whose optical axes are oriented parallel to the radial direction, and poly(butylene terephthalate) (PBT) spherulites, whose optical axes are oriented at 45° with respect to the radial direction. The degree of disorder for PBT was much larger than that for PP. By selecting a parameter associated with the degree of disorder of the optical axes with respect to the radial direction, the patterns calculated as a function of draw ratios were in good agreement with the observed patterns, which changed from four leaves to streaks extended in the horizontal direction. Through a series of observed and calculated patterns, it turns out that an increase in the disorder under the deformation process occurs drastically even for perfect spherulites in an undeformed state.     

Surface enhanced Raman scattering from layered assemblies of close-packed gold nanoparticles

A synthetic method of ordering hydrophilic gold nanoparticles into a close-packed two-dimensional array at a hexane-water interface and subsequent transferring of such structure onto a solid substrate is described. By repeating the transfer process, multilayered gold nanoparticle films are formed without need of linker molecules. Their surface enhanced Raman scattering (SERS) efficiencies are compared as a function of the number of layers. It is shown that both the number of layers and the particle size contribute to SERS phenomenon. Judging from the noticeable dependence of SERS efficiency on the nanometer scale architecture, the close-packed nanoparticle formation at an immiscible interface presents a facile route to the preparation of highly active and relatively clean SERS substrates by controlling both the particle size and the film thickness. Among the investigated samples, the gold nanoparticle film assembled with quintuple layers of 30 nm diameter particles showed the maximum SERS efficiency.     

Scattering from truncated spherulites

A general two-dimensional theory is derived to explain the light scattering from truncated spherulites. The severity of the truncation is expressed by a statistical parameter σ²/ā² which is the ratio of the variance σ² of the size of the spherulite to the square of its average size ā. The H_v light-scattering patterns are calculated for different values of the truncation parameter. It is observed that the truncation decreases the position of maximum scattering intensity of the pattern. It also increases the scattering intensity at small and large angles, but reduces it at intermediate angles. For a spherulitic polyethylene sample, the truncation parameter is found to equal 0.100 ± 0.030 as measured microscopically. The theory can also be used to calculate light-scattering patterns from row-nucleated spherulites. If it is assumed that the interference effect averages out to zero when a large number of spherulites is involved, a single “sliced” spherulite model can be used. Then, the scattering intensity per unit area decreases as the “slice” becomes very thin.     

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.     

Light scattering characterization of constituent copolymers from polyacrylate latices

The method described is based on static light scattering measurement of solutions obtained by the direct dissolution of latex in a suitable organic solvent without intermediate isolation of solids. In the case of latices of acrylate copolymers with acrylic or methacrylic acid, often used in the paint industry, 2-ethoxyethanol proved to be the best solvent for this purpose. Static light scattering can also be used to estimate the mass and size of the dispersion particles prior to their dissolution.     

Light scattering near and from interfaces using evanescent wave and ellipsometric light scattering

The broad range of interface light scattering investigations in recent years shows the power and the versatility of these techniques to address new and open questions in colloid and interface science and the soft condensed matter field. Structural information for polymers, liquid crystals, or colloids close to planar or spherical colloidal interfaces are either captured with long range light scattering resolution, or in a complementary approach by high resolution ellipsometric techniques. Of special interest is the dynamic behavior close to or in interfaces, since it determines material properties and responses to external fields. Due to the broad dynamical range and the high scattering contrast for visible light, interface light scattering is a key to elucidate soft matter interfacial dynamics. This contribution reviews experimental and related theoretical approaches for interface light scattering and further gives an overview of achievements based on such techniques.     

Light scattering from a binary mixture with internal relaxation

The hydrodynamic modes of a binary liquid mixture are investigated for two cases: (1) the bulk viscosity contains a frequency dependent part, and (2) an additional internal variable is introduced. The consequences for the light scat- tering spectrum are discussed and comparisons are made with previous investigations by other authors.     

Light scattering from crystalline superstructure in tubular-extruded polybutene-1 films

Light scattering from polybutene-1 films prepared by tubular extrusion was studied in order to investigate its crystalline superstructure and the deformation mechanism. Analysis of the light-scattering patterns together with electron micrographs, indicate the existence of sheaflike crystalline superstructures. The sheaves are aligned nearly side by side with their axes preferentially oriented perpendicular to the machine direction. The H_v scattering patterns exhibit a “butterfly” appearance. Analysis of the patterns in terms of scattering and azimuthal angles at which the scattering intensity is a maximum yields information on the size and shape of the sheaflike texture. The information should be of importance in studies of anisotropic crystal growth caused by molecular orientation in the melt and of the deformation mechanism of the texture. The deformation behavior should be representative of that of different parts of spherulites, at least qualitatively; the deformation of the texture along the machine and transverse directions corresponds to deformation of equatorial and meridional regions of a spherulite, respectively.