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.     

Small-angle scattering of polarized light. I. comparison of theoretical predictions for isotropic and anisotropic spheres

This paper describes small angle light scattering (SALS) calculations and compares the results for isotropic and anisotropic spheres. For isotropic spheres the exact Mie theory is compared with the Rayleigh-Gans-Debye (RGD) and the anomalous diffraction (AD) approximations in order to study the validity of the approximations. For anisotropic spheres the RGD is compared with the AD approximation. A study of SALS in the RGD approximation shows that the first-order intensity maximum corresponding to a lobe of the four-leaf clover pattern is not only a function of the sphere diameter but also depends on the isotropic and the anisotropic refractive index of the sphere. The practical implications of this are discussed.     

Small-angle scattering of polarized light. IV. Isotropic to birefringent transition for spheres

The Rayleigh-Gans-Debye approximation is used to investigate the small-angle, cross-polarized light scattering by a sphere of radius a, birefringence Δμ and relative index μ. If θ_max is the polar scattering angle of the intensity maxima, the quantity Û_max = 4πa/λ × sin (θ_max/2) behaves in two different ways according to the signs of Δμ and μ ? 1. When Δμ > 0, μ > 1 or Δμ < 0, μ < 1, then Û_max varies from 2.8 to 4.1 as Δμ increases from zero. If Δμ < 0, μ > 1 or Δμ > 0, μ < 1, then Û_max goes from 2.8 to about 6, thereafter decreasing to 4.1. Another interesting result is that the value of Û_max for a highly briefringent sphere is 4.1 only for large diameters. It decreases to 4.0 when the diameter decreases.     

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.     

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.     

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     

Small-angle light scattering from optically anisotropic spheres and disks. Theory and experimental verification

The small-angle light scattering (SALS) theory for optically anisotropic spheres and disks is examined in depth. An error is found in the existing sphere equations. The correct form of the equations is identified and then experimentally verified for dilute starch suspensions. Increased concentrations and solid films of starch granules are used to identify the effect of concentration on the scattering envelope. Spherulitic films of isotactic polypropylene, isotactic polystyrene, nylon 610, PET, and nylon 66 are then used to examine different aspects of the SALS theory. Experimental observations are found to agree with the predictions of the correct SALS equations. Disk theory is interrogated and correlated with predictions for spheres. It is found that the predicted patterns from spheres and disks are very similar under identical optical conditions, in contradiction to earlier predictions. A method is developed for identifying the optical sign of spherulites too small to be seen in the optical microscope. This study constitutes a comprehensive examination of SALS theory and includes many other aspects of the phenomena. A catalogue of theoretical V_v SALS patterns from spheres and disks is also included.     

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.     

Small-angle light scattering from hedrites,ovoids, and spiral ovoids. II. Experimental

Procedures for obtaining hedrites, ovoids, and spiral ovoids in polyoxymethylene are described. Results of morphological studies on these structures by optical and electron microscopy are presented. Small-angle light scattering studies on single isolated supermolecular structures are described. The V_v and H_v diffraction patterns obtained experimentally are discussed in the light of theoretical results of Part I of this study.     

Small-angle x-ray scattering of semicrystalline polymers. II. Analysis of experimental scattering curves

The small-angle x-ray scattering (SAXS) patterns of a number of linear polyethylene (PE) and polyoxymethylene (POM) samples have been measured and compared to the intensity functions of one-dimensional paracrystalline lattices. It was found that the ratio of the angular positions of the second and first scattering maxima (θ₂/θ₁) is generally less than or equal to 2.0, implying that the paracrystalline lattice statistics are symmetric or moderately skewed to larger periods. The Bragg spacing (“long period”) of such samples is within 3% of the identity period of the macrolattice. With quenched POM the ratio θ₂/θ₁ is substantially larger than 2.0, which indicates either extremely asymmetric lattice statistics or coexisting structures within the material. From consideration of the reduced widths of the first scattering maxima, it was found that some broadening is present in addition to that from the paracrystallinity. This excess broadening could result from a finite lattice length of ～1000 Å. The need for careful experimental technique for obtaining the actual position of the scattering maximum is emphasized. In addition, it is demonstrated that the scattering curve and the correlation function of the system yield essentially the same apparent structural periods.     

Small-angle X-ray scattering studies on the X-ray induced aggregation of malate synthase II. Inactivation and aggregation experiments

The X-ray induced inactivation and aggregation of the enzyme malate synthase in aqueous solution were investigated by small-angle X-ray scattering and enzymic tests.Enzymic activity decreases about exponentially with increasing dose. The rate of inactivation depends linearly on the dose rate; the extrapolation to zero dose rate yielded a finite limiting value of the rate constant of inactivation. The inactivation doseD ₃₇ is a linear function of enzyme concentration.Enzymic tests and small-angle X-ray scattering on samples, which had been X-irradiated before the measurements, showed no direct relation between aggregation and inactivation. The substrates glyoxylate and acetyl-CoA and the substrate analogue pyruvate are able to protect the enzyme against radiation damage, however to a different extent against aggregation (pyruvate > glyoxylate > acetyl-CoA) or inactivation (glyoxylate > pyruvate acetyl-CoA; the latter showed no effect). These findings and the protective effect of dithiothreitol against aggregation and inactivation of the enzyme are discussed in context with the formation of hydrogen peroxide. A possible shielding of radiosensitive groups of the enzyme by the substrates and scavenging are also taken into consideration as explanations for the protective effects.While the novel application of small-angle X-ray scattering in the field of radiation biology delivers information on X-ray induced structural changes of biopolymers and on their kinetics, the occurrence of radiation damages in conventional small-angle X-ray scattering measurements on biopolymers can be reduced by a variety of precautions.

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Röntgenkleinwinkeluntersuchungen der durch Röntgenstrahlen induzierten Aggregation der Malatsynthase. II. Inaktivierungs- und Aggregationsexperimente

Zusammenfassung Die durch Röntgenbestrahlung in wäßriger Lösung induzierte Inaktivierung und Aggregation des Enzyms Malatsynthase wurden mit der Methode der Röntgenkleinwinkelstreuung und mit Enzymtests untersucht.Die Enzymaktivität nimmt mit zunehmender Dosis annähernd exponentiell ab. Die Inaktivierungsgeschwindigkeit hängt linear von der Dosisleistung ab; die Extrapolation auf Dosisleistung null ergab einen endlichen Grenzwert der Inaktivierungsgeschwindigkeitskonstante. Die InaktivierungsdosisD ₃₇ ist eine lineare Funktion der Enzymkonzentration.Enzymtests und Röntgenkleinwinkelstreuexperimente an Proben, welche vorher bereits bestrahlt worden waren, zeigten keinen direkten Zusammenhang zwischen Aggregation und Inaktivierung. Die Substrate Glyoxylat und Acetyl-CoA sowie das Substratanaloge Pyruvat vermögen das Enzym gegen Strahlenschäden zu schützen, jedoch in unterschiedlichem Ausmß gegen Aggregation (Pyruvat > Glyoxylat > Acetyl-CoA) oder Inaktivierung (Glyoxylat > Pyruvat Acetyl-CoA; letzteres zeigte keinen Effekt). Diese Befunde und die Schutzwirkung von Dithiothreitol gegen die Aggregation und Inaktivierung des Enzyms werden in Zusammenhang mit der Bildung von Wasserstoffperoxid diskutiert. Als weitere Erklärungen für die Schutzwirkungen werden die mögliche Abschirmung strahlenempfindlicher Gruppen des Enzyms durch die Substrate und der Einfang von Radikalen in Erwägung gezogen.Während die neuartige Anwendung der Röntgenkleinwinkelstreuung auf dem Gebiet der Radiobiologie Aufschluß über strahleninduzierte Strukturänderungen von Biopolymeren und deren Kinetik gibt, läßt sich das Auftreten von Strahlenschäden bei konventionellen Röntgenkleinwinkelmessungen an Biopolymeren durch verschiedene Vorkehrungen reduzieren.

     

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 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.     

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.     

Small-angle light scattering from thin polymer films: Multiple scattering from samples with rodlike morphology

Hartel's theory for multiple scattering has been generalized to the case of small-angle light scattering (SALS) by polymers having a roadlike morphology. It is shown that multiple scattering tends to make the scattering tends to make the scattering patterns more diffuse and leads to an underestimation of the size of the units (rods) measured from such patterns. The error induced by neglecting multiple scattering has been estimated at 10% for a transmittance of 75% and at 22% for a transmittance of 50%. A correction method based on Hartel's procedure is suggested.     

Incoherent subharmonic light scattering in isotropic media

Incoherent subharmonic light scattering in isotropic media is a new kind of nonlinear light scattering, which involves single input photon and multiple output photons of equal frequency. We investigate theoretically the dependence of the subharmonic scattering intensity on the hyperpolarizability of molecules and the incident intensity using nonlinear optics theory similar to that used for Hyper-Rayleigh scattering and degenerate optical parametric oscillators. It is derived that the subharmonic scattering intensities grow exponentially or superexponentially with the hyperpolarizability of molecules and the incident intensity.     

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.