Statistical approach to light scattering from deformed textured heterogeneous polymer materials

A statistical theory of light scattering from deformed isotropic and textured heterogeneous polymer materials is formulated. Two types of textured structures are analyzed: assemblies of optically isotropic and anisotropic rods and a spatially anisotropic distribution of isotropic spherical inclusion centers. The small-angle H_v light-scattering patterns are calculated. The appearance of scattering from isotropic rods and spheres in deformed materials has been demonstrated. The changes of the H_v scattering patterns as a function of elongation and strucuture parameters are discussed. © 1993 John Wiley & Sons, Inc.     

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 light scattering from an anisotropic sphere: Anisotropy and size effects

The recently developed theory of light scattering from an anisotropic sphere (taken as a model for a spherulite) summarizes all information obtainable from such scattering system when the Rayleigh-Gans-Debye approximation is appropriate. The commonly used procedure of size determination from the maximum of the H_v intensity is tested for a number of models differing in radius size, inherent anisotropy δn and mean refractive index ¯n. It has been confirmed, that the parameter (¯n - 1)/δn plays the decisive role in the angular dependence of the H_v intensity and the influence of that parameter on the size determination and resulting accuracy is specified. The results differ for positive and negative spherulites and the stabilizing role of increasing spherulite size in accuracy of procedure is demonstrated. It has been shown that the RGD approximation is appropriate especially for the case of homogeneous spherulite texture (thus implying, that the refractive index of the surrounding is close to the average refractive index of a single spherulite). The results extrapolated outside of the RGD approximation display invariable U_max position for isotropic contribution with increasing sphere size in contrast to the oscillatory character of U_max predicted by the LM solution. It is proposed to construct the anisotropic solution under an approximation recently suggested for thin anisotropic shell. © 1994 John Wiley & Sons, Inc.     

SMALL ANGLE LIGHT SCATTERING MEASUREMENT OF THE ISOTROPIC TO NEMATIC TRANSITION OF A SIDE CHAIN NEMATIC POLYMETHACRYLATE*

The kinetics of I→N transition of a side chain nematic polymethacrylate has been studied by small angledepolarized light scattering intensity measurements using a charge coupled device linear image sensor. The polymer showsthe transition temperatures K52N79I in ℃. The H_v scattering intensity J(q,t) during the transition I (at 80.2℃)→N (at75.8℃) shows that J(q) is independent of q for all t, and during the initial stage (in 6 s) J(t) increases exponentially with t.In the later stage of the transition J(t) approaches a saturation value in 2 min. This experimental result indicates that the I→Ntransition of a liquid crystalline polymer is a spinodal type of phase transition mediated by orientation fluctuation.     

The scattering of light from thin polymer films: Multiple scattering. II. Effect of depolarization

A procedure is described to include the effect of depolarization of the originally plane-polarized incident light beam as it passes through a thin polymer sample on the intensity of multiple light scattering. The multiple scattering gives rise to “polarization scrambling” in which, for example, H_v scattering measurements involve multiple scattered rays which may have undergone some V_v scattering. These phenomena reduce the angular dependence of scattering since large intensities originally occurring at small values of θ are rescattered so as to enhance intensities at other angles. Correction factors for both H_v and V_v scattering are presented.     

A quantum scattering study of collinear state-testate reaction probabilities for the F + H2(v) → HF(v') + H system

A new quantum scattering approach (linear combination of arrangement channels-scattering wavefunction, LCAC-SW) proposed by Deng and his co-workers is used to calculate collinear state-to-state reaction probabilities for the F + H₂(v) → HF(v') + H system. Several interesting problems such M threshold energy, compound states and enhance by translational energy of the reactants and the vibration excitation of products are discussed and they are compared with other theoretical investigations reported in the literature. It is shown that the LCAC-SW approach is the successful one of quantum scattering methods.     

TOF-GISANS investigation of polymer infiltration in mesoporous TiO2 films for photovoltaic applications

The structure of porous TiO₂ films and TiO₂:poly(N-vinylcarbazole) (PVK) composite films is investigated with time-of-flight grazing incidence small-angle neutron scattering (TOF-GISANS). The TiO₂ films have been prepared by application of a sol–gel process with a diblock copolymer as structure directing agent, and the conductive polymer PVK is infiltrated in the porous network by spin coating and solution casting. The films show a hierarchical pore structure with mesopores 52 nm in size and additional large macropores with a diameter of about 180 nm. By matching the scattering contrast of the TiO₂ with the polymer information about the penetration of the polymer in the pores is determined. Whereas in the PVK film prepared by solution casting the pores are filled to a high degree; in the spin coated film, PVK wets only the TiO₂ pore walls and forms a solid overlying layer. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1628–1635, 2010     

Morphology of a liquid-crystalline polyester film

Morphological studies are reported for a thermotropic liquid crystalline polyester. Small angle light scattering studies were carried out as a function of temperature using H_v and V_v polarization with photographic as well as photometric techniques. No scattering was observed from a thin film cast from a dilute solution of the polymer in a highly volatile solvent. When the film was heated, scattering of light was observed above the glass transition temperature of the polyester. The scattering was found to be azimuthally dependent with V_v intensities being much higher than the corresponding H_v intensities. The size of the morphological features responsible for SALS patterns were calculated and were found not to change significantly with temperature ranging from glass transition temperature to the solid-nematic transition temperature of the polyester. The WAXS pattern of solution cast polymer was representative of an amorphous structure. Solution cast films heat treated under various conditions (all above the T_g of the polymer) contained crystalline as well as amorphous structures. The maximum apparent crystallinity for annealed samples was of the order of 30%.     

Kinetic study of the formation reaction of colloidal silica spheres by transmitted-light-intensity and dynamic light-scattering measurements

Kinetic analyses of the formation reaction of colloidal silica spheres which are synthesized from ethyl silicate (EtSi), ammonia and a trace of water in ethanol are made by the transmitted-light-intensity and dynamic light-scattering methods. Sphere size versus time profiles from the two methods agree well especially at the beginning of the reaction. The polymerization starts after a certain induction time (t _i) ranging from several tens of seconds to several minutes. t _i increases as the concentrations of NH₃, EtSi and/or H₂O decrease. The apparent rates of the reaction, v ^′ are estimated from the reciprocal periods between the intersections of the linear line with the initial and final horizontal lines in the cube root of the absorbance versus time plots. Log v ^′ increases linearly with slopes of 1, 2 and 0.5 as the logarithms of the concentrations of EtSi, NH₃ and/or H₂O increase, respectively. These results are consistent with the assumption proposed earlier that the polymerization mechanism of the formation of the small preliminary particles is followed by their coalescence to form large silica spheres. Received: 10 November 1998 Accepted in revised form: 12 January 1999     

Energy resonance and inverse population of the product vibrational states for the reaction F + H2(v = 0) → HF(v′) + H,LCAC‐SW theoretical quantum scattering study

LCAC‐SW (linear combination of arrangement channel‐scattering wavefunction) method was used to calculate collinear state‐to‐state reaction probabilities for the reaction F + H₂(v = 0) → HF(v′) + H on the 6SEC potential energy surface. The results show that reaction probabilities P₀₂ and P₀₃ [i. e., v′ = 2,3 for reaction F + H₂ (v = 0) + HF(v′) + H] are primary, the population of product vibrational states is inverse and the reaction probabilities are oscillatory with collision energies, i.e., there is energy resonance in this reaction, which agrees with a new experiment.     

Dynamic and electrophoretic light scattering of poly(dimethyldiallylammonium chloride) in salt-free solutions

Dynamic and electrophoretic light scattering were used to study the diffusion and electrophoretic mobility of poly(dimethyldiallylammonium chloride) as a function of polymer molecular weight in salt-free solutions. Two relaxation modes characterized as fast diffusion (D_f) and slow diffusion (D_s) were obtained from dynamic light scattering. Although the slow diffusion coefficient D_s strongly depends on molecular weight (M_w), the fast diffusion coefficient D_f was found to be independent of M_w over the range in the study. The fast diffusion was considered as the diffusion of a part of the polymer chain; the slow diffusion was interpreted by multichain diffusion. Electrophoretic light scattering results in the salt-free solution show that the electrophoretic mobility of the polymer is independent of M_w. © 1996 John Wiley & Sons, Inc.     

Filamentous Supramolecular Structures

Summary: The formation of four filament forming proteins was studied mainly by light scattering as a function of the scattering angle. Besides the molar mass M_w and the radius of gyration R_g the contour length L, was determined. The corresponding structure parameters are compared with those of the Aβ-amyloid. A minimum cross-sectional diameter of 2 nm appeared to be necessary for filament stabilization. Bundle and network formation are often observed and are tentatively explained by thermodynamic arguments. The local conformation of the unimer proteins in the filaments remained largely unexplored. Only in one example CD and IR spectroscopy was applied. The analysis disclosed a β-sheet/α-helix transition on de-naturation, as was conjectured before as reason for the Aβ-amyloid formation.     

Synthesis,static, and dynamic light scattering studies of soluble aromatic polyamide

Aromatic polyamide was synthesized via condensation polymerization of 4‐aminophenyl sulfone (APS) with isophthaloyl chloride (IPC) using N,N‐dimethyl acetamide (DMAc) as a solvent under anhydrous conditions. The purified aramid was studied by laser light scattering (LLS) in dimethyl sulfoxide (DMSO), a thermodynamically good solvent at 20°C. Static and dynamic light scattering studies permitted to determine the weight average molecular weight , radius of gyration , second virial coefficient A₂, the hydrodynamic radius R_H, and the diffusion coefficient D. Light scattering experiments were conducted at five concentrations ranging from 0.27 to 2.5 g/L. LLS measurement is also a very useful technique to study the aggregation or association in a polymer system as long as the large “clusters” are reasonably stable in time. The intensity autocorrelation function obtained on the quasi‐elastically scattered light showed a simple diffusive relaxation mode. The ratio of radius of gyration to the hydrodynamic radius, i.e. ～ 1.3 indicates that the polyamide chain has coil conformation in DMSO at 20°C. Copyright © 2008 John Wiley & Sons, Ltd.     

Application of the Lie algebraic approach to diffractionally and rotationally inelastic molecule–surface scattering

The Lie algebraic approach of Alhassid and Levine [Phys. Rev. A 18 , 89 (1978)] is applied to the molecule–surface scattering. Specially, the diffractionally and rotationally inelastic scattering of a diatomic molecule from a solid surface is dealt with. Within the framework of the close-coupling method, we construct a Hamiltonian for the scattering system and use it to generate a dynamical algebra h₆. By solving equations of motion for the group parameters, the scattering wave functions near the surface are obtained. Computed transition probabilities of diffractively and rotationally inelastic scattering of H₂ from LiF(001) surface with the use of Lie algebraic method are seen to agree well with the coupled-channel calculations. The Lie algebraic method thus appears to have a wide range of validity for describing the dynamics of gas–surface scattering. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 981–989, 1997     

Optical studies of the deformation of model filled rubbers

The strain pattern about a spherical glass bead imbedded in a stretched rubber has been calculated and used to predict the birefringence and light scattering. This is compared with experimental measurements of the retardation pattern observed using a polarization microscope and deduced from the low-angle laser H_v light scattering pattern. The agreement with theory is favorable. The light scattering is suggestive of similar origins of light scattering from crystallizing rubbers and from inhomogeneously crosslinked rubbers.     

Effect of Hydrophilic/Hydrophobic Block Ratio and Temperature on the Surface and Associative Properties of Oxyethylene and Oxybutylene Diblock Copolymers in Aqueous Media

Recent development in dispersion science and technology demands block copolymers with a variable block length and composition. To highlight that purpose, the surface active, associative, colloidal, and thermodynamic behavior of three diblock copolymers having different hydrophilic to hydrophobic ratio is reported here. Using surface tension and light scattering measurements, the micellization and adsorption behavior of polyoxyethylene and polyoxybutylene diblock copolymers of the type E_mB_n have been analyzed. Critical micelle concentration (CMC) and related thermodynamic parameters like free energy (ΔG_mic), enthalpy (ΔH_mic), and entropy (ΔS_mic) of micellization were calculated from CMC value using the closed association model. Likewise, the surface active parameters, like surface excess concentration (Γ₂), area per molecule (A₂), and thermodynamic parameters such as free energy (ΔG_ads), enthalpy (ΔH_ads), and entropy (ΔS_ads) of adsorption of polymer at the air/water interface, were also calculated at various temperatures. Static and dynamic light scattering techniques were employed for the determination of the weight-average molar (M_w), association number (N_w), polymer–water interaction (A₂), and micellar size in terms of hydrodynamic radii (R_h) of copolymer micelles. The effect of block length and solution temperature on the surface and micellar properties of these copolymers was also investigated.     

Light absorption due to higher harmonics of molecular vibrations in transparent amorphous polymers for plastic optical fibers

We have studied simple empirical equations to estimate light absorption loss α_v due to harmonics of molecular vibrations of transparent amorphous polymers used in plastic optical fibers (POFs). In the visible region, absorption involves two losses. One is α_v, and the other is the electronic transition absorption loss, α_e. Of the two, α_v is considerably larger than α_e in the wavelength region used for optical communication with POFs. We have clarified relationships between chemical structure of repeat units of polymers and α_v. We find that α_v is proportional to the concentration of specific chemical bonds (C? H, N? H, and Obond;H bonds) in the polymer solid, and we propose empirical equations to estimate α_v from the polymer density and the chemical structure of the repeat unit. These equations are used to estimate α_v of several polymers [i.e., poly(methyl methacrylate), polystyrene, and polycarbonate]. The estimated values are nearly equal to the experimental or reference values. Furthermore, to minimize the attenuation in the POF, we conclude that the POF core polymer should have no N? H, O? H, or aliphatic C? H bonds in its repeat unit.     

Micelle structure and molecular self‐diffusion in isononylphenol ethoxylate–water systems

The structure and dynamic properties of micellar solutions of nonionic surfactants of a series of isononylphenol ethoxylates, C₉H₁₉C₆H₄O(C₂H₄O)_nH (where n = 6,8,9,10, and 12), were studied by NMR diffusometry, dynamic light scattering, and viscosimetry. The sizes of the micelles were determined for different surfactants and at different surfactant concentrations. The numbers of water molecules bound by a micelle and by one oxyethylene group of the surfactant were estimated. Copyright © 2013 John Wiley & Sons, Ltd.     

Deformation of polybutene-1 spherulites

The deformation of fresh and aged polybutene-1 spherulitic samples has been investigated by microscopic observation, interferometry, studying macroscopic and spherulitic birefringence changes, and study of light-scattering patterns. The spherulite deformation is not affine, the microscopic deformation ratio being less than the macroscopic deformation ratio of the sample and greater in the equatorial regions of the spherulite than in the polar regions. The deviation from affine deformation is less for fresh spherulites than for the aged, where void formation occurs in the equatorial part of the spherulite. This gives rise to large scattering by this part of the spherulite and to form birefringence. The spherulite birefringence and its change with elongation is dependent upon the degree of aging of the sample. The spherulite birefringence is more negative for the aged sample. In the polar regions of the spherulite, this negative birefringence decreases and turns positive at higher elongations, characteristic of a reorientation of the crystals with their optic axes turning from being perpendicular to parallel to the spherulite radius. The spherulite birefringence in the equatorial direction becomes somewhat more negative on stretching a fresh sample but less negative on stretching an aged one. Spherulite distortion and orientation changes are apparent from the light-scattering patterns of films possessing small spherulites. The changes in V_v and H_v scattering patterns upon stretch are different for the fresh and aged samples. The V_v patterns of the fresh samples decrease in intensity with time after stretching a fresh sample with the H_v patterns do not.     

Untersuchungen zu den Anisotropie- und Dichtefluktuationen im Polymethylmethacrylat mit Hilfe der Lichtstreuung

Zusammenfassung DieV _r - undH _r -Komponenten des an verschieden vorbehandelten Polymethylmethacrylat-Proben gestreuten Lichtes wurden mit Hilfe eines Lichtstreuphotometers in Abhängigkeit vom Streuwinkel und von der Temperatur gemessen. Aus der Höhe der winkel- und temperaturunabhängigenH _v -Komponente wurde eine obere Grenze von 28 Å für die Größe der im PMMA vorhandenen anisotropen Strukturen errechnet. Tatsächlich dürften sie jedoch wesentlich kleiner sein. Flüssigkeiten mit isotropen Molekülen wie z.B. Tetrachlorkohlenstoff verursachen nämlich bereits eine ähnlich hoheH _v -Komponente.Neben den geringen Anisotropiefluktuationen liegen Dichtefluktuationen vor, die zu einer Winkelabhängigkeit derV _v -Komponente führen. Verantwortlich hierfür sind niedermolekulare Bereiche und Löcher mit Dimensionen von 1000–3000 Å. Zusätzlich sind thermische Dichtefluktutionen vorhanden. Bei großen Streuwinkeln kommt etwa die Hälfte der gestreuten Intensität durch sie zustande.

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Summary TheV _v andH _v components of the light scattered by polymethylmethacrylate samples, which had been subjected to different pretreatments, were measured as a function of the scattering angle and temperature with the help of a light scattering photometer. An upper limit of 28 Å for the size of the anisotropic structures present in PMMA was calculated from the height of the angle- and temperature-independentH _v component. They may however be essentially smaller. In fact, fluids with isotropic molecules, for example carbon tetrachloride, give rise to a similarly highH _v component.In addition to the slight anisotropy fluctuations, density fluctuations are present, which lead to an angular dependence of theV _v component. Lower molecular regions and holes with dimensions of 1000–3000 Å are responsible for this. There exist also thermal fluctuations. Approximately half of the scattered light intensity at large scattering angles is caused by them.