Light scattering from polymer films having optically anisotropic rodlike texture. A quantitative test of theories

The light scattering intensity distribution from rodlike crystalline superstructures is quantitatively investigated theoretically and experimentally. The arithmetic average of theoretical H_v scattered intensities at azimuthal angle μ = 0° and μ = 45° is shown to decrease with increasing scattering angle θ in proportion to W^?1 at high scattering angles for a system composed of a random assembly of rodlike superstructure having very small lateral dimensions relative to the length. The quantity W is defined as 2π(L/λ) sin θ where L is the length of the rod, and λ is the wavelength of light in the medium. A method is proposed to estimate the length L by using the W^?1 dependence. Effects of internal heterogenity, polydispersity in rod length, and finite lateral dimensions of the rodlike superstructure are considered to account for experimental deviation of the scattered intensity distributions from the W^?1 dependence. The effect of finite lateral dimensions turns out to be the most important.     

Laser light-scattering investigation of the density of pauci-chain polystyrene microlatices

The average density (〈ρ〉) of the pauci-chain polystyrene microlatices (PCPS), which contains a few linear polystyrene chains, was investigated by laser light scattering (LLS) including both angular dependence of absolute integrated scattered intensity (static LLS) and of the line-width distribution G(Γ) (dynamic LLS). In static LLS, the weight-average particle mass (M_w) and the z-average radius of gyration (R_g) were measured; and simultaneously in dynamic LLS, the hydrodynamic radius distribution was obtained from Laplace inversion of very precisely measured intensity-intensity time correlation function. A combination of both the static and dynamic LLS results leads us to a value of 〈ρ〉. For comparison, we also determined 〈ρ〉 of conventional multichain polystyrene latex (MCPS) by following the same LLS procedure. It was found that 〈ρ〉_MCPS = 〈_bulk〉 = 1.05 g/cm^3, but 〈ρ〉_PCPS = 0.92 g/cm^3. This difference in density suggests that the intersegmental distance in MCPS or bulk polystyrene is smaller than that in PCPS, even the chains in PCPS are confined to a smaller volume. This might attribute to the fact, namely the intersegmental approaching inside PCPS is mainly the intrachain crossing which is more difficult in comparison with the interchain crossing inside MCPS or bulk polystyrene.     

Syntheses,Crystal Structures,and Properties of Two Novel CL‐20‐based Cocrystals

In recent years, cocrystallization has emerged as an effective way of tuning the properties of compounds and has been widely used in the field of energetic materials. In this study, we have prepared two novel cocrystals of CL‐20 and methylimidazole, including a 1:2 CL‐20 / 2‐mercapto‐1‐methylimidazole ( 1 ) and a 1:4 CL‐20 / 4‐methyl‐5‐nitroimidazole ( 2 ). Cocrystal 1 has good physical and detonation properties (ρ₁ = 1.652 g · cm^–3, D₁ = 7073 m · s^–1, P₁ = 21.6 GPa); however, cocrystal 2 shows higher properties (ρ₂ = 1.680 g · cm^–3, D₂ = 7945 m · s^–1, P₂ = 27.4 GPa). The performance of both cocrystals is better than those of TNT. Thermal performance suggests that both the cocrystals have moderate thermal stabilities. Cocrystal 1 decomposes at 164.9 °C and cocrystal 2 has an exothermic peak at 221 °C. Both cocrystals are insensitive energetic explosives (IS > 40 J, FS > 360 N). Methylimidazole compounds are rarely used as coformers to form cocrystals with CL‐20, which possess good properties for a range of potential applications. Herein, we provide new possible directions for enriching cocrystal speciation.     

Scattered intensity by a cross-linked polymer blend

Cross-linked mixtures of polystyrene and poly(vinyl methyl ether) exhibit a non-vanishing zero-angle intensity in small-angle neutron scattering experiments. A possible explanation is that fluctuations in composition in the mixture may be frozen by the presence of cross-links. Assuming this, we introduce a screening length κ by the condition that the scattered intensity should not be changed by cross-linking. We find κ² ∼ C/(χ − χ_i), where C is an elastic constant, χ and χ_i, respectively, the inverse temperature and that where cross-linking is performed. When the temperature is varied, we find three regimes. In the first one, the scattered intensity is monotonously decreasing. In the second one, it has a finite maximum. In the last one, the maximum eventually diverges.     

A review of some recent applications of small-angle scattering in studies of polydisperse systems and porous materials

Recent progress in two fields of small-angle scattering is reviewed: (a) New procedures have been developed by Kotlarchyk and Chen and by Triolo, Griffith, and Compere for calculating the intensity of the small-angle scattering from polydisperse systems of interacting particles of different sizes. These techniques have significantly increased the quantitative information that can be obtained from the scattering data. (b) The pore boundaries in many porous solids have been found to be fractal surfaces. In a porous solid in which the pores have an average diameter ϵ and the pore boundary surfaces have a fractal dimension D, the scattered intensity for qϵ, >> 1 is proportional to q^−(6-D), where q = πλ⁻¹sin(θ/2), θ is the scattering angle, and λ is the wavelength. Some small-angle scattering studies of fractal porosity are outlined.     

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.     

Measurements of differential cross sections for vibrational quantum transitions in scattering of Li+ on H2

A pulsed monoenergetic ⁷Li⁺ ion beam (lab. energy 10–40 eV) is scattered from a highly collimated (= 1.5°) H₂ nozzle beam. The time-of-flight spectrum of the ions scattered in the forward laboratory direction shows both a fast peak corresponding to forward center-of-mass scattering and a slow peak corresponding to wide-angle center-of-mass scattering. These peaks have been further resolved to show contributions from individual vibrational quantum transitions. From an analysis of the time-of flight spectra the differential inelastic cross sections for a wide range of angles and energies between 2 eV <E_cm < 9 eV have been determined. The spectra also contain information on rotational inelastic cross sections.     

Small-angle light scattering from hedrites,ovoids, and spiral ovoids. I. Theoretical considerations

Taking into consideration results of our microscopy studies and data given in the literature on the structure of hedrites, ovoids, and spiral ovoids, we have developed optical models for these morphological entities. These models are applied to calculations of small-angle scattered light intensity distributions for these structural elements. Analytic formulae computed for the V_v and H_v scattering patterns contain terms dependent only on azimuthal angle μ and vertical angle θ. For hedrites and ovoids, equations are derived relating the characteristic points of scattered light intensity patterns to structural parameters. The corresponding diagrams of light intensity distributions are given.     

UNMIXING KINETICS AND ITS MORPHOLOGY OF POLY ( ETHYLENE OXIDE) WITH POLYETHERSULPHONES BLENDS

Unmixing kinetics in a binary polymer mixture of polyethersulphones with poly (ethylene oxide) by spinodal decomposition has been investigated with time-resolved light scattering and microscope methods. The results showed that time evolution of scattered light intensity is of an exponential growth The maximum growth rate R(qm) of phase separation has been obtained. The experimental data did not satisfy the condition that the plot of R(q)/q~2 vs q~2 should be linear For unmixing system annealing at 30℃for three hours, its morphology manifested dish structure The experimental data of the Bragg spacing D_m can be correlated with a straight line which expresses the power-law relation, D_m=bl~α     

A laser light-scattering study of the structure of agarose gels

Diffusion coefficients of dextran fractions within agarose gels surrounded by dextran solution have been measured by laser light scattering using the autocorrelation method. Plots were made of the diffusion coefficient relative to that in dilute solution, D/D₀, against the logarithm of hydrodynamic diameter logd for each concentration of agarose, and superimposed by displacing horizontally to produce a unified plot. In this way it was shown that D/D₀ is a function of C^bd, where C is agarose concentration, with b = 1/3 and 1/2 for the cases in which the dextrans were mixed in before gelation and allowed to diffuse in afterwards, respectively, the plots being the same for a reference concentration of 0.7%. A value of b = 1/2 is that which would be expected if the molecular weight per unit length of the gel fibers were independent of concentration, and a value of 25 kg mol^?1 nm^?1 is calculated. Mobile concentrations of dextran within the gels relative to those in the surrounding solutions were found by determining the scattered intensity associated with the diffusing dextran molecules from the zero-time value of the autocorrelation function. All results and calculations are discussed in terms of current theories, and compared with earlier work on calcium alginate gels for which a molecular weight per unit length of gel fiber of 0.59 kg mol^?1 nm^?1 was calculated. The nature of the spectral broadening of the light scattered from agarose gels in the absence of dextran is described.     

Spectrum of light scattered from polydisperse polymer solutions

We examine several methods for analyzing the spectrum of light scattered from polydisperse polymer solutions. General expressions are reviewed for the inelastic scattering spectra and integrated intensities due to the pure translational normal mode of motion, using both heterodyne and homodyne detection, in terms of the molecular weights, concentrations, scattering form factors, and diffusion coefficients of the individual polymeric species, These results are used to obtain general expressions for the limiting slopes and intercepts of various rearranged versions of the equation I(v) = (A/π)²/(v² + γ²) that permit linear plotting: I(v) is the intensity of light scattered at frequency v, A is the integrated intensity, and γ is the spectral halfwidth, K²D/2π, where K is the scattering vector and D the diffusion coefficient. These results are applied to the special case of a Schulz-Zimm distribution, neglecting form factors, to obtain explicit expressions relating the average diffusion coefficients determined by these procedures to other measurable quantities: the mean polymer radius; the diffusion coefficient of the weight-average species; and, together with the weight-average sedimentation coefficient, the weight-average molecular weight. Numerical calculations for two particular cases indicate the relative merits of the various data analysis procedures. Homodyne detection gives average values that are closer to weight averages than does heterodyne detection.     

Solvent effects in dense gases

The effects of perturber gases, partial pressures in the range 0–50 atm, on the absorption spectra of high-n Rydbergs, n ≥ 10, in methyl iodide and benzene have been investigated. The perturbers were rare gases and H₂. It has been shown that the spectroscopic energy shift Δ = Δ(ρ, n) is given by Δ = Δ°ρ, where ρ is the number density of the perturber, for n ≥ 10. The shift data can be interpreted using a Fermi model, and values of scattering lengths for perturbers can be extracted. These scattering lengths are internally consistent, independent of the absorber, and in excellent agreement with electron-swarm results. Given that the Fermi model is nonspecific and microscopic, scattering shifts and lengths for mixtures of perturber gases can be predicted. These predictions, having been verified by experiment for He/Ar mixtures, provide a means of “tailoring” any required scattering length. Finally, it is shown empirically that the determinative scattering parameter is the polarizability of the perturber, and a universal relationship a = ?0.26α + 1.18 between scattering length a, in Bohr radii, and polarizability α is found to exist.     

Final report on VAMAS round‐robin study to evaluate a correction method for saturation effects in DSIMS

A Versailles Project on Advanced Materials and Standards round robin test (RRT) has been conducted to evaluate the linearity of the instrumental intensity scale and correction method using an approximation intermediate extended dead time model with parameters derived from two different isotope depth profiles. Nine organizations in five countries participated. An arsenic‐implanted silicon wafer and a film of BN diffused into a Si wafer were supplied by the National Institute of Advanced Industrial Science and Technology along with instructions for the RRT. The instruments used to analyze ¹⁰³(AsSi)^? and ¹⁰⁵(AsSi)^? from arsenic‐implanted samples were five quadrupole‐type SIMS and four magnetic‐sector type SIMS. The instruments used to analyze ¹⁰B⁺ and ¹¹B⁺ from the BN‐diffused samples were three quadrupole‐type SIMS, four magnetic‐sector type SIMS, and one time‐of‐flight type SIMS. We validated the usefulness of the approximation intermediate extended dead time model to correct saturated intensities for all SIMS in this RRT. The optimum extension parameter ρ tends to be affected by the ratio of the maximum reliable intensity to the maximum intensity in raw profiles. From the ratio, ρ may be predicted when the intensity reaches full saturation. On the other hand, ρ is also affected by lateral non‐uniformity of intensity. In practice, because the maximum intensity does not reach full saturation and the intensity is not laterally uniform, ρ is likely to be smaller than its predicted value. Copyright © 2015 John Wiley & Sons, Ltd.     

Investigation on the dynamics of aromatic polyesters by means of high resolution solid state CPMAS 13C NMR

The dynamics of amorphous aromatic polyesters consisting of poly(ethylene terephthalate) (PET), poly(ethylene isophthalate) (PEI), and poly(ethylene 2,6-naphthalenedicarboxylate) (PEN) has been investigated by means of solid state CPMAS ¹³C NMR. Proton T₂, ¹³C T_1ρ, and proton T_1ρ decays have been measured in particular, and the experimental data fitted to suitable model functions to determine best relaxation parameters. The fitting results show for proton T₂ and ¹³C T_1ρ measurements the presence of two components with different relaxation times and intensities, arising from different motional domains. The proton T_1ρ, on the contrary, shows a single component which limits the dimensions of the two regions to less than 20 Angstroms. The dependence of ¹³C T_1ρ values on two different irradiating field strengths (H₁ = 38 KHz, H₁ = 60 KHz) allowed the assignment of each component to relatively rigid and mobile regions. By comparing the three polymers we observe that PEN and PEI have a similar relaxation behavior, while a higher fraction of mobile components was found for PET. These differences are believed to arise mainly from local motions of the aromatic rings. The relaxation measurements have been evaluated to suggest a correspondence to O₂ and CO₂ gas permeabilities in PET, PEI, and PEN. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1557–1566, 1998     

Dynamic light scattering and small-angle neutron scattering studies on organogels formed with a gelator

Small-angle neutron scattering (SANS) and light scattering studies were carried out on an organogel consisting of a gelator, coded P-1, and dimethyl sulfoxide (DMSO). The gelator was made of an oligosiloxane stem and about eight branches of an amino acid derivative combined with a long alkyl chain. The amino acid part, N-n-pentanoyl-L -isoleucylaminooctadecane, was responsible for intermolecular association via hydrogen bonding between amide groups. After the complete dissolution of P-1 in DMSO at 85 °C, the solution was cooled, and the variations of the scattered light intensity were monitored as a function of the temperature. The scattered intensity increased drastically at about 40 °C when the P-1 concentration (C) was 3.5 g/L, and this indicated gel formation. The SANS results showed that the scattering intensity function was a monotonically decreasing function, regardless of C. A master relationship of the scattering intensity was obtained with respect to C. These scattering studies disclosed the following facts. First, gelation could be monitored as an abrupt increase in the intensity. Second, the gel was composed of randomly oriented bundlelike clusters. Third, the structure factor could be reduced by the gelator concentration, and this indicated the presence of a self-similar structure across the gelation threshold. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1841–1848, 2004     

State dependence of rayleigh scattering from an=2 state of hydrogenlike atoms

We consider Rayleigh scattering from a hydrogenlike atom in an arbitrary excitedn=2 state, and we investigate theoretically the dependence of the scattered radiation intensity and Stokes parameters on the state multipoles for the case of unpolarized incident radiation. Because in then=2 case Rayleigh scattering can not be accompanied by the change of the electron angular momentum, only 10 out of the 16 state multipoles influence the scattered radiation attributes. Our study reveals the existence of a measurable quantity which is determined only by Rayleigh scattering from 2p states. For the particular case of excitation by electron impact, some quantitative predictions are made, at the photon scattering angle ?=π/2, based on values for the state multipoles extracted from the literature (Blum and Kleinpoppen, Band). The vicinity of Balmer α and Lyman α resonances are studied in detail.     

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.     

On the Dependence of the Light Scattering Intensity on the Averaged Size of Polydisperse Particles: Comments on the Paper by M.S. Dyuzheva et al. (Colloid J., 2002, vol. 64, no. 1, p. 39)

The second stage in the solution of the inverse problem of dynamic light scattering is analyzed; the dependence of the static scattering intensity on the average fraction size is used to calculate the particle size distribution at this stage. The results of the paper by M.S. Dyuzheva et al. (Colloid J., 2002, vol. 64, no. 1, p. 39) concerning this problem are shown to be erroneous. On the basis of calculations within the framework of the Mie theory, the possibility of a power approximation for the particle size dependence of the scattered intensity and the effect of the particle parameters on the power approximation exponents are discussed.     

Dynamic light scattering from asymmetric block copolymers in neutral good solvents: Evidence of association in the disordered state

Dynamic light scattering (DLS) has been used to explore the properties of asymmetric styrene-isoprene (SI) block copolymers in concentrated solutions. Concentrations were always well below those necessary to access the order–disorder transition in neutral good solvents. The samples include SI (10-50), SI (36-9), and SIS (10-100-10), where the numerical suffixes denote the block molecular weights in kilodaltons; experimental emphasis was placed on SI (10-50). The DLS intensity correlation functions in the neutral good solvents, THF and toluene, were dominated by a slow mode that first appeared at a concentration c⁺ ≈ 4 c*, where c* is the coil overlap concentration. The decay rate of this mode scaled approximately as the third power of the scattering wavevector, and the excess scattered intensity decreased with increased scattering angle. These results were tentatively ascribed to the onset of substantial concentration fluctuations, that exhibited cylindrical, or wormlike structures. Measurements in solvents of known selectivity, dioxane and cyclohexane, and on a copolymer of the opposite composition, SI (36-9), indicated that the intermolecular association was driven by the effectively repulsive interactions between styrene and isoprene segments, rather than by solvent selectivity. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1831–1837, 1998     

Comparison between neutron and quasielastic light scattering by polyacrylamide gels

The authors describe small-angle neutron scattering measurements of the screening length ζ in polyacrylamide-water gels. Although these are inhomogeneous systems, the screening length is clearly observable and is in good numerical agreement with the relation E = 3kT/4πζ³, where E is the longitudinal elastic modulus of the gel obtained from measurements of the intensity of qu-asielastically scattered light. Static light scattering observations reveal a larger-scale (ca. 30 nm) superstructure in the gel.