On the structure of glassy polymers. II. Small-angle x-ray scattering from poly(methyl methacrylate)

The small-angle x-ray scattering (SAXS) from glassy poly(methyl methacrylate) has been measured using a Bonse–Hart system. The data cover the angular range (2θ) between 20 sec and 2 deg. After correcting for absorption, background, and beam divergence, the data have been placed on an absolute basis by comparison with the scattering from a standard silica suspension. The corrected absolute intensity decreases strongly with increasing angle over the range between 20 sec and 30 min, and is nearly constant between 30 min and 2 deg. The magnitude of the scattering in the constant range, 0.6 (electrons)² Å^?3, is within a factor of 1.5 of the value predicted by the thermodynamic fluctuation theory for fluids applied at the glass transition temperature. The increase in intensity at smaller angles cannot be described by structures on the scale of the nodules reported in highly isotactic PMMA (150–200 Å), but can be well represented by small concentrations of heterogeneities, several thousand angstrom units in size, superimposed on the thermal density fluctuations frozen-in at the glass transition. The bulk structure of this material is well described as a random amorphous solid, containing simple thermal fluctuations and a small concentration of relatively large heterogeneities.     

On the structure of glassy polymers. III. Small-angle x-ray scattering from amorphous polyethylene terephthalate

The small-angle x-ray scattering (SAXS) from glassy polyethylene terephthalate has been measured using a Bonse–Hart system. The data cover the angular range (2θ) between 20 sec and 2 deg. After correcting for absorption, background, and beam divergence, the data have been placed on an absolute basis by comparison with the scattering from a standard silica suspension. The corrected absolute intensity decreases strongly with increasing angle over the range between 20 sec and 15 min, decreases more gradually in the range between 15 min and 45 min, and reaches a nearly constant asymptotic value over the range between 45 min and 2 deg. The magnitude of the scattering in the constant range, about 0.4 (electrons)² Å^?3, is very close to the value predicted by the thermodynamic fluctuation theory for fluids applied at the glass-transition temperature [0.34 (electrons)² Å^?3]. The increase in intensity at angles smaller than about 45 min cannot be described by structures on the scale and volume fraction of the nodules reported in amorphous PET (50–100 Å), but can be well represented by small concentrations of heterogeneities, ranging in size from 100 to 2000 Angstroms, superimposed on the thermal density fluctuations frozen-in at the glass transition. The bulk structure of this material seems well described as a random amorphous solid, containing simple thermal fluctuations and a small concentration (<1 vol-%) of heterogeneities covering a range of sizes. The heterogeneities in the small end of the range may well be crystallites which formed on cooling.     

Structure of glassy polymers. V. Small-angle x-ray scattering from polystyrene

Small-angle x-ray scattering (SAXS) from glassy atactic polystyrene has been measured using a Bonse–Hart system. After correcting for absorption, background, and beam divergence, the scattering has been placed on an absolute basis using a standard silica suspension as a reference.The desmeared absolute intensity decreases strongly with increasing scattering angle over the range between 20 sec and 20 min. At larger angles, the intensity decreases much more slowly with increasing angle and approaches the value expected for density fluctuations frozen-in at the glass transition. The angular variation of intensity is well described by the scattering from heterogeneities of various sizes and concentrations superimposed on the scattering from thermal density fluctuations. These heterogeneities range in radius from 10 to 4000 Å. The present SAXS results on glassy polystyrene seem inconsistent with the presence of nodular features as representative of the bulk polymer.     

On the structure of glassy polymers. IV. Small-angle x-ray scattering from rigid polyvinyl chloride

The small-angle x-ray scattering (SAXS) from quenched and annealed rigid polyvinyl chloride (PVC) has been measured using a Bonse–Hart system. After correcting for absorption, background, and beam divergence, the scattering has been placed on an absolute basis using a standard silica suspension as a reference. The scattering from annealed (6 days at 75°C) and unannealed PVC was identical within experimental error, varying with scattering angle in a manner similar to the SAXS from other amorphous polymers. The intensity decreases rapidly with increasing scattering angle over the ranges from 20 sec to 20 min. Beyond 20 min the intensity is fairly constant, decreasing only slightly with increasing angle. At the largest angles of measurement (in the range of 120 min), the measured intensity is close to the value calculated for thermal density fluctuations frozen-in at the glass transition. The angular variation of intensity is well described by the scattering from heterogeneities of various sizes and concentrations superimposed on the scattering from thermal density fluctuations. These heterogeneities range in radius from 50 to 4500 Å and, assuming the crystalline excess density, the total concentration of heterogeneities is less than 0.5%. The mean-square fluctuation in density, determined from the measured intensity invariant, is also consistent with such a distribution of heterogeneities. The present SAXS results on rigid PVC are inconsistent with the presence of nodular features as representative of the bulk polymer. Rather, it is suggested that they are associated with surface effects. It is further suggested that previously indicated volume fractions of crystallinity in rigid PVC (generally in the range of 5–12%) are incorrect, and that the model of a three-dimensional network of crystallites used to explain the rheological behavior of this material should be re-examined.     

Structure of glassy polymers. VII. Small-angle X-ray scattering from epoxy resins

The small-angle x-ray scattering (SAXS) from an Epon 812 and two Epon 828 (one amine-cured and one anhydride-cured) epoxy resins has been measured using a Bonse-Hart system. The data cover the angular range (2θ) between 20 sec and 60 min. After correction for absorption, background and vertical beam divergence, they have been placed on an absolute basis by comparison with the scattering from a previously studied polycarbonate sample. The corrected absolute intensity decreases strongly with increasing angle between 20 sec and 2 min, decreases more gradually between 2 and 20–30 min, and reaches a nearly constant asymptotic value at larger angles. The magnitude of the intensity in the constant-intensity region is close to the value predicted by thermodynamic fluctuation theory for fluids applied at the glass transition temperature. The increase in intensity at angles smaller than 20–30 min is associated with heterogeneities in the cured resins. These heterogeneities cover a range of sizes in all samples, from less than 100 Å to more than 1000 Å, with the most frequently occurring size in the range 100–200 Å.     

Small-angle X-ray scattering in sodium dodecyl sulfate solutions and micelle clustering

The small-angle X-ray scattering (SAXS) in micellar sodium dodecyl sulfate solutions has been studied in the range of overall concentrations c from 8 mM (CMC₁) to 300 mM and the absolute values of scattering vector q from 0.07 to 3.0 nm^–1. The total intensity of isotropic scattering has been revealed to increase with solution concentration. At c > 27 mM, the SAXS spectra have been found to exhibit an interference peak, which testifies a correlation in the arrangement of micelles in the bulk solution. This peak corresponds to the magnitude of q close to 1.55 nm^–1. Using the position of this maximum, average distance r₀ between the centers of micelles has been determined, which is equal to 4.1 nm and remains almost unchanged upon an increase in the overall concentration of sodium dodecyl sulfate. The observed regularities have been explained in terms of the DLVO theory taking into account the electrostatic and molecular intermicellar interaction.     

Small-angle x-ray scattering by crystalline polymer fibers 2. Investigation of the linear paracrystalline model using various materials

The linear position-sensitive detector is well-suited to measure quantitatively the distribution parallel to the fibre axis of the intensity of small-angle x-ray scattering (SAXS) by polymer fibres, except that in the case of four-point patterns their width is greater than that of the detector window. A method is described which overcomes this problem, and which has high angular resolution. Using this method, the variation of scattered intensity with angles from 0.3° to 2.5° has been measured for fibres of poly(ethylene terephthalate), nylon, and low density poly(ethylene) (LDPE), and compared with that predicted by the linear paracrystalline model. In all cases except LDPE, when the distribution of phase lengths was given by the Reinhold function, there was no significant disagreement between the measured and predicted scattering except for a very small range of angles on the low angle side of the peak intensity. With LDPE small but significant discrepancies were found at other angles as well, and these were worse if the symmetrical Gaussian distribution function was used. The method enabled quantitative parameters describing the morphology to be obtained. It is concluded that the morphology of the linear paracrystalline stack is consistent with the SAXS intensity distribution, and that the Reinhold function is a reasonable approximation to the distribution of phase lengths. A small modification so that this decays more rapidly at long lengths might be necessary to explain the scattering for all materials over the entire angular range and other small changes might be needed with LDPE, although the asymmetrical nature of the distribution must be retained.On leave from Department of Physics, University of Technology Malaysia, 81300 Sekudai, Malaysia.     

Small-Angle electron scattering and electron density in carbon dioxide

The total (elastic and inelastic) intensity of electrons scattered by CO₂ was measured in the s range of 1 to 12 Å^?1 and compared with the theoretical intensity calculated from the Hartree-Fock molecular wave function and those calculated for the independent-atom-model (IAM ) molecule. In the range of s ? 4 Å^?1 the electron correlation effect on the total scattered intensity was found to be represented by that for the IAM molecule.     

The microstructure of poly(vinyl chloride) as revealed by x-ray and light scattering

Small-angle x-ray scattering (SAXS) and wide-angle x-ray scattering (WAXS) as well as small-angle light-scattering (SALS) techniques have been applied to investigate the microstructure of a number of commercial poly(vinyl chloride) (PVC) samples. From the wide-angle x-ray scattering, crystallinity and crystal size parameters have been determined. The crystallinity of the samples investigated range from 5% to 10%. Superstructure parameters such as crystallite thickness, distribution functions of crystallite and amorphous thicknesses, and size of ordered regions have been obtained by an analysis of the SAXS curves using the cluster model. The crystallinity agrees well with the WAXS crystallinities indicating that most of the crystals are lamellar shaped, though some rodlike entities are present in the sample as is shown by the small-angle light scattering. From the SAXS analysis, the microstructure is described as clusters of lamella stacks which are identical with the subprimary particles. Their size is determined to be 220–240 Å. Emulsion type PVC also contains lamellar-shaped crystals. The superstructure, however, of this type of PVC is different from that of mass or suspension-polymerized material. The SAXS curve does not reveal any correlation between the crystals.     

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.     

Optical and SAXS characterization of poly(phenylene sulfide) (PPS) oligomers

Previously reported oligomeric PPSs prepared via the melt reaction of sulfur with excess p-diiodobenzene have been examined by optical microscopy and small-angle x-ray scattering (SAXS) techniques. A transition was seen from lamellar crystals for longer chains in the PPS samples of this work to a different type, which probably are extended chain crystals, occurring at about 20 DP. Spherulitic growth was observed optically for 38.8 DP and above. SAXS data established 31.8 DP as the point where a long period peak was first observed. The lamellar thickness of these bulk crystallized samples was established as about 50 Å which corresponds to a DP of 10. Maximum intensity of the SAXS peak increased with oligomer DP indicating increasing crystal perfection. Because of the random nature of the crystallization process, in PPS the average oligomer chain must be longer than three times this lamellar thickness to allow for folding and a spherulitic growth habit. © 1994 John Wiley & Sons, Inc.     

Measurements of inelastic cross sections for the (j,m) = (2,0)→(3,0) rotational transition of CsF in collisions with atoms and molecules

Individual state-to-state rotational transitions have been resolved in small angle scattering of polarized CsF molecules on Ne, Ar, C₂, H₆, N₂, CO, CO₂, CHF₃ at center of mass energies of about 0.1 eV. The absolute inelastic cross sections range from 5Ų up to 600Ų.     

Small‐angle X‐ray scattering study of a weak polyelectrolyte in water

Small‐angle X‐ray scattering (SAXS) was used to obtain solution parameters of a weak polyelectrolyte in water in the absence of any additives, such as neutralizing agents or salt. Poly(acrylic acid) (PAA) was used as a weak polyelectrolyte from which SAXS data were obtained in the dilute region of 1–10 mg cm^?3. An intrinsic viscosity of 15.7 dL g^?1 was obtained from a plot of reciprocal reduced viscosities versus the concentration. The application of the SAXS data, that is, the contour length (L = 1.97 × 10⁴ Å), the persistence length (a* = 58.5 Å), and the molecular weight (M = 5.9 × 10⁵ Da), to the Yamakawa–Fujii equation suggested that PAA in water at 25 °C could be described as a wormlike chain having a cylindrical body of d = 6 Å. An end‐to‐end distance (r = 1.6 × 10³ Å) was calculated from r = 2a*L ? 2(a*)². The nonisotropic expansion factor (α = 2.9) was calculated for PAA expanding from the random coil in dioxane at 30 °C (Θ temperature) to the wormlike chain in water at 25 °C. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1263–1272, 2003     

A Dicationic Organoplatinum(II) Complex Containing a Bridging 2,5‐Bis‐(4‐ethynylphenyl)‐[1,3,4]oxadiazole Ligand Behaves as a Phosphorescent Gelator for Organic Solvents

A dicationic platinum(II) terpyridyl complex, [(tBu₃tpy)Pt(OXD)Pt(tBu₃tpy)](PF₆)₂ (tBu₃tpy=4,4′,4“‐tri‐tert‐butyl‐2,2′:6′,2”‐terpyridyl, OXD=2,5‐bis(4‐ethynylphenyl)[1,3,4]oxadiazole) formed phosphorescent organogels in acetonitrile or in a mixture of acetonitrile and alcohol. The structure and properties of these emissive gels were analyzed by polarizing optical and confocal laser scanning microscopy, and by variable‐temperature ¹H NMR, UV/Vis, and emission spectroscopy. Dry gels were studied by scanning electron microscopy, powder X‐ray diffraction (PXRD), and small‐angle X‐ray scattering (SAXS). SEM images of the dry gel revealed a network of interwoven nanofibers (diameter 12–60 nm, length>5 μm). Intermolecular π–π interactions between the [(tBu₃tpy)PtC≡C] moieties could be deduced from the variable ¹H NMR spectra. The PXRD and SAXS data showed that the assembly of the gelator could be represented by a rectangular 2D lattice of 68 Å × 14 Å. The ability of the complex to gelate a number of organic solvents is most likely due to intermolecular π–π interactions between the [(tBu₃tpy)PtC≡C] moieties.     

Investigation of relaxation processes in linear polyethylene in the 10−9 sec region by means of high-resolution neutron spectroscopy

Results are presented of neutron incoherent scattering experiments on isotropic linear polyethylene samples of high (80%) and low (48%) crystallinity in the temperature range between ?180°C and +85°C for values of the scattering vector between 0.29 Å^?1 and 1.81 Å^?1 obtained with a high resolution backscattering spectrometer (Δ?ω = 0.25 ? 1.0 μeV) and between 0.57 Å^?1 and 2.4 Å^?1 with a time-of-flight spectrometer (Δ?ω = 420 μeV). From a comparison of the results on these samples one concludes that relaxation takes place predominantly in the noncrystalline regions. This motion cannot be adequately accounted for by any of the existing models for the γ-process. Therefore, a more liquidlike motion is suggested. Diffusion of shorter chain segments has also been ruled out since it is too slow to be observed. A simplified model of protonic jumps between equidistant sites located on the periphery of a circle of radius 2.5 Å reproduces the experimental results well. For the average time between successive CH₂-group reorientations one obtains τ₁ = τ₀ exp(E_actRT) with τ₀ = (2.0 ± 1.5) × 10^?13 sec and E_act = (4.5 ± 1.0) kcal/mole. The values join up well with those for the γ-process observed by NMR. It has been concluded that 60–90% of the protons in the noncrystalline regions participate in this motion.     

Lamellar morphology and equilibrium melting temperature of syndiotactic polystyrene in β‐crystalline form

Lamellar morphology and thickness of syndiotactic polystyrene (sPS) samples melt‐crystallized at various temperatures were probed using transmission electron microscopy (TEM) and small‐angle X‐ray scattering (SAXS). In addition, the melting temperature and enthalpy of the crystallized samples were characterized with differential scanning calorimetry. Under appropriate thermal treatments, all the samples investigated in this study were crystallized into β′ crystal modification, as revealed by wide‐angle X‐ray diffraction. From the SAXS intensity profiles, a scattering peak (or shoulder) associated with lamellar features as well as the presence of anomalous scattering at the zero‐scattering vector were evidently observed. The peculiar zero‐angle scattering was successfully described by the Debye–Bueche model, and subtraction of its contribution from the raw intensity profiles was carried out to deduce the intensity profile merely associated with the lamellar feature. The lamellar thickness obtained from Lorentz‐corrected intensity profiles in this manner agrees with that measured from the TEM images, provided that the two‐phase model is applied. On the basis of the Gibbs–Thomson equation, the modest estimations of equilibrium melting temperature and the surface free energy of the fold lamellar surface are 292.7 ± 2.7 °C and 20.2 ± 2.6 erg/cm², respectively, when lamellar thicknesses measured by TEM are applied. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1626–1636, 2002     

SURFACE STRUCTURE OF THE MICELLE OK AN AMPHOTERIC AMPHIPHILE DERIVED FROM LYSINE

ABSTRACT

Micelle structure in aqueous colloid of an amphoteric amphiphile N^αN^α-dimethyl-N^? -lauroyl lysine (DMLL), which was derived from lysine, was studied through light scattering, SAXS and a rheological method. The critical micelle concentration of the colloid system is 216 UM and the weight average molecular weight of the micelle is 2.40 × 10⁴, i.e. the aggregation number is 67.4. The diameter of the micelle is about 43.4 Å and the spherical micelle is likely to be retained in a concentration up to about 20 %, The SAXS measurements show that the electron density Fluctuation in the micelle is almost negligible and that the surface area of the micelle is approximately 3.5 times larger than that of a completely smooth sphere.     

Synthesis and Crystal Structure of Bis(methyltriphenylphosphonium) Hexabromotellurate(IV)‐bis{dibromoselenate(II)}, [PMePh3]2[TeBr6(SeBr2)2], the Salt of a Mixed‐valence Bromotellurate(IV)‐Selenate(II) Anion

Brown crystals of [PMePh₃]₂[TeBr₆(SeBr₂)₂] ( 1 ) were obtained when selenium and bromine (1:1) react in acetonitrile solution in the presence of tellurium(IV) bromide and methyltriphenylphosphonium bromide. The salt 1 crystallizes in the triclinic space group P1¯ with the cell dimensions a = 10.3630(14)Å, b = 11.5140(12)Å, c = 11.7605(17)Å, α = 108.643(9)°, β = 106.171(10)° and γ = 99.077(9)° (296 K). In the solid state the [TeBr₆(SeBr₂)₂]^2— anion contains a nearly regular [TeBr₆] octahedron where the four equatorial bromo ligands each have developed a bond to the Se^II atom of a SeBr₂ molecule. The contacts between the bridging bromo and the Se^II atoms of the SeBr₂ molecules are observed in the range 3.11—3.21Å, and can be interpreted as bonds of the donor‐acceptor type with the bridging bromo ligands as donors and the SeBr₂ molecules as acceptors. The Te^IV—Br distances are in the range 2.67—2.72Å, and the Se^II—Br bond lengths in coordinated SeBr₂ molecules in the range 2.33—2.34Å.     

On-line measurement of molecular weight and radius of gyration of polystyrene in a good solvent and in a theta solvent measured with a two-angle light scattering detector

On-line two-angle (15° and 90°) light scattering measurements with a gel permeation chromatography for linear and branched polystyrene in tetrahydrofuran (a good solvent) and in trans-decalin (a theta solvent) were made and compared with data from a multi-angle light scattering detector and literature values. Theoretically, weight-average molecular weight and the radius of gyration R_g can be determined accurately in the range where R_g²k² is less than 1.2 (rod)∼1.7 (random coil); here, k is the absolute value of the scattering vector for a right angle detector with the Berry square root method. Molecular weight dependence of the radius of gyration obtained from the two-angle light scattering detector for linear and branched polystyrenes under different thermodynamic conditions were measured and found to be almost the same as values measured with a multi-angle light scattering detector and literature values in the appropriate range of molecular weight.     

Enrichment and distribution of counterions in spherical polyelectrolyte brushes probed by SAXS

The spatial correlation of counterions [Li⁺, Na⁺, Rb⁺, Cs⁺, NH₄⁺, (CH₃)₄N⁺] with spherical polyelectrolyte brushes (SPBs), which consist of a PS core and chemically grafted PSS chains, was comprehensively studied through a combination of SAXS, DLS, and Zeta potential. Results show that the SAXS intensity profiles of the brush appears to be “insensitive” to the concentration of Na⁺. By contrast, introducing salt ions with a density lower than sodium [NH₄⁺, (CH₃)₄N⁺ and Li⁺] into the brush layer will cause a decrease in the scattering intensity while introducing those with a higher density than sodium (Rb⁺ and Cs⁺) will cause the opposite result. As verified by the combined results of SAXS, DLS, and Zeta potential, the collapse of the brush and the enrichment of the counterions in the brush layer occur simultaneously. It was further demonstrated that the concentration of counterions enriched in the innermost layer of the brush shell can be enhanced up to hundreds of times compared with the bulk concentration, and the counterion distribution in SPB shell follows a radial attenuation distribution. SAXS is confirmed to be powerful in probing the enrichment and distribution of counterions within SPB. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 738–747