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. I. Small-angle X-ray scattering from polycarbonate

The small-angle x-ray scattering (SAXS) from glassy bisphenol-A polycarbonate 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 vertical beam divergence, they 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, 0.44 (electrons)² Å^?3, is well represented by the thermodynamic 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 this material (50–200 Å), but can be well represented by a small concentration of heterogeneities (0.04% by volume or less), several thousand angstrom units in size, superimposed on the thermal density fluctuations frozen in at the glass transition. It is suggested that the nodular features reported for this material are not representative of bulk material but should be associated with surface effects. The bulk structure can—as far as the SAXS is concerned—be well described as a random amorphous solid, containing simple thermal fluctuations and a small concentration of relatively large heterogeneities.     

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.     

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. 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.     

Analysis of small-angle X-ray scattering from fibers: Structural changes in nylon 6 upon drawing and annealing

The changes in the fibrillar and the lamellar structure in nylon 6 fibers resulting from drawing and annealing were studied by a detailed analysis of their two-dimensional small-angle scattering patterns. The scattering object that gives to rise the diffuse equatorial scattering in the angular range of Q = 0.02 to 0.3 Å⁻¹ is assumed to be a fibril. There are two distinct regimes in the equatorial diffuse scattering. The scattering at Q < 0.1 Å⁻¹ is dominated by scattering due to the longitudinal dimension of the fibril, and that at Q > 0.1 Å⁻¹ to the lateral dimensions/organization of the fibril. The interfibrillar regions, unlike the interlamellar regions that are essentially made of amorphous chain segments, may have microvoids in addition to amorphous chain segments. The intensity distribution within the lamellar reflections was used to obtain the lamellar spacings and the dimension of the lamellar stacks. The length of the fibrils is between 1000 and 3000 Å, the higher values being more prevalent at lower draw ratios. The fibril length is larger than the length of the lamellar stack, and approaches the latter at higher draw ratios. Annealing does not change the lengths of the fibrils, but the length of the lamellar stack increases. The fibrils form crystalline aggregates with a coherence length of ∼200 Å at higher draw ratios. The diameter of the fibrils (50–100 Å) determined from the lamellar reflection using both the Scherrer equation and the Guinier law are consistent with the lateral size of the crystallites derived from wide-angle x-ray diffraction. The longitudinal correlation of the lamellae between the neighboring fibrils improves upon drawing and decreases upon annealing. The degree of fibrillar and lamellar orientation is about the same as the crystalline orientation. Lamellar spacing increases upon drawing (from ∼60 to 95 Å) and annealing (from ∼85 to 100 Å). This is accompanied by an increase in the width of the amorphous domains from 30 to 50 Å in drawn fibers, and from 45 to 55 Å in annealed fibers. The diameter of the fibrils decreases slightly upon drawing and increases considerably upon annealing. © 1996 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.     

Étude par rayons X de copolymères téléchéliques butadiène acide méthacrylique

The telechelic polybutadiene–methacrylic acid copolymer (Hycar CTB) containing 2 mole percent acid and neutralized (5–100%) by alkali ions, Na⁺, K⁺, and Cs⁺, has been studied by small-angle x-ray scattering. Salt groups form clusters, and the average value of the radii of gyration is approximately 8 Å; this value seems to be independent of the nature of the cation and the degree of neutralization. The existence of a low-angle maximum in the scattering intensity gives evidence of a mean distance of 80 Å between clusters in the fully neutralized sample. This distance increases slightly with a decreasing degree of neutralization. A more precise analysis of the small-angle scattering curve gives further information on the cluster structure: the ionic groups may form small bilayer disks while the polymer chains maintain a regular distance of 80 Å between the disks.     

The two-phase structure of segmented block copoly(ether ester)

The annealing induced morphological changes in isotropic block copoly(etherester)s are investigated by small angle X-ray scattering methods. The observed results are consistent with a lamellar model which is comprised of a crystalline core of thickness 35 to 45 Å, a diffuse boundary zone of width 9 Å, and an amorphous layer which is varying strongly in thickness. The enhanced crystallinity of the samples annealed at higher temperatures is mainly due the lateral growth of the lamellae; the long period increases by not more than 20%. The scattering power of the samples is explained by means of an equivalent two-phase model in which the crystalline phase has the same structure as theα-form of poly(butylene terephthalate), whereas the amorphous phase is a mixture of the uncrystallized ester segments and the ether segments. The crystallinity determined from the scattering power is very much higher than that determined from thermoanalytical investigations.     

Deactivation of He 23S by thermal electrons

The rate coefficient for deactivation of the metastable 2³S state of He by impact of thermal electrons is deduced from recent calculations of inelastic electron-He cross sections. The deactivation rate is found to be nearly constant with temperature. Computed values range between 2.82 and 3.03 (10^?9 cm³/sec) for T between 0 and 2000°K. De-excitation cross sections are given for low-energy incident electrons.     

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.     

Sorption of organic vapors into drawn and undrawn polyethylene

Drawing of linear polyethylene at 60°C. to an extension ratio of ten drastically reduces the sorption and diffusion of n-pentane, benzene, methylene chloride, and tetrachloroethylene. Methylene chloride was chosen for more detailed study. The sorption is of the normal Fickean type. It is also fully reversible in the temperature range between 25 and 45°C. if the sorbed amount is kept to below 0.5%. At higher concentrations the sample relaxes so that sorption irreversibly increases. The reversible sorption per gram of amorphous component is about 1/6 of that in undrawn polyethylene. The diffusion constant has a larger temperature and concentration dependence than in the undrawn material. At zero concentration the activation energy for diffusion is 34.4 kcal./mole and the diffusion constant at 25°C. is 8 × 10^?11 cm.²/sec. as compared with 14.4 kcal./mole and 1.5 × 10^?8 cm.²/sec. in undrawn PE. Cold drawing reduces the sorption sites without changing their energy content, but drastically cuts down diffusion and increases the activation energy. A smaller part of the increase of the latter is a consequence of the lower enthalpy of the amorphous material and a larger part is probably due to the increased distance between sorption sites.     

Intramolecular multiple scattering in electron diffraction from fluoro-methyl halides

Relative elastic differential cross sections for scattering of 1 keV electrons from CF₃H, CF₄, CF₃Cl, CH₃F and CH₃Cl molecules were measured for momentum transfer from 3 Å^?1 to 29 Å^?1. The oscillatory residuals remaining after substraction of the atomic scattering and the molecular interference contributions calculated in the independent atom model are ascribed to the influence of intramolecular multiple scattering. The data reflect the dominant contributions of the CF₃-group and show larger oscillations than obtained from triple scattering calculations according to the method of Liu and Bonham using the second Born approximation.     

Gas electron diffraction: the direction of development of the method

The problems of gas phase electron diffraction experiments are considered. The operating conditions for a reconstructed electron diffraction apparatus are determined in a scattering regime with an effective cross section of σ = 1.06 × 10² b on a molecular beam with Kn > 1. On the example of the I₂ molecule it is shown that at a vapor pressure over a substance equal to 10^?3 mmHg, one can sort out a desired signal at scattering angles up to s = 30 Å^?1. A nomographic chart for the choice of the optimal operating conditions of electrons scattering is proposed.     

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.     

Resonance raman and infrared spectra of ClO3 radicals in electron irradiated NaClO3

Resonance Raman and infrared absorption spectra of ClO₃ radicals have been observed from measurements of crystalline NaClO₃ irradiated at 77 K with 1.5 MeV electrons. The ClO₃ radicals occupy two sets of nonequivalent sites; radicals at one site are observed from resonance scattering using 6328 Å excitation while those at the other site are observed from resonance scattering with 5145 Å excitation. The red sensitive radicals decompose at 77 K with a half-life of ≈29 min while the green sensitive radicals are more stable at this temperature.     

State of water in amorphous silica samples from rice hulls: A <Superscript>1</Superscript>H NMR study

Behavior of molecules of adsorbed water in rice hulls, weevil, and amorphous samples of carbon-containing (carbonized, SiO₂ content 47%) and pure silica was studied by ¹H NMR spectroscopy in the temperature range from 200 to 298 K. The temperature dependence of the signal intensity from humid samples shows a decrease in temperature of freezing of the adsorbed water and presence of unfrozen water. This dependence was used for estimating the pore size distribution. For pure amorphous silica, the pore diameter is in the range from 50 to 150 Å with a maximum at about 85 Å.     

The investigation of cancerous human bone (osteoclastoma) by small-angle X-ray scattering

Small-angle X-ray scattering methods were applied to provide a pore analysis of cancerous human bone (osteoclastoma). For experimental measurements of the scattering intensities a small-angle Kratky camera, equipped with a counterattachment and a programmable step-scanning device, was used. By applying the theories of Kratky, Porod, Debye, and Bueche, applicable to a densely packed two-phase system belonging to a general micelle system, macromolecular parameters such as specific inner surface, length of coherence, range of inhomogeneity, void percentage, and transversal lengths l?₁ and l?₂ were evaluated and found to be 4.69 × 10^?4 Å^?1, 21.39 Å, 18.01 Å, 0.21%, 18.01 Å and 8.53 × 10³ Å, respectively. A comparison of these parameters with those of pure human bone revealed a macromolecular dissociation in osteoclastoma.     

Wide-angle neutron scattering studies of mixed crystals of polyethylene and deuteropolyethylene

Wide-angle neutron scattering studies have been made of a series of mixed crystal blends of polyethylene and deuterated polyethylene in the range 0.68 ≤ K = 4πλ^?1 sinθ ≤ 2.02 Å^?1. Recent calculations by Stamm have shown that regularly folded subunits of small numbers (two to ten) of stems should produce an observable modulation of the diffuse scattering pattern of such mixtures in this K range. For both melt- and solution-crystallized blends, no extra signal was observed above the background scattering level. The data are used to place an upper limit (of about four) on the number of stems that could be regularly folded in the (100) and (010) planes for these materials.     

X-ray scattering by water molecules studied by using synchrotron radiation

The energy spectra of free water molecules were measured at scattering angles 2θ ranging from 10.5° to 75.7°, using an angle-dispersive-type diffractometer and synchrotron radiation as an X-ray source. A silicon (111) monochrometer was used to obtain incident X-rays with the wavelengths of (1.543/n) Å (n = 1,3,4,5). Observed inelastic scattering peaks are clearly separated from eleastic ones at s values [s = (4π/λ) sin Å] larger than 8 Å^?1. The increase of the separation with an increasing s value was consistent with the classical theory of the Compton shift. The total (elastic plus inelastic) intensities were obtained over a range of s = 0.74–5.0 Å^?1. Experimental difference intensities Δσ_ee and Δσ_ne were obtained separately by combining the X-ray and high-energy electron scattering data. The experimental results are in reasonable agreement with the theoretical intensities calculated from SCF and CI molecular wave functions with a basis set of double-zeta plus polarization functions. © 1994 John Wiley & Sons, Inc.