Magnetic resonance studies of hydrogen atom transfer

The experimental results obtained on four different types of Raman spectra: pure rotational lines, the I_VV and _VH components of the vibrational Q-branch and the vibrational rotational lines are presented for H₂, D₂, HF and N₂ dissolved at low concentration in inert solvents. The line broadening and motional narrowing due to the solvent interaction is discussed.     

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.     

Quantitative small-angle light scattering studies of the melting of poly(ethylene terephthalate)

Quantitative H_v small-angle light-scattering (SALS) studies of the melting of poly(ethylene terephthalate) (PET) have been performed. The results are compared with those from differential scanning calorimetry (DSC). It is found that fully grown spherulites melt over a temperature range of about 20°C without change in spherulite size, number, or internal disorder. The decrease in H_v SALS intensity is due to a decrease in spherulitic crystallinity over the melting range. The corrected experimental intensities are lower than, but in reasonable agreement with, the theoretically predicted intensities based on the DSC results. Procedures are presented for the quantitative analysis of H_v SALS intensities from spherulitic systems, including the corrections for the experimental, external disorder, and internal disorder effects.     

Vibrational dynamics of some anions in aqueous solutions from isotropic Raman scattering

From the I_VV and I_VH Raman spectra of a totally symmetric vibration, isotropic scattering profiles have been obtained for several anions in dilute aqueous solutions at various temperatures. The Raman spectrometer was connected to an A/D converter and a small computer, which allowed multiple scanning, data accumulation, and numerical processing of these profiles with good precision over a frequency range of about 20 times their full width at half peak height.The theoretical analysis of the isotropic Raman profiles was accomplished by assuming vibrational phase relaxation based on a MARKOV-GAUSS mechanism. Fitting procedures to the experimental data permitted the determination of the vibrational frequency distribution and its modulation time. Temperature effects are discussed in relation to the distribution and motional characteristics of the immediate environment of water molecules of the anions.     

Scattering of light by deformed three-dimensional spherulites

A theoretical calculation of the H_v light-scattering patterns for deformed three-dimensional spherulites is presented. Affine deformation is assumed. The optic axis of the scattering element is allowed to lie at an arbitrary angle ß to the radius which is permitted to change in the course of the deformation in a manner that may depend upon the angular location in the spherulite. The consequences of twisting of the optic axis about the spherulite radius are also explored.     

Small-angle light scattering from an anisotropic sphere: The mueller matrix approach

The explicit form of the Mueller scattering matrix, which characterizes the small-angle light scattering from an anisotropic sphere when the requirements of the Rayleigh-Gans-Debye (RGD) approximation are fulfilled, contains all information obtainable about the RGD scattering from an anisotropic sphere taken as a model for a spherulite. A comparison of angular dependences of single matrix elements for the Lorenz-Mie sphere, the Rayleigh particle, and the simplified form of the presented matrix (taking a sphere without inherent anisotropy, i.e., Δn = 0) shows very good agreement within the limits of RGD approximations. The polarized small-angle light scattering intensities Hυ and Vυ are combinations of the single matrix elements. Their explicit form is in accord with the expressions for Hυ and Vυ intensities recently rederived from a 2 × 2 amplitude scattering matrix. It has been shown that the angular dependence of matrix elements is determined by the (n? — 1)/Δn parameter, where n — is the mean refractive index andδ n is the anisotropy, both measured relative to the surrounding medium. The expressions for Hυ and Vυ intensities derived by Stein and Rhodes fail for a sphere without inherenet anisotropy ( δ n = 0); and the commonly used procedure of size determination from a maximum of Hυ intensity has limited validity (it holds only approximately under the condition of a small phase shift and small (n?-1)/ δ n). Further theoretical work must be done to understand and construct scattering models for situations where the RGD approximately is inappropriate.     

Kinetics of growth of developing spherulites

A model containing two rate constants is presented for the development of spherulites from sheaves. One, G_R, is a radial spherulite growth constant while the other, G_S, describes the rate of increase of apex angle of the sheaf. On the basis of this model, Avrami kinetics are developed which predict a change in the Avrami constant n from 5 to 3 as the sheaf develops into a spherulite. H_V light-scattering patterns are calculated according to this model and are found to compare favorably with those found during the early stages of the crystallization of poly(ethylene terephthalate).     

Scattering from truncated spherulites

A general two-dimensional theory is derived to explain the light scattering from truncated spherulites. The severity of the truncation is expressed by a statistical parameter σ²/ā² which is the ratio of the variance σ² of the size of the spherulite to the square of its average size ā. The H_v light-scattering patterns are calculated for different values of the truncation parameter. It is observed that the truncation decreases the position of maximum scattering intensity of the pattern. It also increases the scattering intensity at small and large angles, but reduces it at intermediate angles. For a spherulitic polyethylene sample, the truncation parameter is found to equal 0.100 ± 0.030 as measured microscopically. The theory can also be used to calculate light-scattering patterns from row-nucleated spherulites. If it is assumed that the interference effect averages out to zero when a large number of spherulites is involved, a single “sliced” spherulite model can be used. Then, the scattering intensity per unit area decreases as the “slice” becomes very thin.     

The effect of spherulitic truncation on small-angle light scattering

The effects of spherulitic truncation on the H_v small-angle light-scattering (SALS) patterns are determined by computer simulation of spherulite nucleation and growth. The simulation is carried out for simultaneous and sporadic nucleation of two-dimensional spherulites and simultaneous nucleation of three-dimensional spherulites. The scattered intensity differences between truncated spherulites and round spherulites are determined as functions of the type of growth and the volume (or area) fraction of spherulites. Methods for the determination of certain geometrical characteristics of spherulites systems by SALS are developed. These characteristics include the volume (or area). fraction of spherulites, the average spherulite radius, and the average spherulite volume (or area). The results of this study are essential in the quantitative analysis of H_v SALS from spherulitic systems. The simulation process is readily extendable to the examination of other morphological phenomena by SALS.     

Multiphase structure of segmented polyurethanes: Its relation with spherulite structure

Small-angle light-scattering (SALS), Polarized light microscopy (PLM), differntial scanning calorimetry (DSC), and small-angle x-ray scattering (SAXS) were used to study morphological changes in segmented polyurethanes with 4,4′-diphenylmethane diisocyanate (MDI) and 1,4-butanediol (BD) as the hard segment. It was found. for the first time, that spherulites could form from the melt by quenching the polyurethanes in the melt state to annealing temperatures between 120°C and T_h, the highest annealing temperature for spherulite formation. T_h ranged from 140°C to ca. 170°C and depended upon the hard-and soft-segment compatibility. Within the range 120°C to T_h, the radius of the spherulite increased with increasing hard-segment content at each fixed annealing temperature. Annealing at 135–140°C gave rise to the largest spherulites. SAXS was used to investigate the phase-separated structures corresponding to the spherulite formation. The interdomain spacing increased with increasing hard-segment content and with increasing annealing temperature.The degree of phase separation first increased with increasing annealing temperature from room temperatures (ca. 25°C), reached a maximum at ca. 107°C, and then decreased with further increase in the annealing temperature. On the basis of these observations, the mechanisms of phase separation, crystallization, and spherulite formation are discussed. © 1993 John Wiley & Sons, Inc.     

Block copolymers of poly(ethylene terephthalate)-poly(butylene terephthalate). II. Small-angle light-scattering studies

Small-angle light-scattering (SALS) studies were carried out on block copolymers of poly(ethylene terephthalate) (PET) and poly(butylene terephthalate) (PBT), the synthesis and characterization of which have been reported in an earlier paper. Samples were crystallized isothermally from the melt at 95°C for predetermined crystallization times in order to follow the formation and growth of crystalline superstructure. During the early stages of crystallization, the block copolymers showed unusual H_v patterns with the four lobes along the polarizer directions, while at later stages they showed the usual H_v patterns with the four lobes at 45° to the polarizer directions. The unusual patterns are characteristic of PBT superstructure, while the usual patterns are characteristic of PET superstructure. These results show that PBT, which is the faster-crystallizing component, crystallizes first and provides nucleation sites for the crystallization of PET, which crystallizes later. Similar behavior was not observed in PET homopolymer and random copolymers of equivalent compositions. In each case the spherulite size increased with the time of crystallization. The ultimate spherulite size decreased with increasing PBT content in the block copolymer, thus showing an increase in nucleation density. It was demonstrated that light scattering is a useful tool to characterize block copolymers of two crystalline components which have different types of superstructure.     

Small-angle light scattering by random assemblies of incomplete spherulites. Systems with partial degree of volume filling

A theory is presented to account for the effect of the impingement of growing spherulites on their H_v small-angle light scattering patterns. The theory is developed on the basis of results of computer-simulated two-dimensional spherulite growth and calculated scattered intensities. The impingement produces a lowering of the intensity of the scattering maximum and the diminishing of the overall sharpness of the scattering peak. The extent of these effects increases with area fraction of spherulites. A procedure is suggested for determining correction factors that may be applied to intensity data obtained during the course of spherulite crystallization. An interpretation is made of the type of average spherulite size determined from the scattering angle of maximum intensity.     

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.     

Kinetics and Mechanism of Certain Acetylation Reactions with Acetamide/Oxychloride in Acetonitrile under Vilsmeier?Haack Conditions

Vilsmeier? Haack (VH) acetylation reactions with benzaldehydes or acetophenones in MeCN followed second‐order kinetics and afforded acetyl derivatives under kinetic conditions, irrespective of the nature of the oxychloride (SOCl₂ or POCl₃) used for the preparation of the VH reagent along with acetamide. The present finding contributes to the understanding of the nature of the reactive species of the VH reagent as well as of the acetylation mechanism.     

A growing 2D spherulite and calculus of variations Part I: A 2D spherulite in a linear field of growth rate

We propose to take the calculus of variations in order to compute the shape of a growing 2D spherulite in an uniaxial field of growth rate. We are concerned with the growth line (a path that is traveled in the shortest possible time from nucleus to a point (x₁, y₁), where a molecule just crystallizes) and the growth front (the times between spherulite and supercooled material). The Euler differential equation—a result of the calculus of variations—is derived for all uniaxial growth ratesv (x). Here we especially investigatev(x)=px+q.     

How does the accuracy of NMR conformational analysis depend on the equilibrium constant?

Analytical expressions are derived for the analysis of the accuracy of NMR determinations of conformational equilibrium constants, K. The relative error, σ_K/K, shows a nearly linear increase with K for two commonly used modifications of the NMR approach to conformational analysis (based on measurements of integral intensities and averaged chemical shifts).     

Light scattering from assemblies of spherulites

A general equation describing the small-angle H_v light-scattering intensity for a system of N undeformed spherulites located at random within the sample and taking into account the truncation and interference effects is given. Scattering contour plots or radial scans are reported for various arrangements of the N spherulites. The results show that the interference effect may explain the speckled appearance of the experimental patterns. Moreover, the interference and truncation effects (for the special cases where truncation is considered here) do not seem to shift the position of the maximum scattering angle of the cloverleaf pattern as calculated from the single spherulite theory. Finally, the calculations show that the truncation effect increases the relative intensity of the pattern at large and low scattering angles and at azimuthal angles 0 and 90°C, as compared with the intensity at the position of maximum scattering angle.     

Algebraic expressions of irreducible bases for molecules C20H20, C80, and C240

Using the symmetrized boson representation technique, concise algebraic expressions of the irreducible bases symmetry adapted to the group chain I_h⊃C₅ for the fullerene molecules C₂₀H₂₀, C₈₀, and C₂₄₀ are derived for the most general cases and those for any specific case can be derived from them easily without a projection procedure. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 283–297, 1999     

Effect of the directionality of the ester group on the formation of hairpins in polyesters containing naphthalene and a flexible spacer

Steady-state fluorescence measurements and molecular dynamics simulations have been used to study the intramolecular formation of excimers in five model compounds for polyesters containing naphthalene groups separated by flexible spacers. The model compounds are derived from 2-hydroxynaphthalene and HOOC (CH₂)_n COOH, n = 2–6. The ratio of the intensity of excimer and monomer emissions, I_D/I_M, is nearly independent of the viscosity of the medium, η, over the range covered in dilute solution. Although I_D/I_M is always very small, it shows an odd–even effect for the first four members of the series, with maxima when n is odd. Molecular dynamics simulations provide an explanation for the small values of I_D/I_M, their weak dependence on η, and the trend of I_D/I_M with n. The results for the present series of model compounds are compared with previous work, which reported larger values of I_D/I_M, and a stronger dependence of I_D/I_M on η, for bichromophoric compounds derived from 2-naphthoic acid and aliphatic glycols, where the direction of the ester groups is reversed. The origin of the difference in the behavior of I_D/I_M in the two series is identified. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1127–1133, 1997