Calculating the tetrahedral bond angle using spherical polars and the dot product

A proof using the methane tetrahedroid bond angle can be obtained by using spherical polar coordinates to calculate the Cartesian coordinates of the hydrogen atoms, then using the dot product of vectors.

Rotational symmetry of a methane molecule and the bond angle

The rotational symmetry of a methane molecule can be used to great advantage to calculate the bond angle. The problem is worked out in this article.

A complete atomistic model of molten polyethylene from neutron scattering data: a new methodology for polymer structure

A new approach to the study of the local organization in amorphous polymer materials is presented. The method couples neutron diffraction experiments that explore the structure on the spatial scale 1–20 Å with the reverse Monte Carlo fitting procedure to predict structures that accurately represent the experimental scattering results over the whole momentum transfer range explored. Molecular mechanics and molecular dynamics techniques are also used to produce atomistic models independently from any experimental input, thereby providing a test of the viability of the reverse Monte Carlo method in generating realistic models for amorphous polymeric systems. An analysis of the obtained models in terms of single chain properties and of orientational correlations between chain segments is presented. We show the viability of the method with data from molten polyethylene. The analysis derives a model with average C-C and C-H bond lengths of 1.55 Å and 1.1 Å respectively, average backbone valence angle of 112, a torsional angle distribution characterized by a fraction of trans conformers of 0.67 and, finally, a weak interchain orientational correlation at around 4 Å.

A detailed single chain model for molten poly(tetrafluoroethylene) from a novel structure refinement technique on neutron scattering data

We present a new methodology that couples neutron diffraction experiments over a wide Q range with single chain modelling in order to explore, in a quantitative manner, the intrachain organization of non-crystalline polymers. The technique is based on the assignment of parameters describing the chemical, geometric and conformational characteristics of the polymeric chain, and on the variation of these parameters to minimize the difference between the predicted and experimental diffraction patterns. The method is successfully applied to the study of molten poly(tetrafluoroethylene) at two different temperatures, and provides unambiguous information on the configuration of the chain and its degree of flexibility. From analysis of the experimental data a model is derived with CC and CF bond lengths of 1.58 and 1.36 Å, respectively, a backbone valence angle of 110° and a torsional angle distribution which is characterized by four isometric states, namely a split trans state at ± 18°, giving rise to a helical chain conformation, and two gauche states at ± 112°. The probability of trans conformers is 0.86 at T = 350°C, which decreases slightly to 0.84 at T = 400°C. Correspondingly, the chain segments are characterized by long all-trans sequences with random changes in sign, rather anisotropic in nature, which give rise to a rather stiff chain. We compare the results of this quantitative analysis of the experimental scattering data with the theoretical predictions of both force fields and molecular orbital conformation energy calculations.

A multispacecraft analysis of a small-scale transient entrained by solar wind streams

The images taken by the Heliospheric Imagers (HIs), part of the SECCHI imaging package onboard the pair of STEREO spacecraft, provide information on the radial and latitudinal evolution of the plasma compressed inside corotating interaction regions (CIRs). A plasma density wave imaged by the HI instrument onboard STEREO-B was found to propagate towards STEREO-A, enabling a comparison between simultaneous remotesensing and in situ observations of its structure to be performed. In situ measurements made by STEREO-A show that the plasma density wave is associated with the passage of a CIR. The magnetic field compressed after the CIR stream interface (SI) is found to have a planar distribution. Minimum variance analysis of the magnetic field vectors shows that the SI is inclined at 54° to the orbital plane of the STEREO-A spacecraft. This inclination of the CIR SI is comparable to the inclination of the associated plasma density wave observed by HI. A small-scale magnetic cloud with a flux rope topology and radial extent of 0.08 AU is also embedded prior to the SI. The pitch-angle distribution of suprathermal electrons measured by the STEREO-A SWEA instrument shows that an open magnetic field topology in the cloud replaced the heliospheric current sheet locally. These observations confirm that HI observes CIRs in difference images when a small-scale transient is caught up in the compression region.

The local adsorption geometry and electronic structure of alanine on Cu{110}

The adsorption of alanine on Cu {110} was studied by a combination of near edge X-ray absorption fine structure (NEXAFS) spectroscopy, X-ray photoelectron spectroscopy (XPS) and density functional theory (DFT). Large chemical shifts in the C 1s, N 1s, and O 1s XP spectra were found between the alanine multilayer and the chemisorbed and pseudo-(3 x 2) alaninate layers. From C, N, and O K-shell NEXAFS spectra the tilt angles of the carboxylate group (approximate to 26 degrees in plane with respect to [1 (1) over bar0] and approximate to 45 degrees out of plane) and the C-N bond angle with respect to [1 (1) over bar0] could be determined for the pseudo-(3 x 2) overlayer. Using this information three adsorption geometries could be eliminated from five p(3 x 2) structures which lead to almost identical heats of adsorption in the DFT calculations between 1.40 and 1.47 eV/molecule. Due to the small energy difference between the remaining two structures it is not unlikely that these coexist on the surface at room temperature. (c) 2006 Elsevier B.V. All rights reserved.

Magnetic coupling in trinuclear partial cubane copper(II) complexes with a hydroxo bridging core and peripheral phenoxo bridges from NNO donor Schiff base ligands

Three new trinuclear copper(II) complexes, [(CuL1)(3)(mu(3)-OH)](ClO4)(2)center dot 3.75H(2)O (1), [(CuL2)(3)(mu(3)-OH)](ClO4)(2) (2) and [(CuL3)(3)(mu(3)-OH)](BF4)(2)center dot 0.5CH(3)CN (3) have been synthesized from three tridentate Schiff bases HL1, HL2, and HL3 (HL1 = 2-[(2-amino-ethylimino)-methyl]-phenol, HL2 = 2-[(2-methylamino-ethylimino)-methyl]-phenol and HL3 = 2-[1-(2-dimethylamino-ethylimino)-ethyl]-phenol). The complexes are characterized by single-crystal X-ray diffraction analyses, IR, UV-vis and EPR spectroscopy, and variable-temperature magnetic measurements. All the compounds contain a partial cubane [Cu3O4] core consisting of the trinuclear unit [(CuL)(3)(mu(3)-OH)](2+) together with perchlorate or fluoroborate anions. In each of the complexes, the three copper atoms are five-coordinated with a distorted square-pyramidal geometry except in complex 1, in which one of the Cu-II ions of the trinuclear unit is six-coordinate being in addition weakly coordinated to one of the perchlorate anions. Variable-temperature magnetic measurements and EPR spectra indicate an antiferromagnetic exchange coupling between the CuII ions of complexes 1 and 2, while this turned out to be ferromagnetic for complex 3. Experimental values have been fitted according to an isotropic exchange Hamiltonian. Calculations based on Density Functional Theory have also been performed in order to estimate the exchange coupling constants in these three complexes. Both sets of values indicate similar trends and specially calculated J values establish a magneto-structural correlation between them and the Cu-O-Cu bond angle, in that the coupling is more ferromagnetic for smaller bond angle values.

A new source of suprathermal O+ions near the dayside polar cap boundary

A new dayside source of O+ ions for the polar magnetosphere is described, and a statistical survey presented of upward flows of O+ ions using 2 years of data from the retarding ion mass spectrometer (RIMS) experiment on board DE 1, at geocentric distances below 3 RE and invariant latitudes above 40°. The flows are classified according to their spin angle distributions. It is believed that the spacecraft potential near perigee is generally less than +2 V, in which case the entire O+ population at energies below about 60 eV is sampled. Examples are given of field-aligned flow and of transversely accelerated “core” O+ ions; in the latter events a large fraction of the total O+ ion population has been transversely accelerated, and in some extreme cases all the observed ions (of all ion species) have been accelerated, and no residual cold population is observed (“toroidal” distributions). However, by far the most common type of O+ upflow seen by DE RIMS lies near the dayside polar cap boundary (particularly in the prenoon sector) and displays an asymmetric spin angle distribution. In such events the ions carry an upward heat flux, and strong upflow of all species is present (H+, He+, O+, O++, and N+ have all been observed with energies up to about 30 eV, but with the majority of ions below about 2 eV); hence, these have been termed upwelling ion events. The upwelling ions are embedded in larger regions of classical light ion polar wind and are persistently found under the following conditions: at geocentric distances greater than 1.4 RE; at all Kp in summer, but only at high Kp in winter. Low-energy conical ions (<30 eV) are only found near the equatorial edge of the events, the latitude of which moves equatorward with increasing Kp and is highly correlated with the location of field-aligned currents. The RIMS data are fully consistent with a “mass spectrometer effect,” whereby light ions and the more energetic O+ ions flow into the lobes and mantle and hence the far-tail plasma sheet, but lower-energy O+ is swept across the polar cap by the convection electric field, potentially acting as a source for the nightside auroral acceleration regions. The occurrence probability of upwelling ion events, as compared to those of low-altitude transversely accelerated core ions and of field-aligned flow, suggests this could be the dominant mechanism for supplying the nightside auroral acceleration region, and subsequently the ring current and near-earth plasma sheet, with ionospheric O+ ions. It is shown that the total rate of O+ outflow in upwelling ion events (greater than 10^25 s^{−1}) is sufficient for the region near the dayside polar cap boundary to be an important ionospheric heavy ion source.

Application of cylindrical distribution functions to wide-angle X-ray scattering from oriented polymers

A systematic approach is presented for obtaining cylindrical distribution functions (CDF's) of noncrystalline polymers which have been oriented by extension. The scattering patterns and CDF's are also sharpened by the method proposed by Deas and by Ruland. Data from atactic poly(methyl methacrylate) and polystyrene are analysed by these techniques. The methods could also be usefully applied to liquid crystals.

Effect of sequence distribution on the morphology, crystallization, melting, and biodegradation of poly(epsilon-caprolactone-co-epsilon-caprolactam) copolymers

Two types of poly(epsilon-caprolactone (CLo)-co-poly(epsilon-caprolactam (CLa)) copolymers were prepared by catalyzed hydrolytic ring-opening polymerization. Both cyclic comonomers were added simultaneously in the reaction medium for the First type or materials where copolymers have a random distribution of counits, as evidenced by H-1 and C-13 NMR. For the second type of copolymers, the cyclic comonomers were added sequentially, yielding diblock poly(ester-amides). The materials were characterized by differential scanning calorimetry (DSC), wide- and small-angle X-ray scattering (WAXS and SAXS), and transmission and scanning electron microscopies (TEM and SEM). Their biodegradation in compost was also studied. All copolymers were found to be miscible by the absence of structure in the melt. TEM revealed that all samples exhibited a crystalline lamellar morphology. DSC and WAXS showed that in a wide composition range (CLo contents from 6 to 55%) only the CLa units were capable of crystallization in the random copolymers. The block copolymer samples only experience a small reduction of crystallization and melting temperature with composition, and this was attributed to a dilution effect caused by the miscible noncrystalline CLo units. The comparison between block and random copolymers provided a unique opportunity to distinguish the dilution effect of the CLo units on the crystallization and melting of the polyamide phase from the chemical composition effect in the random copolymers case, where the CLa sequences are interrupted statistically by the CLo units, making the crystallization of the polyamide strongly composition dependent. Finally, the enzymatic degradation of the copolymers in composted soil indicate a synergistic behavior where much faster degradation was obtained for random copolymers witha CLo content larger than 30% than for neat PCL.

Effect of heat on rheology, surface hydrophobicity and molecular weight distribution of glutens extracted from flours with different bread-making quality

Gluten was extracted from flours of several different wheat varieties of varying baking quality. Creep compliance was measured at room temperature and tan 6 was measured over a range of temperatures from 25 to 95 degrees C. The extracted glutens were heat-treated for 20 min at 25, 40, 50, 60, 70 and 90 degrees C in a water bath, freeze-dried and ground to a fine powder. Tests were carried out for extractability in sodium dodecyl sulphate, free sulphydryl (SH) groups using Ellman's method, surface hydrophobicity and molecular weight (MW) distribution (MWD) using field-flow fractionation and multi-angle laser light scattering. With increasing temperature, the glutens showed a decrease in extractability, with the most rapid decreases occurring between 70 and 90 degrees C, a major transition in tan 6 at around 60 degrees C and a minor transition at 40 degrees C for most varieties, a decrease in free SH groups and surface hydrophobicity and a shift in the MWD towards higher MW. The poor bread-making variety Riband showed the highest values of tan delta and Newtonian compliance, the lowest content of free SH groups and the largest increase of HMW/LMW with increasing temperature. No significant correlations with baking volume were found between any of the measured parameters. (c) 2007 Elsevier Ltd. All rights reserved.

Conformational analysis of oriented non-crystalline polymers using wide angle X-ray scattering

A procedure is presented for obtaining conformational parameters from oriented but non-crystalline polymers. This is achieved by comparison of the experimental wide angle X-ray scattering with that calculated from models but in such a way that foreknowledge of the orientation distribution function is not required. X-ray scattering intensity values for glassy isotactic poly(methylmethacrylate) are analysed by these techniques. The method could be usefully applied to other oriented molecular systems such as liquid crystalline materials.

Constructing the frequency and wave normal distribution of whistler-mode wave power

We introduce a new methodology that allows the construction of wave frequency distributions due to growing incoherent whistler-mode waves in the magnetosphere. The technique combines the equations of geometric optics (i.e. raytracing) with the equation of transfer of radiation in an anisotropic lossy medium to obtain spectral energy density as a function of frequency and wavenormal angle. We describe the method in detail, and then demonstrate how it could be used in an idealised magnetosphere during quiet geomagnetic conditions. For a specific set of plasma conditions, we predict that the wave power peaks off the equator at ~15 degrees magnetic latitude. The new calculations predict that wave power as a function of frequency can be adequately described using a Gaussian function, but as a function of wavenormal angle, it more closely resembles a skew normal distribution. The technique described in this paper is the first known estimate of the parallel and oblique incoherent wave spectrum as a result of growing whistler-mode waves, and provides a means to incorporate self-consistent wave-particle interactions in a kinetic model of the magnetosphere over a large volume.

Energy and pitch-angle dispersions of LLBL/cusp ions seen at middle altitudes: predictions by the open magnetosphere model

Numerical simulations are presented of the ion distribution functions seen by middle-altitude spacecraft in the low-latitude boundary layer (LLBL) and cusp regions when reconnection is, or has recently been, taking place at the equatorial magnetopause. From the evolution of the distribution function with time elapsed since the field line was opened, both the observed energy/observation-time and pitch-angle/energy dispersions are well reproduced. Distribution functions showing a mixture of magnetosheath and magnetospheric ions, often thought to be a signature of the LLBL, are found on newly opened field lines as a natural consequence of the magnetopause effects on the ions and their flight times. In addition, it is shown that the extent of the source region of the magnetosheath ions that are detected by a satellite is a function of the sensitivity of the ion instrument . If the instrument one-count level is high (and/or solar-wind densities are low), the cusp ion precipitation detected comes from a localised region of the mid-latitude magnetopause (around the magnetic cusp), even though the reconnection takes place at the equatorial magnetopause. However, if the instrument sensitivity is high enough, then ions injected from a large segment of the dayside magnetosphere (in the relevant hemisphere) will be detected in the cusp. Ion precipitation classed as LLBL is shown to arise from the low-latitude magnetopause, irrespective of the instrument sensitivity. Adoption of threshold flux definitions has the same effect as instrument sensitivity in artificially restricting the apparent source region.

Non-thermal plasma observations using EISCAT: Aspect angle dependence

Recent observations with the EISCAT incoherent scatter radar have shown large rises in dayside, auroral plasma velocities (>2 km s^{−1}) over a wide range of latitudes and lasting about an hour. These are larger than the neutral thermal speed, and allow, for the first time, observations of a non-thermal plasma over a range of observing angles, revealing a clear angular dependence. The observed ion temperature anisotropy, deduced by assuming a Maxwellian line-of-sight ion velocity distribution, is at least 1.75, which exceeds the theoretical value for a bi-Maxwellian based on a realistic ion-neutral collision model. The aspect angle dependence of the signal spectra also indicates non-Maxwellian plasma.