Molecular mobility of nitroxide spin probes in glassy polymers. Quasi‐libration model

ESR spectra of three spin probes with different molecular volumes: 2,2,6,6‐tetramethyl‐4‐oxopiperidine‐1‐oxyl, di‐p‐anisylnitroxide, and nitroxide derivative of fullerene in glassy polystyrene, polyvinyl trimethylsilane, and Teflon AF‐2400 were calculated numerically within the model of quasi‐libration motions. Temperature ranges, where the model is capable to reproduce spectra within experimental errors, were defined. It was found that simulation of X‐band ESR spectra allows to determine quasi‐libration amplitudes around molecular axes X and Y with accuracy ～ 3° and around Z axis with accuracy ～ 15–20°. A shape of distribution of quasi‐libration amplitudes was also determined qualitatively by ESR spectra simulations. It was established that the average amplitude of quasi‐libration motion depends on the free volume of each polymer and geometrical molecular volume of a spin probe. Quasi‐libration amplitudes increase as the temperature increases, and reach the value of 40 degrees. We found that upon further temperature increase, quasi‐libration model becomes inapplicable for quantitative numerical spectra simulation. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 107–120, 2009     

Dilute gravity flows: A phenomenological model in thin layer theory

We present a simple model for the equations of the motion of turbidity flows. The flow is treated as a deformable geometrical object, parametrized by four characteristic quantities linked to the flow: U, the mean motion velocity of the flow object; l, its length; h, its height; φ, the particles' volumetric concentration. To characterise their temporal evolution, we assume that the gravity flow of a finite volume of particulate mixture reflects the balance between the driving gravity force, the turbulent friction, the spreading due to pressure forces, the incorporation of the ambient fluid, and the deposition and/or the erosion of particles. Special emphasis is placed on the search for analytical solutions over long periods. The study shows the evolution of solutions for three physical cases and includes comparison with numerical and analogical experiments.     

The dynamics of rotational isomerism in crystals as studied by vibrational spectroscopy

Vibrational spectroscopy is uniquely capable of determining the structure and dynamics arising from the rotational degrees of freedom in molecular solids. Vibrational spectroscopy is sensitive to phenomena occurring on a time scale between the slow scale of magnetic, resonance methods and fast scale of diffraction methods; a time scale appropriate for both internal and overall rotation. Rotational motion of molecules in crystals provide examples of very simple reactions. Our understanding of the spectra of reacting molecules can thus be tested on these systems, and we conclude that Redfield equations can describe such spectra.A rich variety of motional effects are described: (1) The libration of the water of hydration in sodium perchlorate which illustrates a simple reacting system. (2) The libration of the adamantane molecule in both its ordered and disordered crystal phases which illustrates intermolecular interactions in organic crystals and the consequences of disorder. (3) The libration of the ammonium ion in crystals of ammonium salts which illustrated both change of orientational position by tunneling and the subtle orientating effects of isotopic substitution. (4) The internal rotation in n-alkane crystals which illustrates the ability to determine conformers and the relationship between the occurrence of disordered conformers and the occurrence of phase transitions.     

Frequency shifts and modulation effects due to solenoidal magnetic field inhomogeneities in ion cyclotron mass spectrometry

Solenoidal (i.e. axially symmetric) magnetic field inhomogeneities, which in addition have symmetry under the operation z → −z are the most important to Fourier transform-ion cyclotron resonance (FT-ICR) mass spectrometry since they introduce frequency shifts at first-order in perturbation theory. Frequency shifts for all three fundamental modes are derived for the leading second-order and fourth-order solenoidal inhomogeneities without any restrictions on the initial conditions. The analytical frequency shifts agree very well with frequency shifts obtained from numerical trajectory calculations using the exact classical equations of motion. The effect of the inhomogeneity on the ion trajectory is solved analytically. For a strong magnetic bottle field, the cyclotron motion is frequency modulated at twice the z-oscillation frequency resulting in sidebands. However, the amplitude of these sidebands is negligibly small for typical inhomogeneity strengths. The effect of a magnetized ICR trap on the homogeneity of the magnetic field is studied by analytical methods. We find that the leading magnetic bottle field decreases as d⁻³, where d is the cylindrical ion trap diameter.     

A pulsed NMR study of molecular motion in solid 5,5-dimethyl-5,6,11,12-tetrahydro-5 H-dibenzo[b,f]silocin

A pulsed NMR study of relaxation times, T₁ and T_1D, and second moments for solid 5,5-dimethyl-5,6,11,12-tetrahydro-5 H-dibenzo[b,f]silocin is reported. The compound was studied over the temperature range ?175 to 50°C. Evidence was obtained for three motions characterized by activation energies, 2.70, 1.2, and ?4 kcal/mole, respectively. The first motion is methyl reorientation. The second motion is not assigned but is probably a relatively small amplitude flexing of the central ring. The third motion is also unassigned and may be large amplitude flexing of the central ring, libration, or anisotropic molecular reorientation. The motions was assigned by comparison of X-ray crystallographic data with NMR second moment data.     

Electrical properties and stoichiometry in La2NiO4

The electrical properties of La₂NiO₄ have been studied with respect to the stoichiometry of the material. The conductivity of reduced compositions has been measured between 20 and 1000 K and compared to that of the air-prepared ones. Nonstoichiometry is present in both cases and produces disorder leading to Anderson localization and to the definition of a mobility edge in the σ_x²−y² itinerant band. Air-prepared compounds contain in addition a large number of Ni³⁺ states which may overlap the itinerant σ_x²−y² band. For reduced materials containing small amounts of Ni³⁺, the electrical properties can be described below 200 K by a hopping conductivity at the Fermi level within a sharply peaked density of states. The results are well described within the frame of the Mott theory of variable range hopping. Above 200 K highly reduced materials exhibit direct excitation of holes from Ni³⁺ states to the mobility edge in the itinerant band. Under conditions appropriate to air-prepared materials, the Fermi level is shifted toward the itinerant band and a major contribution to the conductivity arises from hopping at the Fermi level. At high temperature a progressive excitation of carriers from the localized states is anticipated with an eventual exhaustion region. This last assumption is corroborated with a shift of the conductivity maximum to higher temperature for increasingly reduced materials.     

The itinerant oscillator treated and extended in terms of a mori continued fraction

The angular velocity and orientational autocorrelation function of a disk are evaluated using a four-variable Mori formalism. It is pointed out that the equivalent three-variable formalism is formally identical to the inertia-corrected itinerant oscillator model developed recently by Coffey et al. Therefrom a sound physical interpretation can be given to the four-variable model in terms of a disk (in the 2-D case) surrounded by two annuli, the outermost of which undergoes rotational diffusion.     

Orbiting trajectories and the adiabatic approximation to the capture cross section

For the potentialV(R)=CR ^?4(1+ε(cos²??1/2)) and a planar geometry we compute classical trajectories, which are a good approximation to those trapped orbits which separate collisions with “capture” from those without. Two possible types of such trajectories (rotating or librating in the rotating reference frame) and the transition between both types are discussed. From the limiting impact parameters accurate capture cross sections may be calculated. They can be compared with the popular approximation known as ADO — (average dipole orientation) — theory, but an analysis of the latter shows that it is theoretically not justified. Instead, the adiabatic approximation for planar collisions is developed with and without angular momentum conservation. It fits numerical calculations very well as long as the transition from rotation to libration lies inside the centrifugal wall, i.e. the separating orbit is a rotation. In the opposite case only qualitative agreement is obtained. Finally, a simple approximation to get 3D capture cross sections from planar calculations is discussed.     

Itinerant oscillation with a cosine potential

The equations of motion of the planar itinerant librator are extended to involve a cosine potential rather than a harmonic form for interaction, and are solved numerically to produce the angular velocity autocorrelation function and its Fourier transform (real and imaginary parts). The behaviour of the cosine potential is matched with that of the harmonic potential through these functions and in general conforms more closely to the indication of zero-THz spectroscopy and computer simulation.     

Dielectric properties of a liquid of dipole hard spheres

The Kirkwood factor g _K of a model polar liquid of dipolar hard spheres (DHSs) was approximated by analytical equations using the approximation of the interaction of the second neighbors within the hindered rotation model. The derived equations describe the temperature and density dependences of the dielectric functions of the DHS liquid.     

Parameterization of 241Am and 230Th alpha particle energy in dependence on distance traveled in air

A new method is introduced in this paper for calculating alpha particle energy versus traveled distance (APETD) in air as emitted from ²⁴¹Am and ²³⁰Th sources as well as the alpha range versus its energy and its energy versus distance. This method is to derive the stated relevant equations and in particular to speed up the calculation of E(x) by a Monte-Carlo simulation. By a fitting procedure, an analytical formula E(x) was determined in terms of a series of powers of distance x. Then a randomly sampled x can be quickly transformed into a corresponding energy E. The APETD calculations were run on a Microsoft Windows 7 32?bit operating system with a maximum usable memory of 3?GB. The results of calculations for alphas of the above two radionuclides in air compared to those of others using a different method are in good agreement. The above stated equations as derived in this paper are presented and the process time for applying the new method has been greatly improved.     

Ultrafast intermolecular dynamics of liquid water: a theoretical study on two-dimensional infrared spectroscopy

Physical and chemical properties of liquid water are dominated by hydrogen bond structure and dynamics. Recent studies on nonlinear vibrational spectroscopy of intramolecular motion provided new insight into ultrafast hydrogen bond dynamics. However, our understanding of intermolecular dynamics of water is still limited. We theoretically investigated the intermolecular dynamics of liquid water in terms of two-dimensional infrared (2D IR) spectroscopy. The 2D IR spectrum of intermolecular frequency region (<1000 cm(-1)) is calculated by using the equilibrium and nonequilibrium hybrid molecular dynamics method. We find the ultrafast loss of the correlation of the libration motion with the time scale of approximately 110 fs. It is also found that the energy relaxation from the libration motion to the low frequency motion takes place with the time scale of about 180 fs. We analyze the effect of the hindered translation motion on these ultrafast dynamics. It is shown that both the frequency modulation of libration motion and the energy relaxation from the libration to the low frequency motion significantly slow down in the absence of the hindered translation motion. The present result reveals that the anharmonic coupling between the hindered translation and libration motions is essential for the ultrafast relaxation dynamics in liquid water.     

Analytical formulae for chronoamperometry of a charge neutralisation process under conditions of linear migration and diffusion

The electrochemical reaction of the charge neutralisation of a binary electrolyte ion, at a planar electrode, is a rare example for which analytical formulae for potential step chronoamperometry can be obtained, under conditions of migration-diffusion transport in semi-infinite, one-dimensional space domain. This has been previously shown by Myland and Oldham [Electrochem. Commun. 1 (1999) 467], assuming equal diffusion coefficients. In the present work, a more general analytical solution is obtained, for the case of unequal diffusion coefficients. The effect of the diffusion coefficient ratio D_R/D_C, of the electroactive ion R and the counter-ion C, on the limiting chronoamperometric current, is examined. The effect increases with the growing ratio |z_R/z_C| of the electric charges of these ions, and becomes nonnegligible for |z_R| greater than or equal about 2, and for typical departures of D_R/D_C from unity. Among other things, the formulae obtained can be useful for testing digital simulation methods for the Nernst–Planck equations.     

Long-time overdamped Langevin dynamics of molecular chains

We present a novel algorithm of constrained, overdamped dynamics to study the long-time properties of peptides, proteins, and related molecules. The constraints are applied to an all-atom model of the molecule by projecting out all components of the nonbonding interactions which tend to alter fixed bond lengths and angles. Because the overdamped dynamical equations are first order in time, the constraints are satisfied by inversion of a banded matrix at each timestep, which is computationally efficient. Thermal effects are included through a Langevin noise term in the equation of motion. Because high-frequency components of the motion have been eliminated, the timestep of the algorithm is determined by the nonbonding forces, which are two to three orders of magnitude weaker than the bonding forces. Using polyalanine as a test example, we demonstrate that trajectories simulating a microsecond of motion can be run about 10³ times faster than an equivalent molecular dynamics simulation. © 1994 by John Wiley & Sons, Inc.     

Ensembles of microelectrodes: A digital- simulation

The rate of diffusion to ensembles of microelectrodes is calculated by digital simulation, based on the explicit finite-difference technique. Two limiting cases are shown in the current-time relationship at short times, when the diffusion layer is small in comparison to the radius of each microelectrode, the current behaves as in the case of semi-infinite planar diffusion to the active area on the surface. At long times, when the diffusion layers of adjacent electrodes overlap significantly, the current approaches the case of planar diffusion to the total area of the surface, including the non-active regions. The results are compared with previous calculations based on analytical solutions, which were derived on the basis of different approximations. Good agreement between reported experimental data and results based on simulation is observed.Edge effects arising as a result of contributions of radial components to the total diffusion rate are shown to be significant, even on relatively large electrodes. The errors which arise due to such effects are estimated as a function of the size of the electrode and the duration of measurement.     

Phase behavior of attractive k-mers on two-dimensional lattices: a study from quasi-chemical approximation

The phase behavior of attractive linear rigid k-mers on two-dimensional lattices was studied by theoretical and simulation calculations in the framework of the lattice-gas model. Combining (i) the analytical expression for the partition function of non-interacting k-mers, and (ii) a generalization of the classical quasi-chemical approximation (QCA) in which the adsorbate can occupy more than one adsorption site, the main thermodynamic functions of the system were explicitly obtained. It was found that, for temperatures below a certain condensation temperature, the system undergoes a first-order phase transition which is observed as a clear discontinuity in the adsorption isotherms. The transition was studied in detail by calculating the temperature–density phase diagrams. Comparisons with analytical data from Bragg–Williams approximation and Monte Carlo simulations were performed in order to test the validity of the theoretical model. The results obtained allowed us not only to analyze the effect of introducing the lateral interactions by following the configuration-counting procedure of the QCA, but also to discuss the consequences of choosing the configurational factor associated to adsorption of non-interacting k-mers from different models developed to treat the multisite occupancy adsorption problem.     

Magnetic and crystallographic properties of the system Fe2P1−xAsx

The crystallographic and magnetic properties of the system Fe₂P_1?xAs_x were studied between 0 ? x ? 0.65. The end member Fe₂P was prepared by both direct combination of the elements and electrolysis of fused salts. The products obtained showed similar crystallographic properties and were found to be stoichiometric. Differences in the magnetic properties were attributed to carbide impurities present in the samples prepared by electrolysis. The substitution of arsenic takes place preferentially on the anion_I site. The cell volume was found to increase monotonically with arsenic substitution, and the observed magnetic properties were interpreted on the basis of the Stoner model for itinerant electrons.     

Lacunars: Nonfractal molecules with fractional mass dimension

Mass dimension D has been studied analytically and by computer simulation within the framework of the atomic cluster model for large numbers of lacunary molecules (lacunars) from the class of polycyclic hydrocarbons and polyphenyls. These molecules have a central framework and radial peripheral fragments. Due to the presence of lacunas (voids) between the peripheral fragments and because of growth of lacunas with increasing length of these fragments, these lacunary molecules, which are not self-similar fractal objects, have fractional dimension 1 < D _c < 2 in the region of cores. It is established that D _c(q) depends on the number q and length of peripheral fragments, on the core shape and the local symmetry and local anisotropy of the core, and on the character of space occupation by the molecule. For both classes of molecules, analytical dependences D _c(q) have been obtained that explain the results of computer simulation. Similarity and differences between lacunars and fractals are discussed.     

A mathematical model based on the limit dilution method to obtain linear calibration curves which eliminate the matrix effect in quantitative analysis by X-ray fluorescence

We propose a mathematical model from an analytical application viewpoint inspired in the limit dilution method. The theoretical development of the model and its results are given. The model shows that there is a linear relation between the inverse of fluorescence intensity and the inverse of the dilution factor; each analytic system (sample, diluent and analyte) is characterised by a general linear function which is easily obtained. The analytical applications arising from this linearity are of great importance in X-ray fluorescence analysis. The following immediate applications are proposed: direct procurement of the total correction factor Y/H, rapid calculation of the fluorescence intensity of the analyte in a sample (I_i^s) and direct calculation of the corrected fluorescence intensity (I_i^sF). The suggested model makes it possible to deduce a linear function between the fluorescence intensity of the analyte and the analyte concentration in successive dilutions of a standard; this straight line behaves as a calibration curve with direct application in X-ray fluorescence analysis. The proposed model may be applied to complex samples of geological origin, with elimination of the matrix effect. The results obtained in the determination of Ca, K, Fe and Ti in a standard soil show complete agreement with the certified reference values with a relative error about 0.5%, even using a standard shale with very different chemical composition as reference sample.