The 's theory of the motion of the lunar apse

An analysis of Newton's theory of the lunar apsidal motion in the Principia shows an inadequacy for which he attempted to compensate by adjusting his numerical assumptions.     

Geometric approach to a dilation theorem

Problem: Given operators A_j ? O on Hilbert space $\text{H}$, with ΣA_j = 1, to find commuting projectors E_j on a Hilbert space $\text{H}$ ? $\text{H}$ such that (for all _j) x¹A_jy = x¹E_jy for, x, y ∈ $\text{H}$. This paper gives an explicit construction, quite different from the familiar solution.     

Spin density in the CoCl42− ion

Unrestricted and restricted Hartree-Fock calculations for the tetrachlorocobaltate(II) ion ICoCl₄^2?) are presented. The spin density distributions from these calculations are compared with polarized neutron diffraction results through spin density plots and a population analysis.     

The polar nature of 2,1,3-benzoxadiazole, -benzothiadiazole, -benzoselenadiazole and derivatives as determined by their electric dipole moments

Permanent electric dipole moments have been determined in benzene solutions at 25° for the oxygen, sulfur, and selenium series of 2,1,3-benzodiazoles. The derivatives studied contained 4, 5, and 6 substituted methyl, chloro, nitro, and amino groups. The dipole moment data of the derivatives were analyzed relative to that of the parent species which allowed deductions to be made about the mesomeric structures operating in the compounds. The mesomeric charge transfer increases regularly from the oxygen to the selenium structures, being nearly undetected in 2,1,3-benzoxadiazole derivatives and very pronounced in the 2,1,3-benzoselenadiazoles.     

A study of some parameters relevant to the response of harwell PMMA dosimeters to gamma and electron irradiation

The effects on the radiation response of Harwell polymethylmethacrylate (PMMA) dosimeters of dose-rate, radiation type, temperature during irradiation and post-irradiation storage, and post-irradiation stability, are of importance to the operators of commercial irradiation facilities.

This paper describes recent studies of the effects of some of these parameters on the radiation response of Harwell Red 4034, Amber 3042, and Gammachrome YR Perspex dosimeters, and provides data on batch to batch variation and shelf-life.     

Unitary group approach to the many-electron problem. I. Matrix element evaluation and shift operators

This is the first paper in a series of three directed toward the evaluation of spin-dependent Hamiltonians directly in the spin-orbit basis. In this paper we present a new and complete derivation of the matrix elements of the U(n) generators in the electronic Gel'fand basis. The approach employed differs from previous treatments in that the matrix elements of nonelementary generators are obtained directly. A general matrix element formula is derived which explicitly demonstrates the segment level formalism obtained previously by Shavitt using different methods. A simple relationship between the matrix elements of raising and lowering generators is determined which indicates that in CI calculations, only the matrix elements of raising generators need be calculated. Some results on the matrix elements of products of two generators are also presented.     

Transient absorption studies and numerical modeling of iodine photoreduction by nanocrystalline TiO2 films

We have used transient absorption spectroscopy to study the reaction between photogenerated electrons in a dye-free nanocrystalline titanium dioxide film and an iodine/iodide redox couple. Recombination kinetics was measured by recording the transient optical signal following band gap excitation by a UV laser pulse. In the presence of a methanol hole scavenger in the electrolyte, a long-lived (0.1-1 s) red/infrared absorbance is observed and assigned to photogenerated electrons forming Ti(3+) species. In the presence of iodine and excess iodide in the electrolyte, the signal decays on a millisecond-microsecond time scale, assigned to reduction of the redox couple by photogenerated electrons in the TiO(2). The electron lifetime decreases inversely with increasing iodine concentration, indicating that the back reaction is first order in [I(2)]. No evidence for I(2)(-) is observed, indicating that the reaction mechanism does not involve the formation of I(2)(-) as an intermediate. The shape of the kinetics evolves from monoexponential at low [I(2)] to stretched-exponential as [I(2)] increases. A Monte Carlo continuous-time random walk model is implemented to simulate the kinetics and its [I(2)] dependence and used to address the order of the recombination reaction with respect to electron density, n. The model incorporates the diffusion of oxidized species from the electrolyte toward the TiO(2) surface as well as electron trapping and transport in the TiO(2). In the limit of low [I(2)], the monoexponential kinetics is explained by the recombination reaction being rate limited by the diffusion of the oxidized species in the electrolyte. The stretched-exponential behavior at high [I(2)] can be explained by the reaction being rate limited by the transport of electrons through a distribution of trap states toward reactive sites at the TiO(2)-electrolyte interface, similar to the mechanism proposed previously for the kinetics of electron-dye cation recombination. Such trap-limited recombination can also explain the superlinear dependence of electron recombination rate on electron density, which has been reported elsewhere, without the need for a reaction mechanism that is second order in n. In contrast, a second-order reaction mechanism in a trap-free medium cannot explain the observed kinetics, although a second-order mechanism incorporating electron trapping cannot be conclusively ruled out by the data. We propose that the most likely reaction scheme, that is first order in both [I(2)] and n, is the dissociative reduction of I(2) onto the metal oxide surface, followed by a second electron reduction of the resulting adsorbed iodine radical, and that empirical second-order behavior of the electron lifetime is most likely explained by electron trapping rather than by a second-order recombination mechanism.     

Hydrophobic interactions and osmotic second virial coefficients for methanol in water

A recent theory of the hydrophobic effect together with a simple model for an alcohol molecule is used to calculate the osmotic (McMillan-Mayer) second virial coefficientB ₂ for methanol dissolved in water. We use this calculation to study the validity of common arguments that try to draw microscopic structural information from experimental virial coefficient data. In disagreement with many workers, we find that the hydrophobic interaction between hard spheres in water is attractive and that its strength diminishes as temperature is raised. Models that have come to the opposite conclusions have neglected complications inherent to real solutes such as the role of the hydroxy groups in affecting the correlations between the apolar portions of neighboring alcohols. The calculations reported here indicate that this neglect is a poor approximation for methanol. Our calculations also show that osmotic virial coefficients are sensitive to subtle details in the potentials of mean force. Therefore, slowly varying (e.g., dispersion) interactions may also contribute significantly to the values of these coefficients without significantly changing the solvent structure near the solute molecules.     

The role of solvent fluctuations in hydrophobic assembly

We use a coarse-grained solvent model to study the self-assembly of two nanoscale hydrophobic particles in water. We show how solvent degrees of freedom are involved in the process. By using tools of transition path sampling, we elucidate the reaction coordinates describing the assembly. In accord with earlier expectations, we find that fluctuations of the liquid-vapor-like interface surrounding the solutes are significant, in this case leading to the formation of a vapor tunnel between the two solute particles. This tunnel accelerates assembly. While considering this specific model system, the approach we use illustrates a methodology that is broadly applicable.     

Low-temperature activation conditions for PAMAM dendrimer templated Pt nanoparticles

Surface immobilized polyamidoamine (PAMAM) dendrimer templated Pt nanoparticles were employed as precursors to heterogeneous catalysts. CO oxidation catalysis and in situ infrared spectroscopy were used to evaluate conditions for dendrimer removal. Infrared spectroscopy showed that PAMAM dendrimer amide bonds begin decomposing at temperatures as low as 75 degrees C. Although the amide stretches are completely removed after 3 h of oxidation at 300 degrees C, 16 h were required to reach maximum catalytic activity. Further treatment under oxidizing or reducing atmospheres did not cause substantial changes in activity. Infrared spectroscopy of the activated materials indicated that organic residues, probably surface carboxylates, are formed during oxidation. These surface species passivate the Pt NPs, and their removal was required to fully activate the catalyst. Substantially less forcing activation conditions were possible by employing a CO/O(2)/He oxidation treatment. At appropriate temperatures, CO acts as a protecting group for the Pt surface, helping to prevent fouling of the nanoparticle by organic residues. CO oxidation catalysis and infrared spectroscopy of adsorbed CO indicated that the low temperature activation treatment yielded supported nanoparticles that were substantially similar to those prepared with more forcing conditions.