Continuous‐scan capability at SSRL and applications to X‐ray diffraction

Typical X‐ray diffraction measurements are made by moving a detector to discrete positions in space and then measuring the signal at each stationary position. This step‐scanning method can be time‐consuming, and may induce vibrations in the measurement system when the motors are accelerated and decelerated at each position. Furthermore, diffraction information between the data points may be missed unless a fine step‐scanning is used, which further increases the total measurement time. To utilize beam time efficiently, the motor acceleration and deceleration time should be minimized, and the signal‐to‐noise ratio should be maximized. To accomplish this, an integrated continuous‐scan system was developed at the Stanford Synchrotron Radiation Lightsource (SSRL). The continuous‐scan system uses an in‐house integrated motor controller system and counter/timer electronics. SPEC software is used to control both the hardware and data acquisition systems. The time efficiency and repeatability of the continuous‐scan system were tested using X‐ray diffraction from a ZnO powder and compared with the step‐scan technique. Advantages and limitations of the continuous‐scan system and a demonstration of variable‐velocity continuous scan are discussed.     

Cutting and packing problems for irregular objects with continuous rotations: mathematical modelling and non-linear optimization

We further improve our methodology for solving irregular packing and cutting problems. We deal with an accurate representation of objects bounded by circular arcs and line segments and allow their continuous rotations and translations within rectangular and circular containers. We formulate a basic irregular placement problem which covers a wide spectrum of packing and cutting problems. We provide an exact non-linear programming (NLP) model of the problem, employing ready-to-use phi-functions. We develop an efficient solution algorithm to search for local optimal solutions for the problem in a reasonable time. The algorithm reduces our problem to a sequence of NLP subproblems and employs optimization procedures to generate starting feasible points and feasible subregions. Our algorithm allows us to considerably reduce the number of inequalities in NLP subproblems. To show the benefits of our methodology we give computational results for a number of new challenger and the best known benchmark instances.     

A Formula for the Partition Function That “Counts”

We derive a combinatorial multisum expression for the number D(n, k) of partitions of n with Durfee square of order k. An immediate corollary is therefore a combinatorial formula for p(n), the number of partitions of n. We then study D(n, k) as a quasipolynomial. We consider the natural polynomial approximation \({\tilde{D}(n, k)}\) to the quasipolynomial representation of D(n, k). Numerically, the sum \({\sum_{1\leq k \leq \sqrt{n}} \tilde{D}(n, k)}\) appears to be extremely close to the initial term of the Hardy-Ramanujan-Rademacher convergent series for p(n).     

Effect of π-Extended Substituents on Photophysical Properties of BODIPY Dyes in Solutions

Four boron-dipyrrine (BODIPY) based dyes with π-extended substituents in 8-position of dipyrrin ligand have been synthesized and characterized. Photophysical properties of the obtained compounds have been investigated in different individual solvents. Deposits of solvent polarity and viscosity were evaluated. BODIPY with 8-biphenyl substituent was found to be the fluorescent molecular rotor in contrast to more extended substituents. The complex nature of solvent-solute interactions leads to the poor applicability of standard multiparameter approaches to BODIPY solvatochromic properties. Fluorescence intensity was found to increase in case of solvent polarity growth, it is not typical for BODIPY. Taking that into account the BODIPY with π-extended substituents could be used for fluorescence viscosity measurements, and as the fluorescent media polarity indicators in analytical chemistry and biochemistry.     

Oxidation of some cage hydrocarbons by dioxiranes. Nature of the transition structure for the reaction of C-H bonds with dimethyldioxirane: a comparison of B3PW91 density functional theory with experiment

Dimethyl- (DMD) and methyl(trifluoromethyl)-dioxiranes were used for oxyfunctionalization of spiro{1',7-cyclopropan-(E)-2-methylbicyclo[2.2.1]heptane} (), tricyclo[3.2.2.0(2,4)]nonane (), exo-endo-endo- () and exo-exo-exo- () heptacyclo[9.3.1.0(2,10).0(3,8).0(4,6).0(5,9).0(12,14)]pentadecane, yielding tertiary alcohols as the main products. The rate constants for oxidation of by DMD were measured and the Arrhenius parameters determined. The DFT theory (B3LYP and B3PW91) using restricted and unrestricted methods was employed to study the oxidation reaction of the C-H bond of cage hydrocarbons , adamantane, and acetone with DMD. The kinetic isotopic effect calculated using unrestricted methods agreed with experiment. The reaction mechanism in terms of the concerted oxygen insertion vs. the radical part is discussed.     

Effect of alkyl substituents on excited state intramolecular proton transfer dynamics of jet-cooled bis(benzoxazolyl)phenoles

Structural factors affecting the dynamics of the excited state intramolecular proton transfer (ESIPT) are studied for alkyl derivatives of 2,5-bis(2-benzoxazolyl)phenol. Two fluorescence bands with equal decay times are observed in solution, while only one--emitted by the phototautomer--in supersonic jet. All evidence indicates the existence of a potential barrier in the S(1) state. Upon deuteration of the OH group the laser induced fluorescence (LIF) excitation spectra become much sharper as a result of slowing down the proton transfer reaction. Two conformers (rotamers) of each compound in the ground state were detected using hole burning technique. With a help of theoretical calculations three vibrations were identified as the most active ones in reducing the distance between two heavy atoms, N and O, involved in H-bond formation. The widths of (0,0) transitions in LIF excitation spectra decrease with increasing size or number of alkyl substituents at terminal aromatic rings. The corresponding calculated rate constants of ESIPT reaction ( approximately 10(12) s(-1)) decrease approximately three times upon the substituent effect. In contrast, model compound 2,5-bis(2-benzoxazolyl)-4-methoxyphenol (BBMP) with OCH(3) parasubstituent in central ring slows down the ESIPT reaction to such an extent that double, primary and phototautomeric, fluorescences coexist.     

n-Propylpyridinium chloride-modified poly(dimethylsiloxane) elastomeric networks: preparation, characterization, and study of metal chloride adsorption from ethanol solutions

An n-propylpyridinium chloride-modified PDMS elastomeric network, PDMS/Py(+)Cl(-), was prepared from linear PDMS chains containing Si(CH(3))(2)OH end-groups cross-linked by 3-chloropropyltrimethoxysilane and posterior reaction with pyridine. PDMS/Py(+)Cl(-) material was structurally characterized by infrared spectroscopy (IR) and solid state (13)C and (29)Si NMR. Thermogravimetric analysis of the product showed good thermal stability, with the initial temperature of weight loss at 450 K. The ion-exchange capacity of the PDMS/Py(+)Cl(-) was 0.65 mmol g(-1). Metal halides, MCl(z) [M=Fe(3+), Cu(2+), and Co(2+)], were adsorbed by the modified solid from ethanol solutions as neutral species by forming the surface anionic complexes MCl(z+n)(n-). The nature of the anionic complex structure was proposed by UV-vis diffuse reflectance spectra. The species adsorbed were FeCl(-)(4), CuCl(2-)(4), and CoCl(2-)(4). The specific sorption capacities and the heterogeneous stability constants of the immobilized metal complexes were determined with the aid of computational procedures. The trend in affinities of PDMS/Py(+)Cl(-) for the metal halides were found to be FeCl(3)>CuCl(2) approximately CoCl(2).     

Carbon monoxide laser emitting nanosecond pulses with 10 MHz repetition rate

Actively mode-locked electron-beam-sustained-discharge CO laser producing a train of ∼5-15 ns (FWHM) spikes following with repetition rate 10 MHz for both single-line and multiline mode of operation in the mid-IR range of ∼5 μm was experimentally studied. Total laser pulse duration was ∼0.5 ms for both mode-locked and free-running laser. Specific output energy in multiline CO laser mode of operation was up to 20 Jl⁻¹ Amagat⁻¹ and the laser efficiency up to 3.5%. The active mode-locking was achieved for single-line CO laser mode of operation in spectral range 5.2-5.3 μm. This sort of radiation can be used for pumping an optical parametric amplifier for optical stochastic cooling in relativistic heavy ion collider, for laser ablation, and for studying vibrational and rotational relaxation of CO and NO molecules.