Exact path-integral evaluation of the heat distribution function of a trapped Brownian oscillator

Using path integrals, we derive an exact expression-valid at all times t-for the distribution P(Q,t) of the heat fluctuations Q of a Brownian particle trapped in a stationary harmonic well. We find that P(Q, t) can be expressed in terms of a modified Bessel function of zeroth order that in the limit t > infinity exactly recovers the heat distribution function obtained recently by Imparato et al. Phys. Rev. E 76, 050101(R) (2007)] from the approximate solution to a Fokker-Planck equation. This long-time result is in very good agreement with experimental measurements carried out by the same group on the heat effects produced by single micron-sized polystyrene beads in a stationary optical trap. An earlier exact calculation of the heat distribution function of a trapped particle moving at a constant speed v was carried out by van Zon and Cohen Phys. Rev. E 69, 056121 (2004)]; however, this calculation does not provide an expression for P(Q, t) itself, but only its Fourier transform (which cannot be analytically inverted), nor can it be used to obtain P(Q, t) for the case v=0.

New flame retardant polyarylazo phosphate and phosphoramide esters

Two series of flame retardant polymers, viz. polyarylazo phosphate and phosphoramide esters, were synthesized by solution polycondensation of 4,4′-dihydroxyazobenzene with various aryl phosphorodichlorides and aryl phosphoramidic dichlorides. They were characterized by i.r. 1H-, 13C- and 31P-NMR spectroscopy. The molar mass, thermal and flammability studies were carried out by viscometry, thermogravimetry and limiting oxygen index respectively to examine the influence of the phosphate and phosphoramide linkages. The polyphosphoramide esters possess better thermal and flammability characteristics than the polyphosphate esters.

The short range interactions between two rare gas atoms

The short range interactions in He2, Ne2 and Ar2 have been studied in terms of the electronic forces as functions of their internuclear separations employing their single configuration SCF wave functions. The results show that the constituent molecular orbitals behave differently in terms of the forces they exert on the nuclei during the interaction process. The different behaviour of the orbitals is also reflected in the redistribution of charges.

Synthesis and spectral studies of polyamide-phosphate esters from phosphine-oxide-containing diols with aryl phosphorodichloridates and their thermal and flammability behaviour

Polyamide-phosphate esters were synthesized by interfacial polycondensation of aryl phosphorodichloridates with the diols of phenoxaphosphine and phosphine oxide in the presence of a phase-transfer catalyst. The polymers were characterized by infra-red and 1H, 13C and 31P nuclear magnetic resonance (n.m.r.) spectroscopy. The molecular weights were determined by end-group analysis using 31P n.m.r. spectral data. The phenoxaphosphine-containing polymers showed superior thermostability and flame retardancy over the phosphine-oxide-containing polymers.

Synthesis, characterization, and fire retardancy of ferrocene containing polyphosphate esters

Polyphosphate esters containing ferrocene structures were synthesized from 1,1′-bis (p-hydroxyphenylamido) ferrocene and 1,1′-bis (p-hydroxyphenoxycarbonyl) ferrocene with aryl phosphorodichloridates by interfacial polycondensation using a phase transfer catalyst. The polymers were characterized by infrared, 1H-, 13C-, and 31-NMR spectroscopy. The molecular weights were determined by end group analysis using 31P-NMR spectral data. The thermal stability and fire retardancy were respectively determined by thermogravimetry and limiting oxygen index (LOI) measurements. The polyamide-phosphate esters showed better thermal stability and higher LOI values than the polyester-phosphate esters.

Synthetic, spectroscopic, magnetic, and x-ray structural studies on a vitamin B6-amino acid Schiff base complex, aqua(5'-phosphopyridoxylidenetyrosinato)copper(II) tetrahydrate

A Schiff base metal complex, [Cu(II)(PLP-DL-tyrosinato)(H2O)].4H2O (PLP = pyridoxal phosphate), with the molecular formula CuC17O13N2H27P has been prepared and characterized by magnetic, spectral, and X-ray structural studies. The compound crystallizes in the triclinic space group P1BAR with a = 8.616 (2) angstrom, b = 11.843 (3) angstrom, c = 12.177 (3) angstrom, alpha = 103.40 (2)degrees, beta = 112.32 (2)degrees, gamma = 76.50 (1)degrees, and Z = 2. The structure was solved by the heavy-atom method and refined by least-squares techniques to a final R value of 0.057 for 3132 independent reflections. The coordination geometry around Cu(II) is distorted square pyramidal with phenolic oxygen, imino nitrogen, and carboxylate oxygen from the Schiff base ligand and water oxygen as basal donor atoms. The axial site is occupied by a phosphate oxygen from a neighboring molecule, thus resulting in a one-dimensional polymer. The structure reveals pi-pi interaction of the aromatic side chain of the amino acid with the pyridoxal pi system. A comparative study is made of this complex with similar Schiff base complexes. The variable-temperature magnetic behavior of this compound shows a weak antiferromagnetic interaction.

Nuclear-quadrupole resonance in coordination chemistry- identification of bridiging and therminal chlorines in the mercuric chloride-4-picoline n-oxide complex

The temperature dependence of the chlorine-35 n.q.r. in the mercuric chloride-4-picoline N-oxide complex has been studied from 77 K to room temperature, and the results are used to assign the observed frequencies to terminal and bridging chlorines.

Curing reactions in plastic prepolymers and propellants. I. Polystyrene

Curing reactions of the viscous PS prepolymer and PS/AP propellant slurry have been studied. The molecular weight of the binder (separated from the propellant) and the prepolymer was found to increase to a maximum value, remain constant for some time, and then fall off between 50–125°C. The molecular weight of the binder was found to be less than corresponding prepolymer between 100–150°C but at lower temperatures (50–75°C) the reverse was found to be true. The increase in the molecular weight during curing at lower temperatures has been explained on the basis of Trommsdorff effect which gets support from the estimated activation energy (9 kcal mole−1) for the curing process. Curing was recognized as chain extension where the rate of polymerization becomes diffusion controlled below 75° C.

Antireflection properties of indium tin oxide (ITO) on silicon for photovoltaic applications

The short‐circuit current density (Jsc) of indium tin oxide (ITO/silicon solar cells has been shown both theoretically and experimentally to be a function of the thickness of the ion beam sputtered ITO layer. These results can be accounted for by computing the optical reflection from the ITO/silicon interface.

Dilute solution properties of methyl methacrylate—acrylonitrile copolymer (MA2)

This article deals with studies of the dilute solution properties of methyl methacrylate-acrylonitrile (MMA-AN) copolymer of 0.415 mole fraction (mf) of acrylonitrile composition. Mark—Houwink parameters for this copolymer have been evaluated in acetonitrile (MeCN), 2-butanone (MEK), dimethyl formamide (DMF), and γ-butyrolactone (γ-BL). The Mark-Houwink exponent a in all four solvents at all temperatures is larger than the corresponding values of the parent homopolymers. The solvent power is in the order of DMF < γ–BL < MEK < MeCN; [η] decreases with an increase in temperature, which is behavior characteristic of polymers in good solvent. The unperturbed dimensions (K0) values, obtained by the Stockmayer–Fixman method, are lower than those for the parent homopolymers and depend on solvent as well as temperature. The solute—solvent interaction parameter X1 values are close to 0.5; X1 is independent of temperature. The excess interaction parameter XABvalues are negative. The results for this copolymer system in regard to low second virial coefficient A2, large X1, and high a values suggest that the large extension of these copolymer chains is due to the unusual short-range interactions.

Structural Relationships in 2,3-Bis-n-decyloxyanthracene and 12-Hydroxystearic Acid Molecular Gels and Aerogels Processed in Supercritical CO2

Supercritical carbon dioxide is used to prepare aerogels of two reference molecular organogelators, 2,3-bis-n-decyloxyanthracene (DDOA) (luminescent molecule) and 12-hydroxystearic acid (HSA). Electron microscopy reveals the fibrillar morphology of the aggregates generated by the protocol. SAXS and SANS measurements show that DDOA aerogels are crystalline materials exhibiting three morphs: (1) arrangements of the crystalline solid (2D p6m), (2) a second hexagonal morph slightly more compact, and (3) a packing specific of the fibers in the gel. Aggregates specific of the aerogel (volume fraction being typically phi approximate to 0.60) are developed over larger distances (similar to 1000 angstrom) and bear fewer defaults and residual strains than aggregates in the crystalline and gel phases. Porod, Scherrer and Debye-Bueche analyses of the scattering data have been performed. The first five diffraction peaks show small variations in position and intensity assigned to the variation of the number of fibers and their degree of vicinity within hexagonal bundles of the related SAFIN according to the Oster model. Conclusions are supported by the guidelines offered by the analysis of the situation in HSA aerogels for which the diffraction pattern can be described by two coexisting lamellar-like arrangements. The porosity of the aerogel, as measured by its specific surface extracted from the scattering invariant analysis, is only 1.8 times less than that of the swollen gel and is characteristic of a very porous material.