Recursive method for opacity expansion at finite temperature

Using a reaction operator approach, we derive the multiple-scattering induced gluon number distribution function to all orders in powers of opacity at finite temperature. The detailed balance effect is analyzed by taking into account both gluon emission and absorption in a thermal medium. We also calculate virtual corrections and show that the infrared divergence cancels out in the gluon distribution function at finite temperature.     

Transport of phosphate in a heterogeneous field

A model for the transport of P in an ensemble of vertical homogeneous columns is given. For a single column, the dimensionless concentration of P sorbed to the solid phase, , as a function of dimensionless depth, is approximated with a piston profile. The velocity of the P-front within a column depends on the application rate of P and the retention capacity of the soil. For a field, represented by an ensemble of columns differing with respect to P applied (A _T ) and retention capacity (F _T ), the field average dimensionless concentration , at fixed depth and time, is related to A _T and F _T using probability theory. F _T and A _T are expressed in terms of easily measured variables: oxalate extractable P and Fe + Al. With the probability density functions of these random variables the field-averaged profile is calculated. Experimental and computed profiles are reasonably in agreement and differences can be explained by assuming correlation of F _T and A _T . A parameter analysis shows the increase in field-scale dispersion if the coefficients of variation of the random variables are increased. Negative correlation of A _T and F _T or a positive correlation of successive applications A _i cause an increase in field-scale dispersion. Trends observed for A _T and F _T must be taken into consideration if the model is used for predictive purposes.Notation of variables and parameters A _T Total amount of phosphate (P) applied [mmol/m²] - A Annually applied amount of P [mmol/m²] - C Covariance - CV Coefficient of variation - D Coefficient of molecular diffusion and hydrodynamic dispersion [m²/yr] - D ^* Effective dispersion coefficient for adsorbing solute, D/R [m²/yr] - E Expectation - F Functional relationship of sorption with time and concentration [mmol/xxx - F _m Maximal sorption based on (Fe + Al) _ox [mmol/xxx - F _T Total sorption capacity for P of soil layer with thickness L [mmol/m²] - K Kolmogorov-Smirnov statistic - L Length of column [m] - M Number of applications - N Number of sample locations - P _m Maximal sorption based on P _ox + P _R [mmol/xxx - P _R Extrapolated measured sorption [mmol/xxx - Q Adsorbed amount [mmol/xxx - R Retardation factor - S Precipitated amount [mmol/xxx - VAR Variance - X Generic notation of a random variable - c Concentration of P in solution [mmol/m³] - c ⁰ Feed solution concentration of P [mmol/m³] - f Probability density function - h Separation vector - l _infD ^supf Field scale dispersivity [m] - m Mean, - m Ratio of means, m/m ^R with m ^R for reference situation - t Time [yr] - t ₁ Period in time between successive applications [yr] - t ^* Time required to dissolve solid P [yr] - v Interstitial water velocity [m/yr] - v ^* Effective interstitial water velocity for adsorbing solute, v/R [m/yr] - Time averaged propagation velocity of front [m/yr] - x, y, z Coordinates [m] - Ratio between P _m and (Fe + Al) _OX - Semivariogram - Dimensionless concentration of P in the solid phase - Variable - Coefficient of correlation - _s Soil bulk density [kg/m³] - Standard deviation, (VAR)^1/2 - Ratio of standard deviations, / _R with _R for reference situation - Total time [yr] - Volumetric water content - Coordinate [m] - Dimensionless depth - _p Dimensionless front penetration depth     

Alternating Copolymerization of Propylene Oxide with Biorenewable Terpene‐Based Cyclic Anhydrides: A Sustainable Route to Aliphatic Polyesters with High Glass Transition Temperatures

The alternating copolymerization of propylene oxide with terpene‐based cyclic anhydrides catalyzed by chromium, cobalt, and aluminum salen complexes is reported. The use of the Diels–Alder adduct of α‐terpinene and maleic anhydride as the cyclic anhydride comonomer results in amorphous polyesters that exhibit glass transition temperatures (T_g) of up to 109 °C. The polymerization conditions and choice of catalyst have a dramatic impact on the molecular weight distribution, the relative stereochemistry of the diester units along the polymer chain, and ultimately the T_g of the resulting polymer. The aluminum salen complex exhibits exceptional selectivity for copolymerization without transesterification or epimerization side reactions. The resulting polyesters are highly alternating and have high molecular weights and narrow polydispersities.     

Homolytic C−H Bond Activation by Phosphine−Quinone-Based Radical Ion Pairs

Herein, we present the formation of transient radical ion pairs (RIPs) by single-electron transfer (SET) in phosphine−quinone systems and explore their potential for the activation of C−H bonds. PMes₃ (Mes=2,4,6-Me₃C₆H₂) reacts with DDQ (2,3-dichloro-5,6-dicyano-1,4-benzoquinone) with formation of the P−O bonded zwitterionic adduct Mes₃P−DDQ ( 1 ), while the reaction with the sterically more crowded PTip₃ (Tip=2,4,6-iPr₃C₆H₂) afforded C−H bond activation product Tip₂P(H)(2-[CMe₂(DDQ)]-4,6-iPr₂-C₆H₂) ( 2 ). UV/Vis and EPR spectroscopic studies showed that the latter reaction proceeds via initial SET, forming RIP [PTip₃]⋅⁺[DDQ]⋅⁻, and subsequent homolytic C−H bond activation, which was supported by DFT calculations. The isolation of analogous products, Tip₂P(H)(2-[CMe₂{TCQ−B(C₆F₅)₃}]-4,6-iPr₂-C₆H₂) ( 4 , TCQ=tetrachloro-1,4-benzoquinone) and Tip₂P(H)(2-[CMe₂{oQ^tBu−B(C₆F₅)₃}]-4,6-iPr₂-C₆H₂) ( 8 , oQ^tBu=3,5-di-tert-butyl-1,2-benzoquinone), from reactions of PTip₃ with Lewis-acid activated quinones, TCQ−B(C₆F₅)₃ and oQ^tBu−B(C₆F₅)₃, respectively, further supports the proposed radical mechanism. As such, this study presents key mechanistic insights into the homolytic C−H bond activation by the synergistic action of radical ion pairs.     

Conformational study of jet-cooled L-phenylglycine

We investigated the conformational structures of L-phenylglycine in the gas phase by photoionization and double resonance spectroscopy techniques as well as high-level ab initio calculations. The UV-UV and IR-UV double resonance spectroscopy suggested that there exists only one conformer that has a free OH band for the carboxyl group. Rotational contour analysis combined with ab initio calculation indicated that the conformer we detected by resonant two-photon ionization was not one of those found by Sanz et al. in their microwave spectroscopic study [Chem. Eur. J. 12, 2564 (2006)]. Different methods of vaporization along with different expansion and cooling conditions and different detection methods are believed to be the culprit for such intriguing discrepancy. The identical hydrogen bonding structure of our phenylglycine conformer with the most abundant conformer of glycine found in helium droplets and their nearly identical OH frequencies suggest that the skeletal structure of glycine is not significantly altered by phenyl substitution.     

Thermal stress development of liquid silicone rubber seal under temperature cycling

Liquid Silicone Rubber (LSR) is commonly used as gasket or seal material in many industrial applications. The temperature dependent material property of polymeric rubbers will result in stress relaxation/creep. The development of compressive stress in LSR between two clamping metal plates under temperature cycling is discussed in this paper. It is found that (a) in addition to stress relaxation, thermal expansion or contraction of the material contributes the most in the observed stress variation during temperature change, and (b) the stiffness of LSR appears to change according to temperature history.     

Goal‐oriented error estimation for Cahn–Hilliard models of binary phase transition

A posteriori estimates of errors in quantities of interest are developed for the nonlinear system of evolution equations embodied in the Cahn–Hilliard model of binary phase transition. These involve the analysis of wellposedness of dual backward‐in‐time problems and the calculation of residuals. Mixed finite element approximations are developed and used to deliver numerical solutions of representative problems in one‐ and two‐dimensional domains. Estimated errors are shown to be quite accurate in these numerical examples. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

Structural investigation of HCN polymer isotopomers by solution-state multidimensional NMR

Hydrogen cyanide is considered as an important precursor to amino acids and nucleic acids, and its polymers could have profound implications on prebiotic chemistry. Several structures of HCN polymers are speculated, but these structures are disparate both chemically as well as structurally. Here, we employ solution-state NMR spectroscopy to investigate the structure of HCN polymers with (13)C and (15)N isotopic enrichment. From the multinuclear and multidimensional NMR investigations, we identify some discrete structural units for the most concentrated small molecular components and suggest that the dominating polymers are polyimine chain-like structures, which are formed by base-catalyzed nucleophilic addition reactions.