Deterministic Motion of the Controversial Piston in the Thermodynamic Limit

We consider the evolution of a system composed of N non-interacting point particles of mass m in a cylindrical container divided into two regions by a movable adiabatic wall (the adiabatic piston). We study the thermodynamic limit for the piston where the area A of the cross-section, the mass M of the piston, and the number N of particles go to infinity keeping A/M and N/M fixed. The length of the container is a fixed parameter which can be either finite or infinite. In this thermodynamic limit we show that the motion of the piston is deterministic and the evolution is adiabatic. Moreover if the length of the container is infinite, we show that the piston evolves toward a stationary state with velocity approximately proportional to the pressure difference. If the length of the container is finite, introducing a simplifying assumption we show that the system evolves with either weak or strong damping toward a well-defined state of mechanical equilibrium where the pressures are the same, but the temperatures different. Numerical simulations are presented to illustrate possible evolutions and to check the validity of the assumption.     

Modeling of mass and charge transfer in an inverted rotating disk electrode (IRDE) reactor

In this work, the validation of a newly constructed inverted rotating disk electrode (IRDE) reactor is reported. Compared to the rotating disk electrode (RDE) reactor, the working electrode is changed in position from the top to the bottom of the electrochemical cell. The IRDE reactor is designed to facilitate the actual study of gas evolution reactions. It is studied whether the first-order analytical expression for the velocity field in an RDE reactor is also acceptable for an IRDE configuration. To that purpose, the kinetic parameters of the well-known ferri/ferro cyanide redox system are determined in both configurations and compared. This is done qualitatively by comparing the polarization curves obtained in the inverted and the conventional RDE configuration. Additionally, a statistically founded fitting algorithm is used to quantitatively determine the model parameters of the oxidation and reduction reaction. Not only the diffusion coefficients of Fe²⁺ and Fe³⁺ are calculated, but also the rate constants (k_ox and k_red) and the transfer coefficients (α_ox and α_red) are quantified and compared together with their respective standard deviation. It is found that the parameters of mass and charge transfer in both configurations agree well. So it is concluded that the same analytical equations of mass and charge transfer can be used in both the RDE and the IRDE reactor.     

Calibration of a Multipoint Sampling System Connected with a Photoacoustic Detector

Abstract

Photoacoustic detection of gases in the air phase in combination with a multipoint sampling device transfers about 100 mL of air from each sample location to the next one, causing a considerable disturbance when small systems are sampled. In reactive systems, such as trace gas exchange in soil samples, a correction is required to determine the kinetic behavior of the systems. But this kinetic behavior is required in turn to calculate the correction in a repeated sampling sequence. A model was developed for reaction kinetics (zero-order or first-order) within closed systems and the sample transfer between these systems by a CBISS MK2 multipoint sampling system, connected with a Brüel & Kjær photoacoustic detector. By regression, the reaction kinetics is determined, and by simulation of the system in the absence of sample transfer, corrected data are generated. Comparison of experimental and modeled data revealed that part of the sample is transferred directly two systems further. In addition, a slight memory effect of the detector was revealed. These effects were accounted for in the model. If the correction is not made, biased results are obtained for the reaction kinetics.     

Anilinium Ions: Relations Between pK, σ and Intensity of the UV Transition

Spectroscopists have often assumed, based only on the UV spectrum of the anilinium ion (φNH₃ ⁺), that ammonium groups cannot bring a “mesomeric” effect upon π systems. This assumption^(1–3) which could be justified for the anilinium ion itself, whose OO band of the secondary transition (towards 260 nm) is very weak, has been unduly extended to all the ammonium groups. Actually, the interaction between a π system and (NX_aX_bX_c)⁺ groups has been studied by several authors^(4–8) and we have shown that contrary to what had been assumed by spectroscopists, such an interaction induces strong effects on the UV spectrum of the benzene chromophore^(9–11). Using the MNDO and the CNDO methods, we have studied the quantum factors which play a part in the long range interaction, between: an ω group X on the one hand, N on the other hand, and then φ, in φNH₂ ⁺CH₂X, φNH⁺ (CH₂X_a) CH₂X_b and φNH⁺ (C₂H₄)₂X.     

π-Electron Densities in Molecules ΦCHX1X2 and Correlation with the Intensity of the 00 Band of the Secondary Transition

In molecules such as ΦX₁X₂X₃the intensity of the secondary transition of the benzene chromophore, strongly depends on long range interactions involving a σ·π coupling between orbitals belonging to the C_α-X bonds, and the πΦ system. Such a coupling distorts the symmetry of the π_Φ system(1–5). The secondary transition (towards 260 nm) which is forbidden when the symmetry is D_6h - as in the benzene molecule itself where only the low intensity progression A isobserved - becomes all the more allowed as the substituent is able to distort the πΦ cloud towards a C_2V symmetry. A new progression called B is observed. Its intensity is usually evaluated by the measure of its 00 band. The distorsion of symmetry arises because of the π donating or π withdrawing electronic effects of the substituent(1–7). These phenomena have been explained on the ground of a V shaped function(l) : ε₀₀ = f(σ), where σ is a parameter linked to the electronic effects of the substituents. When the whole substituent is a π donating one, its π donating effect is lowered by an increase of the electron attracting power of the groups X : the perturbation of the D_6h symmetry is lessened and ε₀₀ decreases. On the contrary, when the whole substituent is a π withdrawing one, an increase of the withdrawing power of the groups X increases the withdrawing power of the whole substituent, the distorsion of the D6h symmetry increases and ε₀₀ increases too. The minimum of the V shaped curve correspond to the species for which the π donating tendency of the aliphatic part of the substituent is quenched by the electron withdrawing tendency of the groups X. The D_6h symmetry of the πΦ cloud is restored. The transition is forbidden and the system A only is observed.     

Sr4PbPt4O11, the first platinum oxide containing Pt2 ions

We report the synthesis and crystal structure of the new compound Sr₄PbPt₄O₁₁, containing platinum in highly unusual square pyramidal coordination. The crystals were obtained in molten lead oxide. The structure was solved by X-ray single crystal diffraction techniques on a twinned sample, the final R factors are R=0.0260 and wR=0.0262. The symmetry is triclinic, space group P1¯, with , , , α=90.421(3)°, β=89.773(8)°, γ=90.140(9)° and Z=2. The structure is built from dumbell-shaped Pt₂O₉ entities formed by a dinuclear metal-metal bonded Pt₂⁶⁺ ion with asymmetric environments of the two Pt atoms, classical PtO₄ square plane and unusual PtO₅ square pyramid. Successive Pt₂O₉ entities deduced from 90° rotations are connected through the oxygens of the PtO₄ basal squares to form [Pt₄O₁₀⁸⁻]_∞ columns further connected through Pb²⁺ and Sr²⁺ ions. Raman spectroscopy confirmed the peculiar platinum coordination environment.     

Reversal of the enantiomeric elution order of some aromatic amino acids using reversed-phase chromatographic supports coated with the teicoplanin chiral selector

In this paper, two chiral stationary phases were prepared by coating the surface of both C8 and C18 high-performance liquid chromatography (HPLC) supports with the teicoplanin chiral selector. The hydrophobic C11 acyl side chain, attached to the d-glucosamine group of teicoplanin, served as anchor moiety for the immobilization of the chiral selector on the apolar support material. The retention and enantioselectivity of these coated stationary phases were studied using some aromatic amino acids as probe solutes and an aqueous solution as mobile phase. It was found that the enantiomer elution order on the modified C8 and C18 stationary phases was reversed (l > d) relatively to that classically observed with a teicoplanin covalently immobilized on a silica support (d > l). Such a dynamic coating on the reversed-phase supports was found to be of interest since the apparent enantioselectivity was not significantly changed by the use during an extended period of time or following a long-term storage of the columns.     

Effet-methyle en α d'un site 13C - inversion et prevision

A progressive inversion of α-methyl effects according to the number of β substituents leads to unusual important upfield shifts in ¹³C spectra of alkylcarboxylic acids.     

Stereospecific annelations of ethylenic β-phenylselenoethers by acid catalysis

It will be shown with several examples that it is possible to effect with exceptional ease on monounsaturated ethers, 1.5-phenylseleno group migration, quantitatively, by the action of anhydrous Lewis or Brönsted acids at 0°C. However, the presence of two C-C double bonds lowers the yield of this transformation.This new method of ring-closure is attractive for the synthesis of polycyclic terpenes.