Spontaneous “Distillation.” Approaching Thermodynamic Equilibrium, A Marathon Experiment in Physical Chemistry

If the left side of a sealed tube (shaped like an inverted U) is filled with chloroform, after many months, the chloroform passes spontaneously to the right side of the vessel in accord with the minimum energy principle. A similar experiment with a half-filled disposable lighter can be performed successfully in a much shorter period (6–8 days). The rate of the process (spontaneous transfer of a substance from one side of the vessel to the other side) decays with time. Curve fitting reveals the existence of two independent exponential-decay processes. An explanation of the possible mechanisms for the transfer of the substance is offered in this paper.     

Second order differential inequalities in the complex plane

Let w(z) be regular in the unit disk U and let h(r, s, t) be a complex function defined in a domain of C³. The authors determine conditions on h such that $\text{¦ h(w(z), zw′(z), z}{}^2\text{w″(z))¦ < 1}$ implies $\text{¦ w(z)¦ < 1}$ and such that Re h(w(z), zw′(z), z²w″(z)) > 0 implies Re w(z) > 0. Applications of these results to univalent function theory, differential equations and harmonic functions are given.     

Ginzburg–Landau minimizers with prescribed degrees: dependence on domain

We study minimizers of the Ginzburg–Landau functional in an annular type domain with holes. We assume degrees 1 and ?1 on the boundary of the annulus, degree 0 on the boundaries of the holes. Two types of qualitatively different behavior of minimizers occur, depending on the value of the H¹-capacity of the domain. We also describe the asymptotic behavior of minimizers as the coherency length tends to ∞. To cite this article: L. Berlyand, P. Mironescu, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

A perturbation theoretical method for determination of the dependence of the intramolecular X–H(D) potential on the hydrogen bond strength

A perturbation theoretical method is proposed that allows determination of the function describing the dependence of the intramolecular XH(D) potential on the hydrogen bond strength. Treating the XH(D) oscillators as mixed cubic–quartic oscillators in which the stretch–stretch couplings of the ν(X–H(D)) mode with the internal modes of the radical X may be neglected, and introducing the hydrogen bonding influence through the changes in the harmonic diagonal force constants (as proposed by Sceats and Rice [41]), it is possible to extract the analytical form of the function ) from the experimental versus correlations. The other parameters obtained by the empirical correlations, within this model, also have an exact physical meaning. The method is applicable to weak hydrogen bonds as well as to hydrogen bonds of intermediate strength, and, strictly speaking, to linear X– systems. However, extension to arbitrary geometry may be easily done. This revised version was published online in July 2006 with corrections to the Cover Date.     

Speciation analysis of mercury by solid-phase microextraction and multicapillary gas chromatography hyphenated to inductively coupled plasma-time-of-flight-mass spectrometry

This paper reports the development of an analytical approach for speciation analysis of mercury at ultra-trace levels on the basis of solid-phase microextraction and multicapillary gas chromatography hyphenated to inductively coupled plasma-time-of-flight mass spectrometry. Headspace solid-phase microextraction with a carboxen/polydimethylsyloxane fiber is used for extraction/preconcentration of mercury species after derivatization with sodium tetraethylborate and subsequent volatilization. Isothermal separation of methylmercury (MeHg), inorganic mercury (Hg2+) and propylmercury (PrHg) used as internal standard is achieved within a chromatographic run below 45 s without the introduction of spectral skew. Method detection limits (3 x standard deviation criteria) calculated for 10 successive injections of the analytical reagent blank are 0.027 pg g(-1) (as metal) for MeHg and 0.27 pg g(-1) for Hg2+. The repeatability (R.S.D., %) is 3.3% for MeHg and 3.8% for Hg2+ for 10 successive injections of a standard mixture of 10pg. The method accuracy for MeHg and total mercury is validated through the analysis of marine and estuarine sediment reference materials. A comparison of the sediment data with those obtained by a purge-and-trap injection (PTI) method is also addressed. The analytical procedure is illustrated with some results for the ultra-trace level analysis of ice from Antarctica for which the accuracy is assessed by spike recovery experiments.     

Volume Nonadditivity of Liquid Mixtures: Modifications to Classical Demonstrations

Departures from Raoults law are often found in liquid mixtures resulting in volume nonadditivity. Modifications are proposed for experiments demonstrating volume contraction of water/ethanol and volume expansion of ethyl acetate/carbon disulfide liquid mixtures. A layer of paraffin oil or water is used to prevent mixing of the liquids at an earlier stage then desired. A demonstration of volume expansion in a CS₂/ethyl acetate system is proposed as well. The modifications significantly improve the ease of the demonstrations, which can be made even more impressive by coloring the liquids. A reaction vessel of simple construction is offered for a more vivid demonstration of the phenomenon.     

Computer program for finding all possible cycles in graphs

A new approach is presented for identifying all possible cycles in graphs. Input data are the total numbers of vertices and edges, as well as the vertex adjacencies using arbitrary vertex numbering. A homeomorphically reduced graph (HRG) is constructed by ignoring vertices of degree less than three. The algorithm is based on successive generation of possible edge-combinations in the HRG. If a combination yields a cycle, it is either printed or stored and then finally printed in a list of all possible cycles arranged in the order of increasing ring size. A unique numbering of the cycle is used. The computer program is listed and exemplified. Computing times are given.     

On the origin of the splittings of the ν3(SO4) modes in the specular reflectance IR spectra of gypsum

The IR polarized spectra of gypsum CaSO₄·2H₂O were recorded at incidence angles of approximately 10 and 16 degrees. Band singlet or doublet was observed for the higher frequency ν₃(SO₄²⁻) mode of B_u symmetry type, depending on polarization (n or p). A doublet was observed for the lower frequency ν₃(SO₄²⁻) mode of B_u symmetry type too, irrespectively of the type of polarization. In order to give an explanation for the doublets origin, a model permittivity function was constructed. Quite good agreement exists between the reflectance based on the model permittivity function and the experimentally measured one for the high-frequency doublet. The origin of the lower frequency doublet could not be explained in this way, but may be speculated to result from an Evans type interaction between a combination of a water libration and ν₂(SO₄²⁻), with the lower frequency ν₃(SO₄²⁻) mode.