On the Second Law of Thermodynamics and the Piston Problem

The piston problem is investigated in the case where the length of the cylinder is infinite (on both sides) and the ratio m/M is a very small parameter, where m is the mass of one particle of the gaz and M is the mass of the piston. Introducing initial conditions such that the stochastic motion of the piston remains in the average at the origin (no drift), it is shown that the time evolution of the fluids, analytically derived from Liouville equation in a previous work, agrees with the Second Law of thermodynamics. We thus have a non equilibrium microscopical model whose evolution can be explicitly shown to obey the two laws of thermodynamics.     

Radical Couplings as Key Steps for the Preparation of Derivatives of Nonactic Acid

Summary. Free radical couplings from furan, as cheap starting material, were studied in view of developing a rapid strategy en route to the synthesis of derivatives of nonactin. The chain containing the alcohol function was introduced in one or two steps in 86% yield. For the introduction of the second chain with the ester function two different coupling methods were tested. Starting from the advanced intermediates obtained nonactin derivatives can be prepared by catalytic hydrogenation of the furan ring.     

Unexpected end‐groups of poly(acrylic acid) prepared by RAFT polymerization

Low‐molecular‐weight poly(acrylic acid) (PAA) was synthesized by reversible addition fragmentation chain transfer polymerization with a trithiocarbonate as chain‐transfer agent (CTA). With a combination of NMR spectroscopy and matrix‐assisted laser desorption/ionization time‐of‐flight mass spectrometry, the PAA end‐groups of the polymer were analyzed before and after neutralization by sodium hydroxide. The polymer prior to neutralization is made up of the expected trithiocarbonate chain‐ends and of the H‐terminated chains issued from a reaction of transfer to solvent. After neutralization, the trithiocarbonates are transformed into thiols, disulfides, thiolactones, and additional H‐terminated chains. By quantifying the different end‐groups, it was possible to demonstrate that fragmentation is the rate limiting step in the transfer reaction. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5439–5462, 2004     

Sensitivity of trust-region algorithms to their parameters

In this paper, we examine the sensitivity of trust-region algorithms on the parameters related to the step acceptance and update of the trust region. We show, in the context of unconstrained programming, that the numerical efficiency of these algorithms can easily be improved by choosing appropriate parameters. Recommended ranges of values for these parameters are exhibited on the basis of extensive numerical tests. MSC classification: 65K05, 90C26, 90C30     

Steric effects—III: Composition of the E's parameter. Variation of alkyl steric effects with substitution. Role of conformation in determining sterically active and inactive sites

The steric effect of alkyl groups as parameterized by E'_s covers a range of over seven powers of ten. In this article an attempt is made to portray in mechanism terms the manifold nature of the steric effect as a function of substitution, i.e. the composition of the steric effect. One most consider the contribution of the topological carbon sites as a function of the true coordinates of these atoms. To this end, we evaluate the geometry of these alkyl groups in carboxylic acid indirectly by a search for the probable conformations of these acids. The starting point in this study is the determination of the minimum energy conformations in carboxylic acids using the empirical force field method based on analogous alkylmethyl ketone models.This approach to the ground state behaviour of these acids leads directly to a division of the complete set of alkyl groups into two subsets within which a Conformational sequence or filitation is associated with the substitution process which generates the successive alkyl groups of that subset. It is shown that eclipsed conformations are preferred in the case of secondary and tertiary groups bearing Et and Me sub-groups, giving way to preferred bisected conformations when t-Bu and i-Pr sub-groups are present. For further elucidation of steric perturbation terms these two subsets must be considered independently. These important observations lead to an overall coherent interpretation of steric effects.Three regions of distinct behaviour as a function of substitution have been identified. In Region I (the so-called “mormal” region, where the contribution of the introduction of successive methyl groups to the overall E'_s increases monotonically), besides excellent topological site correlations, an excellent hybrid correlation is proposed. For a conformationally homogeneous (i.e. eclipsed) set of alkyl groups the overall E'_s of groups is well expressed by a linear combination of the weighted contribution of sub-groups and the Newman six-number. This correlation leads to an interpretation of the composition of the overall steric effect of an alkyl group, as measured by the E'_s parameter, in terms of conformationally defined sites and stresses the steric importance of certain privileged sites. This result is consistent with the molecular mechanics viewpoint of preferred conformations but at variance with previous assumptions.The levelling effect (Region II), in the light of conformational information, is understood in terms of sterically active and inactive sites, while the inversion effect (Region III) is considered to be the result of molecular distortion brought about by relief of local internal steric strain within the alkyl groups. The X-ray structure of i-Pr₃CCO₂H illustrates this point.     

Phenylselenolactonisation des acides homogeranique et homonerique

The reaction of PhSeCl and N-PSP with homogeranic acid ($\text{1}$) or homoneric acid ($\text{2}$) affords butanolides in a stereospecific way. Despite the large number of cyclic cases studied in the literature such acyclic systems were remained largely unexplored. PhSe⁺ was unable to realize polycyclization.     

MIL-50, an open-framework GaPO with a periodic pattern of small water ponds and dry rubidium atoms: a combined XRD,NMR, and computational study

A new fluorinated gallium phosphate, MIL-50, has been synthesized under mild hydrothermal conditions using 1,6-diaminohexane. The chemical formula of MIL-50 is Rb(2)Ga(9)(PO(4))(8)(HPO(4))(OH)F(6).2N(2)C(6)H(18).7H(2)O. The structure is a network of hexameric units of Ga(3)(PO(4))(3)F(2) and Ga(3)(PO(4))(2)(HPO(4))F(3) via corner sharing. It creates a three-dimensional open-framework delimiting 6- and 18-ring channels running along the c axis. The diprotonated 1,6-diaminohexane and water molecules are trapped within the 18-ring pores, whereas the rubidium cations reside in the 6-ring ones. A double quantum (31)P NMR experiment and partial charge calculations indicate that water molecules are present under the form of periodic small clusters, lowering the multiplicity of one phosphorus site, P3. Though water hops within the clusters, the motion leaves the water pattern periodic. Rubidium is so tightly embedded into the framework that water moving in the large 18-ring channels does not reach it, leaving it therefore dry. The crystal framework may be ascribed to the orthorhombic space group Cmc2(1) (n degrees 36), a = 32.1510(2), b = 17.2290(3), c = 10.2120(1) A. The periodic water pattern has a different symmetry than that of the framework. A method has been devised to superpose the two sublattices that coexist in the same unit cell in order to have full occupancy of each site and to perform Madelung summations. This original method is of general interest for most zeolitic materials exhibiting a different symmetry for the framework and the template sublattices.     

Ecdysteroid glycosides: identification, chromatographic properties, and biological significance

Ecdysteroid glycosides are found in both animals and plants. The chromatographic behavior of these molecules is characteristic, as they appear much more polar than their corresponding free aglycones when analyzed by normal-phase high-performance liquid chromatography (HPLC), whereas the presence of glycosidic moieties has a very limited (if any) impact on polarity when using reversed-phase HPLC. Biological activity is greatly reduced because the presence of this bulky substituent probably impairs the interaction with ecdysteroid receptor(s). 2-Deoxy-20-hydroxyecdysone 22-O-beta-D-glucopyranoside, which has been isolated from the dried aerial parts of Silene nutans (Caryophyllaceae), is used as a model compound to describe the rationale of ecdysteroid glycoside purification and identification.