On weak spreadability of distributed-parameter systems and its achievement via linear--quadratic control techniques

In this paper, the concept of weak spreadability is introduced.It constitutes an extension of the idea developed by El Jai& Kassara. In the case of linear distributed systems weconsider quadratic control techniques with a conveniently penalizedcriterion which makes the system weakly spreadable. The approachis outlined for a convection—diffusion system, and theresults of a numerical study are also included to illustratethe main features of the considered problem.     

Thickness of a silica-tethered poly(ethylene oxide) layer measured by spin labeling

EPR spectroscopy of labeled poly(ethylene oxide) (PEO) grafted on silica has been used to characterize the conformation and local dynamics of the chains. Grafted molecules of MW 2000 with grafting ratios of 0.045, 0.057, 0.126, and 0.42 molecules/nm² were in contact with benzene. The mobility of the label was compared with that observed for solution of PEO from very diluted to highly concentrated and even bulk PEO. Thus, the concentration inside the grafted layer could be evaluated and also the thickness, which evolves rather linearly with the grafting ratio. © 1995 John Wiley & Sons, Inc.     

Study of modified silicas by inverse gas chromatography. Influence of chain length on the conformation of n-alcohols grafted on a pyrogenic silica

Summary A fumed silica surface was systematically modified by the grafting of n-alkyl chains with increasing carbon numbers. The samples were characterized by the dispersive component of the surface energy, their specific interaction potential and enthalpies of adsorption of polar, in particular, alcohol probes. It is shown that the variation of the surface properties and adsorption capacities depend on the chain length of the graft. For instance, minimum values are recorded when the surface coverage by methylene groups corresponds either to one or two CH₂ surface layers. This behaviour is related to the mobility of the grafted alkyl chains, mobility which was examined by solid state NMR.     

Study of modified silicas by inverse gas chromatography part II: Influence of chain length on surface properties of silicas grafted withα−ω diols

Summary The surface properties of silicas modified with – diols having between 4 and 16 carbon atoms were investigated by inverse gas chromatography. It is shown, that the value of the dispersive component of the surface energy does not change monotonously: a minimum value is recorded when the surface is covered by a monolayer of methylene groups. Further, when measuring the adsorption enthalpies of polar probes, an alternation of their H values is observed: grafts having an odd number of carbon atoms systematically show higher H values than the others. A trans-trans configuration of the grafted chains which allows optimum interactions is proposed, suggesting a preferential diesterification reaction of both terminal hydroxyl groups of odd diols.     

Probing the Helical Secondary Structure of Short-Chain β-Peptides

Structural prerequisites for the stability of the 3₁ helix of β-peptides can be defined from inspection of models (Figs. 1 and 2): lateral non-H-substituents in 2- and 3-position on the 3-amino-acid residues of the helix are allowed, axial ones are forbidden. To be able to test this prediction, we synthesized a series of heptapeptide derivatives Boc-(β-HVal-β-HAla-β-HLeu-Xaa-β-HVal-β-HAla-β-HLeu)-OMe 13–22 (Xaa = α- or β-amino-acid residue) and a β-depsipeptide 25 with a central (S)-3-hydroxybutanoic-acid residue (Xaa = –OCH(Me)CH₂C(O)–) (Schemes 1 3). Detailed NMR analysis (DQF-COSY, HSQC, HMBC, ROESY, and TOCSY experiments) in methanol solution of the β-hexapeptide H(-β-HVal-β-HAla-β-HLeu)₂-OH ( 1 ) and of the β-heptapeptide H-β-HVal-β-HAla-β-HLeu-(S,S)-β-HAla(αMe)-β-HVal-β-HAla- β-HLeu-OH ( 22 ), with a central (2S,3S)-3-amino-2-methylbutanoic-acid residue, confirm the helical structure of such β-peptides (previously discovered in pyridine solution) (Fig.3 and Tables 1–5). The CD spectra of helical β-peptides, the residues of which were prepared by (retentive) Arndt-Eistert homologation of the (S)- or L -α-amino acids, show a trough at 215 nm. Thus, this characteristic pattern of the CD spectra was taken as an indicator for the presence of a helix in methanol solutions of compounds 13–22 and 25 (including partially and fully deprotected forms) (Figs.4–6). The results fully confirm predicted structural effects: incorporation of a single ‘wrong’ residue ((R)-β-HAla, β-HAib, (R,S)-β-HAla(α Me), or N-Me-β-HAla) in the central position of the β-heptapeptide derivatives A (see 17, 18, 20 , or 21 , resp.) causes the CD minimum to disappear. Also, the β-heptadepsipetide 25 (missing H-bond) and the β-heptapeptide analogs with a single α-amino-acid moiety in the middle ( 13 and 14 ) are not helical, according to this analysis. An interesting case is the heptapeptide 15 with the central achiral, unsubstituted 3-aminopropanoic-acid moiety: helical conformation appears to depend upon the presence or absence of terminal protection and upon the solvent (MeOH vs. MeOH/H₂O).     

The ternary system H2O–Fe(NO3)3–Co(NO3)2 isotherms 0 and 15 °C

The solid–liquid equilibria of the ternary system H₂O–Fe(NO₃)₃–Co(NO₃)₂ were studied by using a synthetic method based on conductivity measurements.

Two isotherms were established at 0 and 15 °C, and the stable solid phases which appear are the iron nitrate nonahydrate (Fe(NO₃)₃·9H₂O), the iron nitrate hexahydrate (Fe(NO₃)₃·6H₂O), the cobalt nitrate hexahydrate (Co(NO₃)₂·6H₂O) and the cobalt nitrate trihydrate (Co(NO₃)₂·3H₂O).     

Study of modified silicas by inverse gas chromatography. Part I: Influence of chain length on grafting ratio

Summary Silica has been modified by an esterification reaction using either n-alcohols or - diols. The grafting ratios were evaluated by elemental analysis of carbon or by the weight loss of the grafted silica heated to 700°C. The grafting ratio can be easily fixed by changing the silica to reactant impregnation ratios. In the case of n-alcohols, the grafting ratios do not vary monotonously with the number of carbon atoms of the grafts and the density of the grafted layer is 25% higher for - diols than for n-alcohols. This observation needs further investigation.