Syntheses,characterization of and studies on the electrochemical behaviour of ferrocenyl dithiophosphonates and 4-methoxyphenyl dithiophosphonates

Some 1,3-dithiadiphosphetane 2,4-disulfides (X₂P₂S₄, X: Fc, FcLR; X: CH₃O?C₆H₄?, LR) were allowed to react with alcohols to obtain dithiophosphonic acids (X(OR)PS₂H). These were converted to the corresponding ammonium salts. The salts were of the structures [Fc(OR)PS₂]^?[NH₄]⁺, R: 3-methyl-1-butyl- for I; 1-phenyl-1-propyl- for II; 3-pentyl- for III; 3-phenyl-1-propyl- for IV and [CH₃O?C₆H₄(OR)PS₂]^?[NH₄]⁺, R: 3-methyl-1-butyl- for V and 1-phenyl-1-propyl- for VI. To the best of our knowledge, all the compounds except V were prepared for the first time.

The compounds synthesized were characterized by elemental analysis, NMR (¹H, ¹³C, ³¹P), MS, FTIR, and Raman spectroscopies. Electrochemical behaviors of I–VI at disposable pencil graphite electrode (PGE) were investigated by using cyclic voltammetry (CV) and square-wave voltammetry (SWV). Adsorption and diffusion patterns of all the compounds on the PGE were also studied.

Two electroactive groups were identified in the compounds I–IV and only one in V and VI. The ferrocenyl groups of I-IV were oxidized at around 0.4 V. The same compounds display a second, more intense CV band at 0.8 V. The corresponding band for the compounds V–VI appears at around 0.6 V with a much weaker intensity. It is suggested that the ferrocenyl group introduced into the structures stabilizes the radical species formed as the product of the oxidation of the dithiophosphonato group.     

The intermediate disorder regime for a directed polymer model on a hierarchical lattice

We study a directed polymer model defined on a hierarchical diamond lattice, where the lattice is constructed recursively through a recipe depending on a branching number $b\in \mathbb{N}$ and a segment number $s\in \mathbb{N}$. When $b\le s$ it is known that the model exhibits strong disorder for all positive values of the inverse temperature $\beta$, and thus weak disorder reigns only for $\beta =0$ (infinite temperature). Our focus is on the so-called intermediate disorder regime in which the inverse temperature $\beta \equiv {\beta }_n$ vanishes at an appropriate rate as the size $n$ of the system grows. Our analysis requires separate treatment for the cases $b<s$ and $b=s$. In the case $b<s$ we prove that when the inverse temperature is taken to be of the form ${\beta }_n=\stackrel{?}{\beta }{(b/s)}^{n/2}$ for $\stackrel{?}{\beta }>0$, the normalized partition function of the system converges weakly as $n\to \infty$ to a distribution $L\left(\stackrel{?}{\beta }\right)$ and does so universally with respect to the initial weight distribution. We prove the convergence using renormalization group type ideas rather than the standard Wiener chaos analysis. In the case $b=s$ we find a critical point in the behavior of the model when the inverse temperature is scaled as ${\beta }_n=\stackrel{?}{\beta }/n$; for an explicitly computable critical value ${\kappa }_b>0$ the variance of the normalized partition function converges to zero with large $n$ when $\stackrel{?}{\beta }\le {\kappa }_b$ and grows without bound when $\stackrel{?}{\beta }>{\kappa }_b$. Finally, we prove a central limit theorem for the normalized partition function when $\stackrel{?}{\beta }\le {\kappa }_b$.     

Well‐posedness and regularity results for a 2m‐th order parabolic equation in symmetric conical domains of ℝN+1

In this paper, we use the domain decomposition method to prove well‐posedness and smoothness results in anisotropic weighted Sobolev spaces for a multidimensional high‐order parabolic equation set in conical time‐dependent domains of . Copyright © 2017 John Wiley & Sons, Ltd.     

Application de l'approximation polytropique à la turbulence statistique en moyenne de FavreApplication of the polytropic approximation to turbulence statistics using Favre averaging

The application of the polytropic approximation connecting the quantities of corresponding state, to experimental analysis, is clarified. A method of polytropic determination of the exponent χ (variable but non-fluctuating) in each point of the flow is given. This approximation makes it possible the generation of representative signals of fluctuating quantities, like pressure or density. For heated gases, the problem of measurement of the equations terms written with Favre averaging is thus almost solved. Then, measurement of χ allows the determination by the experiment of crucial terms like turbulent fluxes of mass and momentum, and presso correlation. To cite this article: C. Rey, S. Benjeddou, C. R. Mecanique 332 (2004).     

Effets d'une modulation en phase de température à la frontière sur l'instabilité convective d'une couche liquide viscoélastiqueEffects of a temperature modulation in phase at the frontier on the convective instability of a viscoelastic layer

In this Note we study the effects of the temperature modulation, applied at the horizontal boundaries, on the onset of convection of a horizontal liquid Maxwellian layer. It is assumed that the temperature imposed features a steady component and a time dependent component. To analyse the effect of the temperature modulation, the study is restricted to a linear stability analysis. Thus the Floquet theory and a technique of converting a boundary value problem to an initial value problem are used to solve the system of equations corresponding to the onset of convection. Results obtained may be used to characterize the influence of modulation effects and that of the viscoelastic nature of liquid on the critical Rayleigh number. To cite this article: B. Oukada et al., C. R. Mecanique 334 (2006).     

Biodegradable PEO/cellulose‐based solid–solid phase change materials

A series of poly(ethylene oxide) (PEO) blends with cellulose (CEL) or cellulose derivatives—carboxymethyl cellulose (CMC), cellulose acetate (CAC), and cellulose ether (CET)—has been investigated as phase change materials for thermal energy storage. For PEO/CEL blends solid–solid phase transition has been observed in the whole concentration's range; for PEO/CMC and PEO/CET blends solid–solid phase transition has been found for PEO content 25 or 50 and 25 wt%, respectively. Otherwise, solid–liquid phase transition takes place. MTDSC investigations revealed that for PEO/CEL and PEO/CMC blends transition the strongest recrystallization effect (as evidenced by exothermic effect in reversing heat flow) as melting process occurred. FTIR analysis shows a shift of the stretching vibration bands of both the proton‐donor O? H groups from CEL and PEO due to intermolecular hydrogen interactions between the blends' components. Copyright © 2010 John Wiley & Sons, Ltd.     

Magnetic exchange interactions and magneto-structural correlations in heterobridged μ-phenoxo-μ(1,1)-azide dinickel(II) compounds: a combined experimental and theoretical exploration

This investigation presents the syntheses, crystal structures, magnetic properties, and density functional theoretical modeling of magnetic behavior of two heterobridged μ-phenoxo-μ(1,1)-azido dinickel(II) compounds [Ni(II)(2)(L(1))(2)(μ(1,1)-N(3))(N(3))(H(2)O)]·CH(3)CH(2)OH (1) and [Ni(II)(2)(L(2))(2)(μ(1,1)-N(3))(CH(3)CN)(H(2)O)](ClO(4))·H(2)O·CH(3)CN (2), where HL(1) and HL(2) are the [1+1] condensation products of 3-methoxysalicylaldehyde and 1-(2-aminoethyl)-piperidine (for HL(1))/4-(2-aminoethyl)-morpholine (for HL(2)), along with density functional theoretical magneto-structural correlations of μ-phenoxo-μ(1,1)-azido dinickel(II) systems. Compounds 1 and 2 crystallize in orthorhombic (space group Pbca) and monoclinic (space group P2(1)/c) systems, respectively. The coordination environments of both metal centers are distorted octahedral. The variable-temperature (2-300 K) magnetic susceptibilities at 0.7 T of both compounds have been measured. The interaction between the metal centers is moderately ferromagnetic; J = 16.6 cm(-1), g = 2.2, and D = -7.3 cm(-1) for 1 and J = 16.92 cm(-1), g = 2.2, and D(Ni1) = D(Ni2) = -6.41 cm(-1) for 2. Broken symmetry density functional calculations of exchange interaction have been performed on complexes 1 and 2 and provide a good numerical estimate of J values (15.8 cm(-1) for 1 and 15.35 cm(-1) for 2) compared to experiments. The role of Ni-N bond length asymmetry on the magnetic coupling has been noted by comparing the structures and J values of complexes 1 and 2 together with previously published dimers 3 (Eur. J. Inorg. Chem. 2009, 4982), 4 (Inorg. Chem. 2004, 43, 2427), and 5 (Dalton Trans. 2008, 6539). Our extensive DFT calculations reveal an important clue to the mechanism of coupling where the orientation of the magnetic orbitals seems to differ with asymmetry in the Ni-N bond lengths. This difference in orientation leads to a large change in the overlap integral between the magnetic orbitals and thus the magnetic coupling. DFT calculations have also been extended to develop several magneto-structural correlations in this type of complexes and the correlation aim to focus on the asymmetry of the Ni-N bond lengths reveal that the asymmetry plays a proactive role in governing the magnitude of the coupling. From a completely symmetric Ni-N bond length, two behaviors have been noted: with a decrease in bond length there is an increase in the ferromagnetic coupling, while an increase in the bond lengths leads to a decrease in ferromagnetic interaction. The later correlation is supported by experiments. The magnetic properties of 1, 2, and three previously reported related compounds have been discussed in light of the structural parameters and also in light of the theoretical correlations determined here.     

Fabrication of polymer nanotubes containing nanoparticles and inside functionalization

A polypyrrole nanotube containing nanoparticles is prepared by a dual template approach, and the inside of the nanotube is selectively functionalized with carboxyl and amine groups.     

Cyclo[2]benzimidazole: luminescence turn-on sensing of anions

Cyclo[2]benzimidazole is a new host for anions that turns on its luminescence up to 150 fold upon binding. Photoexcited cyclo[2]benzimidazole undergoes an efficient non-radiative deactivation through an excited-state intramolecular proton-transfer (ESIPT) mechanism. Upon binding an anion, the ESIPT pathway is blocked, resulting in an increase in the luminescence efficiency.     

Extending the applicability of the Gauss–Newton method under average Lipschitz–type conditions

We extend the applicability of the Gauss–Newton method for solving singular systems of equations under the notions of average Lipschitz–type conditions introduced recently in Li et al. (J Complex 26(3):268–295, 2010). Using our idea of recurrent functions, we provide a tighter local as well as semilocal convergence analysis for the Gauss–Newton method than in Li et al. (J Complex 26(3):268–295, 2010) who recently extended and improved earlier results (Hu et al. J Comput Appl Math 219:110–122, 2008; Li et al. Comput Math Appl 47:1057–1067, 2004; Wang Math Comput 68(255):169–186, 1999). We also note that our results are obtained under weaker or the same hypotheses as in Li et al. (J Complex 26(3):268–295, 2010). Applications to some special cases of Kantorovich–type conditions are also provided in this study.