Relationship between basicity and nucleophilicity

The empirical concepts of basicity and nucleophilicity are related but not strictly proportional. Hence, the aim of this study is to help in elucidating the range where both concepts are directly proportional. To do this, the relationship between a recently introduced nucleophilicity index and the proton affinity (PA) of several families of bases has been studied. A good correlation between the PA and the nucleophilicity index using HF and HCN as electrophilic partner has been found. Our studies show that the correlation exists only when the interaction is soft–soft in character and for strong bases with weak acids. However, the relationship is not only valid for exothermic reactions as it has been previously postulated but also for endothermic reactions. Copyright © 2007 John Wiley & Sons, Ltd.     

Antimony dispersion and phase evolution in the Sb2O3-Fe2O3 system

This paper studies the antimony spreading and segregation that occurred along with the oxidation and solid-state reactions in the Fe2O3-Sb2O3 system. XRD, SEM, TG-DSC and particularly XPS were employed for characterizations. Sb2O4 and FeSbO4 are the only new phases detected. The formation of FeSbO4 is a more exothermic but slower reaction than oxidation of Sb2O3. A mechanical grinding of Sb2O3 and Fe2O3 leads to a significant dispersion of Sb2O3 possibly because of its low hardness. Dispersion of reference Sb2O4 in this way is negligible. During the heating of a mixture of Sb2O3 and Fe2O3 with an atomic ratio of Sb/Fe = 0.5 at 200-1000 degrees C in ambient air, the thermal spreading of Sb2O3 onto Fe2O3 increases with increasing temperature until Sb2O3 is oxidized into Sb2O4. The surface atomic ratio of Sb/Fe measured by XPS, R(Sb/Fe), reaches a maximum around 400 degrees C. The complete oxidation of Sb2O3 leads to a decrease in R(Sb/Fe) because of poorer dispersibility of Sb2O4. The formation of FeSbO4 starting at ca. 800 degrees C causes a further decrease in R(Sb/Fe), but the R(Sb/Fe) is still 3.2 times the nominal bulk Sb/Fe ratio when the Sb2O4 is completely transformed into FeSbO4.     

Passive Transport of Ionic Drugs through Membranes with pH-Dependent Fixed Charges

We have studied both theoretically and experimentally the passive transport of ionic drugs through membranes with pH-dependent fixed charge. The system considered constitutes a simplified model for pH-controlled drug delivery through membranes of biochemical and pharmaceutical interest. The theoretical approach employed is based on the Nernst-Planck flux equations and all of the species present in the system (the neutral or ionic drug and the hydrogen and hydroxide ions) have been taken into account together with a Langmuir-type isotherm for the adsorption of the ionic drug onto the membrane surface. The membrane permeabilities of cationic, anionic, and neutral drugs through porous membranes with graft-polymerized weak polyelectrolytes have been measured as a function of the external pH. According to the nature of the grafted polyelectrolyte, the ionized membrane fixed groups can be negative or positive. For the amphoteric membrane, both fixed charge groups are present in the grafted chains. In all cases, the ionization state of the weak polyelectrolyte fixed groups changes with the local pH within the membrane. A comparison of the theoretical results with the experimental data allows one to explain qualitatively the changes of the membrane flux with the external pH and gives new physical insights into the transport problem. Copyright 2000 Academic Press.     

The role of bismuth as promoter in Pd–Bi catalysts for the selective oxidation of glucose to gluconate

Bismuth is a well-established promoter of noble metal-based catalysts for the selective liquid phase oxidation of alcohols, aldehydes and carbohydrates with molecular oxygen. Experiments were carried out to improve the understanding of the promoting role of bismuth in bimetallic Pd–Bi catalysts used for the selective oxidation of glucose to gluconate. In relationship with the fact that these catalysts undergo substantial bismuth leaching under the reaction conditions, particular attention was paid to the possible role played by the soluble fraction of bismuth in the oxidative process. Carbon-supported Pd–Bi/C catalysts characterized by various Bi–Pd compositions (0.33≤Bi/Pd≤3.0,10 wt.%Pd+Bi) were prepared from acetate-type precursors, tested under various experimental conditions and analyzed by X-ray diffractometry and X-ray photoelectron spectroscopy (XPS). Whatever the initial catalyst composition, the surface intensity ratio measured by XPS in used catalysts lies in the range 0.4–0.6, suggesting that the dynamic state of the catalyst involves the association of one Bi and two to three Pd atoms. The leaching process and the promoting effect itself are discussed in line with the formation of Bi–glucose and Bi–gluconate complexes present in solution but also as adsorbed species at the catalyst surface. The performances of a monometallic Pd/C catalyst are significantly improved in the presence of adequate amounts of soluble Bi. The involvement of the soluble fraction of bismuth in the overall mechanistic scheme of glucose oxidative dehydrogenation is suggested. The detrimental effect of large amounts of soluble bismuth is attributed to a too extensive adsorption of Bi–glucose complexes on the surface Pd atoms.     

Theoretical study of the adsorption of H on Si n clusters, (n=3-10)

A recently proposed local Fukui function is used to predict the binding site of atomic hydrogen on silicon clusters. To validate the predictions, an extensive search for the more stable SinH (n=3-10) clusters has been done using a modified genetic algorithm. In all cases, the isomer predicted by the Fukui function is found by the search, but it is not always the most stable one. It is discussed that in the cases where the geometrical structure of the bare silicon cluster suffers a considerable change due to the addition of one hydrogen atom, the situation is more complicated and the relaxation effects should be considered.     

Electrochemical deposition onto self-assembled monolayers: new insights into micro- and nanofabrication

Pattern transfer with high resolution is a frontier topic in the emerging field of nanotechnologies. Electrochemical molding is a possible route for nanopatterning metal, alloys and oxide surfaces with high resolution in a simple and inexpensive way. This method involves electrodeposition onto a conducting master covered by a self-assembled alkanethiolate monolayer (SAMs). This molecular film enables direct surface-relief pattern transfer from the conducting master to the inner face of the electrodeposit, and also allows an easy release of the electrodeposited film due their excellent anti-adherent properties. Replicas of the original conductive master can be also obtained by a simple two-step procedure. SAM quality and stability under electrodeposition conditions combined with the formation of smooth electrodeposits are crucial to obtain high-quality pattern transfer with sub-50 nm resolution.     

Nuclear Fukui functions from nonintegral electron number calculations

Numerical results for the nuclear Fukui function (NFF) based on a nonintegral number of electrons methodology (NIEM) are reported for a series of simple diatomic molecules. A comparison with those obtained from other methodologies is focused on the estimation of the error associated with a finite difference approximation for the evaluation of the NFF. The dependence of NFFs on the type and size of the basis set is also discussed. The NIEM values are in close agreement with those obtained from a finite difference approximation using ΔN = ±1 with large basis sets. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Phragmén-Lindelöf theorems for nonlinear elliptic equations

We obtain theorems of Phragmén-Lindelöf type for the following classes of elliptic partial differential inequalities in an arbitrary unbounded domain \(\Omega \subseteq \mathbb{R}^n ,{\text{ }}n \geqq 2\) (A.1) $$\sum\limits_{i,j = 1}^n {\frac{\partial }{{\partial x_i }}\left( {a_{ij} 9(x)\frac{{\partial u}}{{\partial xj}}} \right)} + \sum\limits_{i = 1}^n {b_i (x,{\text{ }}u,{\text{ }}\nabla u)\frac{\partial }{{\partial x_i }}} \geqq f(x,{\text{ }}u)$$ where a _ij are elliptic in Ω and b _i ε L^∞(Ω) and where also a _ij are uniformly elliptic and Holder continuous at infinity and b _i = O(|x|⁺¹) as x → ∞; (A.2) $${\text{(A}}{\text{.2) }}\sum\limits_{i,j = 1}^n {a_{ij} (x,{\text{ }}u,{\text{ }}\nabla u)\frac{{\partial ^2 u}}{{\partial x_i \partial x_j }}} + \sum\limits_{i = 1}^n {b_i (x,{\text{ }}u,{\text{ }}\nabla u)\frac{\partial }{{\partial x_i }}} \geqq f(x,{\text{ }}u)$$ where a_ijare uniformly elliptic in Ω and b _iε L^∞(Ω); and finally (A.3) $${\text{div(}}\nabla u^p \nabla u {\text{)}} \geqq f{\text{(}}u{\text{), }}p > - 1,$$ where the operator on the left is the so-called P-Laplacian. The function f is always supposed positive and continuous. Moreover u is assumed throughout to be in the natural weak Sobolev space corresponding to the particular inequality under consideration, namely u ε. W _loc ^1,2 (Ω) ∩L _loc ^t8 (Ω) for (A.I), W _loc ^2,n(Ω) for (A.2), and W _loc ^1,p+2 (Ω) ∩ L _loc ^t8 (Ω) for (A.3). As a consequence of our results we obtain both non-existence and Liouville theorems, as well as existence theorems for (A.1).     

Convergence of a level‐set algorithm in scalar conservation laws

This article is concerned with the convergence of the level‐set algorithm introduced by Aslam (J Comput Phys 167 (2001), 413–438) for tracking the discontinuities in scalar conservation laws in the case of linear or strictly convex flux function. The numerical method is deduced by the level‐set representation of the entropy solution: the zero of a level‐set function is used as an indicator of the discontinuity curves and two auxiliary states, which are assumed continuous through the discontinuities, are introduced. We rewrite the numerical level‐set algorithm as a procedure consisting of three big steps: (a) initialization, (b) evolution, and (c) reconstruction. In (a), we choose an entropy admissible level‐set representation of the initial condition. In (b), for each iteration step, we solve an uncoupled system of three equations and select the entropy admissible level‐set representation of the solution profile at the end of the time iteration. In (c), we reconstruct the entropy solution using the level‐set representation. We prove the convergence of the numerical solution to the entropy solution in for every , using ‐weak bounded variation (BV) estimates and a cell entropy inequality. In addition, some numerical examples focused on the elementary wave interaction are presented. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1310–1343, 2015     

A note on the strong maximum principle and the compact support principle

In this note we are concerned with the strong maximum principle (SMP) and the compact support principle (CSP) for non-negative solutions to quasilinear elliptic inequalities of the form