Minimum Distance Between the Faces of Two Convex Polyhedra: A Sufficient Condition

The problem of finding the Euclidean distance between two convex polyhedra can be reduced to the combinatorial optimization problem of finding the minimum distance between their faces. This paper presents a global optimality criterion for this problem. An algorithm (QLDPA) for the fast computation of the distance between convex and bounded polyhedra is proposed as an application of it. Computer experiments show its fast performance, especially when the total number of vertices is large.     

Stable boundary layers in a diffusion problem with nonlinear reaction at the boundary

We prove the existence of nonconstant stable stationary solutions of an evolution problem with a nonlinear reaction acting on the boundary. These solutions present layers at certain points of the boundary. We also study the behavior of these solutions as the small parameter appearing in the equation approaches zero and show some stability properties of the profiles given by these equilibrium solutions.     

Preparation and electrochemical behavior of ordered rh adlayers on Pt(100) electrodes

Rhodium adlayers on Pt(100) substrates have been prepared by electrodeposition from dilute Rh(III) acidic solutions. The initially disordered layer is electrochemically annealed by applying a polarization program consisting of high-sweep-rate multicycle sequences between 0.05 and 0.78 V(RHE) in 0.1 M H(2)SO(4). In this way, a pseudomorphic Rh monolayer can be prepared on Pt(100) substrates. The degree of order of the electrochemically annealed layer has been evidenced not only through voltammetric experiments but also by means of scanning tunneling microscopy with atomic resolution for iodine-protected adlayers, which show a c(2 x 2) structure. The electrochemically induced ordering of the Rh adlayer appears to be a consequence of the repeated cycles of adsorption/desorption of H and, especially, oxygenated species. Voltammetry in sulfuric acid solutions permits examination of the energetics of H/anions and OH/O adsorption as a function of the Rh coverage. The first monolayer adsorbs both hydrogen and oxygenated species more strongly than the second one. This can be explained through an electronic effect caused by the underlying Pt(100) substrate.     

Kinetics of underpotential deposition and nucleation of copper on the Pt(111) face in the presence of acetonitrile

The kinetics of underpotential deposition, three-dimensional nucleation, and growth of copper deposits at cathodic overpotentials on a Pt(111) electrode in solutions containing 0.5 M H₂SO₄, 10 mM CuSO₄, and 0–200 mM acetonitrile (AcN) is studied by the cyclic voltammetry, potentiostatic current transients, and scanning probe microscopy methods. At low volume concentrations of acetonitrile ([AcN] ≤ 4 mM), adsorbed acetonitrile molecules accelerate the formation of a co-adsorption lattice of copper adatoms with anions due to local electrostatic effects at the charged interface. At higher concentrations, the underpotential deposition process is hampered, but the desorption of copper adatoms occurs at potentials more positive than those at low acetonitrile concentrations. This effect is attributed to a stabilizing action of acetonitrile molecules situated on the layer of copper adatoms and, in part, on platinum. At [AcN] = 0.4–40 mM, adsorbed acetonitrile molecules accelerate the growth of the bulk copper deposit, but the nucleation stage is hindered. The dependence of the copper amount on the deposition potential at [AcN] = 40 mM exhibits a maximum at 0.15–0.17 V. This effect was previously observed in weakly acid solutions (pH 1.7–3.0) containing no acetonitrile. The maximum rate of the deposit growth corresponds to an optimum number of crystallites (which is not too great) and an optimum distance between the growing centers in conditions of mixed kinetics “diffusion + electron transfer.” A substantial number of complexes Cu(I)-AcN forms at high acetonitrile concentrations.     

Electrochemical oxidation of aliphatic amines and their attachment to carbon and metal surfaces

The electrochemical oxidation of aliphatic amines (primary, secondary, and tertiary) has been investigated by cyclic voltammetry and preparative electrolysis. The oxidation mechanisms have been established, and the lifetimes of the radical cations have been measured for secondary and tertiary amines. These results have been put in parallel with the attachment of amines to glassy carbon, Au, and Pt electrodes by cyclic voltammetry, X-ray photoelectron spectroscopy (XPS), and infrared reflection-absorption spectroscopy (IRRAS). It is then possible to show that it is not the radical cation but the radical obtained after the deprotonation which reacts with the electrode surface. XPS results also point to the existence of a covalent bond between Au or Pt and the organic moiety.     

New understanding of the nature of OH adsorption on Pt(1 1 1) electrodes

The adsorption of hydroxyl on Pt(1 1 1) single crystal electrodes from aqueous acidic solutions is carefully reinvestigated. The effect of small additions (10⁻⁸–10⁻⁵ M) of chloride and bisulphate anions on the OH adsorption region in perchloric acid solution has been studied. Two regions can be differentiated in the voltammetric profile, that behave differently after the addition of the foreign anion. The initial broad adsorption process is unaffected until the highest concentration is attained. However, the sharper peak at higher potentials is affected even at the lower anion concentration. Since mass transport limitations allow to discard the anion adsorption as the main process giving this peak, we propose that the two processes are due to the dissociative adsorption of two different kinds of water, that are affected by the anion in a different way. From this idea, a new model, based on the Frumkin adsorption isotherm, is proposed, which gives an excellent fit of the experimental results.     

Potential of zero total charge of platinum single crystals: A local approach to stepped surfaces vicinal to Pt(111)

The electrochemical behavior of platinum single-crystal electrodes is revisited, with special emphasis on the determination of the potential of zero charge. We show that the measure of the charge displaced during CO adsorption allows the determination of the potential of zero total charge (PZTC). The estimation of the potential of zero free charge (PZFC) is discussed, with different degrees of approximation. The application of this methodology to the study of the PZTC of platinum stepped surfaces vicinal to Pt(111) reveals a marked decrease of the PZTC due to the introduction of surface steps. This effect is interpreted as the result of the existence of markedly smaller surface potentials localized on step sites. The importance of considering local aspects of the interface is emphasized with the use of N₂O reduction as a sensitive probe to the local structure of the surface. It is proposed that the different local maxima observed in the absolute value of the reduction current correspond to the local values of PZTC. It is shown that there is, in general, good agreement between the overall PZTC, obtained from the CO displacement, and that calculated from the local values inferred from the N₂O reduction. Further insight is obtained with the application of the laser-induced temperature jump method. This technique is useful to calculate the potential of maximum entropy of the double-layer formation. The resulting value of this potential for Pt(111) is discussed in the light of the PZFC value obtained from different approaches. For stepped surfaces vicinal to Pt(111), two local maxima in the entropy of the double layer are observed that are close to the local PZTC values estimated from the N₂O reduction. This result suggests the existence of cooperative effects in the organization of the water dipoles close to the electrode surface. Published in Russian in Elektrokhimiya, 2006, Vol. 42, No. 11, pp. 1275–1292. Based on the report delivered at the 8th International Frumkin Symposium “Kinetics of the Electrode Processes,” October 18–22, 2005, Moscow. The text was submitted by the authors in English.     

Synthesis and Characterization of a [Mn12O12(O2CR)16(H2O)4] Complex Bearing Paramagnetic Carboxylate Ligands. Use of a Modified Acid Replacement Synthetic Approach

Summary.  A new modified approach for the synthesis of Mn₁₂ clusters, based on the use of complex [Mn₁₂O₁₂(O₂C ^t Bu)₁₆(H₂O)₄] (2) as starting material to promote the acidic ligand replacement, is presented here. This new synthetic approach allowed us to obtain complex [Mn₁₂O₁₂(O₂CC₆H₄N(O^•) ^t Bu)₁₆(H₂O)₄] (3), whose preparation remained elusive by direct replacement of the acetate groups of Mn₁₂Ac (1). Complex 3 bearing open-shell radical units, was prepared to increase the total spin number of its ground state, and consequently, to increase T _B , with the expectation that the radical ligands may couple ferromagnetically with the Mn₁₂ core. Unfortunately, magnetic measurements of complex 3 revealed that the sixteen radical carboxylate ligands interact antiferromagnetically with the Mn₁₂ core to yield a S = 2 magnetic ground state. Corresponding author. E-mail: vecianaj@icmab.es Received March 27, 2002; accepted May 2, 2002     

Quantitation in capillary electrophoresis-mass spectrometry

CE-MS has evolved into a strong alternative to LC-MS. Most of CE-MS applications deal with characterization and identification. However, quantitative aspects have gained importance in, e.g., pharmaceutical and biotechnological applications. Here we summarize and evaluate various methodological aspects in order to achieve sensitive and reproducible results. Similar to LC-MS, aspects of matrix influence on the electrospray process need to be carefully addressed when quantitative results are intended by CE-MS. Due to a more complicated coupling special emphasis needs to be put on the CE-MS interface. Generally linearity over more than three orders of magnitude can be achieved by CE-ESI-MS. Furthermore, a literature survey has been performed in order to give an overview over quantitative measurements performed by CE-MS. The precision can be doubled when changing from a structural related to an isotopically labeled internal standard. Thus a level of precision better than 5% RSD can be achieved.     

The effect of the "inert" counteranions in the deprotonation of the dihydrogen complex trans-[FeH(eta 2-H2)(dppe)2]+: kinetic and theoretical studies

Kinetic studies indicate that trans-[FeH(H2)(dppe)2]+ reacts with an excess of NEt3 to form cis-[FeH2(dppe)2] in a single kinetic step. The second-order rate constant is strongly affected by the presence of added salts, an acceleration being observed with BF4- and PF6- salts and a deceleration with BPh4-. Theoretical calculations indicate that the role of the accelerating anions consists of the formation of ion pairs that provide a more effective reaction pathway for deprotonation. However, for the ion pair with the bulky BPh4- anion, steric crowding in the proximities of the dihydrogen ligand hinders the approach of the base, and the reaction is decelerated.