Voltammetric characterization of metal sulfide particles and nanoparticles in model solutions and natural waters

Voltammetric scans in sulfidic natural waters often reveal reduction peaks in the range −0.9 to −1.35 V versus Ag/AgCl. These peaks have been attributed to iron sulfide complexes or clusters. However, sols containing CuS nanoparticles now also are known to produce reduction peaks in this range. Here we investigate the voltammetric behavior of two additional metal sulfides at the Hg electrode in 0.55 M NaCl + 0.03 M NaHCO₃ electrolyte, pH = 8.5. We show that Pb and Hg sulfides, either as suspended powders or as precipitated nanoparticles, also yield cathodic peaks between −0.9 and −1.35 V, similar to peaks obtained with CuS and FeS. For precipitated nanoparticles, the position and shape of these reduction peaks change with ageing. Freshly formed nanoparticles produce less negative reduction peaks than aged nanoparticles. Peaks from aged nanoparticles often consist of two or more superimposed reduction peaks. When all other experimental parameters are held constant, the amount of nanoparticle analyte accumulated on the electrode increases with the amount of ageing (≤1 h). Addition of EDTA or acidification followed by purging can be used to distinguish PbS nanoparticles and Fe sulfide clusters from CuS and HgS nanoparticles or from colloidal S. This test was applied to interpret −0.9 to −1.35 V reduction peaks observed in two meromictic lakes. In conjunction with other evidence, this test suggests that FeS clusters are present in one case whereas colloidal S is present in the other. Interpreting −0.9 to −1.35 V voltammetric peaks observed in sulfidic natural waters requires caution, but these peaks are potentially rich sources of information about trace metal speciation.     

Complexes of N-thiophosphorylthioureas (HL) with copper(I). Crystal structures of [Cu3L3] and [Cu(PPh3)2L] chelates

Reaction of the potassium salts of N-thiophosphorylated thioureas of common formula RC(S)NHP(S)(OiPr)(2) [R = morpholin-N-yl (HL(a)), piperidin-N-yl (HL(b)), NH(2) (HL(c)), PhCH(2)NH (HL(d))] with Cu(PPh(3))(3)I in aqueous EtOH/CH(2)Cl(2) leads to mononuclear [Cu(PPh(3))(2)L-S,S'] complexes. Using copper(i) iodide instead of Cu(PPh(3))(3)I, polynuclear complexes [Cu(n)(L-S,S')(n)] were obtained. The structures of these compounds were investigated by ES-MS, elemental analyses, 1H and 31P NMR in solution, IR and 31P solid-state MAS NMR spectroscopy. The crystal structures of [Cu(3)L(3)(a)] and [Cu(PPh(3))(2)L(b)] were determined by single-crystal X-ray diffraction.     

J-inner matrix functions, interpolation and inverse problems for canonical systems, I: Foundations

This is the first of a planned sequence of papers on inverse problems for canonical systems of differential equations. It is devoted largely to foundational material (much of which is of independent interest) on the theory of assorted classes of meromorphic matrix valued functions. Particular attention is paid to the structure of J-inner functions and connections with bitangential interpolation problems and reproducing kernel Hilbert spaces. Some new characterizations of regular, singular and strongly regular J-inner functions in terms of the associated reproducing kernel Hilbert spaces are presented.D. Z. Arov wishes to thank the Weizmann Institute of Science for hospitality and support; H. Dym wishes to thank Renee and Jay Weiss for endowing the chair which supports his research.     

Calibrating a nanoindenter for very shallow depth indentation using equivalent contact radius

Nanoindenter tips are usually modelled as axisymmetric cones, with calibration involving finding a fitting function that relates contact area to contact depth. For accurate calibration of shallow depth indentation, this is not ideal because it means that deeper indents tend to dominate the fitting function. For an axisymmetric object, it is always possible to define an equivalent contact radius (which, in the case, of nanoindentation is linearly related to the reduced modulus) and to obtain a fitting function that relates this equivalent contact radius to indentation depth. The equivalent contact radius approach is used here to provide shallow depth calibration of a nanoindenter tip at three separate times. The advantage of the equivalent contact radius methodology is that it provides a clearer physical interpretation of the changes in tip shape than a conventional area-based fit. We also show that the minimum depth for a reliable hardness measurement is obtainable and increases as the tip blunts with age but that consistent measurements of very near surface elastic moduli can be made if the blunting of the tip over time is fully accounted for in the tip area function calibration.     

On the anti-Kekulé number of leapfrog fullerenes

The Anti-Kekulé number of a connected graph G is the smallest number of edges that have to be removed from G in such way that G remains connected but it has no Kekulé structures. In this paper it is proved that the Anti-Kekulé number of all fullerenes is either 3 or 4 and that for each leapfrog fullerene the Anti-Kekulé number can be established by observing finite number of cases not depending on the size of the fullerene.     

On decompositions of leapfrog fullerenes

It is shown that given a fullerene F with the number of vertices n divisible by 4, and such that no two pentagons in F share an edge, the corresponding leapfrog fullerene Le(F) contains a long cycle of length 3n − 6 missing out only one hexagon.     

Two canonical passive state/signal shift realizations of passive discrete time behaviors

A discrete time invariant linear state/signal system Σ with a Hilbert state space and a Kren signal space has trajectories (x(),w()) that are solutions of the equation , where F is a bounded linear operator from into with a closed domain whose projection onto is all of . This system is passive if the graph of F is a maximal nonnegative subspace of the Kren space . The future behavior of a passive system Σ is the set of all signal components w() of trajectories (x(),w()) of Σ on with x(0)=0 and . This is always a maximal nonnegative shift-invariant subspace of the Kren space , i.e., the space endowed with the indefinite inner product inherited from . Subspaces of with this property are called passive future behaviors. In this work we study passive state/signal systems and passive behaviors (future, full, and past). In particular, we define and study the input and output maps of a passive state/signal system, and the past/future map of a passive behavior. We then turn to the inverse problem, and construct two passive state/signal realizations of a given passive future behavior , one of which is observable and backward conservative, and the other controllable and forward conservative. Both of these are canonical in the sense that they are uniquely determined by the given data , in contrast earlier realizations that depend not only on , but also on some arbitrarily chosen fundamental decomposition of the signal space . From our canonical realizations we are able to recover the two standard de Branges–Rovnyak input/state/output shift realizations of a given operator-valued Schur function in the unit disk.     

Atom-bond connectivity index of trees

The recently introduced atom-bond connectivity (ABC) index has been applied up to now to study the stability of alkanes and the strain energy of cycloalkanes. Here, mathematical properties of the ABC index of trees are studied. Chemical trees with extremal ABC values are found. In addition, it has been proven that, among all trees, the star tree, S_n, has the maximal ABC value.     

Canonical conservative state/signal shift realizations of passive discrete time behaviors

A passive linear discrete time invariant s/s (state/signal) system Σ=(V;X,W) consists of a Hilbert (state) space X, a Kre?n (signal) space W, a maximal nonnegative (generating) subspace V of the Kre?n space K:=−X[?]X[?]W. The sets of trajectories (x(⋅);w(⋅)) generated by V on the discrete time intervals I⊂Z are defined by