On the origin of Turing instability

A reaction–diffusion system consisting of one, two or three chemical species and taking place in an arbitrary number of spatial dimensions cannot exhibit Turing instability if none of the reaction steps express cross‐inhibition. A corollary of this result – obtained by elementary calculations – underlines the importance of nonlinearity in the formation of stationary structures, a kind of self‐organization on a chemical basis. Relations to global stability of reaction–diffusion systems, and results on multispecies systems are also mentioned. The statements are not restricted to mass action type models. As a by‐product, the solution of a basic inverse problem of formal kinetics is also presented which extends a previous result by Hárs and Tóth (1981) to models with arbitrary – including rational – functions as reaction rates so often occurring, e.g., in enzyme kinetics. This revised version was published online in July 2006 with corrections to the Cover Date.     

Calculation of chemical and phase equilibria via simulated annealing

We present a new class of techniques for the solution of the chemical and phase equilibria problem for reacting species in a closed system. The minimisation of the Gibbs free energy for all the species in the system is conducted using the technique of simulated annealing (SA). The SA objective function incorporates non‐ideal equations of state. This new approach is demonstrably able to solve multi‐species and multi‐phase LTCE problems in ideal‐gas solutions, ideal solutions and mixtures of ideal and non‐ideal solutions. This revised version was published online in July 2006 with corrections to the Cover Date.     

Chemical systems consisting only of elementary steps – a paradigma for nonlinear behavior

We present a new analytic method which allows one to interpret a mass‐action kinetic reaction of arbitrary molecularity as the limit case of a sequence of bimolecular steps. Together with other technics (transformation of an arbitrary ODE into a polynomial ODE [8]; transformation of a polynomial ODE into a form which can be interpreted as a mass‐action kinetic system [10]), it is thus possible to construct an at most bimolecular mass‐action kinetic system with the same dynamic behavior as an arbitrary ODE. Furthermore, we demonstrate necessary improvements of the transformation given in [10]. Is is also shown that an arbitrary single mass‐action kinetic reaction can be understood as a sequence of two reactions with a short‐living intermediate. In particular, it therefore follows that an autocatalytic reaction can always be approximated by two nonautocatalytic ones without changing the dynamics of the whole system. This revised version was published online in July 2006 with corrections to the Cover Date.     

Analysis of nuclear spectra with non-linear techniques and its implementation in the Cambio software application

Popular nuclear spectral analysis applications typically use either the results of a peak search or of the best match of a set of linear templates as the basis for their conclusions. These well‐proven methods work well in controlled environments. However, they often fail in cases where the critical information resides in well-masked peaks, where the data is sparse and good statistics cannot be obtained, and where little is known about the detector that was used. These conditions are common in emergency analysis situations, but are also common in radio‐assay situations where background radiation is high and time is limited. To address these limitations, non‐linear fitting techniques have been introduced into an application called “Cambio” suitable for public use. With this approach, free parameters are varied in iterative steps to converge to values that minimize differences between the actual data and the approximating functions that correspond to the values of the parameters. For each trial nuclide, a single parameter is varied that often has a strongly non‐linear dependence on other, simultaneously varied parameters for energy calibration, attenuation by intervening matter, detector resolution, and peak-shape deviations. A brief overview of this technique and its implementation is presented, together with an example of its performance and differences from more common methods of nuclear spectral analysis.     

Misgivings from the theoretical foundation of the path‐following procedures based on the Elber–Karplus strategy

A mathematical proof against the theoretical foundation of the Elber–Karplus (EK) global reaction path‐following method and the improvements based on the EK strategy have been discussed. According to our arguments the minimization of the average value of the potential energy along a path to two energy minima never defines a reaction path (RP) unless in the chemically irrealistic situation where the points of the curve joining the two minima of reactants and products have constant energy values. Therefore, finding approximate RPs by EK‐strategies for large chemical systems or even in mathematical test examples is impossible or at least strongly doubtful (the larger the system the more doubtful). This revised version was published online in July 2006 with corrections to the Cover Date.     

Mass transfer to tubular electrodes. Part 2: CE process

The kinetic equations for an electrochemical process consisting of a homogeneous first‐order chemical reaction followed by electron transfer at the electrode surface are solved numerically, for linear sweep voltammetry under hydrodynamical conditions in a tubular electrode. Models for both the cases involving reversible as well as irreversible electrode charge transfer reaction are investigated. The influence on current–potential voltammograms of the experimentally measurable parameters like the potential scan rate, axial flow rate and chemical equilibrium parameter is examined and depicted graphically. This revised version was published online in July 2006 with corrections to the Cover Date.     

Determination of plutonium isotope ratios at very low levels by ICP-MS using on-line electrochemically modulated separations

Electrochemically modulated separations (EMS) are shown to be a rapid and selective means of extracting and concentrating Pu from complex solutions prior to isotopic analysis by inductively coupled plasma mass spectrometry (ICP‐MS). This separation is performed in a flow injection mode, on‐line with the ICP‐MS. A three‐electrode, flow‐by electrochemical cell is used to accumulate Pu at an anodized glassy carbon electrode by redox conversion of Pu(III) to Pu (IV&VI). The entire process takes place in 2% (v/v) (0.46 M) HNO₃. No redox chemicals or acid concentration changes are required. Plutonium accumulation and release is redox dependent and controlled by the applied cell potential. Large transient volumetric concentration enhancements can be achieved. Based on more negative U(IV) potentials relative to Pu(IV), separation of Pu from uranium is efficient, thereby eliminating uranium hydride interferences. EMS‐ICP‐MS isotope ratio measurement performance will be presented for femtogram to attogram level plutonium isotope injections.     

On the extension of quantum similarity to atomic nuclei: Nuclear quantum similarity

Quantum similarity is a useful tool to establish comparisons between elements of a quantum object set and, so far applied successfully to molecular physics, is applied here to atomic nuclei. Quantum Similarity Measures (QSM) and Indices (QSI) are introduced to study an arbitrary set of 20 nuclei. From this study, relationships between nuclear overlap‐like self‐similarities and size‐like properties are found. A bidimensional projection of the set is performed, and Mendeleev conjecture is invoked to predict qualitatively some nuclear ground‐state properties, such as total binding energy per nucleon, nuclear radius, nuclear volume, total and partial energies, etc. This revised version was published online in July 2006 with corrections to the Cover Date.     

Dissociative scattering of hyperthermal energy CF3+ ions from modified surfaces

Dissociative scattering of CF3+ ions in collision with a self-assembled monolayer surface of fluorinated alkyl thiol on a gold 111 crystal has been studied at low ion kinetic energies (from 29 to 159 eV) using a custom built tandem mass spectrometer with a rotatable second stage energy analyzer and mass spectrometer detectors. Energy and intensity distributions of the scattered fragment ions were measured as a function of the fragment ion mass and scattering angle. Inelastically scattered CF3+ ions were not observed even at the lowest energy studied here. All fragment ions, CF2+, CF+, F+, and C+, were observed at all energies studied with the relative intensity of the highest energy pathway, C+, increasing and that of the lowest energy pathway, CF2+, decreasing with collision energy. Also, the dissociation efficiency of CF3+ decreased significantly as the collision energy was increased to 159 eV. Energy distributions of all fragment ions from the alkyl thiol surface showed two distinct components, one corresponding to the loss of nearly all of the kinetic energy and scattered over a broad angular range while the other corresponding to smaller kinetic energy losses and scattered closer to the surface parallel. The latter process is due to delayed dissociation of collisionally excited ions after they have passed the collision region as excited parent ions. A similar study performed at 74 eV using a LiF coated surface on a titanium substrate resulted only in one process for all fragment ions; corresponding to the delayed dissociation process. The intensity maxima for these fragmentation processes were shifted farther away from the surface parallel compared to the thiol surface. A new mechanism is proposed for the delayed dissociation process as proceeding via projectile ions' neutralization to long-lived highly excited Rydberg state(s), reionization by the potential field between the collision region and entrance to the energy analyzer, and subsequent dissociation several microseconds after collisional excitation. A kinematic analysis of experimental data plotted as velocity Newton diagrams demonstrates that the delayed dissociation process results from the collisions of the ion with the bulk surface; i.e., the self-assembled monolayer surface acts as a bulk surface. A similar analysis for the highly inelastic collision processes shows that these are due to stronger collisions with a fraction of the thiol molecular chain, varying in length (mass) with the ion energy.     

Shape‐similarity relations based on topological resolution

Shape‐similarities of electron density clouds of molecules provide important clues concerning chemical and physical properties, including information about their reactivities in biochemical systems. The concept of topological resolution is used for quantifying molecular similarities: within a hierarchy of finer and cruder topologies, the crudest topology that already provides discrimination between two objects (such as two fuzzy electron density clouds) is used to define a measure of their similarities. The finer this topology, the more similar the two objects. This approach, the method of topological resolution‐based similarity measures (TRBSM), can be combined with a geometrically motivated resolution‐based similarity measure (RBSM) within a metric space. Some of the relations between these two approaches are discussed in this contribution, with special emphasis on applications to electron densities. This revised version was published online in July 2006 with corrections to the Cover Date.     

Intramolecular energy transfer reactions in polymetallic complexes

A series of polymetallic complexes are being developed for use in converting solar radiation to usable chemical potential energy. The system is made up of three components: 1) A highly-absorbing (antenna) metal center which absorbs visible light but is photochemically unreactive; 2) A second metal center which undergoes a useful chemical reaction from a non-spectroscopic excited state; and 3) A bridging ligand which couples the two metal fragments and facilitates intramolecular energy transfer from the antenna to the reactive fragment. This paper will focus on optimizing the three components of the system.     

An exactly soluble base problem for atomic systems

An exactly soluble base problem for atomic systems is presented which approximates the atomic Hamiltonian as a sum of identical one‐electron operators. The eigenfunctions of the one‐electron operator consist of a radial function multiplied by a spherical harmonic. Energies for many‐electron atoms are found by summing the one‐electron energy eigenvalues according to the Pauli principle. These energies are rigorous lower bounds to the exact energies. This revised version was published online in July 2006 with corrections to the Cover Date.     

The convergence of energy expansions for molecules in electrostatic fields: A linear‐response coupled‐cluster study

The radii of convergence of power series expansions describing energy of a molecule in external electrostatic field are investigated usingD’Alembert ratio test, standard and generalized Cauchy–Hadamardcriteria, and Padé approximants. The corresponding coefficients at various field and field‐gradient components, representing multipole moments and (hyper)polarizabilities and including terms of tenth or even twentieth order, are determined using an ab initio linear responsecoupled‐cluster theory. Most calculations are performed for the HF molecule described by the basis set of double zeta quality, while the role of basis set is discussed by comparing the results with estimates of the radii of convergence obtained with the basis set of [5s3p2d/3s2p] quality. Emphasis is placed on the dependence of the interval of convergence of power series expansion describing energy of a molecule in applied electrostatic field on the nuclear geometry. The results might have important implications for various numerical methods used to calculate electrostatic molecular properties as functions of the internuclear geometry, including the finite‐field andfixed‐point‐charge approaches. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Chemistry of Methane Remediation by a Non‐thermal Atmospheric Pressure Plasma

The destruction of methane by a nonthermal plasma in atmospheric pressure gas streams of nitrogen with variable amounts of added oxygen has been investigated. The identities and concentrations of the endproducts are determined by online FTIR spectroscopy and the plasma chemistry is interpreted using kinetic modelling. For a deposited energy of 118 kJ m^–3, the destruction is 12% in nitrogen decreasing monotonically to 5% in air. The major endproducts are HCN and NH₃ in nitrogen and CO, CO₂, N₂O, NO and NO₂ for gas streams containing oxygen. The chemistry in pure nitrogen is predominantly due to reactions of electronicallyexcited nitrogen atoms, N(²D). The addition of oxygen converts the excited state nitrogen into nitrogen oxides reducing the methane destruction which then arises by O and OH reactions yielding CO and, to a lesser extent, CO₂. The modelling correctly predicts the magnitude of the methane destruction as a function of added oxygen and the concentrations of the endproducts for processing in both nitrogen and air.     

A naive look on the Hohenberg–Kohn theorem

A generalised Hohenberg–Kohn theorem is described in terms of the sign of the secondorder energy variation. Independently, it is also corroborated within the perturbation theoretical framework. An alternative formulation of the Hohenberg–Kohn theorem, based on the relationships involving the matrix representations of density functions and the Hamiltonian operator variations, is shown to extend the validity of the theorem to the excited states of the Hamiltonian operators possessing nondegenerate spectra. Finally, a connection with Brillouin's theorem when energy variation becomes stationary is also outlined.     

Resonance Activation and Collision-Induced-Dissociation of Ions Using Rectangular Wave Dipolar Potentials in a Digital Ion Trap Mass Spectrometer

Collision-induced dissociation (CID) of ions by resonance activation in a quadrupole ion trap is usually accomplished by resonance exciting the ions to higher kinetic energy, whereby the high kinetic energy ions collide with a bath gas, such as helium or argon, inside the trap and dissociate to fragments. A new ion activation method using a well-defined rectangular wave dipolar potential formed by dividing down the trapping rectangular waveform is developed and examined herein. The mass-selected parent ions are resonance excited to high kinetic energies by simply changing the frequency of the rectangular wave dipolar potential and dissociation proceeds. A relationship between the ion mass and the activation waveform frequency is also identified and described. This highly efficient (CID) procedure can be realized by simply changing the waveform frequency of the dipolar potential, which could certainly simplify tandem mass spectrometry analysis methods.

Theoretical aspects of the radiation effects of polymers

The Millar–Wall–Charlesby empirical rule of radiation effects on polymers was theoretically examined. The theoretically calculated adiabatic potential curves of the main chain scission and side chain cleavage revealed that the effects of radiation on polymers are clearly interpreted as chemical reactions in the excited states; namely, that degradation occurs when little or no activation energy is required in the main chain cleavage reaction in the excited states, or, in other words, stabilization of the excited polymer molecule leads to the main chain cleavage. Crosslinking occurs when moderate or large activation energy is required in the main chain cleavage reaction in any electronic state and little or no activation energy is needed in the C? H bond cleavage reaction in the excited states. Therefore stabilization of the excited polymer molecule leads to the formation of a polymer radical that crosslinks. It was concluded that Millar–Wall–Charlesby's rule is exact only when the shape of the adiabatic potential curve in the ground state reflects those in the excited states.     

Study on kinetics of combustion of brick-shaped carbonaceous materials

Combustion of brick-shaped carbonaceous materials (carbon deposits from coke oven, coke and electrographite) was carried out in thermobalance in static air. Analysis of kinetics of the process was carried out using both classical (Arrhenius law) and newer (three-parametric equation) methods. In classical approach two types of kinetic equations were used in calculations: differential and integral. The results obtained show that, independently on kinetic variables (α – conversion degree or m – mass of sample) used in differential equations, kinetics of combustion of brick-shaped carbonaceous materials is characterized by only one pair of Arrhenius coefficients: activation energy (E) and pre-exponential constant (A). At the same time the integral equation demonstrates distinction in relation to methods based on differential equations, generating higher activation energies and separate isokinetic effect (IE). Parallel IE shows that kinetic analysis has to encompass activation energy in connection to second coefficient, pre-exponential constant A, depending on assumptions made for kinetic equations. On the other hand three-parametric equation allows describing kinetic of combustion in alternative way using only one experimental value – initial temperature in form of point of initial oxidation (PIO) – and also offers new methods of interpretation of the process.     

Collision-induced dissociation of the lower alcohols. A thermochemical study

Collision-induced dissociation of the molecular ions and of some of the fragment ions foremed on ionization of methanol, ethanol and n-propnol have been studied at high energy resolution in a mass spectrometer. The translational energy lost upon collision and the kinetic energy releasedupon fragmentation of the collisionally excited species have been measured by the methods of ion kinetic energy spectromety. The results of the translational energy loss measurements compare well with excitation energies predicted for each reaction form breakdown curves showing the relative abundances of the ionsas a fuction of internal energy. This correspondence is evidebce that the ionic reactions following electron-impact excitation and those following collisional excitation with neutral molecules at relative traslational energies in the range of several kilovolts are at least qualitatively independent of the method of excitation. The occurrence of the corresponding spontaneous fragmentations in the alcohols has also been studied and the kinetic energy releases accompanying these reactions have been determined. In a few cases, metastable peaks were observed which did not increase in intensity when collision gas added and this phenomenon is associated with particular features of the reaction thermochemistry. Reactions which generally occur to very small extents in mass spectromety, such as methylene elimination, have been observed in highly excited ions. The methods developed in this study allow the decription of the thermochemistry of the reaction of highly excited ions, indlcuding the experimental determination of the partitioning of the nonfixed energy of the activated complex. This procedure complemets and extends energy partitioning studies made on metastable ions in which the partitioning of the reverse activation energy is the more readily accessible.