Influence of the peak height distribution on separation performances: Discrimination factor and effective peak capacity

Summary A new index of performance of the chromatographic separation between two adjacent peaks, the discrimination factor, d₀, is defined. It is normalized between 0 and 1 and is directly and easily determined from the chromatogram. It does not depend on any assumption regarding peak shape, except that the peak profiles of individual sample components have a single mode. Its value depends on the relative heights of the two peaks as well as on their separation. The separation power of a chromatographic system is classically measured by its peak capacity, defined on the basis of constant resolution between adjacent peaks. A previously developed statistical theory of the composition of mixtures makes it possible to extend the concept of peak capacity by taking into account the peak height distribution in typical average chromatograms. A new parameter, the effective peak capacity, is defined for this purpose on the basis of a constant discrimination factor between adjacent peaks. It allows to take into account the distribution of peak heights in statistical theories of the evaluation of complex chromatograms and in the measurement of the limit of determination in quantitative analysis. The characteristics of the two new parameters, the discrimination factor and effective peak capacity, are discussed and compared with those of their classical homologs, resolution and peak capacity, in the case of gaussian component peaks of equal widths.     

On the statistical independence of various column contributions to band broadening. Part 1: Second moment contributions from statistically independent,longitudinal diffusion in both phases

The total length-based second moment contribution from longitudinal sample diffusion in both phases on a column, σD , is derived by adding individual partial differential contributions to a partial differential equation accounting for the longitudinal diffusion processes only. Although each diffusion-dispersed sample part is equilibrated between two phases, the resulting σ,D (= 2D _mt _m + 2D _st _s) can be interpreted as the sum of two independent contributions in accordance with the variance addition rule. (D _m and D _s are the mean diffusion coefficients and t _mand t _s the mean residence times of the sample in the mobile and stationary phases, respectively.) The same σD expression is derived from the random walk model of Giddings by treating the diffusional process in each phase as statistically independent of the other processes. Under these conditions the broadening contribution from longitudinal diffusion in the mobile phase is shown to be independent of the velocity profile.     

Superstability estimates for anharmonic systems

We consider an anharmonic crystal described by variablesS _x ,x ^d ,S _x , with one-body interaction ¦S _x ¦ and nearest neighbor (n.n.) two body interaction ¦S _x –S _y ¦. We prove that, for ^d bounded, , where is the correlation function for the free boundary condition Gibbs state in ,>0 and are suitable constants independent of and . This generalizes previous results obtained in the case.Research partially supported by Consiglio Nazionale delle Ricerche.     

On the theory of radiative transitions in centrosymmetric complexes

The theory of radiative transitions, in centrosymmetric complexes, is examined in great detail, within the framework of the crystal field method.In connection with radiative transitions, the current method of calculations, with and without invoking closure approximation, are considered from a purely theoretical point of view, by taking advantage of the irreducible tensor method put forward by Griffith.Explicit equations are derived throughout the course of this work to account for the vibronic electric dipole moments, associated with d-d and f-f type of excitations.At high Academy of Pedagogic Sciences, Santiago, Chile.     

Solution of periodic Poisson's equation and the Hartree–Fock approach for solids with extended electron states: Application to linear augmented plane wave method

We formulate a Hartree–Fock‐LAPW method for electronic band structure calculations. The method is based on the Hartree–Fock–Roothaan approach for solids with extended electron states and closed core shells where the basis functions of itinerant electrons are linear augmented plane waves. All interactions within the restricted Hartree–Fock approach are analyzed and in principle can be taken into account. In particular, we obtained the matrix elements for the exchange interactions of extended states and the crystal electric field effects. To calculate the matrix elements of exchange for extended states, we first introduce an auxiliary potential and then integrate it with an effective charge density corresponding to the electron exchange transition under consideration. The problem of finding the auxiliary potential is solved by using the strategy of the full potential LAPW approach, which is based on the general solution of periodic Poisson's equation. Here, we use an original technique for the general solution of periodic Poisson's equation and multipole expansions of electron densities. We apply the technique to obtain periodic potentials of the face‐centered cubic lattice and discuss its accuracy and convergence in comparison with other methods. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Vibronisches Spektralverhalten von Molekülen: XIV. Zum Einfluß der vibronischen Kopplung auf die S0-S1-Absorption und Fluoreszenz von ausgewählten 1,3-Diketonato-bor-komplexen im Rahmen der Herzberg-Teller-Näherung

Summary Based upon completely-optimized S₀ and S₁ molecular geometries the vibrational structures of S₀-S₁ absorption and fluorescence transitions of selected 1,3-diketonato boron complexes being differently substituted, are calculated within the Herzberg-Teller approach taking into account vibronic coupling contributions. In dependence on substituted diketone as well as on the co-ligand, the influence of vibronic coupling and the consequences of intensity borrowing on the spectral behaviour in absorption and fluorescence are found to be quite different for the studied boron complexes. Consequently, for some complexes their spectroscopic properties may be interpreted exclusively by means of the Herzberg-Teller approach. An analysis of the relevant vibrational modes is given.

     

Modelling of polymer aggregates in solution

The self-consistent mean field model of Scheutjens and Fleer is used to model spherical aggregates of homopolymers and monomer—polymer particles in solution. For homopolymer aggregates we found that the chain ends are preferentially located at the exterior side of the polymer/solvent interface. The distribution of the end segments may be an important parameter in latex film formation. For monomer—polymer particles a “core-shell” structure is found with an extended core containing a monomer—polymer mixture and a thin shell a few nanometres thick strongly enriched with monomer. The monomer-enriched shell seems to function as a solvating envelope for the dangling chain ends. These results are compared with other simulations based on a single chain in a spherical-cavity model.     

Gold nanoparticle arrays directly grown on nanostructured indium tin oxide electrodes: Characterization and electroanalytical application

This work describes an improved seed-mediated growth approach for the direct attachment and growth of mono-dispersed gold nanoparticles on nanostructured indium tin oxide (ITO) surfaces. It was demonstrated that, when the seeding procedure of our previously reported seed-mediated growth process on an ITO surface was modified, the density of gold nanospheres directly grown on the surface could be highly improved, while the emergence of nanorods was restrained. By field emission scanning electron microscopy (FE-SEM) and cyclic voltammetry, the growth of gold nanoparticles with increasing growth time on the defect sites of nanostructured ITO surface was monitored. Using a [Fe(CN)₆]³⁻/[Fe(CN)₆]⁴⁻ redox probe, the increasingly facile heterogeneous electron transfer kinetics resulting from the deposition and growth of gold nanoparticle arrays was observed. The as-prepared gold nanoparticle arrays exhibited high catalytic activity toward the electrooxidation of nitric oxide, which could provide electroanalytical application for nitric oxide sensing.     

Advanced statistical evaluation of the complex formation constants from electrophoretic data II: Diastereomeric ion-pairs of (R,S)-N-(3,5-dinitrobenzoyl)leucine and tert-butylcarbamoylquinine

Intermolecular association and ion-pair formation, respectively, between a cationic chiral selector, viz. o-9-(tert-butylcarbamoyl) quinine (CQN), and the both enantiomers of anionic N-(3,5-dinitrobenzoyl)leucine, (R)-DNB-Leu and (S)-DNB-Leu, were investigated by affinity capillary electrophoresis (ACE). Thus, binding constants of the both diastereomeric ion-pairs, (R) and (S)-DNB-Leu/CQN associates, were determined by different experimental setups and correction of nonlinear effects. A reciprocal setup was employed for the high-affinity (S)-enantiomer, and the experimental mobility data obtained for CQN at variable (S)-DNB-Leu concentrations in the background electrolyte were linearized and evaluated by advanced statistical model. A binding constant of K_S=125.1 l mol⁻¹ was afforded. The constant for the (R)-enantiomer, which is outside the range suitable for direct affinity CE, was obtained from indirect affinity CE utilizing the separation of the DNB-Leu racemate at a single appropriate CQN concentration in the BGE (resolution method) taking advantage of the known constant for the (S)-enantiomer yielding a binding constant of K_R=2.51 l mol⁻¹. Thereby, the so-called “constant time method” was adopted for the required precise measurement of the effective mobilities of the both enantiomers. A combined approach of reciprocal affinity CE with racemic DNB-Leu as additive and the resolution method confirmed the results. The resulting constants evidence excellent enantioselectivity of the tert-butylcarbamoyl derivative of the cinchona alkaloid quinine as chiral selector for N-(3,5-dinitrobenzoyl) derivatives of amino acids.     

Three-dimensional quantum dynamics study of vibrational predissociation of HeI_2 van der Waals molecule for low vibrational excitation using the time-dependent wave packet method

Three-dimensional quantum mechanical calculations for vibrational predissociation of HeI2(B) van der Waals molecules are presented using the time-dependent wave packet technique within the golden rule approxima tion.The total and partial decay widths,lifetimes,rates and their dependence on initial vibrational states were obtained for HeI2 at low initial vibrational excited levels.Our calculations show that the calculated tota decay widths,lifetimes and rates agree well with those extrapolated from experimental data available The predicted total decay widths as a function of initial vibrational states exhibit highly nonlinear behavior.The very short propagation time (less.than 1 ps) required in the golden rule wave packet calculation is determined by the duration time of the final state inter-action between the fragments on the vibrationally deexcited adiabatic potential surface.The final state interaction between the fragments is shown to play an important role in determining the final rotational distri