Review of Chemometrics Applied to Spectroscopy: 1985-95, Part 3 — Multi-way Analysis

INTRODUCTION

In this third part of a review on chemometrics in spectroscopy we will describe a recent methodology that has attracted increasing interest in spectroscopy. namely multi-way analysis. The application of multi-way analysis in spectroscopy is still relatively new. hence many methodological improvements are being investigated currently. Part of thls review will also be used to describe the algorithmic improvements gained the last decade.     

Asymptotic behaviour of the ratio of density gradient to electron density for atomic systems

The asymptotic behaviour of the negative ratio of the density gradient to the electron density, q(r), for neutral and singly charged atoms has been investigated. The results show that, for large r, q(r) can approach its limit √8?, where ? is the first ionization potential, from either above or below depending on the specific system considered.     

Oscillatory structure of confined fluids

The confinement of fluids in pores and wedges is associated with exponentially damped oscillatory packing structure, as observed with the surface forces apparatus. This paper reviews the statistical mechanics of confined fluids and then illustrates the results with density functional data for hard-sphere solvent. The free energy of the pore fluid and its functional derivatives with respect to thermodynamic fields all oscillate, as a function of pore width, with a wavelength close to the solvent diameter. In contrast, the density at the centre of pores oscillates with twice this wavelength, as a function of pore width. The development of a unified physics of confined fluids is considered. Approximations based on one-dimensional physics do extraordinarily well in planar symmetry at three-dimensions.     

Exploring complex CIDEP of p-benzosemiquinones with time resolved CW-EPR

The time and magnetic field dependent magnetization of polarized signals in the presence of chemically induced magnetization transfer is described by means of a kinetic matrix incorporated into the Bloch equations. The approach is transformed into a computer algorithm accounting for all hyperfine lines present in the system. Solutions are readily obtained by numerical methods. Calculations are applied to the time resolved EPR (TR-EPR) spectroscopic signals of p-benzoquinone after laser flash photolysis. In an aqueous alcoholic solution at pH 2.0, chemical exchange via intermolecular proton transfer is found present between neutral semiquinones. At pH 8.3, the TR-EPR spectrum shows only a uniform signal of the semiquinone. At pH 5.4, a superposition of neutral and anionic radicals is observed together with a protonation-deprotonation equilibrium. A two-step hydrogen atom transfer, consisting of electron transfer followed by protonation, is proposed to account for the formation of both neutral and anionic semiquinone species prior to observation. Experiments in partly deuterated solvent mixtures indicate the existence of three semiquinone forms: BQH^?, BQ^?-, and BQD^? prior to observation. The origin of the proton/deuteron transferred to the anion radical in the precursor state is discussed.     

Eigenvalues of the difference and product of projections

There is an isomorphism between the matrices over the Boolean algebra of subsets of a k-element set and the k-tuples of Boolean binary (i.e. zero-one) matrices. This isomorphism allows many problems concerning nonbinary Boolean matrices to the referred to the binary ease. However, there are some features of the general (i.e. nonbinary) case that have not been mentioned, although they differ somewhat from the binary case. We exhibit characterizations of the linear operators that preserve several invariants of matrices over finite Boolean algebras to illustrate the differences and similarities of the general vs. the binary cases. We employ a canonical form that is useful in applying the isomorphism.     

Standard Molar Volumes and Heat Capacities of Aqueous Solutions of Trifluoromethanesulfonic Acid at Temperatures up to 573 K and Pressures to 30 MPa

Densities and heat capacities of dilute aqueous solutions (0.025 to 0.4 mol⋅kg⁻¹) of trifluoromethanesulfonic acid (triflic acid) were measured with original high-temperature, high-pressure instruments at temperatures and pressures up to 574 K and 31 MPa, respectively. Standard molar volumes and standard molar heat capacities were obtained via extrapolation of the apparent molar properties to infinite dilution. The evolution of these standard derivative properties of triflic acid with temperature and pressure is qualitatively compared with that of other acids of different strengths.     

A simple sensitive recording differential refractometer for column chromatography

Light passes through a hollow prism containing the sample liquid and is then focussed on a position-sensitive photodiode. Movement of the image due to a change in the refractive index of the sample produces an electrical signal which is recorded directly on a potentiometer recorder.     

Mass spectrometry of metal chelates-III Further studies on metal oxinates

The mass spectra of the oxmates of gallium, dysprosium, beryllium, samarium, cadmium, neodymium, indium, bismuth, lanthanum, yttrium and gadolinium have been recorded. The results have been correlated with the structures proposed m the literature. The integrated ion current method has been applied to determine submicrogram quantities of some of these compounds. Oxinates insoluble in organic solvents or undergoing reaction on solution were precipitated directly in the evaporation probe. The factors which determine the suitability of metal chelates for the estimation of metals by this method are discussed together with the instrumental factors which determine the ultimate sensitivity.     

Adsorption of calcium and magnesium ions on surfaces

The adsorption of calcium and magnesium ions at trace levels in solution on borosilicate glass and polypropylene is described. The rate and extent of adsorption increases with increasing pH and the process is not completely reversible. The apparent energies of activation for the adsorption of calcium and magnesium ions on borosilicate glass are 17.5 and 10.5 kJ mol^?1, respectively. The corresponding half-lives are 568 and 127 h. For polypropylene the half-lives increase to 5775 and 537 h, respectively.