An entropy-based uncertainty principle for a locally compact abelian group

We classify all functions on a locally compact, abelian group giving equality in an entropy inequality generalizing the Heisenberg Uncertainty Principle. In particular, for functions on a real line, we proof a conjecture of Hirschman published in 1957.     

Vacancy ion-exclusion chromatography of carboxylic acids on a weakly acidic cation-exchange resin

In this preliminary study, a new approach to ion-exclusion chromatography is proposed to overcome the relatively poor conductivity detection response which occurs in ion-exclusion chromatography when acids are added to the eluent in order to improve peak shape. This approach, termed vacancy ion-exclusion chromatography, requires the sample to be used as eluent and a sample of water to be injected onto a weakly acidic cation-exchange column (TSKgel OApak-A). Vacancy peaks for each of the analytes appear at the retention times of these analytes. Highly sensitive conductivity detection is possible and sharp, well-shaped peaks are produced, leading to efficient separations. Retention times were found to be affected by the concentration of the analytes in the eluent, and also by the presence of an organic modifier such as methanol in the eluent. Detection limits for oxalic, formic, acetic, propionic, butyric and valeric acids were 0.1, 0.2, 0.3, 0.3, 0.4 and 0.5 microM, respectively, and linear ranges for some acids extended over two orders of magnitude. Precision values for retention times were 0.21% and for peak areas were <1.90%. The vacancy ion-exclusion chromatography method was found to give detection responses four to 10 times higher than conventional ion-exclusion chromatography using sulfuric acid eluent and two to five times higher than conventional ion-exclusion chromatography using benzoic acid eluent.     

Molecular dynamics averaging of Xe chemical shifts in liquids

The Xe nuclear magnetic resonance chemical shift differences that afford the discrimination between various biological environments are of current interest for biosensor applications and medical diagnostic purposes. In many such environments the Xe signal appears close to that in water. We calculate average Xe chemical shifts (relative to the free Xe atom) in solution in eleven liquids: water, isobutane, perfluoro-isobutane, n-butane, n-pentane, neopentane, perfluoroneopentane, n-hexane, n-octane, n-perfluorooctane, and perfluorooctyl bromide. The latter is a liquid used for intravenous Xe delivery. We calculate quantum mechanically the Xe shielding response in Xe-molecule van der Waals complexes, from which calculations we develop Xe (atomic site) interpolating functions that reproduce the ab initio Xe shielding response in the complex. By assuming additivity, these Xe-site shielding functions can be used to calculate the shielding for any configuration of such molecules around Xe. The averaging over configurations is done via molecular dynamics (MD). The simulations were carried out using a MD technique that one of us had developed previously for the simulation of Henry's constants of gases dissolved in liquids. It is based on separating a gaseous compartment in the MD system from the solvent using a semipermeable membrane that is permeable only to the gas molecules. We reproduce the experimental trends in the Xe chemical shifts in n-alkanes with increasing number of carbons and the large chemical shift difference between Xe in water and in perfluorooctyl bromide. We also reproduce the trend for a given solvent of decreasing Xe chemical shift with increasing temperature. We predict chemical shift differences between Xe in alkanes vs their perfluoro counterparts.     

Ion-exclusion chromatography with conductimetric detection of aliphatic carboxylic acids on a weakly acidic cation-exchange resin by elution with benzoic acid-beta-cyclodextrin

In this study, an aqueous solution consisting of benzoic acid with low background conductivity and beta-cyclodextrin (beta-CD) of hydrophilic nature and the inclusion effect to benzoic acid were used as eluent for the ion-exclusion chromatographic separation of aliphatic carboxylic acids with different pKa values and hydrophobicity on a polymethacrylate-based weakly acidic cation-exchange resin in the H+ form. With increasing concentration of beta-cyclodextrin in the eluent, the retention times of the carboxylic acids decreased due to the increased hydrophilicity of the polymethacrylate-based cation-exchange resin surface from the adsorption of OH groups of beta-cyclodextrin. Moreover, the eluent background conductivity decreased with increasing concentration of beta-cyclodextrin in 1 mM benzoic acid, which could result in higher sensitivity for conductimetric detection. The ion-exclusion chromatographic separation of carboxylic acids with high resolution and sensitivity was accomplished successfully by elution with a 1 mM benzoic acid-10 mM cyclodextrin solution without chemical suppression.     

NMR and UV studies of 3'-S-phosphorothiolate modified DNA in a DNA : RNA hybrid dodecamer duplex; implications for antisense drug design

High-resolution NMR spectroscopy has been used to establish the conformational consequences of the introduction of a single 3[prime or minute]-S-phosphorothiolate link in the DNA strand of a DNA : RNA hybrid. These systems are of interest as potential antisense therapeutic agents. Previous studies on similarly modified dinucleotides have shown that the conformation of the sugar to which the sulfur is attached shifts to the north (C(3[prime or minute])-endo/C(2[prime or minute])-exo). Comparisons made between NOESY cross-peak intensities, and coupling constants from PE-COSY spectra, for both non-modified and modified duplexes confirm that this conformational shift is also present in the double helical oligonucleotide system. In addition it is noted that in both the dinucleotides and the modified duplex, the conformation of the sugar ring 3[prime or minute] to the site of modification is also shifted to the north. That this pattern is observed in the small monomeric system as well as the larger double helix is suggestive of some pre-ordering of the sequences. The conclusion is supported by consideration of the (1)H chemical shifts of the heterocyclic bases near the site of the modification. The enhanced stability that these conformational changes should bring was confirmed by UV thermal melting studies. Subsequently a series of singly and doubly 3[prime or minute]-S-phosphorothiolate-modified duplexes were investigated by UV. The results are indicative of an additive effect of the modification with thermodynamic benefit being derived from alternate spacing of two modified linkers.     

Second-order perturbation theory for the angular pair correlation function in molecular fluids

Second-order perturbation theory is used to calculate spherical harmonic coefficients of the angular pair correlation function g(rω₁ω₂) for a liquid in which the molecules interact with a pair potential that is the sum of Lennard-Jones and quadrupole-quadrupole parts. The theory is compared with both molecular dynamics results and with the predictions of the GMF ≡ LHNC, QHNC and first-order perturbation theories. Second-order perturbation theory gives excellent results for the harmonic coefficient g(224,r), but is poorer for g(222,r) and g(202,r).     

Molecular dynamics simulations of gas separations using faujasite-type zeolite membranes

Gas separations with faujasite zeolite membranes have been examined using the method of molecular dynamics. Two binary mixtures are investigated, oxygen/nitrogen and nitrogen/carbon dioxide. These mixtures have been found experimentally to exhibit contrasting behavior. In O(2)/N(2) mixtures the ideal selectivity (pure systems) is higher than the mixture selectivity, while in N(2)/CO(2) the mixture selectivity is higher than the ideal selectivity. One of the key goals of this work was to seek a fundamental molecular level understanding of such divergent behavior. Our simulation results (using previously developed intermolecular models for both the gases and zeolites investigated) were found to replicate this experimental behavior. By examining the loading of the membranes and the diffusion rates inside the zeolites, we have been able to explain such contrasting behavior of O(2)/N(2) and N(2)/CO(2) mixtures. In the case of O(2)/N(2) mixtures, the adsorption and loading of both O(2) and N(2) in the membrane are quite competitive, and thus the drop in the selectivity in the mixture is primarily the result of oxygen slowing the diffusion of nitrogen and nitrogen somewhat increasing the diffusion of oxygen when they pass through the zeolite pores. In N(2)/CO(2) systems, CO(2) is rather selectively adsorbed and loaded in the zeolite, leaving very little room for N(2) adsorption. Thus although N(2) continues to have a higher diffusion rate than CO(2) even in the mixture, there are so few N(2) molecules in the zeolite in mixtures that the selectivity of the mixture increases significantly compared to the ideal (pure system) values. We have also compared simulation results with hydrodynamic theories that classify the permeance of membranes to be either due to surface diffusion, viscous flow, or Knudsen diffusion. Our results show surface diffusion to be the dominant mode, except in the case of N(2)/CO(2) binary mixtures where Knudsen diffusion also makes a contribution to N(2) transport.     

Vacancy ion-exclusion chromatography of aromatic carboxylic acids on a weakly acidic cation-exchange resin

Determination of aromatic carboxylic acids by conventional ion-exclusion chromatography is relatively difficult and methods generally rely on hydrophobic interaction between the solute and the resin. To overcome the difficulties in determining aromatic carboxylic acids a new approach is presented, termed vacancy ion-exclusion chromatography, which is based on use of the sample as mobile phase and an injection of aqueous 10% methanol onto a weakly acidic cation-exchange column (TSKgel OApak-A). Highly sensitive conductivity detection occurred with sharp and well-shaped peaks, leading to very efficient separations. The effects of sulfuric acid concentration added to the mobile phase, flow-rate, and column temperature on the retention volume of tested aromatic carboxylic acids was investigated. Retention times were found to be affected by the concentration of the analytes in the mobile phase and to some extent also by the addition of an organic modifier such as methanol to the injected water sample. Separation of sulfuric acid (SA), naphthalenetetracarboxylic acid (NTCA), phthalic acid (PA) and benzoic acid (BA) was satisfactory using this new approach. Detection limits were 0.66, 0.67, 0.42 and 0.86 microM and detector responses were linear in the range 1-100, 1-80, 2.5-100 and 10-40 microM, for SA, NTCA, PA and BA, respectively. Precision for retention times was 0.36% and for peak areas was 1.5%.     

Monolithic octadecylsilyl-silica gel column for the high-speed ion chromatographic determination of acidity

A monolithic ODS-silica gel column modified by saturating it with lithium dodecylsulfate (Li-DS) was used to demonstrate the high-speed separation of H+ from other mono- and divalent cations, such as Na+, NH4+, K+, Mg2+ and Ca2+ using ion chromatography (IC). Using a 5 mM EDTA-2K solution containing 0.10 mM Li-DS (pH 4.80) as eluent, H+ was eluted with a sharp and symmetrical peak within 1.0 min before other cations at a flow-rate of 1.5 ml min(-1). The rapid elution of H+ and its conductimetric detection could be attributed to the presence of EDTA (HY2-), which can convert H+ ions as anions. i.e. H(+) + H2Y(2-) --> H3Y(-). The acidity of rainwater and deionized water samples was determined using this IC system with satisfactory results.     

On using the NMR chemical shift to assess polar–nonpolar cross-intermolecular interactions

The possibility of using the NMR chemical shift to evaluate and develop intermolecular potentials for cross-interactions between polar and nonpolar molecules has been examined using the method of molecular dynamics. Such interaction potential models are known to be notoriously difficult to develop. Our work has shown that chemical shift can be obtained quite efficiently in simulations and converges much faster than other properties traditionally used for such evaluations (for example, the infinite dilution activity coefficients, Henry’s constants or the solubility of solutes in solvents). We have also found chemical shift to be quite sensitive to the intermolecular potentials which makes it a rather promising property to investigate polar–nonpolar interactions in fluids.