The inside outside intersection problem for hexagon triple systems

We give a complete solution of the following two problems:

1. (1)
   For which (n, x) does there exist a pair of hexagon triple systems of order n having x inside triples in common?
    
2. (2)
   For which (n, x) does there exist a pair of hexagon triple systems having x outside triples in common?
    

     

Osmotic compression and expansion of highly ordered clay dispersions

Aqueous dispersions of nanometric clay platelets (Laponite) have been dewatered through different techniques: centrifugation, mechanical compression, and osmotic stress (dialysis against a polymer solution). The positional and orientational correlations of the particles have been determined through small-angle neutron scattering. Uniaxial compression experiments produce concentrated dispersions (volume fraction > 0.03) in which the platelets have strong orientational and positional correlations. The orientational correlations cause the platelets to align with their normal along a common axis, which is the axis of compression. The positional correlations cause the platelets to be regularly spaced along this direction, with a spacing that matches the average volume per particle in the dispersion. The swelling law (volume fraction versus separation distance) is one-dimensional, as in a layered system. Changes in the applied osmotic pressure cause the water content of the dispersion to either rise or decrease, with time scales that are controlled by interparticle friction forces and by hydrodynamic drag. At long times, the dispersions approach osmotic equilibrium, which can be defined as the common limit of swelling and deswelling processes. The variation of the equilibrium water content with the applied osmotic pressure has been determined over 1 decade in volume fractions (0.03 < phi < 0.3) and 3 decades in pressures. This equation of state matches the predictions made from the knowledge of the forces and thermal agitation for all components in the dispersion (particles, ions, and water).     

Influence of shell thickness and cross-link density on the structure of temperature-sensitive poly-N-isopropylacrylamide-poly-N-isopropylmethacrylamide core-shell microgels investigated by small-angle neutron scattering

Swelling properties of doubly temperature sensitive core-shell microgels consisting of two thermosensitive polymers with lower critical solution temperatures (LCTS) at, respectively, 34 degrees C in the core and 44 degrees C in the shell have been investigated by small-angle neutron scattering (SANS). A core-shell form factor has been employed to evaluate the structure, and the real space particle structure is expressed by radial density profiles. By this means, the influences of both shell/core mass composition and shell cross-linker content on the internal structure have been revealed at temperatures above, between, and below the LCSTs. Higher shell/core mass ratios lead to an increased expansion of the core at temperatures between the LCSTs, whereas a variation of cross-linker in the shell mainly effects the dimensions of the shell. The influence on the core structure was interpreted as resulting from an elastic force developed from the swollen shell. At temperatures below the core LCST, the core cannot swell to its native size (i.e., in the absence of a shell), because the maximum expanded shell network prohibits further swelling. Thus, depending on temperature, the shell either expands or compresses the core.     

Structural characterisation of the core oligosaccharides isolated from the lipooligosaccharide fraction of Agrobacterium tumefaciens A1

Three different oligosaccharide structures from the lipooligosaccharide fraction of Agrobacterium tumefaciens strain A1 were determined by means of chemical and spectrometrical methods. The peculiar feature of this oligosaccharide family consisted of its unusual length, that was very close to the that minimal requested for the external membrane functionality as exemplified from oligosaccharide 3, where the inner core is glycosylated from only one sugar moiety onwards.     

Deuterium isotope effects observed during competitive binding chiral recognition electrospray ionization--mass spectrometry of cinchona alkaloid-based systems

Deuterium isotope effects are reported for binding between tert-butylcarbamoyl-quinine/quinidine chiral selectors and isotopomeric quasienantiomers of N-(3,5-dinitrobenzoyl)leucine measured using electrospray ionization-mass spectrometry (ESI-MS) and competitive binding. Evaluation of mixtures of each selector with one labeled and one unlabeled enantiomeric selectand of identical configuration showed a significant difference in measured ion abundances of diastereomeric complexes between the selector and each selectand. It was found that in some cases, the complex containing the nondeuterated selectand was 15% more abundant than its deuterated counterpart. On the basis of an assessment of solution- and gas-phase isotope effects reported in the literature, a series of control experiments were performed to study the origin of the effects. On the basis of these measurements, our preliminary conclusion is that the differing gas-phase physicochemical nature of the deuterated versus nondeuterated selectand represents the strongest contribution to the observed effect in this chiral molecular recognition system.     

Power Spectrum of a Noisy System Close to a Heteroclinic Orbit

We consider a two-dimensional dynamical system that possesses a heteroclinic orbit connecting four saddle points. This system is not able to show self-sustained oscillations on its own. If endowed with white Gaussian noise it displays stochastic oscillations, the frequency and quality factor of which are controlled by the noise intensity. This stochastic oscillation of a nonlinear system with noise is conveniently characterized by the power spectrum of suitable observables. In this paper we explore different analytical and semianalytical ways to compute such power spectra. Besides a number of explicit expressions for the power spectrum, we find scaling relations for the frequency, spectral width, and quality factor of the stochastic heteroclinic oscillator in the limit of weak noise. In particular, the quality factor shows a slow logarithmic increase with decreasing noise of the form \(Q\sim [\ln (1/D)]^2\). Our results are compared to numerical simulations of the respective Langevin equations.     

Increments to chiral recognition facilitating enantiomer separations of chiral acids, bases, and ampholytes using Cinchona-based zwitterion exchanger chiral stationary phases

The intramolecular distances of anion and cation exchanger sites of zwitterionic chiral stationary phases represent potential tuning sites for enantiomer selectivity. In this contribution, we investigate the influence of alkanesulfonic acid chain length and flexibility on enantiomer separations of chiral acids, bases, and amphoteric molecules for six Cinchona alkaloid-based chiral stationary phases in comparison with structurally related anion and cation exchangers. Employing polar-organic elution conditions, we observed an intramolecular counterion effect for acidic analytes which led to reduced retention times but did not impair enantiomer selectivities. Retention of amphoteric analytes is based on simultaneous double ion pairing of their charged functional groups with the acidic and basic sites of the zwitterionic selectors. A chiral center in the vicinity of the strong cation exchanger site is vital for chiral separations of bases. Sterically demanding side chains are beneficial for separations of free amino acids. Enantioseparations of free (un-derivatized) peptides were particularly successful in stationary phases with straight-chain alkanesulfonic acid sites, pointing to a beneficial influence of more flexible moieties. In addition, we observed pseudo-enantiomeric behavior of quinine and quinidine-derived chiral stationary phases facilitating reversal of elution orders for all analytes.     

Comparison of the photoelectrochemical oxidation of methanol on rutile TiO2 (001) and (100) single crystal faces studied by intensity modulated photocurrent spectroscopy

The photooxidation of methanol as a model substance for pollutants on rutile TiO(2) (001) and (100) surfaces was investigated using intensity modulated photocurrent spectroscopy (IMPS). The results are analyzed in view of the influence of the surface structure, the methanol concentration and the electrode potential on the rate constants of charge transfer and recombination. The obtained results have been explained with a model combining the theory of IMPS for a bulk semiconductor surface and the nature of the surface-bound intermediates (alternatively mobile or immobile OH˙ radicals). The results indicate that water photooxidation proceeds via mobile OH˙ radicals on both surfaces, while methanol addition gives rise to the involvement of immobile OH˙ radicals on the (100) surface. Detailed analysis in view of the surface structures suggests that the latter observation is due to efficient electron transfer from bridging OH˙ radicals on the (100) surface to methanol, while coupling of two of these radicals occurs in the absence of methanol, making them appear as mobile OH˙ radicals. In the case of the (001) surface, the coupling reaction dominates even in the presence of methanol due to the smaller distance between the bridging OH˙ radicals, leading to more efficient water oxidation, but less efficient methanol photooxidation on this surface.     

Molecular recognition principles and stationary-phase characteristics of topoisomer-selective chemoaffinity materials for chromatographic separation of circular plasmid DNA topoisomers

We recently discovered the molecular recognition capability of a quinine carbamate ligand attached to silica as a powerful chemoaffinity material for the chromatographic separation of circular plasmid topoisomers of different linking numbers. In this paper we develop structure-selectivity relationship studies to figure out the essential structural features for topoisomer recognition. By varying different moieties of the original cinchonan-derived selector, it was shown that intercalation by the quinoline moiety of the ligand as assumed initially as the working hypothesis is not an essential feature for topoisomer recognition during chromatography. We found that the key elements for topoisomer selectivity are the presence of a rigid weak anion-exchange site and a H-donor site separated from each other in a defined distance by a 4-atom spacer. Additionally, incorporation of the weak anion-exchange site into a cyclic ring structure provides greater rigidity of the ligand molecule and turned out to be advantageous, if not mandatory, for (close to) baseline separation.     

Synthesis and Optical Properties of Diaza‐ and Tetraazatetracenes

A series of functionalized diaza‐ and tetraazatetracenes was synthesized, either by condensation of an aromatic diamine with an ortho‐quinone/diethyloxalate followed by chlorination with POCl₃ to give diazatetracenes or by palladium‐catalyzed coupling of a phenylenediamine with various 2,3‐dichloroquinoxalines to give tetraazatetracenes (after oxidation with MnO₂). Representative examples included halogenated and nitrated derivatives. The optical properties of these azatetracenes were discussed with respect to their molecular structures and substitution patterns. The diazatetracenes and tetraazatetracenes formed two different groups that had significantly different electronic structures and properties. Furthermore, 1,2,3,4‐tetrafluoro‐6,11‐bis((triisopropylsilyl)ethynyl)benzo[b]phenazine was synthesized, which is the first reported fluorinated diazatetracene. Single‐crystal X‐ray analysis of this compound is reported.