Orbifolds, Sheaves and Groupoids

We characterize orbifolds in terms of their sheaves, and show that orbifolds correspond exactly to a specific class of smooth groupoids. As an application, we construct fibered products of orbifolds and prove a change-of-base formula for sheaf cohomology.     

Large effect of polydispersity on defect concentrations in colloidal crystals

We compute the equilibrium concentration of stacking faults and point defects in polydisperse hard-sphere crystals. We find that, while the concentration of stacking faults remains similar to that of monodisperse hard-sphere crystals, the concentration of vacancies decreases by about a factor of 2. Most strikingly, the concentration of interstitials in the maximally polydisperse crystal may be some six orders of magnitude larger than in a monodisperse crystal. We show that this dramatic increase in interstitial concentration is due to the increased probability of finding small particles and that the small-particle tail of the particle size distribution is crucial for the interstitial concentration in a colloidal crystal.     

Separation strategy for acidic chiral pharmaceuticals with capillary electrochromatography on polysaccharide stationary phases

The effect of five factors on the capillary electrochromatographic enantioseparation of acidic compounds was studied using an experimental design. The studied factors were pH, acetonitrile content in the mobile phase, temperature, buffer concentration, and applied voltage. These experiments allowed defining a generic separation strategy applicable on acidic compounds with chemical and structural diversity. The starting screening conditions consist of a 45 mM ammonium formate electrolyte at pH 2.9 mixed with 65% acetonitrile, an applied voltage of 15 kV, and a temperature of 25 degrees C. The screening phase occasionally can be followed by an optimization procedure. Evaluation of the proposed strategy pointed out that it allows achieving baseline resolution within a relatively short time when a beginning of separation is obtained at the starting conditions. This strategy revealed enantioselectivity for 11 compounds out of 15, of which 10 could be baseline-separated after the proposed optimization steps.     

Light-driven molecular motors: stepwise thermal helix inversion during unidirectional rotation of sterically overcrowded biphenanthrylidenes

To investigate the unidirectional rotation of chiral overcrowded biphenanthrylidenes in more detail, the size of the substituent next to the double bond responsible for the unidirectionality of rotation was varied. The thermal and photochemical isomerization of three sterically overcrowded alkenes is described. The behavior of the biphenanthrylidenes with methyl and ethyl substituents is rather similar, and these compounds undergo a unidirectional 360 degrees rotation around the central double bond in a four-step sequence involving two photochemical cis-trans isomerizations and two thermal helix inversions. The only difference between these two true molecular motors was a small entropic effect, which causes the ethyl substituted molecular motor to rotate slightly faster. The behavior of the i-propyl substituted compound differs significantly from that of the other two. Although not all different isomers of the i-propyl substituted molecular motor were detected spectroscopically, experimental data led to the conclusion that this compound can also be considered as a molecular motor and is capable of performing a 360 degrees unidirectional rotation. (1)H NMR and X-ray analysis show a meso-like form as an intermediate in the unidirectional rotation, which proves that the thermal helix inversion is a stepwise process.     

Carbon skeletal rearrangements in 2-phenylthiophene and 2,5-diphenylthiophene under conditions of electron-impact

The mass spectra of ¹³C-labelled 2-phenylthiophenes and 2,5-diphenylthiophenes were studied. The label distributions for the [HCS]⁺, [C₂H₂S]^+·, [C₈H₆]^+·, [C₉H₇]⁺ and [C₇H₅]S⁺ ions from 2-phenylthiophene and the [HCS]⁺, [C₉H₇]⁺, [C₇H₅S]^+·, and [C₁₅H₁₁]⁺ ions from 2,5-diphenylthiophene were interpreted in terms of both carbon skeletal rearrangements in the thiophene ring and migration of the phenyl substituent. The degree of carbon scrambling in the thiophene ring appeared to be almost independent of the electron beam energy. The formation of some of the fragment ions studied seems to be so fast that no carbon scrambling could be detected at all; in neither case was complete scrambling of the carbon atoms of the thiophene ring observed.     

Ring expansion and hydrogen scrambling in the molecular ion of 3-methylthiophene

The ratio [M ? D]/{[M-D] + [M ? H]} in the 70 eV mass spectra of six deuterated 3-methylthiophenes has been determined. From these values the mole fractions of the molecular ions that lose hydrogen atoms specifically from the various positions of the molecule were calculated, as well as the mole fraction in which the hydrogen atoms are fully scrambled before hydrogen elimination. It appears that hydrogen atoms are mainly lost from a fully scrambled [C₅H₆S]⁺· ion and from the α-position of the original molecular ion. A deuterium isotope effect of 1·60 to 1·72 was calculated for the hydrogen elimination. The reaction was also studied at low electron energies. In order to determine the degree of scrambling in the [C₅H₅S]⁺ ions, some decomposition reactions of this ion were investigated.     

A chiroptical molecular switch with perfect stereocontrol

A modified version of the first generation unidirectional molecular motor showed >99% stereoselectivity in photo-induced isomerizations in both directions, thus functioning as a perfect chiroptical molecular switch.     

Tuning intermolecular interactions in a rodlike polymer assembled at surfaces and in solution

The isolation of single polyelectrolyte chains of water-soluble poly(isocyanodipeptide)s (PICs) bearing carboxylic acid terminated side chains occurring both at surfaces and in solution was accomplished by reducing the intermolecular interactions through complexation with cations or positively charged surfactants.Scanning force microscopy and viscosity analyses revealed that this method allows to tune the conformation of the macromolecule, which is of importance for tailoring the physicochemical properties of the material.This is particularly significant for the use of these polymer chains as seed for biomineralization processes.     

A comparison of boundary element and finite element methods for modeling axisymmetric polymeric drop deformation

A modified boundary element method (BEM) and the DEVSS‐G finite element method (FEM) are applied to model the deformation of a polymeric drop suspended in another fluid subjected to start‐up uniaxial extensional flow. The effects of viscoelasticity, via the Oldroyd‐B differential model, are considered for the drop phase using both FEM and BEM and for both the drop and matrix phases using FEM. Where possible, results are compared with the linear deformation theory. Consistent predictions are obtained among the BEM, FEM, and linear theory for purely Newtonian systems and between FEM and linear theory for fully viscoelastic systems. FEM and BEM predictions for viscoelastic drops in a Newtonian matrix agree very well at short times but differ at longer times, with worst agreement occurring as critical flow strength is approached. This suggests that the dominant computational advantages held by the BEM over the FEM for this and similar problems may diminish or even disappear when the issue of accuracy is appropriately considered. Fully viscoelastic problems, which are only feasible using the FEM formulation, shed new insight on the role of viscoelasticity of the matrix fluid in drop deformation. Copyright © 2001 John Wiley & Sons, Ltd.