Functions and Shapes in the Light of the International System of Units

Famously, Galilei made the ontological claim that the book of nature is written in the language of mathematics. Probably, if only implicitly, most contemporary natural scientists share his view. This paper, in contradistinction, argues that nature is only partly written in the language of mathematics; partly, it is written in the language of functions and partly in a very simple purely qualitative language, too. During the argumentation, three more specific but in themselves interesting theses are put forward: first (in Section 3), there are more shapes than real numbers; second (in Section 4), the metrological notion ‘amount of substance’ can profitably be exchanged for ‘number of entities’; third (in Section 5), prototypical concepts will always be scientifically important.     

Über singuläre Elementarflächen und das Dehnsche Lemma II

Ohne Zusammenfassung     

Dendrimers in thiol‐ene crosslinked networks and the effect of subsequent generations on thermoset properties

A series of well‐defined allyl‐ether functionalized polyester dendrimers has been synthesized via the divergent approach using traditional esterification reactions. Two commercially available trifunctional thiols, trimethylolpropane tri(3‐mercaptopropanoate) (TRIS) and ethoxylated trimethylolpropane tri(3‐mercaptopropanoate) (ETTMP), were incorporated with the dendrimers into the thiol‐ene polymer networks. The thiol‐ene reactions were conducted at room temperature and cured by UV light without the addition of photoinitiatior. Highly crosslinked films were obtained and characterized with respect to mechanical (DMA) and thermal (DSC and TGA) properties. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 589–601, 2009     

Synthesis and thiol–ene photopolymerization of allyl‐ether functionalized dendrimers

Well‐defined, allyl‐ether functional, first‐generation dendrimers have been synthesized. The convergent growth approach was utilized, using the anhydride of the allyl‐ether terminated building block. Three different core moieties were used: trimethylolpropane, trisphenol, and ditrimethylolpropane. The coupling reactions proceeded in good yields and all compounds were characterized by NMR, MALDI‐TOF, and SEC. The allyl‐terminated dendrimers were crosslinked by thiol–ene chemistry, using a multifunctional thiol, TriThiol, to give clear and smooth films. The photopolymerization was conducted in the presence of a photoinitiator, Irgacure 651, and no traces of either allyl‐ether groups or thiols were observed by FT‐Raman after cure. All crosslinked films were characterized with respect to mechanical (DMA) and thermal (DSC) properties. It was found that homogeneous networks were formed and that the core functionality and structure had little effect on the network properties. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 1339–1348, 2008     

Angle-resolved photoemission study of a vacancy-induced state in substoichiometric VC

A vacancy induced state has been identified at about 1.8eV binding energy on the (100) face of VC_0.80 using angle-resolved photoelectron spectroscopy. The recorded spectra are compared with calculated spectra for VC_1.0 and the results show that the origin of the observed state cannot be accounted for by the energy band structure of VC_1.0. Photoemission spectra recorded after exposing the clean surface to O₂ and CO are also presented and used in a discussion of the sensitivity of the vacancy induced state to surface contamination.     

Three-stage auto-ignition of n-heptane and methyl-cyclohexane mixtures at lean conditions in a flat piston rapid compression machine

One approach to enhancing the thermal efficiency of combustion systems is to burn fuels at ultra-lean conditions (equivalence ratio below 0.5). It has been recently reported that the auto-ignition of some hydrocarbon fuels, under specific temperature, pressure, and mixture conditions, releases heat in three distinctive stages. The three auto-ignition stages can be divided as a first low-temperature auto-ignition stage with conventional low temperature, and a high-temperature stage separated into two sub-stages. This study presents ignition delay time measurements of n-heptane and methyl-cyclohexane (MCH) mixtures in a flat piston rapid compression machine (RCM) under ultra-lean conditions. It provides experimental evidence of three-stage auto-ignition. This phenomenon of delayed high-temperature heat release is seldom reported in the literature and this is the first time to be reported for these types of fuels. The experiments cover two binary n-heptane/MCH mixtures of 15/85 and 70/30 by volume, pressures of 11 bar and 16 bar, temperature range of 700 to 900 K, and equivalence ratio of 0.4. The RCM optical access was utilized for high-speed chemiluminescence imaging. Detailed chemical kinetic simulations in a homogenous batch reactor with variable volume were conducted to further interrogate the three-stage auto-ignition phenomenon. Chemiluminescence shows that three-stage auto-ignition occurs in the adiabatically compressed end-gas, which indicates that this phenomenon is chemically-driven and is not induced by a thermal stratification in the RCM experiments. The model predicts the features of three-stage auto-ignition, which were experimentally observed at temperatures approximately below 750 K. As expected, significant discrepancies are observed in the ignition delays of experiment and simulation in the negative temperature coefficient (NTC) region. The simulation of the n-heptane/MCH 70/30 mixture shows better agreement with experiments in the Positive Temperature Coefficient (PTC) region compared to the 15/85 mixture.     

Coordination of imidazoles by Cu(II) and Zn(II) as studied by NMR relaxometry, EPR, far-FTIR vibrational spectroscopy and ab initio calculations: effect of methyl substitution

Synthetic imidazole ligands are typically substituted at the N(1) ((1)-Im) position while natural imidazole ligands are substituted at the C(4) ((4)-Im) position. To outline the difference in coordination properties, the methyl-substituted imidazoles Me(4)-Im and Me(1)-Im were complexed with CuCl(2) and ZnCl(2) and investigated by NMR relaxometry, electron paramagnetic resonance, far-Fourier transform IR vibrational spectroscopy, and ab initio calculations. Me(4)-Im, Me(1)-Im, and Im in excess form the usual tetragonal D(4h) [CuL(4)X(2)] complexes with CuCl(2) whereas the methylated imidazoles form pseudotetrahedral C(2v) complexes instead of the usual octahedral O(h) [ZnIm(6)](2+) complex. All imidazoles display a high degree of covalence in the M-L σ- and π-bonds and the π-interaction strength affects the relative energies of complexation. Opportunities to tailor complexes by the chemical properties of the substituents are envisaged due to the role of the inductive and hyperconjugative effects, rather than position.     

Determining scaling in known phase diagrams of nonionic microemulsions to aid constructing unknown

Microemulsions based on nonionic surfactants of the ethylene oxide alkyl ether type C_mE_n, have been studied thoroughly for around 30 years. Thanks to the considerable amount of published data available on these systems, it is possible to observe trends to make predictions of phase diagrams not yet determined. Strey and Kahlweit, and subsequently Sottmann and Strey, with coworkers have studied and published phase diagrams for systems with a fixed ratio of oil to water, varying the surfactant, the so-called Kahlweit fish-cut diagrams. Some properties of the phase diagrams can be scaled to become general and not system dependent. Here are shown two examples of scaling data from phase diagrams and the use of trends to determine phase diagrams, both inside and outside a dataset. The trends of microemulsions with fixed ratio of surfactant to oil, the so-called Lund-cut diagrams, are also investigated. The trends are used to determine a new phase diagram and this is compared with previously unpublished experimental data on C₁₂E₅-Octadecane-Water system. The scalings and trends make it possible to get good estimations of many of the important properties of the phase diagrams, both temperatures and surfactant concentrations of interest, by investigating one sample in the 3-phase region of the balanced fish-cut diagram.     

Luminescence Enhancement from Silica-Coated Gold Nanoparticle Agglomerates Following Multi-photon Excitation

Multi-photon absorption induced luminescence (MAIL) from bare gold nanoparticles, silica-coated particles, as well as silica-coated agglomerated gold nanoparticles suspended in aqueous solution was studied by using time-resolved and steady-state luminescence spectroscopy. The nanoparticles were excited by femtosecond pulses of wavelengths ranging from 630 nm to 900 nm. The luminescence from the particles exhibits a broad spectrum in the UV and VIS region. The time-resolved measurements indicate a luminescence lifetime of a few ps, limited by the response of the experimental system. The studied dependence of the MAIL efficiency on the excitation wavelength showed that the luminescence from silica-coated agglomerates was enhanced over the whole range of excitation wavelengths, when compared to the luminescence from individual gold nanoparticles. The agglomerates show an almost excitation wavelength independent efficiency of the MAIL, while for individual nanoparticles a rapid decrease of the MAIL efficiency was observed with increasing excitation wavelength. The observed enhancement of the MAIL from the agglomerated nanostructures can be attributed to the presence of localized surface plasmon resonances in the spectral region corresponding to the excitation wavelengths. The high MAIL efficiency from the agglomerated nanoparticle structures in the near-infrared could be an advantage in the expanding field of luminescence-based-imaging, as well as in biosensor technology.