The exponential power law: partial wetting kinetics and dynamic contact angles

An equation for the kinetics of partial drop spreading is proposed. This equation was empirically derived from experimental data for the spreading kinetics of partially wetting liquids in terms of the wet area versus time. The equation has the form of an exponential power law (EPL), and transforms into the well-known power law for complete wetting, when the equilibrium contact angle approaches zero. The EPL fits very well available experimental data. To lend additional support to the validity of this generalized equation, it will be demonstrated that when it is transformed to present the dynamic contact angle (DCA), it fits very well DCA experimental data for other wetting processes, such as capillary flow and tape coating.     

Probing local environments in paramagnetic europium-substituted Keggin solids by 31P magic angle spinning NMR spectroscopy

Paramagnetic Eu-substituted Keggin oxopolytungstates crystallize in different forms, determined by the nature of the counterions. The crystal packing is in turn responsible for the variations in the geometry of paramagnetic Eu sites with respect to the anion core. We probed the paramagnetic environments in a series of Eu-substituted Keggin solids, by 31P magic angle spinning NMR spectroscopy. 31P spinning sideband envelopes are dominated by the electron-nuclear dipolar interaction. For the compounds under investigation, both the magnitude and the asymmetry parameter of the electron-nuclear dipolar coupling tensor are sensitive to the mutual arrangements of paramagnetic Eu sites in the crystal lattice. and also report on the stoichiometry of the anion. The electron-nuclear dipolar coupling tensors were calculated from the crystallographic coordinates and the experimentally determined effective magnetic moments, assuming a point dipole approximation. The computed tensors are in very good agreement with the experimental spectra. Furthermore, the P-Eu distance estimates, accurate to within 0.06-0.12 A, can be obtained directly from the magnitude of the electron-nuclear dipolar coupling. This work demonstrates that 31P MAS NMR spectroscopy is a useful probe for investigating local environments in paramagnetic Keggin solids.     

Solutions of Doubly and Higher Order Iterated Equations

Michael Fisher once studied the solution of the equation f(f(x))=x ²–2. We offer solutions to the general equation f(f(x))=h(x) in the form f(x)=g(ag ^–1(x)) where a is in general a complex number. This leads to solving duplication formulas for g(x). For the case h(x)=x ²–2, the solution is readily found, while the h(x)=x ²+2 case is challenging. The solution to these types of equations can be related to differential equations.     

Synthesis of (S)-Propranolol by Chemicoenzymatic Approach

(S)-Propranolol, [1-isopropylamino-3-(1-naphthoxy)-2-propanol], which possesses important β-adrenergic blocking activity, has been synthesized by a chemicoenzymatic approach. The 2S-absolute configuration was created by the enzyme-mediated asymmetric hydrolysis of the (±)-2-acetoxy-1-chloro-3-(1-naphthoxy)-2-naphthoxy)-2-propanol. The enzymatically produced chiral intermediate was then chemically converted to optically pure (S)-propranolol.     

Long-lived radical cations as model compounds for the reactive one-electron oxidation product of vitamin E

Heterocyclic compounds with structures similar to vitamin E, but without the hydroxyl hydrogen atom, were synthesized and their electrochemical behavior examined in acetonitrile solutions and as solids in aqueous solutions of varying pH by attaching the compounds to the surface of a glassy carbon electrode. Compound 1, containing a fully methylated aromatic ring was found to be the most long-lived following one-electron oxidation, with its radical cation (1+*) surviving in acidic aqueous solutions and able to be isolated as a salt, 1+*(SbF6-), when reacted with NOSbF6 in CH3CN. Electrochemical, UV-vis and FTIR experiments on 1+*, in addition to the results from theoretical calculations, indicated that the electrochemical, electronic and structural properties of 1+* are very similar to those of the radical cation of vitamin E.     

First FEL Winter School in Taiwan

The free electron laser (FEL) is widely regarded as the core technology of the fourth-generation light source in the international scientific community, as the development of such technology is making remarkable progress in recent years. FEL offers scientists the means to probe the nano-scale and outer-space world beyond the fullest extent of the existing scientific boundary. Compared to the cost of building a large-scale advanced research facility, the investments of the most ambitious FEL facilities, such as the Linac Coherent Light Source (LCLS) in the U.S. and SPring-8 Angstrom Compact Free Electron Laser (SACLA) in Japan, are much more expensive. However, there is great interest in the development of smaller and more affordable FELs.