Quadratic-Like Dynamics of Cubic Polynomials

A small perturbation of a quadratic polynomial f with a non-repelling fixed point gives a polynomial g with an attracting fixed point and a Jordan curve Julia set, on which g acts like angle doubling. However, there are cubic polynomials with a non-repelling fixed point, for which no perturbation results into a polynomial with Jordan curve Julia set. Motivated by the study of the closure of the Cubic Principal Hyperbolic Domain, we describe such polynomials in terms of their quadratic-like restrictions.     

PASADENA hyperpolarization of succinic acid for MRI and NMR spectroscopy

We use the PASADENA (parahydrogen and synthesis allow dramatically enhanced nuclear alignment) method to achieve 13C polarization of approximately 20% in seconds in 1-13C-succinic-d2 acid. The high-field 13C multiplets are observed as a function of pH, and the line broadening of C1 is pronounced in the region of the pK values. The 2JCH, 3JCH, and 3JHH couplings needed for spin order transfer vary with pH and are best resolved at low pH leading to our use of pH approximately 3 for both the molecular addition of parahydrogen to 1-13C-fumaric acid-d2 and the subsequent transfer of spin order from the nascent protons to C1 of the succinic acid product. The methods described here may generalize to hyperpolarization of other carboxylic acids. The C1 spin-lattice relaxation time at neutral pH and 4.7 T is measured as 27 s in H2O and 56 s in D2O. Together with known rates of succinate uptake in kidneys, this allows an estimate of the prospects for the molecular spectroscopy of metabolism.     

Electrochemical characterization of 17β-estradiol with fast-scan cyclic voltammetry

We have developed a sensitive and stable electrochemical method for 17β-estradiol (E2) detection using fast-scan cyclic voltammetry (FSCV). Recently, E2 was proposed to function as a rapid synaptocrine signaling molecule in the brain; however, methods to directly monitor subsecond fluctuations in E2 are currently unavailable, limiting our understanding of the dynamics and mechanism of rapid E2 release. FSCV at carbon-fiber microelectrodes enables subsecond detection of electroactive neurochemicals directly in tissues like the brain. Here, we have electrochemically characterized E2 using FSCV for use in a tissue matrix. The limit of detection of E2 is 31.2±2.5 nM with FSCV, which will enable low nanomolar fluctuations in extracellular E2 to be monitored with hundred millisecond temporal resolution. We also identify specific parameters for waveform modification to improve future detection. This method will significantly improve E2 sensing capabilities and will have far-reaching impacts on improving our understanding of dynamic E2 signaling in the brain.     

Highly active mesostructured silica hosted silver catalysts for CO oxidation using the one-pot synthesis approach

A facile one-pot approach gave isolated silver nanoparticles anchored on a mesostructured silica matrix in a self-assembled way; these gave 100% CO conversion in CO oxidation at room temperature, which is higher than or comparable to the conversion obtained using noble metal catalysts.     

Finite sample effect in temperature gradient focusing

Temperature gradient focusing (TGF) is a new and promising equilibrium gradient focusing method which can provide high concentration factors for improved detection limits in combination with high-resolution separation. In this technique, temperature-dependent buffer chemistry is employed to generate a gradient in the analyte electrophoretic velocity. By the application of a convective counter-flow, a zero-velocity point is created within a microchannel, at which location the ionic analytes accumulate or focus. In general, the analyte concentration is small when compared with buffer ion concentrations, such that the focusing mechanism works in the ideal, linearized regime. However, this presumption may at times be violated due to significant sample concentration growth or the use of a low-concentration buffer. Under these situations the sample concentration becomes non-negligible and can induce strong nonlinear interactions with buffer ions, which eventually lead to peak shifting and distortion, and the loss of detectability and resolution. In this work we combine theory, simulation, and experimental data to present a detailed study on nonlinear sample-buffer interactions in TGF. One of the key results is the derivation of a generalized Kohlrausch regulating function (KRF) that is valid for systems in which the electrophoretic mobilities are not constant but vary spatially. This generalized KRF greatly facilitates analysis, allowing reduction of the problem to a single equation describing sample concentration evolution, and is applicable to other problems with heterogeneous electrophoretic mobilities. Using this sample evolution equation we have derived an understanding of the nonlinear peak deformation phenomenon observed experimentally in TGF. We have used numerical simulations to validate our theory and to quantitatively predict TGF. Our simulation results demonstrate excellent agreement with experimental data, and also indicate that the proper inclusion of Taylor dispersion is important for the accurate modeling of TGF. This work is an important first step towards the understanding and prediction of the more complex, nonlinear, and multi-species interactions which often occur in on-chip electrophoretic assays such as TGF.     

Alkali metal complexes of a naphthylamine-substituted phosphanide

The reaction between {(Me3Si)2CH}PCl2 and one equivalent of [C10H6-8-NMe2]Li, followed by in situ reduction with LiAlH4, gives the secondary phosphane {(Me3Si)2CH}(C10H6-8-NMe2)PH(1) in good yield as a colourless crystalline solid. Metalation of 1 with Bu(n)Li in diethyl ether gives the lithium phosphanide [{[{(Me3Si)2CH}(C10H6-8-NMe2)P]Li}2(OEt2)](2), which undergoes metathesis with either NaOBu(t) or KOBu(t) to give the heavier alkali metal derivatives [[{(Me3Si)2CH}(C10H6-8-NMe2)P]-Na(tmeda)](3) and [[{(Me3Si)2CH}(C10H6-8-NMe2)P]K(pmdeta)](4), after recrystallisation in the presence of the corresponding amine co-ligand [tmeda = N,N,N',N'-tetramethylethylenediamine, pmdeta = N,N,N',N",N"-pentamethyldiethylenetriamine]. Compounds 2-4 have been characterised by 1H, 13C{1H} and 31P{1H} NMR spectroscopy, elemental analyses and X-ray crystallography. Dinuclear 2 crystallises with the phosphanide ligands arranged in a head-to-head fashion and is subject to dynamic exchange in toluene solution; in contrast, compounds 3 and 4 crystallise as discrete monomers which exhibit no dynamic behaviour in solution. DFT calculations on the model compound [{[(Me)(C10H6-8-NMe2)P]Li},(OMe2)] (2a) indicate that the most stable head-to-head form is favoured by 15.0 kcal mol(-1) over the corresponding head-to-tail form.     

Analysis of dielectric and conductive dispersion above Tg in glass-forming molecular liquids

Dynamics of the nonassociated supercooled liquids N-methyl-epsilon-caprolactam (NMEC) and glycerol in the frequency domain are investigated using full complex-nonlinear-least-squares fitting of immittance spectroscopy data for appreciable temperature ranges above the glass transition. Such fitting, not previously used for these materials, helps to identify physical processes responsible for the data and elements of their common behavior. Several different fitting models were applied to find a physically plausible best-fitting one to distinguish quantitatively between the dielectric effects of dipoles and the conductive effects of mobile ions. The utility of many composite fitting models was investigated, and although a pure conductive-system dispersive (CSD) fitting model led to good but physically unrealistic fits of all data sets, the dielectric-system dispersive (DSD) Davidson-Cole model best fitted the alpha-dispersion part of the responses. Nevertheless, the series combination of such a DSD model and a separate CSD model (one not associated with electrode effects) was found to yield much better fitting of the data for both materials. Although the CSD model plays somewhat the role of the conventional parallel DSD Johari-Goldstein beta-response, it is here in series and arises from mobile impurity-ion effects rather than from dipolar ones. Previous analyses of data of the present and other molecular materials have often involved two DSD models in parallel, but fitting with such a composite model led here to less physically plausible parameter values and ones with appreciably more uncertainties. Surprisingly, the series DSD and CSD composite-model fits led to comparable estimated values of the NMEC and glycerol dielectric strength parameters, as well as to the nearly equal small thermal activation energies of these parameters.