Solving eigenvalue problems on curved surfaces using the Closest Point Method

Eigenvalue problems are fundamental to mathematics and science. We present a simple algorithm for determining eigenvalues and eigenfunctions of the Laplace–Beltrami operator on rather general curved surfaces. Our algorithm, which is based on the Closest Point Method, relies on an embedding of the surface in a higher-dimensional space, where standard Cartesian finite difference and interpolation schemes can be easily applied. We show that there is a one-to-one correspondence between a problem defined in the embedding space and the original surface problem. For open surfaces, we present a simple way to impose Dirichlet and Neumann boundary conditions while maintaining second-order accuracy. Convergence studies and a series of examples demonstrate the effectiveness and generality of our approach.     

Effects of various boundary conditions on the response of Poisson-Nernst-Planck impedance spectroscopy analysis models and comparison with a continuous-time random-walk model

Various electrode reaction rate boundary conditions suitable for mean-field Poisson-Nernst-Planck (PNP) mobile charge frequency response continuum models are defined and incorporated in the resulting Chang-Jaffe (CJ) CJPNP model, the ohmic OHPNP one, and a simplified GPNP one in order to generalize from full to partial blocking of mobile charges at the two plane parallel electrodes. Model responses using exact synthetic PNP data involving only mobile negative charges are discussed and compared for a wide range of CJ dimensionless reaction rate values. The CJPNP and OHPNP ones are shown to be fully equivalent, except possibly for the analysis of nanomaterial structures. The dielectric strengths associated with the CJPNP diffuse double layers at the electrodes were found to decrease toward 0 as the reaction rate increased, consistent with fewer blocked charges and more reacting ones. Parameter estimates from GPNP fits of CJPNP data were shown to lead to accurate calculated values of the CJ reaction rate and of some other CJPNP parameters. Best fits of CaCu(3)Ti(4)O(12) (CCTO) single-crystal data, an electronic conductor, at 80 and 140 K, required the anomalous diffusion model, CJPNPA, and led to medium-size rate estimates of about 0.12 and 0.03, respectively, as well as good estimates of the values of other important CJPNPA parameters such as the independently verified concentration of neutral dissociable centers. These continuum-fit results were found to be only somewhat comparable to those obtained from a composite continuous-time random-walk hopping/trapping semiuniversal UN model.     

Calorimetric Investigation of the Complexation of Didodecylcalix[4]arene-crown-6 with Alkali Metal and Ammonium Cations in Acetonitrile

Abstract

The Cs⁺ selectivity of some calix-crown ligands makes them excellent candidates for use in separation systems such as liquid membranes. Separation performance can be understood and predicted from thermodynamic data for cation complexation. We have therefore determined the log K, ΔH and ΔS for the interaction of Na⁺, K⁺, Rb⁺, Cs⁺ and NH₄ ⁺ with didodecyl-calix[4]arene-crown-6 in acetonitrile at 25°C by titration calorimetry. The ligand is strongly selective for Cs⁺, and the selectivity trend results entirely from the enthalpy contribution, with entropy effects opposing the trend. These results are discussed in light of some corresponding data obtained by other researchers with similar ligands.     

Temperature driven annealing of perforations in bicellar model membranes

Bicellar model membranes composed of 1,2-dimyristoylphosphatidylcholine (DMPC) and 1,2-dihexanoylphosphatidylcholine (DHPC), with a DMPC/DHPC molar ratio of 5, and doped with the negatively charged lipid 1,2-dimyristoylphosphatidylglycerol (DMPG), at DMPG/DMPC molar ratios of 0.02 or 0.1, were examined using small angle neutron scattering (SANS), (31)P NMR, and (1)H pulsed field gradient (PFG) diffusion NMR with the goal of understanding temperature effects on the DHPC-dependent perforations in these self-assembled membrane mimetics. Over the temperature range studied via SANS (300-330 K), these bicellar lipid mixtures exhibited a well-ordered lamellar phase. The interlamellar spacing d increased with increasing temperature, in direct contrast to the decrease in d observed upon increasing temperature with otherwise identical lipid mixtures lacking DHPC. (31)P NMR measurements on magnetically aligned bicellar mixtures of identical composition indicated a progressive migration of DHPC from regions of high curvature into planar regions with increasing temperature, and in accord with the "mixed bicelle model" (Triba, M. N.; Warschawski, D. E.; Devaux, P. E. Biophys. J.2005, 88, 1887-1901). Parallel PFG diffusion NMR measurements of transbilayer water diffusion, where the observed diffusion is dependent on the fractional surface area of lamellar perforations, showed that transbilayer water diffusion decreased with increasing temperature. A model is proposed consistent with the SANS, (31)P NMR, and PFG diffusion NMR data, wherein increasing temperature drives the progressive migration of DHPC out of high-curvature regions, consequently decreasing the fractional volume of lamellar perforations, so that water occupying these perforations redistributes into the interlamellar volume, thereby increasing the interlamellar spacing.     

Kinetics of bacterial potentiometric titrations: the effect of equilibration time on buffering capacity of Pantoea agglomerans suspensions

Several recent studies have made use of continuous acid-base titration data to describe the surface chemistry of bacterial cells as a basis for accurately modelling metal adsorption to bacteria and other biomaterials of potential industrial importance. These studies do not share a common protocol; rather they titrate in different pH ranges and they use different stability criteria to define equilibration time during titration. In the present study we investigate the kinetics of bacterial titrations and test the effect they have on the derivation of functional group concentrations and acidity constants. We titrated suspensions of Pantoea agglomerans by varying the equilibration time between successive titrant additions until stability of 0.1 or 0.001 mV s(-1) was attained. We show that under longer equilibration times, titration results are less reproducible and suspensions exhibit marginally higher buffering. Fluorescence images suggest that cell lysis is not responsible for these effects. Rather, high DOC values and titration reversibility hysterisis after long equilibration times suggest that variability in buffering is due to the presence of bacterial exudates, as demonstrated by titrating supernatants separated from suspensions of different equilibration times. It is recommended that an optimal equilibration time is always determined with variable stability control and preliminary reversibility titration experiments.     

Alkali Metal Dihydropyridines in Transfer Hydrogenation Catalysis of Imines: Amide Basicity versus Hydride Surrogacy

Catalytic reduction of a representative set of imines, both aldimines and ketimines, to amines has been studied using transfer hydrogenation from 1,4-dicyclohexadiene. Unusually, this has been achieved using s-block pre-catalysts, namely 1-metallo-2-tert-butyl-1,2-dihydropyridines, 2-tBuC₅H₅NM, M(tBuDHP), where M=Li–Cs. Reactions have been monitored in C₆D₆ and tetrahydrofuran-d₈ (THF-d₈). A definite trend is observed in catalyst efficiency with the heavier alkali metal tBuDHPs outperforming the lighter congeners. In general, Cs(tBuDHP) is the optimal pre-catalyst with, in the best cases, reactions producing quantitative yields of amines in minutes at room temperature using 5 mol % catalyst. Supporting the experimental study, Density Functional Theory (DFT) calculations have also been carried out which reveal that Cs has a pathway with a significantly lower rate determining step than the Li congener. In the postulated initiation pathways DHP can act as either a base or as a surrogate hydride.     

Halide Chemistry in Tin Perovskite Optoelectronics: Bottlenecks and Opportunities

Tin halide perovskites (Sn HaPs) are the top lead-free choice for perovskite optoelectronics, but the oxidation of perovskite Sn²⁺ to Sn⁴⁺ remains a key challenge. However, the role of inconspicuous chemical processes remains underexplored. Specifically, the halide component in Sn HaPs (typically iodide) has been shown to play a key role in dictating device performance and stability due to its high reactivity. Here we describe the impact of native halide chemistry on Sn HaPs. Specifically, molecular halogen formation in Sn HaPs and its influence on degradation is reviewed, emphasising the benefits of iodide substitution for improving stability. Next, the ecological impact of halide products of Sn HaP degradation and its mitigation are considered. The development of visible Sn HaP emitters via halide tuning is also summarised. Lastly, halide defect management and interfacial engineering for Sn HaP devices are discussed. These insights will inspire efficient and robust Sn HaP optoelectronics.