The eigenpairs of a Sylvester–Kac type matrix associated with a simple model for one-dimensional deposition and evaporation

A straightforward model for deposition and evaporation on discrete cells of a finite array of any dimension leads to a matrix equation involving a Sylvester–Kac type matrix. The eigenvalues and eigenvectors of the general matrix are determined for an arbitrary number of cells. A variety of models to which this solution may be applied are discussed.     

Effects of structural properties of silicon carbide-derived carbons on their electrochemical double-layer capacitance in aqueous and organic electrolytes

High surface area silicon carbide-derived carbons (Si-CDCs) synthesized by chlorination of beta silicon carbide (βSiC) with two different particle sizes (6 μm and 50 nm) show different porosities with graphitic structure. Transmission electron microscopy, Raman spectroscopy and argon (Ar) and carbon dioxide (CO₂) sorption analyses are used to examine the textural properties of the Si-CDCs. The results show that the particle size of the precursor affects the surface area and porosity of carbons. Furthermore, an additional heat treatment of the Si-CDC with 50-nm particle size for 24 h at 1,000 °C results in a collapse of the pore structure and reduces the surface area. The capacitive behaviours are investigated in H₂SO₄ and in tetraethyl ammonium tetrafluoroborate (TEABF₄)/acetonitrile (AN). The electrochemical performance of the Si-CDCs is influenced by the particle size, surface area, pore volume and pore size distribution. The Si-CDCs exhibit capacitances in 1 M H₂SO₄ of up to 179 F g^?1 and very stable charge–discharge performance over 5,000 cycles. This study shows the crucial importance of ultramicropores less than 1 nm combined with nanosized particles for achieving high capacitance in aqueous electrolyte. Moreover, the graphitic degree at the surface of the Si-CDCs enhances considerably the rate capability and stability in both electrolytes.     

Copper-Photocatalyzed Hydrosilylation of Alkynes and Alkenes under Continuous Flow

Herein, the photocatalytic hydrosilylation of alkynes and alkenes under continuous flow conditions is described. By using 0.2 mol % of the developed [Cu(dmp)(XantphosTEPD)]PF₆ under blue LEDs irradiation, a large panel of alkenes and alkynes was hydrosilylated in good to excellent yields with a large functional group tolerance. The mechanism of the reaction was studied, and a plausible scenario was suggested.     

Chromatography Modeling Software Applicability for Non-Conventional Columns: a Case Study of Calixarene- and Resorcinarene-Bonded Stationary Phases

In this study a systematic evaluation of the applicability of DryLab for calixarene- and resorcinarene-bonded stationary phases and some other relatively new reversed-phase columns with the presence of conventional alkyl-bonded phases was carried out. Calixarene- and resorcinarene-bonded stationary phases belong to the reversed-phase materials. However, depending on the analytes, they show some additional interactions, since their steric, polar and ionic properties are different compared to those of conventional alkyl-bonded phases. Three different mixtures of model analytes, consisting of alkyl substituted benzene derivatives, 4-hydroxybenzoic acid esters and polycyclic aromatic hydrocarbons, were used to verify the accuracy of DryLab prediction of retention times and to compare the results of 20 different liquid chromatographic phases. The type and the content of the organic modifier as well as the temperature and the gradient time were systematically changed using same conditions for all stationary phases. The results showed that the prediction on the calixarene- and resorcinarene-bonded stationary phases as well as on other reversed-phase columns is highly accurate in both isocratic and gradient modes. The predictions and real experiments were highly correlated with an average absolute error (∆t _R) of 0.027 min (<2 s) and an average percent absolute error (%∆t _R) of 0.38 on the calixarene- and resorcinarene-bonded stationary phases, and ∆t _R of 0.04 min (<3 s); %∆t _R of 0.51 on the other reversed-phase columns in this study. As a result, DryLab could be applied with very accurate predictions in method development using calixarene- and resorcinarene-bonded stationary phases, which were used as an example for “new” stationary phase materials.