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.