An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy

Using the approach of Rulla (1996 SIAM J. Numer. Anal. 33, 68-87)for analysing the time discretization error and assuming moreregularity on the initial data, we improve on the error boundderived by Barrett and Blowey (1996 IMA J. Numer. Anal. 16,257-287) for a fully practical piecewise linear finite elementapproximation with a backward Euler time discretization of amodel for phase separation of a multi-component alloy.     

Spatially resolved sources of dark current from TiO2 nanoparticle electrodes

The properties of TiO(2) and polyphenyl oxide (PPO) blocking layers were compared using a highly positive redox shuttle in dye-sensitized solar cells. The dark current versus applied potential curve was found to be composed of two separate current features. Cyclic voltammetric and impedance measurements were performed to identify the source of the two features. The first feature results from electron transfer from the TiO(2) blocking layer and the first layer of the TiO(2) nanoparticle film contacting the substrate. The second onset of dark current results from the transport resistance in the nanoparticle film decreasing, thus allowing electron transfer to occur throughout the film. It is further demonstrated that PPO prevents back electron transfer from the conductive substrate to the redox shuttle across the entire potential range studied; however, the TiO(2) blocking layer is active and participates in electron transfer at rates similar to those of the TiO(2) nanoparticle film.     

Finite element approximation of a model for phase separation of a multi-component alloy with a concentration-dependent mobility matrix

We consider a model for phase separation of a multi-componentalloy with a concentration-dependent mobility matrix and logarithmicfree energy. In particular we prove that there exists a uniquesolution for sufficiently smooth initial data. Further, we provean error bound for a fully practical piecewise linear finiteelement approximation in one and two space dimensions. Finallynumerical experiments with three components in one space dimensionare presented.