Electron diffusion and back reaction in dye-sensitized solar cells : the effect of nonlinear recombination kinetics

The electron collection efficiency in dye-sensitized solar cells (DSCs) is usually related to the electron diffusion length, L = (Dτ)^1/2, where D is the diffusion coefficient of mobile electrons and τ is their lifetime, which is determined by electron transfer to the redox electrolyte. Analysis of incident photon-to-current efficiency (IPCE) spectra for front and rear illumination consistently gives smaller values of L than those derived from small amplitude methods. We show that the IPCE analysis is incorrect if recombination is not first-order in free electron concentration, and we demonstrate that the intensity dependence of the apparent L derived by first-order analysis of IPCE measurements and the voltage dependence of L derived from perturbation experiments can be fitted using the same reaction order, γ ≈ 0.8. The new analysis presented in this letter resolves the controversy over why L values derived from small amplitude methods are larger than those obtained from IPCE data.

Corrected mean-field models for spatially-dependent advection-diffusion-reaction phenomena

In the exclusion-process literature, mean-field models are often derived by assuming that the occupancy status of lattice sites is independent. Although this assumption is questionable, it is the foundation of many mean-field models. In this work we develop methods to relax the independence assumption for a range of discrete exclusion process-based mechanisms motivated by applications from cell biology. Previous investigations that focussed on relaxing the independence assumption have been limited to studying initially-uniform populations and ignored any spatial variations. By ignoring spatial variations these previous studies were greatly simplified due to translational invariance of the lattice. These previous corrected mean-field models could not be applied to many important problems in cell biology such as invasion waves of cells that are characterised by moving fronts. Here we propose generalised methods that relax the independence assumption for spatially inhomogeneous problems, leading to corrected mean-field descriptions of a range of exclusion process-based models that incorporate (i) unbiased motility, (ii) biased motility, and (iii) unbiased motility with agent birth and death processes. The corrected mean-field models derived here are applicable to spatially variable processes including invasion wave type problems. We show that there can be large deviations between simulation data and traditional mean-field models based on invoking the independence assumption. Furthermore, we show that the corrected mean-field models give an improved match to the simulation data in all cases considered.

Nanostructured metal oxides as adsorbents and photocatalysts

This research underlines the extensive application of nanostructured metal oxides in environmental systems such as hazardous waste remediation and water purification. This study tries to forge a new understanding of the complexity of adsorption and photocatalysis in the process of water treatment. Sodium niobate doped with a different amount of tantalum, was prepared via a hydrothermal reaction and was observed to be able to adsorb highly hazardous bivalent radioactive isotopes such as Sr2+ and Ra2+ions. This study facilitates the preparation of Nb-based adsorbents for efficiently removing toxic radioactive ions from contaminated water and also identifies the importance of understanding the influence of heterovalent substitution in microporous frameworks. Clay adsorbents were prepared via a two-step method to remove anionic and non-ionic herbicides from water. Firstly, layered beidellite clay was treated with acid in a hydrothermal process; secondly, common silane coupling agents, 3-chloro-propyl trimethoxysilane or triethoxy silane, were grafted onto the acid treated samples to prepare the adsorption materials. In order to isolate the effect of the clay surface, we compared the adsorption property of clay adsorbents with ƒ×-Al2O3 nanofibres grafted with the same functional groups. Thin alumina (£^-Al2O3) nanofibres were modified by the grafting of two organosilane agents 3-chloropropyltriethoxysilane and octyl triethoxysilane onto the surface, for the adsorptive removal of alachlor and imazaquin herbicides from water. The formation of organic groups during the functionalisation process established super hydrophobic sites along the surfaces and those non-polar regions of the surfaces were able to make close contact with the organic pollutants. A new structure of anatase crystals linked to clay fragments was synthesised by the reaction of TiOSO4 with laponite clay for the degradation of pesticides. Based on the Ti/clay ratio, these new catalysts showed a high degradation rate when compared with P25. Moreover, immobilized TiO2 on laponite clay fragments could be readily separated out from a slurry system after the photocatalytic reaction. Using a series of partial phase transition methods, an effective catalyst with fibril morphology was prepared for the degradation of different types of phenols and trace amount of herbicides from water. Both H-titanate and TiO2-(B) fibres coated with anatase nanocrystal were studied. When compared with a laponite clay photocatalyst, it was found that anatase dotted TiO2-(B) fibres prepared by a 45 h hydrothermal treatment followed by calcination were not only superior in performance in photocatalysis but could also be readily separated from a slurry system after photocatalytic reactions. This study has laid the foundation for the development of the ability to fabricate highly efficient nanostructured solids for the removal of radioactive ions and organic pollutants from contaminated water. These results now seem set to contribute to the development of advanced water purification devices in the future. These modified nanostructured materials with unusual properties have broadened their application range beyond their traditional use as adsorbents, to also encompass the storage of nuclear waste after concentrating from contaminated water.

Drug diffusion from polymeric delivery devices : a problem with two moving boundaries

An existing model for solvent penetration and drug release from a spherically-shaped polymeric drug delivery device is revisited. The model has two moving boundaries, one that describes the interface between the glassy and rubbery states of polymer, and another that defines the interface between the polymer ball and the pool of solvent. The model is extended so that the nonlinear diffusion coefficient of drug explicitly depends on the concentration of solvent, and the resulting equations are solved numerically using a front-fixing transformation together with a finite difference spatial discretisation and the method of lines. We present evidence that our scheme is much more accurate than a previous scheme. Asymptotic results in the small-time limit are presented, which show how the use of a kinetic law as a boundary condition on the innermost moving boundary dictates qualitative behaviour, the scalings being very different to the similar moving boundary problem that arises from modelling the melting of an ice ball. The implication is that the model considered here exhibits what is referred to as ``non-Fickian'' or Case II diffusion which, together with the initially constant rate of drug release, has certain appeal from a pharmaceutical perspective.

Numerical simulation for the variable-order Galilei invariant advection diffusion equation with a nonlinear source term

In this paper, we consider the variable-order Galilei advection diffusion equation with a nonlinear source term. A numerical scheme with first order temporal accuracy and second order spatial accuracy is developed to simulate the equation. The stability and convergence of the numerical scheme are analyzed. Besides, another numerical scheme for improving temporal accuracy is also developed. Finally, some numerical examples are given and the results demonstrate the effectiveness of theoretical analysis. Keywords: The variable-order Galilei invariant advection diffusion equation with a nonlinear source term; The variable-order Riemann–Liouville fractional partial derivative; Stability; Convergence; Numerical scheme improving temporal accuracy