A mathematical model for the anodic half cell of a dye-sensitised solar cell

We present a mathematical model of the steady-state current produced by the anodic half cell of a dye-sensitised solar cell (DSC) under both illuminated and non-illuminated conditions. A one-dimensional transport model that describes the transport of charged species via migration and diffusion within the electrolyte filled pores and the porous semiconductor that constitutes the porous anode of the DSC is given. This model is coupled to an interfacial model, developed previously by the authors, that describes charge transfer across the semiconductor–dye–electrolyte interface by explicitly accounting for each reaction at the interface involving dye molecules, electrolyte species, and semiconductor electrons. An equivalent circuit extension to the anode model (in the form of a boundary condition) is developed in order to validate some of the simulation results of the anode model with experimental results obtained from a full DSC specifically commissioned for the study. Parameter values associated with the model are obtained from the literature or experimentally from the specifically commissioned cell. A comparison of the numerical simulation results with experimental results shows a favourable correspondence without the need to fit parameter values.     

Modelling of stratified gas–liquid two-phase flow in horizontal circular pipes

This paper reports numerical and experimental investigation of stratified gas–liquid two-phase flow in horizontal circular pipes. The Reynolds averaged Navier–Stokes equations (RANS) with the k–ω turbulence model for a fully developed stratified gas–liquid two-phase flow are solved by using the finite element method. A smooth interface surface is assumed without considering the effects of the interfacial waves. The continuity of the shear stress across the interface is enforced with the continuity of the velocity being automatically satisfied by the variational formulation. For each given interface position and longitudinal pressure gradient, an inner iteration loop runs to solve the non-linear equations. The Newton–Raphson scheme is used to solve the transcendental equations by an outer iteration to determine the interface position and pressure gradient for a given pair of volumetric flow rates. Favorable comparison of the numerical results with available experimental results indicates that the k–ω model can be applied for the numerical simulation of stratified gas–liquid two-phase flow.     

Degradation of transparent metal–insulator–semiconductor solar cells due to heating effects

All the output parameters of the metal–insulator–semiconductor solar cells are degraded after heating. Also the dark current and the non-ideality factor are increased with heating. A reduction in the built-in potential has been detected. The capacitance–voltage–frequency measurements indicate the presence of interface states. These states are heavily occupied by electrons. Heating will increase the density of these states and consequently reduce the barrier height and the overall cell efficiency.     

Effect of interface recombination on solar cell parameters

A model is presented for p–n hetero-junction solar cells in which interface recombination is the dominant diode current transport mechanism. The model explains the large diode ideality factor (n>2) and the increased saturation current density in terms of increased density of interface states N_ir. Furthermore, the model allows us to explain the non-translation between illuminated and dark J–V characteristics. The explanation is based on the assumption that, for high interface state density values, both the depletion layer width and the diffusion voltage in the p- and n-side of the junction are functions of N_ir. The interface recombination leads to lower values of the open-circuit voltage, short-circuit current density, and fill factor. These results are illustrated by numerical calculations of solar cell parameters and compared with experimental data achieved for ZnO/CdS/CuGaSe₂ single-crystal solar cells.     

Density of interface states, excess capacitance and series resistance in the metal–insulator–semiconductor (MIS) solar cells

Dark and illuminatied current–voltage (I–V) characteristics of Al/SiO_x/p-Si metal–insulator–semiconductor (MIS) solar cells were measured at room temperature. In addition to capacitance–voltage (C–V) and conductance–voltage (G–V), characteristics are studied at a wide frequency range of 1 kHz–10 MHz. The dark I–V characteristics showed non-ideal behavior with an ideal factor of 3.2. The density of interface states distribution profiles as a function of (E_ss−E_v) deduced from the I–V measurements at room temperature for the MIS solar cells on the order of 10¹³ cm⁻² eV⁻¹. These interface states were responsible for the non-ideal behavior of I–V, C–V and G–V characteristics. Frequency dispersion in capacitance for MIS solar cells can be interpreted only in terms of interface states. The interface states can follow the a.c. signal and yield an excess capacitance, which depends on the relaxation time of interface states and the frequency of the a.c. signal. It was observed that the excess capacitance C_o caused by an interface state decreases with an increase of frequency. The capacitances characteristics of MIS solar cells are affected not only in interface states but also series resistance. Analysis of this data indicated that the high interface states and series resistance leads to lower values of open-circuit voltage, short-circuit current density, and fill factor. Experimental results show that the location of interface states and series resistance have a significant effect on I–V, C–V and G–V characteristics.     

Sb–Cu–Li electrochromic mirrors

Switchable mirrors offer significant advantages over traditional electrochromic devices for control of incident light in architectural and aerospace applications due to their large dynamic ranges in both transmission and reflection in the visible and near infrared regimes. Here we describe construction and spectroscopic characterization of a complete electrochromic mirror device consisting of an antimony–copper alloy (40 at% Cu) active electrode coupled with an optically passive vanadium oxide counter electrode and a crosslinked polymer gel electrolyte. Transmittance and reflectance spectra in the visible–near IR (300–2500 nm) in both mirror and transparent states are reported. The photopic transmittance of the complete device varied from less than 3% to more than 20% during cycling, requiring about 40 min for complete switching in each direction. At the same time, the photopic reflectance varied from 40% to 25%. The crosslinked polymer improves the stability of the mirror electrode relative to that in a liquid electrolyte.     

An analysis of the electrical characteristics of DSC under inhomogeneous solar illumination

A simple model to describe the dye sensitized solar cell (DSC) is presented in which simultaneous occurrence of diffusion and charge transfer processes, power loss due to inhomogeneous excitation resulted from absorption of the dye and the electrolyte, and power gain due to the direct excitation (not via dye molecules) of semiconductor particles are taken into consideration. About 35% and 2.2% decrease in power is estimated for the dye and the electrolyte absorption, respectively, while 2.9% increase of power is obtained by the direct excitation of TiO₂ at maximum power point (MPP) under AM1.5 solar illumination. Some numerical results are also presented to demonstrate the influence of the material parameters for the cell characteristics.     

Photocurrent in CdTe NIP solar cells

A simple analytical model for the voltage dependence of the photocurrent in CdTe n–i–p solar cells is presented. The physical model is corroborated with a numerical solution of Poisson and the two continuity equations under illumination and shows excellent agreement with the numerical data. The new model is compared with previously reported models of Bube and Crandall. The new model illuminates the loss mechanism of carriers near the front interface of CdTe solar cells. It is shown that the photocurrent is high when the carrier velocity due to the electric field is higher than the product of the absorption coefficient and the diffusion coefficient, almost regardless of the interface recombination velocity value. At lower electric field values, the interface recombination velocity has a stronger effect on the photocurrent. Experimental conditions leading to a reduction of the electric field and a corresponding decrease in the collection efficiency in CdTe n–i–p solar cells are discussed.     

On the modeling of the dye-sensitized solar cell

A simplified electric model of the dye-sensitized electrochemical solar cell (DSC) is presented. It permits the calculation of internal steady-state cell characteristics like particle density distributions or the electric field as a function of the (measured) external current I_ext. The cell is modeled as an one-dimensional pseudo-homogeneous medium of thickness L, where all the electroactive particles involved in the current supporting process move according to different effective transport coefficients (i.e. effective diffusivities D and effective mobilities μ). The electroactive particles are the electrons e⁻ injected into the nanoporous TiO₂ layer after light absorption by the dye, the reduced and the oxidized counterpart of the redox electrolyte El_Red and El_Ox, and the positively charged cation Kat⁺ being brought into the cell together with the electrolyte. By applying the continuity equation, the transport-equation and Poisson's equation to all the electroactive species involved (e⁻, El_Red, El_Ox and Kat⁺) and by assuming a linear Boltzmann relaxation approximation for the back reaction, a system of differential equations is derived, describing particle densities, particle currents and the electric field within the cell. The underlying simplifying assumptions as well as the resulting limits of the model are stated, and some possible extensions are given. This paper aims to outline the general ideas and limitations of the proposed electric modeling, numerical calculations have been successfully implemented, but will be presented in a future paper.     

Experimental investigation on melting characteristics of ethanolamine–water binary mixture used as PCM

An experimental investigation of the melting process of ethanolamine–water binary mixture used as PCM (phase change material) in a rectangular enclosure with a heated vertical wall is reported in this work. The liquid–solid interfaces were captured and the instantaneous liquid fraction was presented. The effect of natural convection was studied in terms of the molten fraction and the shape of the solid–liquid interface. The correlations of molten fraction and time-averaged Nusselt number are obtained so that the time of the melting process can be predicted. The results indicate that natural convection enhances the rate of melting compared with the pure conduction model and that pure conduction mechanism only occurs at the initial stage of melting. Conduction–convection coupled model is necessary for predicting melting process exactly.     

Effect of structure on porous gas-diffusion electrodes for phosphoric acid fuel cells

This investigation is concerned with the variation of structure in the catalyst layer for porous gas-diffusion electrodes. The pore-size distribution and the total pore volume of the electrode are measured by a mercury penetration method. A model that accounts for this incomplete wetting electrode is solved by an orthogonal collocation method and matched with experimental observations. The numerical solution indicates that the effectiveness factor drops noticeably under high current density when the agglomerate radius is greater than 40 μm. When the agglomerate radius is smaller than 1.2 μm, however, the effect of ionic transport becomes important. The maximum reaction rate occurs at carbon-paper/ catalyst-layer interface when the effective conductivity of the electrolyte is larger than that of the solid phase. If the effective conductivity of the electrolyte is smaller, then the maximum reaction rate occurs at the electrode/electrolyte interface.     

Spatial variation of heat flux at the metal–mold interface due to mold filling effects in gravity die-casting

Most of the research work pertaining to metal–mold heat transfer in casting solidification either assumes no spatial variation in the air gap formation or limits the study to only those experimental systems in which air gap formation is uniform. However, in gravity die-casting, filling effects induce variation in thermal field in the mold and casting regions. In this paper, we show that this thermal field variation greatly influences the time of air gap initiation along a vertical mold wall, which subsequently leads to the spatial variation of air gap and in turn, the heat flux at the metal–mold interface.In order to study the spatial variation of heat flux at the metal–mold interface, an experimental setup that involved mold filling was devised. A Serial-IHCP (inverse heat conduction problem) algorithm was used to estimate the multiple heat flux transients along the metal–mold interface. The analysis indicates that the fluxes at different mold segments (bottom, middle, and top) of the metal–mold interface reaches the peak value at different time steps, which shows that the initiation of air gap differs along the mold wall. The experimental and numerical results show that the heat transfer in the mold is two-dimensional during the entire period of phase change, which is initially caused by the filling effects and further enhanced by the spatial variation of the air gap at the metal–mold interface.     

Estimation de la résistance thermique de contact durant la solidification du verre

Estimation of the thermal contact resistance during glass solidification. This paper presents an experimental study of thermal contact conditions during glass moulding. Our goal was to develop an experimental setup to simulate the real contact conditions during the glass solidification and to build a numerical procedure to estimate the thermal parameters characterizing heat transfer at the contact interface (mould–glass). The semi-transparent character of glass was taken into account when building the theoretical heat transfer model. Thus a heat radiation–conduction model was built to simulate heat transfer at the interface during the glass cooling. The study shows that when the coupled conduction–radiation effect is taken into account, the parameter estimation is better. Thermal contact resistance mold–glass was estimated and the quality of heat transfer at the interface was analyzed.     

Degradation mechanisms in a dye-sensitized solar cell studied by UV–VIS and IR spectroscopy

By deliberately causing degradation of components in a dye-sensitized solar cell we have studied failure mechanisms of such cells. The dye, bis(tetrabutylammonium) cis–bis(thiocyanato)bis(2,2^′-bipyridine-4-carboxylic acid, 4^′-carboxylate)ruthenium(II), adsorbed to a nanostructured TiO₂ film was studied with UV–VIS and IR spectroscopy after being exposed to visual and ultra-violet radiation, increased temperature, air, electrolyte, and water in the electrolyte. The thiocyanate ion ligand is lost in air, at temperatures equal to and above 135 °C, in electrolyte and possibly upon UV irradiation. The loss of the SCN⁻ ligand in air was accelerated under visual illumination. From working electrodes immersed in the electrolyte or in degraded complete solar cells it was observed that the absorption peak from the thiocyanate ion ligand at around 2100 cm⁻¹ had broadened, blue-shifted and decreased. One failure mechanism is thus that the thiocyanate ion ligand is lost from the dye together with the electrolyte. Together with water in the electrolyte (5 v%) the SCN⁻ ligand is exchanged with H₂O and/or OH⁻. The ligand exchange between SCN⁻ and H₂O/OH⁻ was accelerated under visual illumination.     

Analysis of photocurrent in the i-layer of GaAs-based n–i–p solar cell

A numerical investigation of the intrinsic layer effect on the improvement of GaAs n–i–p solar cell performances is presented. Solution of Poisson's equation together with continuity equations for electrons and holes allows the determination of carrier's density, electric field and recombination profiles within the i-layer. The analysis examines the effect of i-layer thickness on the electric field, recombination rate and collection efficiency. It is found that increasing the i-layer thickness increases the absorption while it reduces the electric field and increases the recombination rate. The three competing parameters have to be monitored simultaneously so as to obtain an optimal thickness. To achieve this, the variation of the total photocurrent is used as indicator. The photocurrent shows a sharp increase in the domain of very thin i-layers (<0.5 μm) then a saturation is reached for thicker layers (>1 μm), the simulation is performed for thicknesses up to 2 μm.     

A two-phase model for studying the role of microporous layer and catalyst layer interface on polymer electrolyte fuel cell performance

In this work, a two-phase, two-dimensional model is developed to investigate the role of interfacial voids at the microporous layer (MPL) and catalyst layer (CL) interface on the polymer electrolyte fuel cell (PEFC) performance. The model incorporates the MPL|CL interfacial region as a separate domain and simulates two-phase transport within the interfacial voids. Different case studies, including the experimentally-measured MPL|CL interface and a perfect contact interface, are conducted. Model simulations indicate that the MPL|CL interfacial morphology has a significant effect on performance, particularly in the high current density region (>1.0 A/cm²). The interfacial voids at the MPL|CL interface are found to retain liquid water during operation and induce mass transport resistance, resulting in nearly a 20% reduction in the limiting current density when compared to perfect interfacial contact. The liquid water saturation retained at the interface and the magnitude of the mass and charge transport resistance induced by the interface are found to be highly dependent upon the geometry and size of the interfacial voids. Finally, simulations indicate that the morphology of the MPL|CL interface affects the location where reactions tend to occur in the CL, and also has a direct impact on the temperature distribution within the cathode.     

Organic–inorganic hybrid composites for photovoltaics: Organic guest molecules embedded in μc-Si and ZnSe host matrices

The concept of organic–inorganic hybrid composites for bulk sensitization of inorganic semiconductors by organic dye molecules is introduced. The idea is either to increase the absorptivity of e.g. indirect semiconductors as μc-Si or to expand in a two-step process the absorption spectrum of wide gap semiconductors to photons of energy smaller than the band gap. The composites are prepared by vacuum-based codeposition. Raman and optical spectroscopy, and photoemission have been used to prove the stability of the organic molecules ZnPc and F₁₆ZnPc for the applied growth conditions. Enhancement of photoconductivity has been shown for ZnPc–Si bilayer. As a crucial parameter for the transfer of excited charges, the alignment of dye HOMO–LUMO states versus semiconductor band edges has been determined using photoelectron spectroscopy.     

Soft switching bidirectional DC–DC converter for ultracapacitor–batteries interface

In this paper a new soft switching bidirectional DC–DC converter is introduced which can be applied as the interface circuit between ultracapacitors and batteries or fuel cells. All semiconductor devices in the proposed converter are soft switched while the control circuit remains PWM. Due to achieved soft switching condition, the energy conversion through the proposed converter is highly efficient. The proposed converter is analyzed and a prototype converter is implemented. The presented experimental results confirm the theoretical analysis.     

A comprehensive analytical solution of macromolecular transport within an artery

Macromolecule transport within an artery is investigated and a comprehensive analytical solution is presented. The transport within the lumen and the arterial wall are coupled. Arterial wall is modeled as a four-layer porous wall. The layers are all treated as macroscopically homogeneous porous media. The volume-averaged porous media equations are employed to solve for transport through the porous arterial layers. Staverman filtration coefficient is incorporated to account for selective permeability of each porous layer to macromolecules. The problem encompasses complex interfacial transport phenomena involving various porous–porous as well as porous–fluid interfaces. The method of matched asymptotic expansions is employed to solve for the fluid flow field and species concentration distributions. For comparison purposes, the physiological and transport parameters associated with each porous layer are obtained from the literature. The analytical results are in excellent agreement with previous numerical studies. The results presented in this work provide the first comprehensive analytical solution representing arterial transport phenomena.     

Electrical and photovoltaic properties of devices based on PbPc–TiO2 thin films

The electrical, optical and photovoltaic properties of organic–inorganic hybrid devices consisting of Al/TiO₂/PbPc/ITO and Al/PbPc/TiO₂/ITO structures have been investigated through analyzing the current–voltage characteristics, optical absorption and photocurrent action spectra of the devices. The combined presence of oxygen, light and an electric field in the photocurrent decay of Al/TiO₂/PbPc/ITO device have been studied. It is observed that under illumination, the oxygen radical anions and excitons are formed, which subsequently drift towards the interface with TiO₂, where an internal electric field is present. The excitons that reach to the interface are subsequently dissociated into free charge carriers due to the electric field present at the interface. The exciton diffusion length for PbPc calculated from the dependence of luminescence with the PbPc film is about 13 nm. We have also studied the effect of PbPc thickness and hole mobility on the device performance of organic photovoltaic device consisting of PbPc as an optically active layer, TiO₂ as the electron–transporting layer and ITO and Al used as electrodes. We have shown that the power conversion efficiency in the device is primarily limited by the short-exciton diffusion length combined with the low-hole mobility in PbPc layer. The model of charge transport in Al/TiO₂/PbPc/ITO device explained the experimental results where the total current density is a function of injected carriers at electrode–organic semiconductor surface, the leakage current through the organic layer and collected photogenerated current that results from the effective dissociation of excitons.