The obstructed diffusion of the I3− ion in mesoscopic TiO2 membranes

doi:10.1016/S0927-0248(97)00229-8

Solar Energy Materials and Solar Cells

Volume 51, Issues 3–4, 27 February 1998, Pages 291-303

https://doi.org/10.1016/S0927-0248(97)00229-8 Get rights and content

Abstract

The diffusional permeability of I⁻₃ ion in acetonitrile in free standing TiO₂ membrane with a porosity of 55% was examined. The apparent diffusion coefficient, D_app at 25°C of the ion was found to be 3.4×10⁻⁶ cm² ⁻¹, an order of magnitude smaller than the free diffusion at the same temperature. The temperature dependency of D_app was measured in the range 0–30°C and analysed in terms of the Walden product. The diffusional activation energy was found to be 13.5 kJ/mol. The parameters of interest for the efficiency of mesoscopic wet solar cells are discussed. A back of an envelope calculation shows that although the obstructed diffusion coefficient of the I⁻₃ ion was an order of magnitude smaller than the free diffusion the diffusional flux is still sufficient to meet a current density of 50 mA cm⁻². At incident photon flux of 1 kW m⁻² and at a photopotential of 0.6 V this would correspond to a solar energy efficiency of approximately 30%.

Introduction

A limiting factor at high light intensities in dye-sensitised thin film solar cell devices 1, 2may be the transport of charge through the electroyte. Due to the specific properties of the electrode material in such devices – the electrolyte penetrating the mesoscopic thin film all the way to the back contact – the diffusion and migration of charge carriers in the electrolyte will depend on the viscosity of the solvent but it will also be obstructed by the network formed by the nanoparticles in the mesoscopic film electrode. To get valid parameters to feed into an overall model for a solar cell based on mesoscopic thin films, we are currently studying the obstructed diffusion of reversible redox couples through free standing membranes of TiO₂. Parameters of interest in these studies are e.g., particle size, film thickness, porosity of the mesoscopic film and temperature. One of the most efficient and commonly used electrolyte solutions in the dye-sensitised solar cell prototypes is the iodide/triiodide (I⁻/I⁻₃) redox couple in acetonitrile.

The aim of the present work was therefore, to detemine the apparent diffusion coefficient of this electrolyte, in particular I⁻₃, in acetonitrile in pressed free-standing TiO₂ membranes [3]. We believe that general discussion we do and the information gained will be of importance for the modelling and optimisation of not only the dye-sensitised solar cells, but also for the optimisation and performance of other devices, such as smart window devices, displays and batteries [4], based on nanostructured semiconducting film electrodes.

Section snippets

Preparation of TiO₂ membrane

The membranes of different thickness were prepared at the tip of Pyrex glass tubes (diameter 5 mm) from known amount of TiO₂ powder (P25, Degussa AG, Germany, a mixture of ca. 30% rutile and 70% anatase) by pressing with an appropriate pressure. The pressures were typically in the range 200–800 N cm⁻². The pressing was performed by introducing titanium dioxide powder between Kel-F surfaces of a pressing tool. The thickness of the membrane was varied by either applying the same pressure on

The TiO₂ membrane

The P25 Degussa powder has frequently been used for the preparation of film electrodes for solar cells 2, 5. Those films were prepared from suspensions of TiO₂ powder in which a detergent and a carbowax were used to stabilise the solution. The porosity of such films are typically around 50% and in the same range as the films prepared in the present investigation. It was found that when increasing the amount of powder to get thicker films the porosity at constant pressure was increased. A 350 μm

Summary

In TiO₂ mesoscopic membranes with porosity 55%, prepared by pressing Degussa powder P25 into free-standing films the apparent diffusion coefficient of I⁻₃ dissolved in acetonitrile at 25°C is typically an order of magnitude lower than the free diffusion in the same solvent. The apparent diffusion coefficient is however sufficiently large to meet the demands for current efficiencies of a mesoscopic wet solar cell.

Under the simple assumptions that the photoactive porous film was of thickness of 10

Acknowledgements

We are grateful to The EU Joule II program and the Swedish Research Council for Engineering Science (TFR) for financial support of the present work. One of us Z.K. is grateful to the Swedish Institute, the Department of Physical Chemistry, Uppsala University, and Kotebe College of Teacher Education, Addis Abada, Ethiopia, for financial support, provision of laboratory facility and offer of research leave, respectively. Thanks also to Prof. Hans Vink for helpful discussions concerning migration

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¹: On leave of research from Kotebe College of Teacher Education, P.O. Box 31248, Addis Ababa, Ethiopia.

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The obstructed diffusion of the I3− ion in mesoscopic TiO2 membranes

Abstract

Introduction

Section snippets

Preparation of TiO2 membrane

The TiO2 membrane

Summary

Acknowledgements

Cells

J. Membrane Sci.

J. Membrane Sci.

J. Membrane Sci.

Nature

J. Am. Chem. Soc.

Physical Chemistry

J. Elecrochem. Soc.

J. Am. Chem. Soc.

Nature

J. Am. Chem. Soc.

Nature

J. Am. Chem. Soc.

The obstructed diffusion of the I₃⁻ ion in mesoscopic TiO₂ membranes

Preparation of TiO₂ membrane

The TiO₂ membrane