Nanostructured Materials for Electrochemical Energy Production and Storage (Nanostructure Science and Technology)

Nanostructured Materials for Electrochemical Energy Production and Storage

Nanostructure Science and Technology Series Editor: David J. Lockwood, FRSC National Research Council of Canada Ottawa, Ontario, Canada

For other titles published in this series, go to www.springer.com/series/6331

Edson Roberto Leite Editor

Nanostructured Materials for Electrochemical Energy Production and Storage

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Edson Roberto Leite Universidade Federal de S˜ao Carlos Centro de Ciˆencias Exatas e de Tecnologia Caixa Postal 676 S˜ao Carlos-SP Brazil [email protected]

Series Editor David J. Lockwood National Research Council of Canada Ottawa, Ontario Canada

ISBN: 978-0-387-49322-0 e-ISBN: 978-0-387-49323-7 DOI: 10.1007/978-0-387-49323-7 Library of Congress Control Number: 2008 941657 c Springer Science+Business Media, LLC 2009 ° All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper springer.com

Preface

The major problem facing new energy conversion and storage technologies remains device efficiency. Projects based on nanostructured materials can yield improved performance in devices involving electrochemical reactions and heterogeneous catalysis, such as fuel and solar cells, batteries, etc. Nanoscale structures dramatically alter the surface reaction rates and electrical transport throughout the material, causing a dramatic improvement in energy storage, conversion, and generation. Furthermore, the design of nanoscale materials to be applied in alternative energy devices is a predictable way to develop a wide range of new technologies for a more sustainable future. Therefore, the goal of this book is to present basic fundamentals and the most relevant properties of nanostructured materials in order to improve alternative energy devices. This book begins with a chapter by Gr¨atzel summarizing the use of mesoscopic thin films and hybrid materials in the development of new kinds of regenerative photoelectrochemical devices. Applications include high-efficiency solar cells. In chapter two, Ribeiro and Leite describe assembly and properties of nanoparticles. The chapter presents a review on the properties and main features of nanoscale materials, emphasizing the dependence of key properties on size for energy purposes. A general description is also given of nanoparticle synthesization methods (mainly oxides), focusing on advances in tailoring controlled shape nanostructures. Bueno and Gabrielli present the basic principles of nanotechnology in general and integrate fundamental electrochemistry with nanostructured materials in particular. The main focus of this chapter, therefore, is on novel strategies that exploit nanoscale architectures to enhance the efficiency of alternative energy conversion and storage devices and on the basic principles of electrochemistry governing the effects of nanoscale structures on electrodes and electrolytes. Heinzel and K¨onig summarize the impact of nanostructured materials on fuel cell technology, mainly in the area of polymer electrolyte membrane fuel cells. This chapter illustrates how nanostructured materials can modify component performance such as electrocatalyst materials and membrane.

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Preface

Dong and Dunn describe advances resulting from the use of sol-gel technology on energy storage devices. This chapter reviews the importance of aerogel nanoarchitecture in achieving high performance electrochemical properties. Results obtained with vanadium oxide aerogels are highlighted as these materials exhibit a number of desirable characteristics for secondary lithium batteries. A chapter focusing on the use of nanocomposites in electrochemical devices is presented by Schoonman, Zavyalov, and Pivkina. A wide range of metal (metal oxide)/polymer nanocomposites has been synthesized using Al, Sn, Zn, Pd, and Ti as a metal source and poly-para-xylylene (PPX) as a polymeric matrix. The properties of the nanocomposites were studied by comparing structure, morphology, electrical properties, oxidation kinetics, and electrochemical parameters. As the rapid development of nanostructured materials continues, this book illustrates the impact of this class of materials on performance improvements of alternative energy devices, particularly those based on electrochemical processes. The authors make a powerful case for nanomaterials and nanotechnology as a way to transform such alternative energy sources into significant contributors to the future global energy mix.

Contents

Recent Applications of Nanoscale Materials: Solar Cells . . . . . . . . . . . . . . . Michael Gr¨atzel

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Assembly and Properties of Nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Caue Ribeiro and Edson R. Leite Electrochemistry, Nanomaterials, and Nanostructures . . . . . . . . . . . . . . . . 81 Paulo Roberto Bueno and Claude Gabrielli Nanotechnology for Fuel Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 Angelika Heinzel and Uwe K¨onig Vanadium Oxide Aerogels: Enhanced Energy Storage in Nanostructured Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 Winny Dong and Bruce Dunn Nanostructured Composites: Structure, Properties, and Applications in Electrochemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 Joop Schoonman, Sergey Zavyalov, and Alla Pivkina Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

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Contributors

Paulo Roberto Bueno, Instituto de Qu´ımica, Departamento de F´ısico-Qu´ımica, Universidade Estadual Paulista, C. Postal 355, 14801-907, Araraquara, S˜ao Paulo, Brazil, [email protected] Winny Dong, Chemical and Materials Engineering, California State Polytechnic University, Pomona, CA 91768 Bruce Dunn, Department of Materials Science and Engineering, University of California, Los Angeles, CA 90095, USA, [email protected] Claude Gabrielli, UPR 15 du CNRS, Physique des Liquides et Electrochimie, Universit´e Pierre et Marie Curie, 4 place Jussieu, 75252 Paris, France Michael Gr¨atzel, Laboratory of Photonics and Interfaces, Ecole Polytechnique F´ed´erale de Lausanne, CH-1015, Lausanne, Switzerland, [email protected] Angelika Heinzel Centre for Fuel cell Technology (ZBT gGmbH), Carl-Benz-Str. 201, 47057 Duisburg, Germany Uwe K¨onig Centre for Fuel cell Technology (ZBT gGmbH), Carl-Benz-Str. 201, 47057 Duisburg, Germany Edson R. Leite, LIEC – Universidade Federal de S˜ao Carlos, Departamento de Qu´ımica, Rod. Washington Luiz, km 235 – 13565-905, S˜ao Carlos, SP, Brazil Alla Pivkina, Semenov Institute of Physical Chemistry, Russian Academy of Science, Kosygin st. 4, 119991, Moscow, Russia Caue Ribeiro, EMBRAPA Instrumentac¸a˜ o Agropecu´aria, Rua XV de Novembro, 1452 – 13560-970, CP 741, S˜ao Carlos, SP, Brazil Joop Schoonman, Delft University of Technology, Delft Institute for Sustainable Energy, P.O. Box 5045, 2600 GA Delft, The Netherlands, [email protected] Sergey Zavyalov, Karpov Institute of Physical Chemistry, Vorontsovo Pole, 10, 103064 Moscow, Russia

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Recent Applications of Nanoscale Materials: Solar Cells Michael Gr¨atzel

Abstract Photovoltaic cells have been dominated so far by solid state p-n junction devices made from silicon or gallium arsenide wavers or thin film embodiments based on amorphous silicon, CdTe and copper indium gallium diselenide (CIGS) profiting from the experience and material availability of the semiconductor industry. Recently there has been a surge of interest for devices that are based on nanoscale inorganic or organic semiconductors commonly referred to as “bulk” junctions due to their interconnected three-dimensional structure. The present chapter describes the state of the art of the academic and industrial development of nanostructured solar cells, with emphasis in the development of the dye-sensitized nanocristalline solar cell.

1 Introduction Photovoltaic cells have been dominated so far by solid state p–n junction devices made from silicon or gallium arsenide wavers or thin film embodiments based on amorphous silicon, CdTe and copper indium gallium diselenide (CIGS) profiting from the experience and material availability of the semiconductor industry. Recently there has been a surge of interest for devices that are based on nanoscale inorganic or organic semiconductors commonly referred to as “bulk” junctions due to their interconnected three-dimensional structure. Research in this field has gained significant momentum with hundreds of groups being active to develop new mesoscopic solar cell variants and improve their performance. These devices are formed from junctions of, for example, nanocrystalline, inorganic oxides and chalcogenides or fullerenes with organic electrolytes, ionic liquids, or inorganic and organic hole conductors and conducting polymers, offering the prospect of very M. Gr¨atzel Laboratory of Photonics and Interfaces, Ecole Polytechnique F´ed´erale de Lausanne, CH-1015, Lausanne, Switzerland e-mail: [email protected] E.R. Leite (ed.), Nanostructured Materials for Electrochemical Energy Production and Storage, Nanostructure Science and Technology, DOI 10.1007/978-0-387-49323-7 1, c Springer Science+Business Media LLC 2009 

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low cost fabrication without expensive and energy-intensive high-temperature and high-vacuum processes. They are compatible with flexible substrates and a variety of embodiments and appearances to facilitate market entry, both for domestic devices and in architectural or decorative applications. Thus, it appears possible now to depart completely from the concept of classical, flat p–n junction cells to replace them with interpenetrating network junctions. The nanoscale morphology produces an interface with a huge area, endowing these systems with extraordinary optoelectronic properties. Despite their disordered structure these novel solar cells have shown strikingly high conversion efficiencies competing with those of conventional devices while at the same time offering advantages of ease of production, lower cost and shorter energy payback times. The first embodiment and prototype of this family of devices is the dye-sensitized solar cell (DSC), invented in the author’s laboratory at the Ecole Polytechnique F´ed´erale de Lausanne [1–3]. At the heart of the DSC is a mesoscopic film composed by, for example, nanoparticles, nanorods or nanotubes of a wide band gap semiconductor oxide (typically ZnO, SnO2 or TiO2 ) that is covered by a monolayer of sensitizer. During the illumination of the cell the photo-excited dye molecules adsorbed on the nanoparticle surface inject electrons into the conduction band of the oxide. The sensitizer is regenerated by hole injection into a redox electrolyte or a solid-state p-type conductor. Although many organic or inorganic sensitizers, including semiconductor quantum dots are known to date and their performance is rapidly improving, ruthenium poly-pyridyl complexes have maintained so far a lead as the most efficient and stable sensitizers. Published first in 1993 [4], cisRuL2 (SCN)2 (L = 2, 2 -bipyridyl-4,4 -dicarboxylic acid), coded N3 or N719 for the fully protonated or half protonated form, respectively, has become the paradigm of a charge transfer sensitizer capturing a large domain of the visible spectrum. The structure of the N3 dye is shown in Fig. 1.

Fig. 1 Structure of the N3 dye cis − RuL2 (SCN)2 (L = 2,2-bipyridyl-4,4 dicarbo-xylate). See Color Plates

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Incident photon-to-electron conversion efficiencies (IPCEs) attaining almost unity have been obtained with this sensitizer in the wavelength range near its absorption maximum corresponding to quantum yields for electric current generation near 100% when light losses due to the conducting glass current collector are taken into account [4–8]. The DSC is the only solar cell that uses a molecule to absorb photons and convert them into electric charges without the need of excitonic transport. It also is the only photovoltaic device that separates the two functions of solar light harvesting and charge carrier transport, whereas conventional cells perform both operations simultaneously resulting in stringent demands on the purity of materials and much higher production costs. In the DSC, the molecular sensitizer or semiconductor quantum dot is placed at the interface between an electron and hole conducting material. Upon photo-excitation the negative charge carriers are injected by the excited dye into an electron (n) conductor and the positive charges in a hole (p) conductor or an electrolyte. Therefore, the electrons and holes are charges that move in different phases to the front and back contacts of the photocell. Their recombination occurs across the interface separating the electron and the hole conductor materials. The open circuit photo-voltage developed by the cell corresponds to the difference of the quasi-Fermi level of the electrons and holes in their respective transport medium. The great advantage of this cell configuration is that the solar energy conversion process involves only majority charge carriers. Electron and holes are generated in different phases and their recombination across the interface is blocked to a significant extent by the presence of the sensitizer. However, in order to harvest solar light efficiently, the use of a bulk or interpenetrating network junction of mesoscopic dimension is necessary since the optical cross section of a dye or QD is much smaller than the area it occupies. The challenge one faces with these systems is to make adequate provisions for contacting a large area of the junction by a suitable hole conductor or electrolyte in order to regenerate the sensitizer following lightinduced electron injection and conduct the positive carriers to the back contact of the photovoltaic cell. The validated solar to electric power conversion efficiency of the liquid electrolyte-based DSC stands currently at 11.1% under standard reporting conditions (AM1.5 global sunlight at 1,000 W/m2 intensity, 298 K temperature) [9] rendering it a credible alternative to conventional p–n junction photovoltaic devices. Solid-state DSC equivalents using organic hole conductors have reached over 5% efficiency with ruthenium-based sensitizers [10] and over 4% with organic dyes [11] whereas nanocomposite films composed of inorganic materials, such a TiO2 and CuInS2 have achieved efficiencies between 5 and 6% [12, 13]. New dyes showing increased optical cross sections and capable of absorbing longer wavelengths are currently under development. Similarly, the performance of mesoscopic TiO2 films employed as electron collectors is benefiting greatly from recent advances in nanomaterial research. Taking advantage of the highly transparent nature of the sensitized nanocrystalline oxide film, tandem structures employing a DSC and CIGS top and bottom cell reached a conversion efficiency of >15% [14].

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Obtaining long-term stability for DSCs at temperatures of 80–85◦ C had remained a major challenge for many years and has only been achieved in 2003 [15]. Solvent-free electrolytes such as ionic liquids or solid polymers have been introduced to provide systems that are suitable for practical applications. Stabilization of the interface by using self-assembly of hydrophobic sensitizers alone or in conjunction with amphiphilic co-adsorbents has been particularly rewarding. Stable operating performance under both prolonged thermal stress (at 85◦ C) and AM 1.5 light soaking conditions (at 60◦ C) has now been demonstrated [16–18]. These recent devices retained 98% of their initial power conversion efficiency after 1,000 h of high-temperature aging. Long-term accelerated testing shows that DSCs can function in a stable manner for over 20 years, if sealing and the interfacial engineering issues are properly addressed. The present review is on the state of the art of the academic and industrial development of nanostructured solar cells, with emphasis being placed on the work performed in the author’s laboratory.

2 Band Diagram and Operational Principle of Nanocrystalline Solar Cells Figure 2 shows a band diagram of the dye-sensitized nanocrystalline solar cell (DSC) and explains its operational principle. Sunlight is harvested by the sensitizer that is attached to the surface of a large band gap semiconductor, typically a film constituted by titania nanoparticles. Photo-excitation of the dye results in the Conducting glass TiO2

Injection

Dye

Electrolyte

Cathode

S*

−0.5

hν

0 E vs NHE (V) 0.5

Red

Maximum Voltage Mediator Ox Diffusion

1.0

S /S+ e-

e-

Fig. 2 Energy band diagram of the DSC. Light absorption by the dye (S) produces an excited state (S∗ ) that injects an electron into the conduction band of a wide band gap semiconducting oxide, such as TiO2 . The electrons diffuse across the oxide to the transparent current collector made of conducting glass. From there they pass through the external circuit performing electrical work and re-enter the cell through the back contact (cathode) by reducing a redox mediator (ox). The reduced form of the mediator (red) regenerates the sensitizer closing the cyclic conversion of light to electricity. See Color Plates

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injection of electrons into the conduction band of the oxide. The dye is regenerated by electron donation from an organic hole conductor or an electrolyte that is infiltrated into the porous films. The latter contains most frequently the iodide/triiodide couple as a redox shuttle although other mediators such as cobalt(II/III) complexes [19, 20] or the TEMPO/TEMPO + redox couple [21] have also been developed + recently as an alternative to the I− /I− 3 system. Reduction of S by iodide regenerates the original form of the dye under production of triiodide ions. This prevents any significant buildup of S+ , which could recapture the conduction band electron at the surface. The iodide is regenerated in turn by the reduction of the triiodide ions at the counter electrode, where the electrons are supplied by migration through the external load completing the cycle. Thus, the device is regenerative producing electricity from light without any permanent chemical transformation. The voltage produced under illumination corresponds to the difference between the quasi-Fermi level of the electron in the solid and the redox potential of the electrolyte or the work function of the hole conductor.

3 The Importance of the Nanostructure The nanocrystalline morphology of the semiconductor film is essential for the efficient operation of all mesoscopic photovoltaic devices. A whole range of nanostructures has been tested so far ranging from simple assemblies of nanoparticles to nanorods [19], tetrapods [20] and nanotubes [21, 22]. The use of mesocopic interpenetrating network junctions has also overcome the fundamental problem posed by the notoriously short diffusion length of excitons or charge carriers that are encountered in organic and hybrid photovoltaic cells. For example in the well-known fullerene/polyhexylthiophene (P3HT) [23] or CdTe/P3HT [24] cells the excitons produced by light excitation of the polymer diffuse only over a distance of a few nanometers during their lifetime while the light absorption length in these films is several hundred nanometers. In a flat junction geometry the excitons recombine before they reach the junction where they dissociate into electrons and holes that produce the photocurrent. On the other hand, in a mesoscopic junction, the diffusion path to reach the interface is shortened to a few nanometers allowing generation of charge carriers from the excitons before they recombine. The use of interpenetrating network junctions is essential for the DSC. On a flat surface a monolayer of dye absorbs at most a few percent of light because it occupies an area that is several hundred times larger than its optical cross section. Using multi-layers of sensitizer does not offer a viable solution to this problem. Only the molecules that are in direct contact with the oxide surface would be photoactive – the remainder filtering merely the light. Apart from poor light harvesting a compact semiconductor film would need to be n-doped to conduct electrons. In this case energy transfer quenching of the excited sensitizer by the electrons in the semiconductor would inevitably reduce the photovoltaic conversion efficiency. For this reason the conversion yields obtained from the sensitization of flat electrodes

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100 nm

Fig. 3 Transmission electron microscope picture of a mesoscopic TiO2 (anatase) film. Note the bipyramidal shape of the particles having (101) oriented facets exposed. The average particle size is 20 nm

have been notoriously low. The use of nanocrystalline films to support the dye and collect the photo-injected electrons has permitted to overcome these problems resulting in a dramatic improvement of the performance of sensitized hetero-junction devices. Figure 3 shows a scanning electron microscopy picture of a mesoscopic TiO2 (anatase) layer. The particles have an average size of 20 nm and the facets exposed have mainly (101) orientation, corresponding to the anatase crystal planes with the lowest surface energy (ca. 0.5 J/m2 ). Employing such oxide nanocrystals covered by a monolayer of sensitizer as light harvesting units allows overcoming the notorious inefficiency problems, which have haunted all solar energy conversion devices based on the sensitization of wide band gap semiconductors.

3.1 Light Harvesting by a Sensitizer Monolayer Adsorbed on a Mesoscopic Semiconductor Film Consider a 10-μm thick mesoscopic oxide film composed of 20-nm-sized particles whose real surface area is over 1,000 times greater than the projected one. Because of the small size of the particles such films show high transparency and negligible

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light scattering. Lambert Beer’s law can be applied to describe the light absorption by the adsorbed dye monolayer yielding for the reciprocal absorption length.

α = σ c.

(1)

Here, σ and c are the optical absorption cross section of the sensitizer and its concentration in the mesoporous film, respectively. The value of σ can be derived from the decadic extinction coefficient ε of the sensitizer using the relation:

α = 1, 000ε (cm2 /mol).

(2)

For example, the optical cross section of the N3 dye cis–RuL2 (SCN)2 (L = 2,2bipyridyl-4,4 dicarboxylate) is 1.4 × 107 cm2 /mole at 530 nm, where it has an absorption maximum, and its concentration in the nanocrystalline film at full monolayer coverage is typically 2 × 10−4 mol/cm3 . Hence α = 2.8 × 103 cm−1 and the absorption length 1/α is 3.6 μm for 530-nm light. The light harvesting efficiency LHE is derived from the reciprocal absorption length via: LHE(λ ) = 1 − 10−d ,

(3)

where d is the thickness of the nanocrystalline film. Using d = 10 μm and α = 2.8 × 103 cm−1 one obtains LHE = 99.8%. On a flat surface the N3 dye would have only absorbed 0.3% of the incident 530-nm light. The dramatic difference of the light harvesting efficiency is illustrated by the deep coloration of the nanocrystalline TiO2 layers shown in Fig. 4, despite of the fact that they are covered only by a monolayer of sensitizer. On a flat surface the N3 dye would have remained invisible to the eye. A film exhibiting ordered mesoporous structure, such as shown in Fig. 5 has an even higher internal surface area than one that is composed of randomly associated nanoparticles [24]. Because more sensitizer is adsorbed for the same film

Fig. 4 Uptake of N3 dye by a nanocrystalline TiO2 film, which is immersed in the dye solution. The resulting deeply red-colored film is the photoactive part of the DSC. See Color Plates

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Fig. 5 Top scanning electron microscope view of an ordered mesoporous TiO2 (anatase) film produced by a block-copolymer templating method [25]

Fig. 6 Scanning electron microscope view of a film constituted of titania nanotubes. The length of the tubes is about 5 μm

thickness its concentration in the mesoscopic TiO2 layer is increased, reducing the absorption length and enhancing the absorption of solar light over that of a dyecovered layer of randomly associated colloidal TiO2 particles of the same thickness. The problem with mesoporous films of the type shown in Fig. 5 is that ordered structures can only be realized so far up to a thickness of 1 μm, which is not enough to produce cells with conversion efficiencies over 5%. One-dimensional nanostructures such as the titania nanotubes shown in Fig. 6 and ZnO nanorods have been the focus of much recent interest [19,21,22,26]. These studies are motivated by the expectation that the transport of charge carriers along the tubes is more facile than within a random network of nanoparticles where the

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electrons have to cross many particle boundaries. Hence, one-dimensional nanostructures should produce a lower diffusion resistance than the nanoparticle films facilitating the collection of photo-generated charge carriers.

3.2 Enhanced Red and Near IR Response by Light Containment The light harvesting by the surface adsorbed sensitizer can be further improved by exploiting light localization and optical enhancement effects. This increases the absorption of solar light in particular in the red and near IR region of the spectrum where currently used ruthenium complexes show only weak light absorption. For example, incorporating 200–400-nm-sized anatase particles enhances significantly the absorption of red or near infrared photons by the film. A scanning electron micrograph of such particles is shown in Fig. 7. These light management strategies employ scattering and photonic band gap effects [27–29] to localize light in the mesoporous structure augmenting the optical pathway significantly beyond the film thickness and enhancing the harvesting of photons in a spectral region where the optical cross section of the sensitizer is small. The benefits from using such a photon capture strategies are clearly visible below, where the light scattering layer is shown to enhance the photocurrent response of the DSC in the near IR and visible region of the solar spectrum. The gain in short circuit photocurrent through these optical containment effects can be as high as 30%.

Fig. 7 Scanning electron micrograph showing anatase crystals of ca. 400 nm size, employed as light scattering centres to enhance the red response of the DSC (courtesy of Dr. Tsuguo Koyanagi, Catalysts & Chemicals Ind. Co. Ltd., Japan). See Color Plates

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3.3 Light-Induced Charge Separation and Conversion of Photons to Electric Current The incident photon to current conversion efficiency (IPCE) sometimes referred to also as external quantum efficiency (EQE) corresponds to the number of electrons measured as photocurrent in the external circuit divided by the monochromatic photon flux that strikes the cell. The following product expresses this key parameter: IPCE(λ ) = LHE(λ )φinj ηcoll .

(4)

Here, LHE(λ ) is the light harvesting efficiency for photons of wavelength λ , φinj is the quantum yield for electron injection from the excited sensitizer in the conduction band of the semiconductor oxide and ηcoll is the electron collection efficiency. Having analyzed above the light harvesting efficiency of dye-loaded mesoscopic films we discuss now the other two parameters. The quantum yield of charge injection (φinj ) denotes the fraction of the photons absorbed by the dye that are converted into conduction band electrons. Charge injection from the electronically excited sensitizer into the conduction band of the semiconductor is in competition with other radiative or radiationless deactivation channels. Taking the sum of the rate constants of these nonproductive channels together as kdeact gives: (5) (φinj ) = kinj /(kdeact + kinj ). Typical kdeact values lie in the range from 103 to 1010 s−1 . Hence, injection rates in the picosecond range may have to be attained in order to obtain φinj values close to 1. The currently used sensitizers satisfy this requirement. These dyes incorporate functional groups e.g. carboxylate, hydroxamate or phosphonate moieties [30] that attach the sensitizer to the oxide surface. Figure 8 shows the side and top view of the RuL2 (NCS)2 (N3) sensitizer anchored to the (101) surface plane of TiO2 through coordinative binding of two carboxyl groups to the titanium ions. The green and red spheres present titanium and oxygen, respectively. Note that the left carboxylate group straddles two Ti(IV) surface ions from adjacent titanium rows corresponding to a bidentate bridging configuration while the right one forms a monodentate ester bond with one Ti(IV) ion. The structure shown represents the lowest energy configuration derived from molecular dynamics calculations [30] yielding for the area occupied by one adsorbed N3 molecule a value of 1.64 nm2 . By undergoing strong coordinative bonding with the titanium surface ions, these groups enhance electronic coupling of the sensitizer LUMO with the Ti(3d) orbitals forming the conduction band of the semiconductor. The lowest energy electronic transition for ruthenium polypyridyl complexes, such as the N3 dye is of MLCT (metal to ligand charge transfer) character, albeit with significant delocalization of the highest occupied molecular orbital (HOMO) over the SCN groups [27]. Upon optical excitation an electron is shifted from the Ru (SCN)2 moiety of the complex to the lowest unoccupied molecular orbital (LUMO) of the carboxylated bipyridine ligands moving in close vicinity to the titania surface. In a second step, the electron is injected from the LUMO into the conduction band of the nanocrystalline

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Top view

Side view

Fig. 8 Side and top view of the RuL2 (NCS)2 (N3) sensitizer anchored to the (101) TiO2 anatase surface through coordinative binding of two carboxyl groups to surface titanium ions. The green and red spheres present titanium and oxygen, respectively. Note that the left carboxylate group straddles two Ti(IV) surface ions from adjacent surface titanium rows while the right one forms an ester bond. The structure shown represents the lowest energy configuration derived from molecular dynamics calculations and the area occupied by one adsorbed N3 molecule being 1.64 nm2 . See Color Plates

1e−

Fig. 9 Calculated shift in electron density during optical excitation and charge injection from the N3 sensitizer into the conduction band of a TiO2 (anatase) cluster [31] consisting of 38 titanium ions. The surface of the cluster corresponds to the (101) plane. See Color Plates

titania particles. Figure 9 shows the results from time-dependant DFT calculations [32] indicating the vectorial charge displacement from the HOMO of the sensitizer to the T(3d) orbitals of the oxide during the optical excitation and electron injection process while Fig. 10 presents a schematic of the energy levels involved in the sensitization. Shown in Fig. 11 is the transient absorption signal following femtosecond laser excitation of the N-719 dye adsorbed on the surface of nanocrystalline titania [33]. The formation of the oxidized sensitizer and conduction band electrons due

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Fig. 10 Interfacial electron transfer involving a ruthenium complex bound to the surface of TiO2 via a carboxylated bipyridyl ligand. Orbital diagram for the forward electron injection (rate constant kf ) from the π∗ orbital of the bipyridyl ligand into the empty t2g orbitals forming the TiO2 conduction band and the backward electron transfer from the conduction band of the oxide into the Ru(III) d orbitals. See Color Plates

to heterogeneous charge transfer from the excited ruthenium complex into the conduction band of the oxide occurs on a femtosecond time scale. Figure 11 indicates that the reaction is completed within the femtosecond laser excitation pulse. Fitted data provide a cross-correlation time of 57 fs that is consistent with the instrument response measured by Kerr gating in a thin glass window. Hence, this temporal resolution does not allow determination of the rate of the injection process accurately but its time constant can be estimated as being definitely shorter than 20 fs corresponding to a rate constant kinj > 5 × 1013 s−1 . Such high rate can be rationalized in terms of electronic coupling of the π∗ sensitizer LUMO with the t2g wavefunction of the Ti(3d) conduction manifold and a large density of acceptor states in the semiconductor. Since nuclear motion in the molecule and its environment takes place within a time frame of at least 20 fs, the observed charge injection dynamics is certainly beyond the scope of vibration-mediated electron transfer models [34–39]. The process rate is therefore likely to be limited only by the electron dephasing in the solid. Interestingly, much slower injection kinetics extending into

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Fig. 11 Transient absorption signal for N719 adsorbed on nanocrystalline titania (open circle) (pump wavelength 535 nm, probe 860 nm). Fitted instrument response is 57 fs (straight line). Simulated exponential rises with time constants of 20 fs (dashed line) and 50 fs (dotted line) and convoluted with the same instrument response are shown

the picosecond time domain were observed when the sensitizer was present in an aggregated form at the surface of the titania films [40]. As the next step of the conversion of light into electrical current, a complete charge separation must be achieved. On thermodynamic grounds, the preferred process for the electron injected into the conduction band of the titanium dioxide films is the back reaction with the oxidized sensitizer. Naturally this reaction is undesirable, since instead of electrical current it merely generates heat. For the characterization of the recombination rate, an important kinetic parameter is the rate constant kb . It is of great interest to develop sensitizer systems for which the value of kinj is high and that of kb low. While for the N3-type sensitizer the forward injection is a very rapid process occurring in the femtosecond time domain, the back reaction of the electrons with the oxidized ruthenium complex occurs on a much longer timescale of micro- to milliseconds. One of the reasons for this striking behaviour is that the electronic coupling element for the back reaction is one to two orders of magnitude smaller for the back electron transfer. As the recapture of the electrons by parent sensitizer involves a d-orbital localized on the ruthenium metal the electronic overlap with the TiO2 conduction band is small and is further reduced by the spatial contraction of the wavefunction upon oxidation of Ru(II) to Ru(III). A second important contribution to the kinetic retardation of charge recombination arises from the fact that this process is characterized by a large driving force and small reorganization energy – the respective values for N-719 being 1.5 and 0.3 eV, respectively. This places the electron recapture clearly in the inverted Marcus region reducing its rate by several orders of magnitude [41, 42]. For the same reason the

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interfacial redox process is almost independent of temperature and is surprisingly insensitive to the ambience that is in contact with the film [43]. Charge recombination is furthermore inhibited by the existence of an electric dipole field at the surface of the titanium dioxide film. While the depletion layer field within the oxide is negligible due to the small size of the particles and their low doping level, a dipole layer is established at the surface by proton transfer from the carboxylic acid groups of the ruthenium complex to the oxide surface. In aprotic media, Li+ or Mg2+ are potential determining ions for TiO2 [44] as they charge the oxide positively. The local potential gradient from the negatively charged sensitizer to the positively charged oxide drives the injection in the desired direction and inhibits the electrons from re-exiting the solid. Finally, the back reaction dynamics are strongly influenced by the trapping of the conduction band in the mesoscopic film. If the diffusion of trapped electrons to the particle surface is rate determining, the time law for the back reaction is a stretched exponential [45]. If, by contrast the interfacial back electron transfer is so slow that it becomes rate determining then the back reaction follows first order kinetics.

3.4 Charge Carrier Collection The question of charge carrier percolation over the mesoscopic particle network is presently attracting a great deal of attention. This important process leads to nearly quantitative collection of electrons injected by the sensitizer. The large band gap semiconductor oxide films used in dye sensitized solar cells are insulating in the dark, however, a single electron injected in a 20-nm-sized particle produces an electron concentration of 2.4 × 1017 cm−3 . This corresponds to a specific conductivity of 1.6 ×10−4 S/cm if a value of 10−4 cm2 /s is used for the electron diffusion coefficient [46]. In reality the situation is more complex as the transport of charge carriers in these films involves trapping unless the Fermi level of the electron is so close to the conduction band that all the traps are filled and the electrons are moving freely. Therefore, the depth of the traps that participate in the electron motion affects the value of the diffusion coefficient. This explains the observation [47, 48] that the diffusion coefficient increases with light intensity. Recent Monte Carlo modelling gives an excellent description of the intricacies of the electron transport in such mesoscopic semiconductor films [49]. Of great importance for the operation of the DSC is the fact that charges injected in the nanoparticles can be screened on the mesoscopic scale by the surrounding electrolyte, facilitating greatly electron percolation [50]. The electron charge is screened by the cations in the electrolyte, which eliminates the internal field, so no drift term appears in the transport equation. Figure 12 illustrates this local screening effect. The electron motion in the conduction band of the mesoscopic oxide film is coupled with interfacial electron-transfer reaction and with ion diffusion in the electrolyte. Bisquert [51] has introduced a transmission line description to model these processes. The mesoscopic film is thought to be composed of a string of oxide nanoparticles (Fig. 12). Apart from recapture by the oxidized dye, the electrons can

Recent Applications of Nanoscale Materials: Solar Cells

Dye

RS

Dye Dye

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rtrans

rtrans

rct

rct

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cch

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cch

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15

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cch

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Electrolyte Dye Dye

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Dye Dye

Dye

Dye Dye

Dye

Dye

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Dye Dye Dye Dye

Dye Dye

Dye Dye

Dye

Dye Dye Dye

Fig. 12 Equivalent electric circuit diagram of a solar cell based on a nanocrystaline semiconductor film in contact with an electrolyte. Two transmission lines are used to model the motion of the conduction band electron motion through a network of mesoscopic semiconductor particles and the charge compensating flow of redox electrolyte. The electrical equivalent circuit treats each particle as a resistive element. Interfacial electron transfer from the conduction band of the nanoparticle to the triodide is modelled by a charge transfer resistance rct connected in parallel with their chemical capacitance cch . The latter is defined as the electric charge (measured in Coulomb) that is required to move the Fermi level of the of the semiconductor nanoparticles by 1 eV. Zd is the Warburg diffusion resistance describing the motion of triiodide ions through the porous network to the counter electrode while RCE and CCE are the charge transfer resistance for the reduction of triodiodide and the double-layer capacitance of the counter electrode, respectively The red dots present cations from the electrolyte. See Color Plates

be lost to the electrolyte by the reaction with the oxidized from of the redox mediator, e.g. triiodide ions: − − (6) I− 3 + 2e cb(TiO2 ) → 3I . The equivalent electrical circuit shown in the lower part of the figure treats each particle as a resistive element coupled to the electrolyte through the interface. The latter is presented by the chemical capacitance (cch ) connected in parallel with the resistance (rct ) for interfacial electron transfer. The red dots denote electrolyte cations. It is clear from Fig. 12 that the movement of electrons in the conduction band of the mesoscopic films must be accompanied by the diffusion of charge-compensating cations in the electrolyte layer close to the nanoparticle surface. The cations screen the Coulomb potential of the electrons avoiding the formation of uncompensated local space charge, which would impair the electron motion through the film. This justifies using an ambipolar or effective diffusion coefficient, which contains both contributions from the electrons and charge-compensating cations [48, 52] to

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e− + * 3 S /S

−

1

Oxidation Potential

2

−

e

5 + TiO2

4 S+/S

Red/Ox Couple

Fig. 13 Photo-induced processes occurring during photovoltaic energy conversion at the surface of the nanocrystalline titania films. 1: sensitizer (S) excitation by light, 2: radiative and nonradiative deactivation of the sensitizer, 3: electron injection in the conduction band followed by electron trapping and diffusion to the particle surface, 4: recapture of the conduction band electron by the oxidized sensitizer (S+ ), 5: recombination of the conduction band electrons with the oxidized form of the redox couple regenerating the sensitizer and transporting the positive charge to the counterelectrode. Grey spheres: titania nanoparticles, red dots: sensitizer, green and blue dots: oxidized and reduced form of the redox couple. See Color Plates

describe charge transport in such mesoscopic interpenetrating network solar cells although at the high electrolyte concentrations employed the electron diffusion is the dominating factor. Figure 13 summarizes the injection and recombination processes. Mastering the interface to impair the unwanted back reactions remains a key target of current research [53]. The efficient interception of recombination by the electron donor, e.g. iodide: (7) 2S + 3I− → 2S + I− 3 is crucial for obtaining good collection yields and high cycle life of the sensitizer. In the case of N3 or its amphiphilic analogue Z-907 time-resolved laser experiments have shown the interception to take place with a rate constant of about 105 –107 s−1 at the iodide concentrations that are typically applied in the solar cell [54]. This is more than a hundred times faster than the recombination rate and >108 times faster than the intrinsic lifetime of the oxidized sensitizer in the electrolyte in absence of iodide.

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To reach IPCE values close to 100%, provisions must be made to collect all photo-generated charge carriers. A key parameter is the electron diffusion length: √ Ln = De τr , (8) where De and tr are the diffusion coefficient and lifetime of the electron, respectively. Collection of charge carriers is quantitative if the electron diffusion length exceeds the film thickness (d): (9) Ln > d The film in turn needs to be significantly thicker than the light absorption length (1/α ) in order to ascertain nearly quantitative harvesting of the light in the spectral absorption range of the quantum dot or the molecular sensitizer: d > 1/α .

(10)

The thickness of the nanocrystalline layer required to satisfy the last conditions is typically of the order of a few microns depending on the optical cross section of the sensitizer and its concentration in the film as discussed earlier. A simple consideration shows that the electron collection efficiency is related to the electron transport (tτ ) and recombination time (tr ) or the respective electron transfer and recombination resistances (Rt and Rct ) by the equation [55]:   1 τt 1 1 Rt ηcc = + = 1− . (11) = 1− τt τt τr τ t + τr Rct + Rt The transport time of conduction band electron across a 10-μm thick nanocrystalline titania film is typically a few milliseconds while for good cells the recombination time is in the range of seconds. This explains why practically all the injected electrons reach the current collector before they recombine. These time constants or resistances can be measured by impedance spectroscopy, which provides a powerful tool for analyzing the circuit elements of nanocrystalline solar cells [56, 57].

3.5 Quantum Dot Sensitizers Semiconductor quantum dots (QDs) can replace dyes as light harvesting units in the DSC [58, 59]. Light absorption produces excitons or electron–hole pairs in the QD. The electron is subsequently injected in the semiconducting oxide support while the hole is transferred to a hole conductor or an electrolyte present in the pores of the nanocrystalline oxide film. Efficient and rapid hole injection from PbS quantum dots into triarylamine hole conductors has already been demonstrated and IPCE values exceeding 50% have been reached without attempting to optimize the collector structure and retard interfacial electron hole recombination [59]. QDs have much higher optical cross sections than molecular sensitizers, depending on their size. However, they also occupy a larger area on the surface of the mesoporous electrode

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decreasing the QD concentration in the film. As a result, the value of the absorption length is similar to that observed for the dye-loaded films. A recent exciting discovery shows that multiple excitons can be produced from the absorption of a single photon by a quantum dot via impact ionization (IMI) if the photon energy is three times higher than its band gap [60, 61]. The challenge is now to find ways to collect the excitons before they recombine. As recombination occurs on a femtosecond time scale, the use of mesoporous oxide collector electrodes to remove the electrons presents a promising strategy opening up research avenues that ultimately may lead to photovoltaic converters reaching efficiencies beyond the Shockley Queisar limit of 31%.

4 Photovoltaic Performance of the DSC Having dealt with the fundamental features of operation of a DSC we present now recent performance data obtained with this new type of thin film photovoltaic cell. A cross sectional view of the cell structure used in these experiments is shown in Fig. 14. Both the front and back contact are made of sodium lime float glass covered by a transparent conducting oxide. The latter material is fluorine-doped tin dioxide (FTO) having a sheet resistance of 10–15 Ω/square and has an optical transmission of 80–90% in the visible including reflection losses. The back contact is coated with a small amount of Pt to catalyze the interfacial electron transfer from the SnO2 electrode to triiodide the typical loading being 50 mg/m2 . The nanocrystalline TiO2 film is deposited by screen printing onto the FTO glass serving as front electrode followed by a brief sintering in air at 450◦ C to remove organic impurities and enhance the interconnection between the nanoparticles. Adsorption of the sensitizer monolayer occurs from solution by self-assembly. The cell is sealed using a Bynel (Dupont) hot melt. Redox electrolyte is introduced by injection through a hole on the back contact.

Fig. 14 Cross-sectional view of the embodiment of DSC used in the laboratory for photovoltaic performance measurements. See Color Plates

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4.1 Photocurrent Action Spectra Mesoscopic TiO2 films are currently prepared mainly by hydrothermal methods, which have been standardized to yield films composed of 15–20 nm-sized anatase. The mesocopic morphology has a dramatic effect on the performance of a dye-sensitized solar cell. Figure 15 compares the photocurrent action spectrum obtained from a single crystal of anatase to that of a nanocrystalline film, both being sensitized by the standard N-719 ruthenium dye i.e. cis-RuL2 (SCN)2 (L = 2,2bipyridyl-4,4 dicarboxylate). The incident photon-to-current conversion efficiency (IPCE) or external quantum efficiency is plotted as a function of wavelength. The IPCE value obtained with the single crystal electrode is only 0.13% near 530 nm, where the N-719 sensitizer has an absorption maximum, while it reaches 88% with the nanocrystalline electrode. As a consequence, in sunlight the photocurrent augments more than 1,000 times when passing from a single crystal to a nanocrystalline electrode. This striking improvement defies expectation as such large-area junctions

Fig. 15 Conversion of light to electric current by dye-sensitized solar cells. The incident photon to current conversion efficiency is plotted as a function of the excitation wavelength. Left: single crystal anatase cut in the (001) plane. Right: nanocrystalline anatase film. Pictures of the two electrodes used as current collectors are also presented. The electrolyte consisted of a solution of 0.3 M LiI and 0.03 M I2 in acetonitrile

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should fare poorly in photovoltaic energy conversion the presence of defects at the disordered surface enhancing recombination of photo-generated charge carriers. Taking into account the optical losses in the FTO glass that serve as a front contact, the conversion of incident photons is practically quantitative in the 500– 600 nm range were the sensitizer has an absorption maximum. It is apparent from (5) that the light harvesting, electron injection- and charge carrier collection efficiency must be close to unity to achieve this result. Impedance studies have shown the diffusion length of the conduction band electrons in the DSC to be typically in the 20–100-μm range. This exceeds the thickness of the nanocrystalline TiO2 film explaining why all photo-induced charge carriers can be collected.

4.2 Overall Conversion Efficiency Under Global AM 1.5 Standard Reporting Condition The overall conversion efficiency of the dye-sensitized cell is determined by the photocurrent density measured at short circuit (JSC ), the open-circuit photo-voltage (Voc ), the fill factor of the cell (FF) and the intensity of the incident light (Is ).

ηglobal = Jsc ×Voc × f f /Is .

(12)

Under full sunlight (air mass 1.5 global, intensity Is = 1, 000 W/cm2 ), short circuit photo-currents ranging from 16 to 22 mA/cm2 are reached with state-of-the art ruthenium sensitizers, while Voc is 0.7–0.86 V and the fill factor values 0.65–0.8. A certified overall power conversion efficiency of 10.4% was attained [62] in 2001. A new record efficiency over 11.2% was achieved recently [3], and Fig. 16 shows the current voltage curve obtained with this cell.

Fig. 16 Photocurrent density vs. voltage curve for a DSC employing the N-719 dye adsorbed on a double layer of nanocrystalline TiO2 and scattering particles. The iodide/triiodide-based redox electrolyte employed a mixture of acetonitrile and valeronitrile as a solvent. The conversion efficiency in AM 1.5 sunlight was 11.18%

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4.3 Increasing the Open Circuit Photovoltage We have identified additives, such as guanidinium ions, which are able to suppress the dark current at the titania electrolyte junction. Although these effects remain yet to be fully understood it appears that these ions assist the self-assembly of dye molecules at the TiO2 surface, rendering it more impermeable and reducing in this fashion the dark current of the cell. In addition guanidinium butyric acid was found to suppress the number of surface states acting as a recombination centers [63]. The ruthenium dye N-719 i.e. cis-RuL2 (SCN)2 (L = 2,2-bipyridyl-4,4 dicarboxylate) is adsorbed at the TiO2 surface via two of the four carboxylate groups. The spatial configuration of the adsorbed dye at the (111) oriented surface of the TiO2 nanocrystals has been assessed by FTIR analysis and molecular dynamics calculation. The dye monolayer is disordered and the lateral repulsion of the negatively charged dye molecules is attenuated by spontaneous co-adsorption of cations. It is desirable to increase the order of the dye monolayer at the interface and render it denser. The goal here is to make the dye layer insulating in order to block the dark current across the interface. The resulting gain in open circuit voltage can be calculated from the diode equation: Voc = (nRT /F) ln[(isc /io ) − 1],

(13)

where n is the ideality factor, whose value is between 1 and 2; io is the reverse saturation current and R and F are the ideal gas and Faraday’s constant, respectively. Increasing the injection and lowering the recombination rates are critical for maximizing the open circuit voltage of a cell as shown by (11). Using 1.5 as a value for the ideality factor in DSC, the reduction of the dark current by a factor of 10 would result in a voltage increase of 90 mV, boosting the conversion efficiency of the cell by at least 15%. The fact that the dye itself blocks the dark current of the DSC has been confirmed recently [64].

5 Development of New Sensitizers and Redox Systems While the improvements in DSC performance obtained recently are remarkable, it would be very difficult to reach much higher efficiencies with the standard N-719 sensitizer unless the redox system is changed. Because of the mismatch of the redox levels of the N-719 and the iodide/triiodide couple the regeneration reaction of the sensitizer consumes too large a fraction of the absorbed photon energy as is apparent from the band diagram shown in Fig. 2. Work on alternative redox systems whose Nernst potential is better adapted to that of the N-719 dye is currently being done [65, 66] and should ultimately lead to DSCs exhibiting Voc values above 1 V. Alternatively, if the present iodide-based redox system is maintained, introducing panchromatic sensitizers or dye mixtures can boost the efficiency of cells further. To give 15% conversion efficiency, these should be designed to yield at least 24 mA/cm2 short circuit current under full sunlight and fill factor as well as open

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M. Gr¨atzel COOH O HOOC

N N

N Ru S

C

N

N N C S

O

Scheme 1 K-19 sensitizer with an extended p-system in one of its ligands. See Color Plates

circuit voltage values similar to those that are presently obtained. To achieve such photocurrents the light harvesting in the 650–900-nm range needs to be significantly improved. Scheme 1 shows the structure of a heteroleptic ruthenium complex coded K-19, which due to the extension of the π-system in one of its ligands has an enhanced absorption coefficient. An analogue of this dye with long alkyl side chains on the bipyridyl group, named Z-907, showed excellent light conversion performance and cell stability [16]. These dyes of Z-series have proved themselves to be very useful to solid-state DSC, where their hydrophobic nature indeed became a helpful factor. Subsequently, they enhanced the performance of systems containing ionic electrolytes and hole conductors. The K-19 dye also exhibits excellent conversion yield and stability [17, 18].

6 Solid-State DSCs Solid-state DSCs employing the lithium-coordinating K-67 dye and the holeconductor spiro-OMeTAD [67] in conjunction with additives such as Li(CF3 SO2 )2N, and t-butyl pyridine have shown 54% energy conversion efficiency under AM 1.5 global illumination [10]. Here again the self-assembly of the dye molecules to a dense layer on the TiO2 surface plays an important role, with the COOH groups serving as anchors and the lithium coordination to the sensitizer affording local electrostatic screening assisting charge separation.

7 DSC Stability While long-term accelerated light soaking carried tests have confirmed the intrinsic stability of current DSC embodiments [67] stable operation under high-temperature stress 80–85◦ C has been achieved only recently by judicious molecular engineering of the sensitizer used in conjunction with a robust and non-volatile electrolyte.

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7.1 Criteria for Long-Term Stability of the Dye Figure 17 shows the coupling of two redox cycles involved in the solar energy conversion process. In analogy to natural photosynthesis, light acts as an electron pump initiating charge flow from the sensitizer via the conduction band of the oxide semiconductor to the external circuit. The dye is regenerated by electron donation from iodide producing iodine or triiodide. The latter diffuses to the counter electrode where the electrons injected into the circuit by the sensitizer reduce it back to iodide, thus closing the two redox cycles involved in the energy conversion process. The turnover frequency of the sensitizer is 25 s−1 in full sunshine and during 20 years of outdoor service it must support 100 million turnovers. Scheme 2 illustrates the catalytic cycle that the sensitizer performs during cell operation. Critical for stability are any side reactions that may occur from the excited state S* or the oxidized state of the dye (S+ ), which would compete with electron injection from the excited dye into the conduction band of the mesoscopic oxide and with the regeneration of the sensitizer. These destructive channels are assumed to follow first or pseudo-first order kinetics and are assigned the rate constants k1 and k2 . By introducing the two branching ratios, P1 = kinj /(k1 + kinj ) and P2 = kreg /(k2 + kreg ) where kinj and kreg are the first order or pseudo-first order rate constants for the injection and regeneration processes, respectively. The fraction of the sensitizer molecules that survive one cycle can be calculated as the product P1 × P2 . Also, the upper limit for the sum of the two branching ratios can be calculated for a cell operation of 20 years and is shown to be 1 × 10−8 . The turnover frequency, averaged over seasons and day–night time, of the dye has been derived as 0.155 s−1 .

Light

I

Conduction Band

–

e–

e–

S

1

2 I2

S* e –

e–

e–

S+ Semiconducting Membrane

e– Electrical Work

Fig. 17 The two coupled redox cycles involved in the generation of electricity from light in a dye-sensitized solar cell. See Color Plates

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Scheme 2 The catalytic cycle of the sensitizer during cell operation

7.2 Kinetic Measurements As indicated earlier, for most of the common sensitizers the rate constant for electron injection from the excited state to the conduction band of the TiO2 particles is in the femtosecond range. Assuming kinj = 1 × 1013 s−1 , a destructive side reaction with k1 < 105 s−1 could be tolerated. Ruthenium sensitizers of the N3 type readily satisfy this condition. They can undergo photo-induced loss or exchange of the thiocyanate ligand, which however occurs at a much lower rate than the 105 s−1 limit. It is also debatable whether this pathway is destructive as the product formed still acts as a charge transfer sensitizer. In ethanolic solution prolonged photolysis of N3 dye leads to sulphur loss and formation of the cyanato-ruthenium complex probably via photoxidation by oxygen. However, this reaction is not observed when the dye is adsorbed on oxide surfaces. Precise kinetic information has also been gathered for the second destructive channel involving the oxidized state of the sensitizer, the key parameter being the ratio k2 /kreg of the rate constants for the degradation of the oxidized form of the sensitizer and its regeneration. The S+ state of the sensitizer can be readily produced by chemical or electrochemical oxidation and its lifetime determined independently by absorption spectroscopy. Data from a recent study of Z-907 shows that the formation of its oxidized form occurs over the first 8–10 min after the addition of an oxidant. The subsequent decay occurs with a lifetime of 75 min corresponding to k2 = 2.2 × 10−4 s−1 . The regeneration rate constant for this sensitizer in a typical iodide/triiodide redox electrolyte is at least 2 × 105 s−1 . Hence the branching ratio is about 10−9 that is well below the limit of 10−8 admitted to achieve the 100 million turnovers and a 20-year lifetime for the sensitizer.

7.3 Recent Experimental Results on DSC Stability Many long-term tests have been performed with the N3-type ruthenium complexes confirming the extraordinary stability of these charge transfer sensitizers. For example, a European consortium financed under the Joule program [41,42] has confirmed

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cell photocurrent stability during 10,000 h of light soaking at 2.5 sun corresponding to ca. 56 million turnovers of the dye without any significant degradation. These results corroborate the projections from the kinetic considerations made earlier. A more difficult task has been to reach stability under prolonged stress at higher temperatures, i.e. 80–85◦ C. Recent stabilization of the interface by using self-assembly of sensitizers in conjunction with amphiphilic coadsorbents has been particularly rewarding by allowing the DSC to meet for the first time the specifications laid out for outdoor applications of silicon photovoltaic cells. For example, the new amphiphlic sensitizer K-19 shows increased extinction coefficients due to extension of the π conjugation of the hydrophobic bipyridyl and the presence of electrondonating alkoxy groups. Taking advantage of the enhanced optical absorption of this new sensitizer and using it in conjunction with decylphoshponic acid (DPA) as co-adsorbent and a novel electrolyte formulation, a ≥ 8% efficiency DSC has been realized showing strikingly stable performance under both prolonged thermal stress and light soaking [16]. Hermetically sealed cells were used for long-term thermal stress test of cells stored in the oven at 80◦ C. The VOC of such a device drops only by 25 mV during 1,000-h aging at 80◦ C while there was a ∼70-mV decline for a device stained with the K-19 sensitizer alone. The stabilizing effect of the DPA is attributed to the formation of a robust and compact molecular monolayer at the mesoscopicTiO2 surface, reducing the amount of adsorbed water and other interfering impurities. This stabilization of the VOC allowed the solar cell to sustain the high conversion efficiency during extended heat exposure [16]. Figure 18 shows results from a recent long-term illumination experiment carried out at Dyesol with two cells over a period of close to 14 months. After 10,000 h of continuous illumination 0.56 million coulombs of charge had passed per square centimeter of electrode surface corresponding to a turnover number of 60 million. During this time the measured JSC increased from initially 12 to 15 mA/cm2 while

Fig. 18 Temporal evolution of short circuit photocurrent and open circuit photo-voltage under long-term light soaking of a Z907-sensitized DSC using a non-volatile electrolyte (courtesy of Dyesol)

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the Voc decreased slightly from 0.72 to 0.65 V. The opposite change of Jsc and Voc reflects probably a small positive shift of flat-band potential of the mesoporous titania film under the thermal stress, which can result in a net enhancement of photoinduced charge separation efficiency in the DSC.

8 First Large-Scale Field Tests and Commercial Developments During recent years industrial interest in the dye-sensitized solar cell has surged and the development of commercial products is progressing rapidly. A number of industrial corporations, such as G24 Innovations (http://www.g24i.com), Aisin Seiki in Japan, and well as Solaronix in Switzerland are actively pursuing the development of both flexible- and glass-based modules. Particularly interesting are applications in building integrated photovoltaic elements such as electric power-producing glass tiles. The Australian company Dyesol (http://www.dyesol.com) has produced such tiles on a large scale for field testing and several buildings have been equipped with a wall of this type. Aisin Seiki in Japan in collaboration with Toyota Research laboratory has started DSC prototype production. The layout of these modules is shown in Fig. 19. Note the monolithic design is using carbon as interconnect and cathode material to keep the cost down.

Fig. 19 Production of DSC prototypes by Aisin Seiki in Japan. Note the monolithic design of the PV modules and the use of carbon as interconnect and counter electrode material. The red dye is related to N-719 while the black dye has the structure RuL (NCS)3 where L = 2, 2 , 2 -terpyridyl4,4, 4 tricarboxylic acid. See Color Plates

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Field tests of such modules have already started several years go and the results of these tests revealed advantages of the DSC with regards to silicon panels under realistic outdoor conditions. Thus, for equal rating under standard test conditions (STC) the DSC modules produced 20–30% more energy than the polycrystalline silicon (pc-Si) modules [68]. The superior performance of the DSC can be ascribed to the following factors: • The DSC efficiency is practically independent of temperature in the range of 25–65◦ C while that of mono and pc-Si declines by ca. 20% over the same range. • Outdoor measurements indicate that the DSC exhibits lower sensitivity to light capture as a function of the incident angle of the radiation, although this needs to be further assessed. • The DSC shows higher conversion efficiency than pc-Si in diffuse light or cloudy conditions. While it is up to the commercial supplier to set the final price for such modules it is clear that the DSC shares the cost advantage of all thin film devices. In addition it uses only cheap and readily available materials [26]. Finally, in contrast to amorphous silicon and CIGS cells the DSC avoids high vacuum production steps that are very cost intensive. Given these additional advantages at comparable conversion efficiency, module costs well below 1 are realistic targets even for plants having well below GW capacity. The DSC has thus become a viable contender for large-scale future solar energy conversion systems on the bases of cost, efficiency, stability and availability as well as environmental compatibility. These DSC panels have been installed in the walls of the Toyota dream house shown in Fig. 20, offering a building-integrated source of solar power to the inhabitants.

The Toyota Dream House

DSC made by AISIN -SEIKI

Fig. 20 The Toyota “Dream House” featuring DSC panels made by Aisin Seiki. For details see web announcement http://www.toyota.co.jp/jp/news/04/Dec/nt04 1204.html. See Color Plates

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Fig. 21 First commercial flexible lightweight cell produced by G24 Innovation on a large scale for us as telephone chargers. See Color Plates

G24 innovation has been the first to realize large-scale, role-to-role production of lightweight flexible cells, which are sold presently on the market for mobile telephone charging. A photograph of such a cell is shown in Fig. 21.

9 Future Prospects Reaching much beyond 12% conversion efficiency for DSC, by relying mainly on panchromatic and IR absorbing dyes or surface modifications will require enhanced light collection in the 700–900-nm region. An alternative and promising approach will be the use of a tandem concept, where the top and bottom cells are judiciously chosen to absorb complimentary components of the available light including the IR region. Such a device was recently tried in our laboratory and obtained 15% conversion efficiency

10 Summary Using a principle derived from natural photosynthesis, mesoscopic injection solar cells and in particular the DSC have become a credible alternative to solid-state p–n junction devices. Conversion efficiencies over 11% and 15% have already been

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obtained with single junction and tandem cells, respectively, on the laboratory scale, but there is ample room for further amelioration. Future research will focus on improving the Jsc by extending the light response of the sensitizers in the near IR spectral region. Substantial gains in the Voc are expected from introducing ordered oxide mesostructures and controlling the interfacial charge recombination by judicious engineering on the molecular level. Hybrid cells based on inorganic and organic hole conductors are an attractive option in particular for the flexible DSC embodiment. Nanostructured devices using purely inorganic components will be developed as well. The mesoscopic cells are well suited for a whole realm of applications ranging from the low power market to large-scale applications. Their excellent performance in diffuse light gives them a competitive edge over silicon in providing electric power for stand-alone electronic equipment both indoor and outdoor. Application of the DSC in building integrated PV has already started and will become a fertile field of future commercial development. Acknowledgements Financial support from the EU and Swiss sources (ENK6-CT2001-575 and SES6-CT-2003-502783), as well as the United States Airforce (USAF contract No. FA8655-0313068) is acknowledged.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

B.O’ Regan, M. Gr¨atzel, Nature 1991, 335, 7377 M. Gr¨atzel, Nature 2001, 414, 338–344 M. Gr¨atzel, Chem. Lett. Chem. Lett. 2005, 34, 8–13 M.K. Nazeeruddin, A. Kay, I. Rodicio, R. Humphrey-Baker, E. M¨uller, P. Liska, N. Vlachopoulos, M. Gr¨atzel, J. Am. Chem. Soc. 1993, 115, 6382 M. Gr¨atzel, J. Photochem. Photobiol. A: Chem. 2004, 164, 3–14 M. Gr¨atzel, Inorg. Chem. 2005, 44, 6841 M.K. Nazeeruddin, F. De Angelis, S. Fantacci, A. Selloni, G. Viscardi, P. Liska, S. Ito, B. Takeru, M. Gr¨atzel, J. Am. Chem. Soc. 2005, 127, 16835 Q. Wang, S. Ito, M. Gr¨atzel, F. Fabregat-Santiago, I. Mora-Sero, J. Bisquert, T. Bessho, H. Imai, J. Phys. Chem. B 2006, 110, 25210 Y. Chiba, A. Islam, Y. Watanabe, R. Komiya, N. Koide, L. Han, Jpn. J. Appl. Phys. Part 2, 2006, 45, 24–28 H.J. Snaith, M. Gr¨atzel, Nano. Lett. 2007, 7, 3372–3376 U. Schmidt-Mende, R. Bach, T. Humphry-Baker, H. Horiuchi, S. Miura, S. Ito, M. Uchida, Adv. Mat. 2005, 17, 813–815 M. Nanu, J. Schoonman, A. Goossens, Adv. Mat. 2004 16, 453. M. Nanu, J. Schoonman, A. Goossens, Adv. Funct. Mat. 2005, 15, 95 P. Liska, R. Thampi, D. Br´emaud, D. Rudmann, H.M. Upadhyaya, A.N. Tiwari, M. Gr¨atzel. Appl. Phys. Lett. 2006, 88, 203103 P. Wang, S.M. Zakeeruddin, J.E. Moser, M.K. Nazeeruddin, T. Sekiguchi, M. Gr¨atzel Nat. Mat. 2003, 2, 402 P. Wang, C. Klein, R. Humphry-Baker, S.M. Zakeeruddin, M. Gr¨atzel, Appl. Phys. Lett. 2005, 86, 123508 D. Kuang, C. Klein, S. Ito, J.E. Moser, R. Humphry-Baker, N. Evans, F. Duriaux, C. Gr¨atzel, S. M. Zakeeruddin, M. Gr¨atzel, Adv. Mater. 2007, 19, 1133 D. Kuang, C. Klein, Z. Zhang, , S. Ito, J-E. Moser, S.M. Zakeeruddin, M. Gr¨atzel, Small 2007, 3, 2094–2102

30

M. Gr¨atzel

19. E. Galoppini, J. Rochford, H. Chen, G. Saraf, Y. Lu, A. Hagfeldt, G. Boschloo, J. Phys. Chem. B 2006, 110, 16159–16161 20. L. Fang, J.Y. Park, Y. Cui, P. Alivisatos, J. Shcrier, B. Lee, L.W Wang, M. Salmeron, J. Chem. Phys. 2007, 127, 184704/1–184704/6 21. K. Shankar, J. Bandara, M. Paulose, H. Wietasch, O.K. Varghese, G.K. Mor, T.J. LaTempa, M. Thelakkat, C.A. Grimes, Nano Lett. 2008, 8, 1654–1659 22. J.M. Macak, A. Ghicov, R. Hahn, H. Tsuchiya, P. Schmuki, J. Mat. Res. 2006, 21, 2824–2828 23. G. Dennler, N.S. Sariciftci, C.J. Brabec, Semiconducting Polym. (2nd Edition) 2007, 2 455–530 24. W.U. Huyn, J.J. Dittmer, A.P. Alivisatos, Science 2002, 295, 2425 25. M. Zoukalova, A. Zoukal. L. Kavan, M.K. Nazeeruddin, P. Liska, M. Gr¨atzel Nanolett. 2005, 5, 1789–1792 26. M. Law, L.E. Greene, J.C. Johnson, R. Saykally, P. Yang, Nat. Mat. 2005, 4, 455–459 27. S. Nishimura, N. Abrams, B. Lewis, L.I. Halaoui, Th.E. Mallouk, K.D. Benkstein, J. van de Lagemaat, J A.J. Frank, J. Am. Chem. Soc. 2003, 125, 6306 28. L.I. Halaoui, N.M. Abrams, T.E. Mallouk, J. Phys. Chem. 2005, 109, 6334 29. S. Hore, P. Nitz, C. Vetter, C. Prahl, M. Niggemann, R. Kern, Chem. Comm. 2005, 15, 2011 30. V. Shklover, M.K. Nazeeruddin, M. Gr¨atzel, Yu.E. Ovshinikov. Appl. Organometallic Chem. 2002, 16, 635–647 31. F. De Angelis, S. Fantacci, A. Seloni, Md.K. Nazeeruddin, M. Gr¨atzel, J. Am. Chem. Soc. 2007, 129, 14156 32. A. Hagfeldt, M. Gr¨atzel, Acc. Chem. Res. 2000, 33, 269–277 33. D. Kuang, S. Ito, B. Wenger, C. Klein, J.-E. Moser, R. Humphry-Baker, S.M. Zakeeruddin, M. Gr¨atzel, J. Am. Chem. Soc. 2006, 128, 4146–4154 34. Y. Tachibana, J.E. Moser, M. Gr¨atzel, D.R. Klug, J.R. Durrant, J. Phys. Chem. 1996, 100, 20056 35. J.E. Moser, M. Gr¨atzel, Chimia 1998, 52, 160 36. G. Benk¨o, J. Kallioinen, J.E.I. Korppi-Tommola, A.P. Yartsev, V. Sundstr¨om, J. Am. Chem. Soc. 2002, 124, 489 37. J. Kallioinen, G. Benk¨o, V. Sundstr¨om, J.E.I. Korppi-Tommola, A.P. Yartsev, J. Phys. Chem. B, 2002, 106, 4396 38. G. Benk¨o, J. Kallioinen, P. Myllyperki¨o, F. Trif. J.E.I. Korppi-Tommola, A.P. Yartsev, V. Sundstr¨om, J. Phys. Chem. B. 2004, 108, 2862 39. K. Schwarzburg, R. Ernstorfer, S. Felber, F. Willig, Coord. Chem. Rev. 2004, 248(13–14), 1259–1270 40. B. Wenger, M. Gr¨atzel, J.E. Moser, Am. Chem. Soc. 2005, 127, 12150–12151 41. J.M. Lanzafame, R.J.D. Miller, A.A. Muenter, B.A. Parkinson, J. Phys. Chem. 1992, 96, 2820 42. R. Huber, J.E. ’Moser, M. Gr¨atzel, J. Wachtveitl, Proc. SPIE 2003, 5223, 121 43. J.E. Moser, and M. Gr¨atzel, Chem. Phys. 1993, 176, 493 44. G. Redmond, and D. Fitzmaurice, J. Phys. Chem. 1993, 97, 11081 45. J. Nelson, R.E. Chandler, Coord. Chem Rev. 2004, 248, 1181–1194 46. H.G. Agrell, G. Boschloo, A. Hagfeldt, J. Phys. Chem. B 2004, 108, 12388 47. M.J. Cass, A.B. Walker, D. Martinez, L.M. Peter, J. Phys. Chem. B 2005, 109, 5100 48. A.J. Frank, N. Kopidakis, J. van de Lagemaat, Coord. Chem. Rev. 2004, 248, 1165 49. M.J. Cass, F.L. Qiu, A.B. Walker, A.C. Fisher, and L.M. Peter J. Phys. Chem. B 2003, 107 (1), 113–119 50. W. Kubo, T. Kitamura, K. Hanabusa, Y. Wada, S. Yanagida, Chem. Commun. 2002, 374-375 51. J. Bisquert, J. Phys. Chem. B 2002, 106, 325–333 52. S. Nakade, W. Kubo, Y. Saito, T. Kanzaki, T. Kitamura, Y. Wada, S.J. Yanagida, Phys. Chem. B 2003, 107, 4374–4381 53. P. Wang, S.M. Zakeeruddin, J.E. Moser, R. Humphry-Baker, P. Comte, V. Aranyos, A. Hagfeldt, M.K. Nazeeruddin, M. Gr¨atzel, Adv. Mat. 2004, 16, 1806 54. P. Wang, B. Wenger, R. Humphry-Baker, J.-E. Moser, J. Teuscher, W. Kantlehner, J. Mezger, E.V. Stoyanov, S.M. Zakeeruddin, M. Gr¨atzel, J. Am. Chem. Soc. 2005, 127, 18

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31

55. Q. Wang, Z. Zhang, S. M. Zakeeruddin, M. Gr¨atzel J. Phys. Chem. C 2008, 112 (17), 7084–7092 56. F. Fabregat-Santiago, J. Bisquert, G. Garcia-Belmonte, G. Boschloo, A. Hagfeldt, Solar Energy Mat. Solar Cells 2005, 87, 117 57. Q. Wang, J.-E. Moser, M. Gr¨atzel, J. Phys. Chem. B 2005, 109, 14945–14953 58. R. Plass, S. Pelet, J. Kr¨uger, M. Gr¨atzel, U. Bach. J. Phys. Chem. B 2002, 106, 7578–7580 59. A.J. Nozik, Quantum dot solar cells, Next Generation Photovoltaics 2004, 196–222 60. R. Schaller, V.I. Klimov, Phys. Rev. Lett. 2004, 92, 186601 61. M.C. Beard, K.P. Knutsen, P. Yu, J.M. Luther, Q. Song, W.K. Metzger, R.J. Ellingson, A.J. Nozik, Nano. Lett. 2007, 7, 2506–2512 62. M.K. Nazeeruddin, P. Pechy, T. Renouard, S.M. Zakeeruddin, R. Humphry-Baker, P. Comte, P. Liska, L. Cevey, E. Costa, V. Shklover, L. Spiccia, G.B. Deacon, C.A. Bignozzi, M. Graetzel, J. Am. Chem. Soc. 2001, 123, 1613–1624 63. Z. Zhang, S.M. Zakeeruddin, B.C. O’Regan, R. Humphry-Baker, M. Gr¨atzel, J. Phys. Chem. B 2005, 109, 21818–21824 64. S. Ito, P. Liska, P. Comte, R. Charvet, P. Pechy, U. Bach, L. Schmidt-Mende, S.M. Zakeeruddin, A. Kay, M.K. Nazeeruddin, M. Gr¨atzel, Chem. Comm. (Cambridge, UK) 2005, 4351–4353 65. H. Nusbaumer, S.M. Zakeeruddin, J.-E. Moser, M. Gr¨atzel, Chem. Europ. J. 2003, 9, 3756–3763 66. M. Brugnati, S. Caramori, S. Cazzanti, L. Marchini, R. Argazzi, C.A. Bignozzi, Int. J. Photoenergy 2007, 2, 80756/1–80756/10 67. A. Hinsch, J.M. Kroon, R. Kern, I. Uhlendorf, J. Holzbock, A. Meyer, J. Ferber, Prog. Photovoltaics 2001, 9, 425–438 68. T. Toyoda, T. Motohiro, Seramikkusu 2004, 39, 465–468

Assembly and Properties of Nanoparticles Caue Ribeiro and Edson R. Leite

Abstract A short review is presented on the properties and main features of nanoscale materials, emphasizing the dependence of key properties on size for energy purposes. A general description is also given about nanoparticle synthesization methods (mainly oxides), focusing on advances in tailoring controlled shape nanostructures.

1 Introduction Most of today’s energy needs are still met by fossil fuels (finite reserves). However, fossil fuels may be abandoned far earlier than generally believed in favor of clean renewable energy sources, as soon as the latter become environmentally and economically more attractive alternatives. The main problem of new energy conversion and storage technologies remains the efficiency of devices. Designs based on nanoscale-range materials can provide new or improved technologies for devices involving electrochemical reactions and heterogeneous catalysis such as fuel and solar cells, batteries, etc. Nanoscale structures dramatically alter surface reaction rates and electrical transport throughout the material, considerably improving its ability to store, convert, and generate energy. Furthermore, the design of nanoscale materials for application in alternative energy devices is a predictable way to develop a wide range of new technologies for an environmentally friendlier future. The physical and chemical properties of nanoscale materials (usually defined in the 1–100 nm range) are of immense interest and increasing importance for future technological applications. Nanoparticles or nanocrystals (in this work, the terms nanoparticles and nanocrystals are synonymous) generally display properties E.R. Leite () LIEC – Universidade Federal de S˜ao Carlos, Departamento de Qu´ımica, Rod. Washington Luiz, km 235 – 13565-905, S˜ao Carlos, SP, Brazil e-mail: [email protected] E.R. Leite (ed.), Nanostructured Materials for Electrochemical Energy Production and Storage, Nanostructure Science and Technology, DOI 10.1007/978-0-387-49323-7 2, c Springer Science+Business Media LLC 2009 

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that differ from those of bulk material. The literature provides several examples of properties, such as magnetic and optical properties, melting point, specific heat, and surface reactivity, which can be affected by particle size [1–6]. A material’s properties are usually very substantially modified in the 1–10 nm sizes. These changes are known as quantum size effects, and their origin is directly related to the type of chemical bond in the crystal [7]. The correlation between properties and particle size has been known since the nineteenth century, when M. Faraday demonstrated that the color of colloidal Au particles can be modified, changing the Au particle size [8]. However, despite the subject’s long history, interest in nanoparticles has only grown considerably over the last decade. The driving force for this increase in research activities is the ability to control a material’s properties by controlling the size and shape of crystals and the arrangement of such particles. These developments can lead to new technologies, including energy conversion [9–14], catalysis and sensors [15, 16], ultrahigh density data storage media [17–19], nanoparticle light-emitting diodes [20,21], and special pigments [22]. From the standpoint of energy, nanostructured materials offer a way for alternative energy devices such as solar and fuel cells to become truly feasible and for the performance of batteries and super-capacitors for energy storage to be dramatically improved. The future of these new technologies is strictly dependent on the development of synthetic routes to process metal, metal oxides, and semiconductor nanoparticles, as well as processes that allow such nanoparticles to be manipulated and controlled. This introductory chapter discusses basically two topics, i.e., the properties of nanoparticles or, more precisely, how size modifies a material’s properties, and how to synthesize nanocrystals with a controlled morphology. Special attention is given to fundamental subjects such as quantum confinement, phase transformation and nucleation, and growth processes.

2 Nanoparticles Surfaces The surface of a material plays a key role in many of its characteristics, ranging from chemical reaction rates to optical properties [2]. Simply stated, this is due to the fact that an inner atom in the particle will interact with other atoms in its surroundings, whereas the surface atoms do not have neighbors in a given direction [23]. This interaction enables nanoparticles to contribute substantially to the material’s surface disorder and, hence, to its properties. Gilbert and coworkers [24] applied wide-angle X-ray scattering technique (WAXS) on 3.4 nm ZnS nanoparticles, attributing pair distribution functions (PDF) to the nanoparticles. Their results revealed structural disorder caused by nanoparticle strain and contraction of the bond lengths at the surface. These interesting results confirm that any observation of nanoparticles must take into account the surface effects, especially in very small particles. The dependence of the surface area on size is, therefore, the simplest way to observe the modulation of properties in nanoparticles. The correlation between the surface area and volume of a spherical particle can be determined by the formula

Assembly and Properties of Nanoparticles

35

4π R2p Area 3 = = , 3 Volume 4/3π Rp Rp

(1)

where Rp is the particle radius. To normalize the relation for a given mass (to obtain the surface area in area/weight), it is useful multiply the result by the material’s density, ρ . Since nanoparticles are not true spheres, we can derive a geometric expression to give the number of atoms in a near-spherical shape, as follows [25]: N=

R3p , ra3

(2)

where ra is the radius of an atom deduced from the atomic volume. Since the nanoparticle volume is proportional to N and (by analogy) the number of atoms in surface scales is quadratically proportional to Rp , a similar result is obtained for the ratio of surface atoms and inner atoms in a given particle. Thus, (1) can be interpreted as being related to the proportion of atoms on the particle’s surface. Therefore, the relation assumes a constant value (close to zero) only for large particles; however, in very small particles, the relation tends to infinity, i.e., the majority of the atoms forming a particle are at the surface. Practical conclusions can be observed in properties intrinsically related to the coordination of atoms in space. One of the first properties studied extensively as a function of particle size was the solid–liquid transition, i.e., the variation of melting point with size [26–32]. A decrease in the melting temperature has been observed with decreasing nanocrystal size in a wide range of materials. In CdS nanocrystals, Goldstein and coworkers [31] observed a temperature depression of over 50% for nanocrystals in the 15 nm range. Comparing the final results with the reported bulk melting temperature – about 1,690◦ C – the smaller nanoparticles melted at ≈ 600◦ C. This phenomenon must be interpreted in light of the fact that given their high surface energy, surface atoms tend to be unsaturated. This surface energy is always lower in the liquid phase than in the solid, and in the liquid phase, these atoms tend to move to minimize energy. In the rigid geometry of a solid, the surface atoms are constrained, and melting is a way to reduce the total surface energy. In higher surface areas, the contribution of surface energy will be higher, and melting temperature will be reduced. According to the liquid-drop model, the total cohesive energy (Eb ) of a nanoparticle with N atoms is equal to the volumetric or bulk energy av N minus the surface energy, the latter term arising from the presence of atoms on the surface. Hence, the cohesive energy per atom, i.e., Eb /N = av,Rp , is given by av,Rp = av −

4π ra2 γ = av − as N −1/3 , N 1/3

(3)

where av represents the bulk’s cohesive energy and γ is the material’s surface energy. This expression is the same as that of the binding energy per nucleon obtained from the liquid-drop model. Since the number of atoms in a near-spherical nanoparticle with radius Rp is known (2), we can write

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av,Rp = av −

12υ0 γ , Rp

(4)

where υ0 is the atomic volume. This expression gives a qualitative view of the size dependence of the amount of energy required to remove an atom from a cluster. Since empirical studies [26] have established a linear relation between the melting point (Tm ) and the cohesive energy av , we can write a relation of Tm /T0 and the nanoparticle radius, as follows [25]: 2βE,υ ,T0 Tm = 1− T0 Rp

(5)

where βE,υ ,T0 is a constant dependent upon surface energy, atomic volume, and the bulk melting temperature, T0 . Similar results have been obtained from classical thermodynamic treatments. The linear relationship between Tm and R−1 was compared with experimental data for Pb and In nanoparticles, and for several metals in molecular–dynamic simulations [25]. The results showed that this simple approach efficiently demonstrates the melting point’s dependence on size. Figure 1 gives an example of melting temperature depression in sodium clusters [32], where the approach seems to be valid. Other aspects of the high surface area in nanoparticles appear in catalytic studies. In fact, it is well known that, in heterogeneous catalysis, the rate of reaction is assumed to be proportional to the surface coverage [33]. Therefore, the greater

Fig. 1 Melting of sodium nanoparticles (from Martin et al. [32]). The metal has bulk melting temperature Tm,bulk = 371 K

Assembly and Properties of Nanoparticles

37

the material’s surface area the greater is its catalytic activity. Several reports discuss this enhancement of catalytic activity, mainly in metallic nanoparticles such as Pt, Rh, Pd, and Co [34–38]. However, it is not easy to separate the effects intrinsically dependent on size from those dependent on the shape of nanoparticles [39]. Irregular shapes will strongly interfere in the vicinity of the surface atoms, especially at the corners and edges. In fact, the sphere is the most stable geometry, and any other shape will have a higher surface area to a given volume. Also, the distribution of crystallographic planes differs in each shape. Narayanan and El-Sayed [38–40] compared the activation energy in the electron transfer reaction between hexacyanoferrate (III) ions and thiosulfate ions catalyzed by Pt nanoparticles, mainly tetrahedral, cubical, and spherical. Tetrahedral Pt nanoparticles are composed of (111) facets, with sharp edges and corners, while cubical nanoparticles comprise (100) facets whose edges and corners are less sharp than the tetrahedral ones, and spherical (or near-spherical) nanoparticles consist of numerous (111) and (100) facets with smooth corners and edges. The authors observed lower activation energy in the above described reaction in tetrahedral nanoparticles (14.0 ± 0.6 kJ mol−1 ) than in cubical (26.4 ± 1.3 kJ mol−1 ) and spherical (22.6 ± 1.2 kJ mol−1 ) nanoparticles. The lower activation energy of spherical particles was attributed to the lower particle size when compared with the cubical (4.9 against 7.1 nm). However, the comparison with tetrahedral particles (4.8 nm) is consistent and clearly shows the dependence on shape, which ultimately means the corners/edges and the crystallographic planes at the surface. Another interesting feature to be pointed out is the instability of these anisotropic shapes [41]. The dissolution and poisoning of atoms in heterogeneous catalysis has been found to occur primarily in the corners and edges because of the higher activity attributed to these atoms in the structure. This fact allows one to conclude that, when it comes to nanoparticles of comparable sizes, the spherical ones display the lowest catalytic activity but the greatest stability. Another aspect of this topic is the colloidal stability of nanoparticles, mainly in metal oxides. In water, the most common liquid medium, metal oxide surface chemistry is controlled by the surface hydroxyl groups [42–44]. The following surface equilibrium condition must therefore be considered: +  MOH+ 2  MOH + H MOH   MO− + H+

(6) (7)

These two conditions of equilibrium are described by pK1 and pK2 values, respectively. The surface charge, together with the zero point of charge or zeta potential (pHζ ), are important properties that determine the stability of a colloid. In principle, the surface area interferes in the absolute number of dispersed charges, but does not affect the zeta potential [45]. However, two effects on this scale are not negligible: the adsorption of any counter ion is enhanced and can shift pHζ in more than two units [45] (this effect was explored by several authors to manipulate nanoparticles by attaching them to organic molecules [46, 47]); and dipole interactions may affect the particle-to-particle interaction [48–50]. The classical equation for the energy of dipole attraction in spheres (aligned dipoles), E = −μD /2πε0 x(x2 − 4R2p )

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(μD is dipole moment and x is the distance between the spheres) shows that this energy can assume significant values in small particles. Estimating these values for CdTe nanoparticles ranging from 2.5 to 5.6 nm in diameter, Tang and coauthors [48] reported values of about 8–10 kJ mol−1 . These values are substantially higher than the regular molecular dipole–dipole attraction (≈1.5 kJ mol−1 ). The authors pointed out that this effect can explain relative orientation in nanoparticulate colloids (such as those reported in the same paper and in others), like “pearl necklaces”. On the one hand, in fact, some papers report ordered agglomeration or significant enhancement of viscosity or rheological properties in nanoparticulate colloids [51,52] when compared with microparticulate in the same solid load [44]. On the other hand, Tohver et al. [53,54] reported that the same charge localization can interfere in the agglomeration of larger particles by repelling others. They observed this behavior in dynamic viscosity measurements in binary colloids of SiO2 microspheres (≈0.285 μ m) and ZrO2 nanoparticles (≈3 nm). The authors proposed that the total interparticle energy Vtotal would have an additional contribution beyond the van der Waals interaction and the repulsive electrostatic potential, a depletion term due to the interaction between the micro and nanoparticles. This interaction implies that the nanoparticles avoided agglomeration of the larger ones, reducing the expected viscosity.

3 Quantum Size Effects Nanoparticles have few atoms that suffice only to form an identifiable (crystal) interior and the interactions among these atoms in a small limited size bring the properties close to the discrete conditions displayed by isolated molecules or atomic pairs. These phenomena are commonly related to quantum size effects, and are revealed mainly in optical and electrical properties. Basic quantum mechanics provides an excellent example of energy level dependence on size: the particle-in-a-box model. For an one-dimensional system, Schr¨odinger’s equation is:   h¯ 2 d2 +V Ψ = EΨ, (8) − 2m dx2 where m is the particle mass, V is the potential energy barrier, E is the energy of the particle, and Ψ is the associated wave function. In a box with length L, the general solution for the equation (according to Levine [55]) is given by  nπ  x , (9) Ψ = 2/L sin L and the energy of the particle is given by E=

n2 π 2 h¯ 2 , 2mL2

(10)

Assembly and Properties of Nanoparticles

39

Fig. 2 The energy of the three first levels (n = 1–3) of a particle with mass = electron mass in a 1-dimensional box with length L. Inside the box V = 0 and outside V = ∞ (the particle is confined in the box)

where n is an integer. The expression shows a strong dependence of the energy level on the size (as seen in Fig. 2): at large L values, all the energy levels tend toward a single level (level superposition), eliminating the quantum regime. Enhancement of the particle energy is easily observed in small sizes. Although the model is commonly referred to as only theoretical, its implications were recently observed through scanning tunneling microscopy (STM) by F¨olsch et al. [56] in linear Cu chains and by Nilius and coworkers [57] in linear Pd chains. The dependence of the length L was observed in both studies, as illustrated in Fig. 2, by the number of atoms in the chain. Another way to explain the influence of size on electronic properties can be through the semiempirical methods utilized to estimate interactions between molecules [55]. In these methods, the contribution of each atom is postulated as α , while the contribution of the interaction with neighboring atoms is postulated as β , and the interactions of nonneighbors are neglected (assumed to be zero). The wave functions will have a number of solutions equal to the number of atoms in the molecule. The general solution for the energies is given by Ek = α + 2β cos

kπ , N +1

(11)

where N is an integer and k = 1 · · · N. Let us assume a particle with N equal atoms and two energy levels – a fundamental level and an excited one, with α , α  and β , β  ,

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C. Ribeiro and E.R. Leite

respectively. The Fermi energy depends only on the density of electrons n, following a free-electron model (EF = h¯ 2 (3π 2 ne /2m)2/3 ) and is therefore independent of the particle size [58]. However, small particles have few conduction electrons ne and a smaller number of electronic states at T = 0. Since the density of electronic states is proportional to the volume, the space between the filled states, δ , is inversely proportional to the particle size – for spherical particles, the level spacing scales with d −3 . More precisely, δ = 4EF /3ne . Now let us take a single particle at a given temperature where kB T δ (where kB is the Boltzmann constant). In this situation, the Fermi energy would probably be found in a gap between adjacent levels, and the particle would reveal a nonmetallic state. For a semimetal (such as carbon), this feature is clearly visible in a qualitative plot of the (11) for k = 1 and k = N in the two cases (fundamental and excited), as shown in Fig. 3. As can be seen, the metallic behavior appears only in a cluster with a significant number of atoms; in the presence of fewer atoms, the particle’s behavior is similar to that of a semiconductor, i.e., it shows a forbidden band dependent on the number of atoms in the particle. The discreteness of the electronic level structure was discussed in detail by Kubo and Kawabata [59, 60], and reviewed by Halperin [58]. In semiconductors, the existence (even in the bulk) of the characteristic band gap requires a better understanding of the conduction mechanism, which differs entirely from that of metals, to describe their quantum size effects [61–63]. By definition, the band gap is the energy necessary to create an electron (e− ) and hole (h+ ). Thus, the ionization potential Ei of a semiconductor can be treated as Ei = Eg + Ea , where Eg is the band gap energy and Ea is the ionization energy from the edge of the conduction band [61].

Fig. 3 Diagram of levels in a single-atom metal according to semiempirical methods

Assembly and Properties of Nanoparticles

41

The S eigenfunctions (in spherical coordinates) and their energy levels in a charged particle (electron or hole) with effective mass m∗ confined in a spherical well of infinite depth and radius Rw are defined in classical quantum mechanics by the equations Ψn (r) = C En =

sin(nπ r/Rw ) , r

h¯ 2 π 2 n2 . 2m∗ R2w

(12) (13)

The internal motion in a small particle can be interpreted by a specific eigenfunction, Φ, given by a direct expansion of Ψn , as defined by (12). Assuming some error, we can write Φ ≈ Ψ1 + ∑ Ψn , or, for the total energy E≈

h¯ 2 π 2 n2 e2  + P, ∗ 2 2m Rw 2Rw

(14)

where P is an average over the 1S function [61]. This interesting result is equal to the ionization potential or electron affinity of a small particle with radius Rp (making Rw = Rp ). Both terms decrease with the size Rp of the particle, and the charge – the electron or the hole – is less stable in small sizes. Consequently, the barrier to the ionization Ea lowers with size. However, the small size implies the approximation of the carriers (e− and h+ , with radius re and rh , respectively), which may form a bond state, an exciton [64]. On the basis of this assumption, the pair can be described approximately by a hydrogenic Hamiltonian [62–64]: 2 2 e2

= − h¯ ∇2h − h¯ ∇2e − H , 2mh 2me ε |re − rh |

(15)

where mh , me are the effective masses of the hole and electron, and ε is the semiconductor dielectric constant. By analogy, the band gap energy is the ionization limit of the hydrogenic electron–hole bound states. In small sizes (assumed to be spherical), one must consider polarization terms due to the Coulomb interaction in the presence of the crystalline surface. Hence, the Schr¨odinger equation is written as follows   h¯ 2 h¯ 2 − +V0 (Se , Sh ) Φ((Se , Sh ) = EΦ(Se , Sh ), (16) − 2me 2mh where Se and Sh are the electron and hole positions inside the sphere (V0 is considered infinity outside the sphere). At small values of Rp , the eingenfunction will be dominated by the carrier confinement, and the solution can be obtained by the variational method using the S wave function for a particle in a sphere (12 and 13) as a tentative function. Thus, the simple uncorrelated function may be an acceptable approximation (especially for direct-gap semiconductors):

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Φ0 = Ψ1 (Se )Ψ1 (Sh ).

(17)

In this condition, and using the reduced mass of the electron–hole pair μ , one has the effective band gap energy, E eff (keeping in mind that the energy of the lowest excited state E is the shift of Eg , i.e., the bandgap energy): E eff = Egap + E = Egap +

h¯ 2 π 2 n2 1.8e2 e2 + Ψ1 . − 2μ R2 εR R

(18)

The first term represents the quantum energy of carrier confinement or localization, and the second term represents the Coulomb attraction. The third term is the energy loss given by the solvation in the surrounding medium, and will depend not only on the semiconductor’s dielectric constant, ε , but also on that of the surrounding medium. Ψ1 is an average sum over a Ψ1 function [62]. Finally, the diameter-range where these size effects are expected can be determined by an exciton Bohr radius, as follows [64]: aB = ε

h¯ 2 . μ e2

(19)

When the crystal size approaches aB , the pair becomes confined and the effects are observable. This model is a simplification, since other correlation functions (with more complex solutions) are possible. However, several experimental works have demonstrated the validity of the expression for near-spherical nanoparticles [65–79]. More complex solutions may be necessary for anisotropic shapes, as experimentally demonstrated by Buhro and Covin [80] for InAs. In general, the third term of (18) is neglected and the second term is only significant when aB ≤ Rp [79]. In these particles, the mode is known as strong confinement, whereas for larger, albeit still small particles, the mode is known as weak confinement [64]. Rossetti and coworkers [65, 66] compared experimental results of absorbance in the UV–Vis range for CdS and ZnS nanocrystals in colloidal suspensions with predictions from classical Mie scattering theory [81], using bulk crystal properties. This theory provides an exact solution to Maxwell’s equations, assuming that small crystallites are characterized by the same wavelength-dependent dielectric constant as that of the bulk material. For particles that are much smaller than the optical wavelength λ in the external medium, only the electric dipole term needs to be considered and the crystallite absorption cross section is given by σ = (8π 2 R3 )/λ · ℑ[(ε  − 1)/(ε  )]. ε  is the ratio of the complex dielectric coefficient of the bulk crystal to the real dielectric coefficient of the external medium. Although the authors found a general shape congruent with the spectra obtained with the Mie curves, some unpredicted plateaus or peaks were observed, and the curves were displaced to higher energies, indicating that the small particles had higher band gap energies than the bulk. The peak was subsequently reported to be a resonance peak resulting from the creation of the electron–hole pairs [63, 64, 82]. The authors concluded that the classical treatment of the Mie theory was invalid, since ε is a collective property of the macroscopic material (the small crystal does not support the

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43

continuous distribution of electron or hole momenta due to the boundary conditions imposed by the surface). Using (18), the authors estimated the effective band gaps of some particle sizes ranging from 2 to 7.5 nm, concluding that the observed spectra was the sum of widely differing spectra corresponding to various sizes. They pointed out that the model predicts that the absorption coefficient is independent of size, and that the crystallite size distribution itself should be used to predict the experimental absorption threshold data. In fact, the broadening of particle size distribution can interfere sufficiently in the absorbance spectrum near the onset to deviate gap measurements significantly by the onset of extrapolation. Pesika and collaborators [77, 78] proposed the inverse observation, i.e., particle size distribution by absorbance spectra measurements. The absorbance A at any wavelength λ in the quantum regime is related to the total volume of particles with radius greater than or equal to the size corresponding to the onset of absorption, in a diluted concentration limit (absorbance will occur continuously since the critical size is reached). For spherical particles, assuming that the absorption coefficient is independent of particle size, we have A(r) ∝

 ∞ 4 Rp

3

π R3p n(Rp )dRp ,

(20)

where n(Rp ) is the particle size distribution. The expression can be rearranged, keeping in mind that when r → ∞, n(Rp ) = 0: n(Rp ) ∝ − 4

dA dRp

3 3 π Rp

.

(21)

The derivative dA/dRp is obtained by the slope of the absorbance curve (converting the energy axis to Rp using (18)). The authors tested the assumptions on ZnO nanoparticles, comparing them with direct size measurements by TEM. A good agreement with the statistical data was achieved; however, considerable deviations were observed in very small radii. The effect was explained by the resonance exciton peak, more pronounced for sharp particle size distributions. On the basis of these observations, the authors concluded that only small fractions of the overall distribution are affected and, in many cases, the exciton’s contribution is negligible. This deviation is observed in SnO2 nanocrystals: the very small calculated Bohr radius (aB ≈ 2.7 nm) implies that, in most cases, the experimentally detectable effects are related to a weak confinement regime. Absorbance measurements in water were carried out on nanoparticles synthesized by the hydrolysis of hydrated SnCl2 and were compared with size distribution measured by TEM (at least 200 particles), as illustrated in Fig. 4 [83]. An acceptable agreement was found for particles over 1.3 nm, but the smaller ones were not detected. According to Pesika, the results were probably strongly affected by the sharp exciton peak (at 283 nm, in the inset of the graph). The case of SnO2 illustrates the experimental problems observed in width gap materials (as is the case of many oxides), for it is sometimes difficult to make a

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Fig. 4 Comparison between statistical measurement of SnO2 particle sizes by TEM and absorbance spectra derived distribution (21). On the inset, the obtained absorbance spectra, showing the sharp exciton peak [83]

good estimate of the band gap. The confinement effect in this oxide was studied by photoluminescence measurements, with better results for the average particle size in several conditions. The photoluminescence peak was considered a good estimate of the band gap, since it relates to the emission of the lower excited level to the ground state, whereas absorbance of the photon will occur continuously, as discussed earlier herein. The results depicted in Fig. 5 show a good congruence with the theory and also the weak confinement regime in this oxide.

4 Phase Stability and Transformation Something commonly seen in the synthesis of nanomaterials is that many metastable structures appear stable in the nanometric range. A typical case is the synthesis of TiO2 polymorphs. TiO2 has three crystalline polymorphs, anatase, brookite, and rutile [84]. Although several papers report on the synthesis of nanocrystalline anatase [12, 85–89], few report on nanocrystalline rutile [90, 91] as an example. However, several papers state that the rutile formation passes through the three metastable phases, and it has been established that rutile is the most stable TiO2 polymorph (observations of micrometric anatase are scarce) [92–96].

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Fig. 5 Comparison between application of (18) to tin dioxide and experimental data – Eeff g obtained by photoluminescence emission and particle radius by TEM measurements (from Lee et al. [79]). The inset in the figure shows an scheme of the photoluminescence emission (adapted from [82])

It is well known that crystallization generally follows a sequence of metastable phases before the most stable phase is attained (known as Ostwald step rule) [94,97]. Although this final crystalline polymorph is the most thermodynamically stable, the others are often only slightly metastable by a few kilojoules per mole. One must keep in mind that the stability of a given nucleus or small cluster (in homogeneous nucleation) is given by the balance between the free energy of formation, ΔGV , and the work given by the new surface, γ A (the product of the surface free energy and the surface area), as follows for a sphere [23, 97, 98] 4 ΔG = − π R3p .ΔGV + 4π R2p γ . 3

(22)

Making the first derivative of the expression equal to zero, d(ΔG)/dR = 0, we have the minimum ratio for a stable nucleus (Rp,crit ): Rp,crit =

2γ . ΔGV

(23)

At this moment, we can consider that ΔGV is independent of size (we will further analyze the equation later on herein). On the basis of this assumption, phases with higher γ values will need larger nucleus to become stable in solution or melt. Thus, the immediate problem is to determine the surface energy of polymorphs.

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Table 1 Surface enthalpies and transformation enthalpies relative to bulk stable polymorph for oxides (adapted from Navrotsky [94]) Oxide

α -Al2 O3 γ -Al2 O3 TiO2 rutile TiO2 brookite TiO2 anatase ZrO2 monoclinic ZrO2 tetragonal ZrO2 amorphous Zeolitic SiO2 SiO2 amorphous

Surface enthalpy (J m−2 )

Transformation enthalpy (kJ mol−1 )

2.6 ± 0.2 1.7 ± 0.1 2.2 ± 0.2 1.0 ± 0.2 0.4 ± 0.1 6.5 ± 0.2 2.1 ± 0.05 0.5 ± 0.05 0.09 ± 0.01 0.1

0 13.4 ± 2.0 0 0.7 ± 0.4 2.6 ± 0.4 0 9.5 ± 0.4 34 ± 4 8–15 9

Calorimetric measurements are a way to determine this property [84, 99]. At room pressure, the effect of the volume variation, PΔV , is expected to be small, and the surface entropy is also expected to be slight. On the basis of this assumption, the surface free energy can be approximated to the surface enthalpy (the variable that is properly measured in calorimetry). Table 1 shows surface enthalpies and transformation enthalpy data for some oxides and their polymorphs. An initial analysis of the data reveals (in accordance with the literature) that the surface enthalpy (or energy) decreases as the phase becomes more metastable (higher transformation enthalpy relative to the bulk stable polymorph), i.e., smaller surface energies lead to lower barriers to stabilization [93, 94]. This analysis (albeit not at all correct) indicates that metastable phases tend to nucleate more easily than stable ones, so it is coherent with Ostwald’s step rule. We can interpret the same result by stating that metastable phases have a lower activation energy ΔG∗ , obtained by substituting the value Rp,crit in (22) [23, 97]: 16πγ 3 ΔG∗ = (24) 3ΔG2V In a reactional medium (such as water, for several materials), the competition between dissolution and reprecipitation renders this interpretation more complex. Even though the main ideas remain valid, the first stages of the formation of a crystal may be the coalescence of two fairly large clusters, eliminating water, protons, and OH − groups from the surface [2, 94]. This step – often referred to as polycondensation [43,100] – has no clear activation energy and may differ significantly from classical nucleation. Hence, a conclusion dictated by common sense may hold true in some cases: the metastable structure of the nanoparticle comes from a memory of the precursor or, in the case of amorphous nanoparticles, the precursor nanostructure constrains the atoms in positions such that crystallization is impossible. At the surface, the low coordination of atoms unbalances the bonding forces and generally causes any phase transformation to be easier at the surface. Under such conditions, phase transformations will depend on particle–particle contact,

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while the kineticrate constant of the process may also be size-dependent (as shown experimentally) [92, 101–107]. The unbalanced forces in small particles can be understood as an excess of pressure upon the whole solid particle, and may be approximated using such expressions as Laplace-Young’s equation [92, 108, 109]: Peff =

2σ , Rp

(25)

where σ is the surface tension. Zhang and Banfield [92] assumed that the increase in activation energy would be proportional to the excess pressure, Ea = E∞ +CPeff = E∞ +C Rp , where Ea is the effective activation energy, E∞ is the bulk energy activation, and C, C are proportionality constants. The authors confirmed this assumption for the transition of TiO2 -anatase to rutile in the 5–100 nm range, with a good correlation. The difference in Ea to the total range was ≈60 kJ mol−1 , a significant value in view of the estimated bulk activation energy (E∞ = 185 kJ mol−1 ). Excess pressure is also observable in pressure-driven phase transformations. Tolbert and Alivisatos [2, 110, 111] showed that a significant increase in pressure induced wurtzite to transform into rock salt (from the less dense to the denser phase) in CdSe nanocrystals, following a scaling law of the type Ptransf ≈ 1 + C /Rp . They observed an increase of ≈35% in transition pressure in 10 nm nanoparticles in relation to 21 nm nanoparticles (3.6–4.9 GPa). The transformations were found to be fully reversible, albeit with some hysteresis, showing an energy barrier to direct transformation, which is coherent with the excess pressure at the surface. However, other factors may predominate and may also be related to the aforementioned phenomena. Solid surfaces of different crystallographic orientations have different surface energies and different affinities for absorbed ions and molecules [112] (as exemplified for SnO2 , in Table 2 [113–116]). The fact is that shape is an important variable in the stability of nanocrystals, since the total amount of surface energy depends on the exposed crystallographic planes [117]. To adapt this feature, Barnard and Zapol [109] proposed a general model for the phase stability of any nanoparticle based on the Gibbs free energy of an arbitrary particle. According to the authors, the correct treatment of the free energy must include contributions from the edges and corners rather than only from the bulk and surface. As an example, a Si cubic nanocrystal with 200 atoms will have 9% of the

Table 2 Surface energies for SnO2 calculated for several crystallographic planes in vacuum (adapted from Beltran et al. [113]) Surface (110) (010), (100) (101), (101) (201) (001)

Ref. [113]

Ref. [114]

Ref. [115, 116]

1.20 1.27 1.43 1.63 1.84

1.04 1.14 1.33 – 1.72

1.30–1.40 1.66–1.65 1.55 – 2.36

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atoms in edges; with 103 atoms, 4% will be in the edges and with 105 only 0.3% will remain. These estimates highlight the importance of the small terms, in some cases. For a given x nanoparticle, the free energy can be expressed as a sum of individual contributions, i.e., + Gsurface + Gedge + Gcorners . G0x = Gbulk x x x x

(26)

The first term is defined as the standard free energy of formation, Gbulk = x ΔG0x (T ), which is dependent on the temperature. The second term is expressed in terms of surface energy γi for each i plane on the surface and molar surface area A. Using the relations of density ρ , molar mass M and surface to volume ratio q, one has M = γ (T )A = q ∑ fi γi (T ), (27) Gsurface x ρ i where fi is a weight factor of the facets i in the crystal (∑ fi = 1). In the above formulation, the expression takes into account the crystallographic alignment of the properties and, indirectly, the shape. The edge and corner energies can be described by similar expressions: = ξ (T )L = Gedge x

M p g j ξ j (T ), ρ ∑ j

(28)

Gcorner = τ (T )W = x

M w hk τk (T ), ρ ∑ k

(29)

where ξ (T ), τ (T ) are the edge and corner free energies, L is the total length of edges and W is the total number of corners, p, w the edge and the corner to volume ratios, and g j , hk weight factors. Substituting and rearranging the terms, (26) becomes G0x = ΔG0x (T ) +

M q fi γi (T ) + p ∑ g j ξ j (T ) + w ∑ hk τk (T ) . ρ ∑

(30)

However, as proposed by Zhang and Banfield [92], the effective pressure must be taken into account. The volume dilation ed is given as ΔV = ed = Peff βV , V

(31)

where βV is the material’s compressibility. Peff can be estimated by (25) above. Although it is known that σ = γ + A(∂ γ /∂ A), when the dependence of γ on A is small, the approximation σ = γ is acceptable. The anisotropy should be included in the determination of γ , as done in (27). Using these approximations, (30) becomes  

M 2βV σ G0x = ΔG0x + q ∑ fi γi + p ∑ g j ξ j + w ∑ hk τk . (32) 1− ρ R

Assembly and Properties of Nanoparticles

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Table 3 Surface free energies γ (in J m−2 ), for the clean, partially hydrogenated and fully hydrogenated low index surfaces of TiO2 anatase and rutile (adapted from Barnard and Zapol [96]) Anatase

Rutile

Surface

Clean

Partial

Full

Surface

Clean

Partial

Full

(001) (100) (101)

0.51 0.39 0.35

0.86 0.55 0.51

0.84 0.65 0.63

(100) (110) (011)

0.60 0.47 0.95

0.71 0.56 1.02

1.82 0.84 1.19

Although the Laplace–Young equation (25) is only applicable to spherical particles, the approach was tested successfully in simulations for Si, Ge, nanodiamonds, and TiO2 polymorphs. The authors predicted faceted shapes (e.g., cubes or tetrakaidecahedrons) as preferred shapes in very small sizes for most cases, which is contradictory to common sense (i.e., spheres). This strong dependence on surface, corner, and edge energies can induce unexpected phase transformations through interactions with the medium. Gilbert et al. [118–120] reported the reversible transition of ZnS wurtzite to a structure close to spharelite by the gradual substitution of methanol medium (from synthesis) by water. The authors explained the water-driven transformation through MD simulations, showing that interactions between water and ZnS reduce the surface energy. This aspect can be explored by including the contribution of absorbed ions or molecules at each surface i, i.e. [96, 121], 1  (33) γi = A · ENsurf − NE bulk − Ny μy , 2 where ENsurf and E bulk are the total energy for the surface and bulk for a given area A, N is number of units in the stoichiometric cell (considering a minimal slab), Ny is the number of absorbed molecules or ions and μy is the chemical potential of the y molecule or ion. Taking in account these parameters, the surface energies for some crystallographic planes of clean, partially and fully hydrogenated TiO2 anatase and rutile were obtained by density functional calculations (as shown in Table 3 [96]). The slight variations of some values caused by ion adsorption can be extremely significant in small particles and in anisotropic shapes, as experimentally observed.

5 Synthetic Methods After reviewing the fundamentals of nanoparticle properties, in the following sections we discuss some of the fundamentals involved in nanoparticle synthesis, and review some methods commonly employed to produce such particles, with emphasis on methods for synthesizing nanoparticles for energy purposes.

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5.1 Nucleation and Growth Many of the synthesization methods to produce nanoparticles are based on coprecipitation steps, or nucleation and growth in reactional media [98, 108]. Precipitation reactions involve the simultaneous occurrence of these steps, as well as coarsening and agglomeration processes [122, 123]. Because of the difficulties in isolating each process for independent study, the fundamental mechanisms of precipitation are still not entirely understood. However, a good understanding of the nucleation step is fundamental for grasping the nature of nanosize particles. In the section below, we discuss the correlation between the critical nucleus and surface energy (23). A more complete analysis of precipitation must take into account the chemical potential of the nucleus formed in equilibrium with the reactional media. In such a condition, the nucleus possesses free Gibbs energy, as follows [23, 98, 108, 124]: (34) dG = μ0 dn + ∑ γi dSi , i

where μ0 is the chemical potential of the bulk nucleus, n is the number of moles, γi is the surface energy and Si is the area for each surface i. The equation can be rearranged to dSi . (35) μ = μ0 +Vm ∑ γi dV i since dn = dV /Vm (where Vm is the molar volume). For a particle of any shape, the surface area Si and the volume V can be written as generic equations for a given Z characteristic dimension, as follows: Si = κi Z 2 ,

(36)

V = ςZ .

(37)

3

where κi are ς are geometric constants. Taking the derivative of the two expressions as Z, and applying it to a chain rule, one has: dSi /dZ dSi 2Si = = . dV /dZ dV 3V

(38)

As proposed by (27), the surface energy can be inserted as an average surface tension. Here we will not consider the contributions from edges and corners, although this contribution (as discussed) may be important. For the sake of simplicity, we can rearrange the expression as follows:

γ=

∑ γi Si . ∑ Si

(39)

Inserting the (38) and (39) into (35) and rearranging them, one has:

μ = μ0 + αF

2Vm γ , 3Z

(40)

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where αF is a shape factor defined as ∑ κi /ς . This equation describes the chemical potential of the formed nucleus. The chemical potential of the substance μ  (or reactional product) in solution or melt is

μ  = μ0 + RT ln a,

(41)

where R is the universal gas constant, a is the activity in solution, and μ0 is the standard chemical potential in solution. We can assume that the standard chemical potential μ0 in the particle is μ0 = μ0 + RT ln a0 , where a0 is the saturation activity. Comparing the equilibrium condition for precipitation, i.e., μ = μ  , and rearranging it, one has: 2Vm γ a . (42) ln = αF a0 3ZRT This equation is remarkable, since it describes a general form to express the relation among surface energies, chemical potential and dimension Z. For a spherical particle, Z = Rp and αF = 3, (42) reduces to Rp =

2Vm γ , RT ln aa0

(43)

which is easily compared with (23). The approximation in the equation of activity to the concentration, a ≈ c, is usual and commonly accepted as valid. We can correct the set of equations to consider the reduction of surface energy by contact with other surfaces (which represents a heterogeneous nucleation process) by substituting γ to γeff , an effective surface energy obtained by contact with another surface [125]. Applying the geometric relations of the contact with a cluster and a surface, we can consider the decrease of activation energy to nucleation (as given in (24)), i.e., ΔG∗het = ΔG∗ (2 + cos θ )(1 − cos θ )2 )/4, where θ is the contact angle with the two surfaces. The heterogeneous nucleation is preferable only if the geometric relation is less than 1. While the nucleation process takes place, the growth process can be concurrent in some ways: transport of reactive species in solution, adsorption in the crystal– solution interface, interface reactions – in each case, the growth corresponds to the ordering of ions or molecular species (monomers) over the nucleus surface [42, 124, 126–128]. The growth rate is governed by empirical power laws, which are described as a function of the slowest mechanism present [129, 130]. To obtain nanoparticles in solution, it is usually necessary to stop the growth mechanisms or at least to control them to prevent uncontrollable growth and, hence, undesirable particle sizes. All the reactional parameters can be controlled by the proper selection of reactant relations [43,131]. As an example, in precipitation by hydrolysis, a large excess of water in relation to the metal source reactant leads to nanoparticles due to the fact that all the monomers present in solution are captured in primary nucleus – also, in these cases, the initial particle size is closer to Rp,crit . Special cases that must be analyzed are the growth mechanisms in equilibrium, i.e., not dependent on reactional processes but dependent on diffusional parameters

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and on the particles’ relative mobility. Initially, (43) can be rearranged assuming the activity a is equal to the solubility of the formed particle Sp , and the saturation activity a0 as the bulk solubility Sb,0 [70]:   2Vm γ 1 Sp = Sb,0 exp . (44) RT Rp This relation, widely known as the Ostwald-Freundlich equation, describes the dependence of the solubility of a formed particle on its size. This dependence is particularly important in very small particles, since dissolution and reprecipitation phenomena can easily occur [132]. Usually the argument in exponential terms is too small, and the equation can be linearized to Sp ≈ Sb,0 · (1 + 2Vm γ /RT ) · 1/Rp . If particles dissolve and grow readily without being limited by the rate of interfacial reactions, the growth rate of the particles is likely to be limited by diffusion through a surrounding medium and can be described by Fick’s first law. This supposition is clearly valid in colloids and in reactional media. A convenient form of Fick’s first law for a particle in a diffusion field is given as (in spherical coordinates) [133]: 4π R2p

dRp dc = D4π r2 , dt dr

(45)

where D is the diffusivity and dc/dr is the gradient in concentration at distance r. Considering that, in a distance r Rp , the solubility is the same as that of the average particle size (Rp ), (45) can be rewritten for evaluation at r = Rp , after integration of the right-hand side:   

dRp D 1 c0 D 2Vm γ 1 =− c(Rp ) − c(Rp ) = − − . (46) dt Rp Rp RT Rp Rp The concentration values are substituted by using (44) linearized, assuming c = Sp and c0 = Sb,0 . Figure 6 shows a schematic distribution of growth rates for some arbitrary values of particle radii. Clearly, the maximum growth rate will occur in a defined range of particles. If we take the second derivative d2 Rp /dt 2 = 0, we discover that, when Rp = 2Rp , we have the condition of maximum growth rate, as plotted in Fig. 6 by the straight line. If we assume that growth (in a closed system) is governed by the fastest growing particles, we can write dRp = dRp . Substituting these values in (46) and integrating them, we obtain [23, 125, 134]: 3

3

Rp − Rp,0 =

3c0 DVm γ t. 4RT

(47)

This growth mechanism, known as Ostwald ripening, provides a good description of the growth behavior of a wide range of nanoparticles [71, 76, 135–137]. A thorough analysis of the fundamental equations (44 and 45) leads to a general expression of the type [138–140] n

n

Rp − Rp,0 ∝ t,

(48)

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Fig. 6 Growth rate in Ostwald ripening of particles with arbitrary radius. The straight line refers to the maximum growth rate, when Rp = 2Rp

where n is an exponent dependent on the boundary conditions assumed in the growth [137, 139]: for n = 2, it is inferred that crystal growth is controlled by ion diffusion throughout the particle to its vicinity (the solution of a matrix, in solid compounds); for n = 3, the growth is controlled by the volume diffusion of ions in the vicinity; and when n = 4, it is deduced that growth is controlled by dissolution kinetics at that particle–vicinity interface. Despite the good applicability of the Ostwald ripening model, recent studies have demonstrated that this mechanism cannot be considered responsible for the growth process in some systems [141–145], since the main postulates of the theory are frequently neglected. The oriented attachment mechanism was proposed as another significant process, which may occur during nanocrystal growth [146–150]. By this mechanism, nanocrystals can grow by the alignment and coalescence of neighboring particles, by eliminating a common boundary. The driving force for this mechanism is clearly the decrease in the surface and grain boundaries’ free energies. By the localized nature of oriented attachment, the mechanism leads to the formation of nanoparticles with irregular morphologies, which are not expected in precipitation-based growth. Several studies indicate that oriented attachment is very significant, even in the early stages of nanocrystal growth, and may lead to the formation of anisotropic nanostructures in suspensions, such as nanorods, by the consumption of nanoparticles as building blocks [48, 151–154]. This mechanism has already been theoretically studied [155–158] and experimentally observed in micrometer-sized metallic systems for several years [159–162]. Recently, it was modeled by Moldovan et al. [163–166], investigated by molecular dynamics

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studies [102, 128, 167, 168], and confirmed experimentally [169–172]. In all of the above-mentioned theoretical studies, the authors assumed that the nanoparticles were in contact with each other. Oriented attachment occurred by means of relative rotations between the particles or by plastic deformation associated with displacement motion, until a thermodynamically favorable interface configuration (i.e., crystallographic alignment) was reached. Figure 7 shows the oriented attachment of a SnO2 nanoparticle on the surface of a SnO2 nanoribbon. Edge discordances in the nanoparticle–nanoribbon interface evidence the attachment. However, in nanoparticle synthesis, an aspect of particular interest is controlled growth under colloidal conditions. Considerable efforts have reportedly been dedicated to building adequate models to describe the coalescence of nanoparticles in suspension and at surfaces [173]. Penn and Banfield proposed that dispersed nanoparticles can be treated as molecules or molecular clusters [142] in solution. This treatment was already used by Huang et al. [104, 174] in the development of a kinetic model serving to explain ZnS nanoparticle growth induced by hydrothermal treatments. Penn also developed a kinetic model for oriented attachment growth, considering the electrostatic interaction between particles in solution [175]. Ribeiro et al. [176] proposed another mechanism for oriented attachment growth in dispersed nanoparticles. The authors considered that coalescence may also occur

Fig. 7 Example of a SnO2 nanoparticle attached to a single-crystalline surface (a SnO2 nanoribbon) by the oriented attachment mechanism

Assembly and Properties of Nanoparticles

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when particles with similar crystallographic orientations (or with slight differences) collide, which explains the growth behavior in SnO2 colloidal suspensions. This mechanism is based on the assumption that nanoparticles dispersed in a liquid medium present a very high degree of freedom for rotation and translation motions. Hence, in suspensions where agglomeration does not take place, growth by means of oriented collisions should be more effective than by surface mechanisms (i.e., coalescence induced by relative rotations between particles in contact). Dispersed nanoparticles should present a high velocity in response to the Brownian motion, so nanoparticles in suspension are expected to present a high frequency of collisions. Therefore, growth by coalescence may be interpreted statistically, since collisions can be considered effective (i.e., leading to coalescence) or ineffective (i.e., an elastic event). This mechanism is similar to Smoluchowsky’s coagulation model [126,177–182], which is extensively used to explain polycrystalline colloidal growth and aggregation mechanisms in suspension. If we assume that all of the aforementioned considerations are valid, the coalescence of two particles in suspension may be interpreted as the following chemical equation 49: k

A + A −−−→ B

(49)

where A is a primary nanoparticle and B is the product of coalescence of two nanoparticles. Figure 8 shows a generic scheme of the two proposed ways in which the oriented attachment mechanism works. Several papers have discussed the role of oriented attachment in the anisotropic growth of nanocrystals. A recent paper by Cho and coauthors [50] discusses the oriented attachment process as the main mechanism involved in the construction of anisotropic PbSe nanocrystals in several shapes. The authors used the proposition of

Fig. 8 Scheme of oriented attachment mechanism: a attachment by collision of two particles with similar crystallographic orientations; b attachment induced by rotation and alignment of particles in contact

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the alignment of preformed nanoparticles by dipole–dipole interactions as the mechanism responsible for the anisotropy associated with the attachment (as discussed before). The process was observed concomitantly to the synthesis of the nanocrystals. A similar experiment was proposed by Yu et al. [183] for the synthesis of ZnS. The authors suggested that the formation of ZnS nanorods occurred through the oriented attachment of spherical nanoparticles formed in a precursor solution to preformed nanorods in solution. An interesting feature was the subsequent coarsening (Ostwald ripening) of the final nanorods, smoothing the nanoribbon surface. Anisotropic nanoparticle shapes are often desirable in charge-carrier devices such as solar cells or electrodes [184, 185]. A strategy developed by Vayssieres [186–195], called purpose-built materials (PBM), appears to be a promising route for growth-oriented 3D crystalline nanorods in several kinds of substrates. This strategy allows one to obtain 3D arrays of several semiconducting metal oxides using controlled aqueous chemical processing at low temperatures (usually in the range of 90–95◦ C) and inexpensive precursors [194]. The PBM strategy is based on the heterogeneous nucleation of the desired phase on a substrate. The substrate decreases the activation energy in the crystallization process, promoting heterogeneous nucleation at the surface of the solid. The kinetics of nucleation and growth is controlled by the temperature and the hydrolysis rate, whereby the nucleation and growth processes can be separated. The experimental conditions are adjusted to obtain the most stable thermodynamic structure. The growth mechanism is controlled basically by a dissolution–precipitation process, and the direction of crystal growth is controlled by the surface energy of the oxide crystalline phase. This argument explains the epitaxial growth of single-crystalline metal oxide nanorods perpendicular to the substrate. This growth process is usually associated with the Ostwald-ripening mechanism, but the oriented attachment mechanism may be involved.

5.2 Synthesis of Transition Metal Nanocrystals The development of metal nanocrystals is fundamental for devices where catalytic heterogeneous reactions take place, such as fuel cells. The bottom-up methods of wet chemical nanocrystal synthesis are based on the chemical reduction of the salts, or the controlled decomposition of metastable organometallic compounds in an organic or water solution. These reactions are always carried out in the presence of a large variety of stabilizers, which are used basically to control the growth of the initial nanocluster and to prevent particle coagulation or agglomeration. As discussed, the mechanism of nanoparticle formation is generally based on a process of nucleation, growth, and agglomeration. This process was proposed by Turkevich and is based on the synthesis of metal nanoparticles by salt reduction [34,196]. This model still is valid and has recently been refined. A recent review authored by B¨onnemann and Richards [197] contains a good discussion about the refined model, and supplementary references on this subject are also available.

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Since nanocrystals are unstable from the standpoint of agglomeration and bulk, coagulation and agglomeration are the paths that nanoparticles follow to decrease their high surface area, thus becoming more stable. In the absence of any extrinsic impediment, the unprotected particle coagulates, basically under the action of van der Waals forces. To prevent the coagulation process from occurring, the particle surface can be protected by electrostatic stabilization and/or steric stabilization [44]. Electrostatic stabilization is based on the Coulombic repulsion between particles, promoted by a double layer composed of ions adsorbed on the particle surface. The electrostatic stabilization process can be modified by several parameters, such as ionic strength of the dispersing media, ion concentration, and the presence of neutral adsorbate, which may replace the adsorbed ion on the particle surface. Steric stabilization is based on the steric hindrance caused by organic molecules that are attached to the particle surface, forming a protective layer that prevents particle coagulation or agglomeration. This type of stabilizing system can be viewed as a nanocomposite material, since the organic layer forms a nanometric scale second phase [198, 199]. Several kinds of protective groups can be used as steric stabilization agents, among them polymers and block-polymers, P, N, and S donors (phosphanes, amines, thioethers), surfactants, organometallic compounds, and solvents. A detailed description of the several types of steric stabilizers used during the synthesis of metal nanocrystals is given by Bradley [42]. The synthesis of transition metal nanocrystals can be divided basically into two major groups: salt reduction and decomposition method. Examples of these methods are described below. The salt reduction method is a process whereby a reduction agent reduces the metal salt, in solution, to metal. These reactions can be done in water or in an organic solution. In an organic solution, the solvent can also act as a reduction agent. Alcohols are generally useful reduction agents, particularly hydrogen-containing alcohols. In this process, the alcohol is oxidized to the corresponding carbonyl group. An example of this kind of synthesis is the processing of palladium nanoparticles through the reduction of palladium acetate by methanol [200]. Teranishi and Miyake [37] reported on the reduction of H2 PdCl4 by alcohols to synthesize Pd nanoparticles, demonstrating that the mean diameter of Pd nanocrystals can be controlled from 1.7 to 3.0 nm in a one-step process by changing the amount of protective polymer, poly(N-vynil-2-pyrrolidone) (PVP) and the kind and/or concentration of alcohol in the solvent. The solvent they used was water. They also showed that the reduction rate of [PdCl4 ]− ions is an important factor in the production of smaller Pd particles. The reduction rate was controlled using different kinds of alcohol. The reduction of metal salts by the addition of a reducing agent in a nonreducing solvent is a well-established synthetic route for the preparation of aqueous suspensions of metal nanocrystals. Faraday, for instance, used phosphorous vapor to promote the reduction of [AuCl4 ]− in aqueous solution to synthesize gold nanoparticles [8]. Different kinds of reducing agents have been used to process gold nanocrystals, allowing for the processing of particles ranging from 1 to 100 nm in diameter. Turkevitch and coworkers [196] established the first reproducible standard protocol for the synthesis of gold nanoparticles. Their processing

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of gold nanoparticles by the reduction of [AuCl4 ]− with sodium citrate, for example, became a standard for histological staining applications [201] and for undergraduate experiments in surface and nanomaterials chemistry [202]. Platinum nanoparticles can also be synthesized by the reduction of metal salts, using a reducing agent [36, 203]. Van Rheenen et al. [203] demonstrated that the morphology of platinum particles could be controlled by controlling the synthetic parameters, such as temperature, protective polymer, time, pH, reagent concentration, and the sequence of reagent additions. These authors used various reducing agents and chloroplatinic acid as platinum salt. An interesting synthetization route was recently developed based on the reduction of organometallic compounds by dihydrogen at low pressure and temperature [204–208]. The organometallic compounds used were low-valent alkene or a polyene complex of the desired metal. Using this process, well-dispersed nanoparticles of Ru, Pt, Ni, and Co with a narrow size distribution were synthesized. The particles were stabilized by the presence of poly(vinylpyrrolidone) (PVP). On the basis of a similar process, Ould Ely et al. [209] synthesized nanoscale bimetallic Cox Pt1 − x particles, using Co(η 3–C8 H13 )(η 4–C8 H12 ) and Pt2 (dba)3 (dba = bis-dibenzylidene acetone) as organometallic compounds. They found that the alloy’s composition was determined by the initial ratio of the two organometallic precursors. Recently, the so-called polyol process [210] has been used successfully to process magnetic nanoparticles with a very narrow particle size distribution [211,212]. This process is based on the reduction of metallic salt in solution, at a high temperature (100 < T < 300◦ C), by the addition of a polyol (such as ethylene glycol), resulting in nanometric particles. In this process, surfactants such as oleic acid are used to control particle growth and stabilize the nanoparticles. Park and Cheon [213] discussed an interesting synthetization route to process solid solution and core-shell type cobalt-platinum nanoparticles via redox transmetallation reaction, reporting they had obtained nanoparticles of solid solution and core-shell structures smaller than 10 nm. These alloys were formed by redox transmetallation reactions between the reagents without the addition of reducing agents. The reaction between Co2 (CO)8 and Pt(hfac)2 (hfac = hexafluoroacetylacetonate) resulted in the formation of solid solution, while the reaction between Co nanoparticles and Pt(hfac)2 in solution resulted in “Co-core – Pt-shell” type nanoparticles. Narrow particle size distributions were achieved in both processes. The organometallic compounds of transition metals usually display low thermal stability, decomposing into their respective metals even under mild conditions. Owing to these properties, organometallic compounds can be considered good sources to process metal nanoparticles. Metal carbonyl pyrolysis has been used for the synthesis of several metal nanoparticles, although a broad particle size distribution is usually obtained [127, 214]. Park et al. [215] reported on the synthesis of iron nanorods and spherical nanoparticles using the thermal decomposition of Fe(CO)5 , in the presence of surfactant. They found that rod-like particles, with a higher aspect ratio, could be obtained by changing the concentration of didodecyldimethylammonium bromide (DDAB) during the reaction process. Puntes et al. [216] recently reported on the control of the size and shape of Co nanocrystals.

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A synthetization route, based on the principles applied to the synthesis and control of CdSe nanocrystals, was used [143]. These authors discussed the synthesis of Co nanoparticles with high crystallinity, narrow particle size distribution and a high degree of shape control. The nanocrystals are produced by injecting an organometallic precursor (Co2 (CO)8 ) into a hot (T ≈ 180◦ C) surfactant mixture (oleic acid and trioctylphosphine oxide (TOPO)) under an inert atmosphere. An interesting approach to synthesize metal alloy nanocrystals is the use of simultaneous salt reduction and thermal decomposition processes. Sun et al. [18] reported on the synthesis of iron–platinum (FePt) nanoparticles through the reduction of platinum acetylacetonate by a diol, and decomposition of iron pentacarbonyl (Fe(CO)5 ) in the presence of a surfactant mixture (oleic acid and oleyl amine). On the basis of a similar approach, Chen and Nikles [217] synthesized ternary alloy nanoparticles (Fex Coy Pt100−x−y ), using a simultaneous reduction of acetylacetonate and platinum acetylacetonate and thermal decomposition of Fe(CO)5 and obtaining an average particle diameter of 3.5 nm and narrow particle size distribution. The general process of metal nanocrystal synthesis can be divided, for didactic purposes, into five steps. The first step (step I) consists of the reduction of the metallic precursor (M+ X− ), which results in metal atoms (Mo ). These metallic atoms, ions, and metallic clusters will interact (step II), resulting in a metallic cluster growth process. Steps I and II are reversible. When the cluster grows to a critical size (step III), the process becomes irreversible (thermodynamic condition). Particle size can be controlled with the aid of stabilizers (step IV). The presence of only one stabilizer can result in a spherical particle. The origin of this morphology is thermodynamic. In fact, and as extensively discussed earlier, the cluster will grow in a geometrical arrangement to minimize the surface energy. The presence of two simultaneous stabilizers may give rise to a preferential growth process caused by the preferential adsorption of one of the stabilizers. This process, which leads to the formation of anisotropic particles such as nanorods, occurs under a kinetic condition. Particle agglomeration, basically, is prevented by steric stabilization under the influence of the molecules attached to the particles’ surface (step V). Step V is essential to control nanoparticle deposition. Thus, colloidal metal dispersion can be used as a building block to produce functional materials [218]. The nanocrystal self-assembly process requires a monodispersion system (particle size deviating by less than 10% from the average size) [219] and can be achieved by solvent evaporation [18, 217] or polymer-mediated nanocrystal assembly [220].

5.3 Metal Oxide Nanocrystals Metal oxides represent an important class of materials with a variety of technological applications. In general, transition metal oxides are vital for a series of technologies, such as solar cells and Li ion batteries. Several reports in the literature describe the effects of size on the various properties of this class of materials. Nanocrystalline metal oxide semiconductors such as TiO2 , SnO2 and ZnO, for example, display

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a quantum confinement effect, with enlargement of the band gap as the particle size decreases [73, 135, 221]. Colloidal nanocrystals with quantum size effects are promising building blocks for novel electrical and optoelectronic devices [2, 222]. Based on the above analysis, the development of metal oxides of nanometric dimensions can result in devices and materials with superior performance. However, these developments are directly related to the development of synthetic methods that allow for controlled particle size, particle morphology, and deposition. Once again, the bottom-up methods of wet chemical nanocrystal synthesis are apparently the most viable approach to achieve such control. Compared with the control attained in the synthesis of metal and II-IV semiconductor nanocrystals, the control of metal oxide nanocrystals is still incipient, particularly insofar as the synthesis of complex metal oxide nanocrystals (oxides formed of more than one cation) is concerned. The synthesis of metal oxide nanocrystals by wet chemical processes can be divided basically into two major groups: (a) chemical synthesis method based on the hydrolysis of metal alkoxides or metal halides; (b) chemical synthesis based on the nonhydrolytic method. Examples of these methods are described below. The chemical synthesis of metal oxide nanocrystals based on hydrolysis falls into two major groups: hydrolysis of metal alkoxides; hydrolysis of metal halides, and other inorganic salts. Metal alkoxide compounds are defined as compounds that have metal–oxygen–carbon bonds. Si(OC2 H5 )4 (tetraethyl orthosilicate or TEOS), for instance, is an alkoxide compound. This class of compound is highly reactive with water. Because the hydroxyl ion (OH− ) becomes bonded to the metal of the organic precursor, this reaction is called hydrolysis. Equation (50) shows a typical hydrolytic reaction of an alkoxide compound [100]: M − OR + H2 O → M − OH ↓ + ROH

(50)

where M represents Si, Ti, Zr, Al, and other metals, R is a ligand such as an alkyl group, and ROH is an alcohol. Hydrolytic reactions are strongly dependent on water content and catalysts. Because of the high reactivity of alkoxide compounds with water, hydrolytic reactions must be carried out in an atmosphere devoid of water vapor and the solvents used must have very low water content. A partially hydrolyzed metal alkoxide molecule can react with other partially hydrolyzed molecules by a polycondensation reaction, as described in (51) and (52): M − OH + M − OR → M − O − M + ROH M − OH + M − OH → M − O − M + ROH

(51) (52)

This type of reaction leads to the formation of an inorganic polymer or a threedimensional network formed of metal oxianions. The above-described process is called metal alkoxide-based sol–gel. The literature contains excellent reports providing in-depth analyses of this method [100, 223]. The sol–gel process allows for very good chemical homogeneity and offers the possibility of obtaining metastable phases, including the amorphous phase. This process normally promotes the formation of amorphous metal oxides, which require thermal or hydrothermal treatment to promote crystallization. Several factors affect the sol–gel process, including the kind

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of metal alkoxide, pH of the reaction solution, water/alkoxide ratio, temperature, nature of the solvent and stabilizers [100]. By varying these parameters, particles can be synthesized with controlled size, morphology, and agglomeration. When the metal alkoxide’s hydrolytic reaction rate is too fast, particle size and morphology are more difficult to control. A good alternative to overcome this problem is to use organic additives, which act as chelating ligands (carboxylic acids, β -diketones, and others) and decrease the precursor’s reactivity [224]. The sol–gel process can generally be divided into three steps: (1) precipitation of hydrous oxide particles, (2) control of hydrous oxide particle coagulation, and (3) crystallization of the hydrous oxide particle. Thus, the sol–gel process requires control of the particle size and morphology during the precipitation and coagulation steps and during the heat or hydrothermal treatment to promote crystallization. The precipitation of amorphous metal oxide (step 1) is well described by the LaMer and Dinegar theory [225]. Following this model, the supersaturation of hydrous oxides increases continuously (by a change in temperature or pH) until a critical concentration is reached. In this condition, nucleation occurs very rapidly and leads to precipitation. Then, the applicability of the nucleation theory discussed above, in this case, is only achieved by considering the as-mentioned monomer, i.e., the solvated metallic ion. Precipitation decreases the supersaturation to levels below the critical concentration, preventing further nucleation and precipitation. After nucleation occurs, the nuclei thus formed grow, reducing the concentration until an equilibrium concentration is achieved. The growth of particles may then occur especially by the Ostwald ripening mechanism (48). Controlled hydrolysis is one of the most popular methods for processing silica spheres in the range of 10–1,000 nm. The method was developed by St¨ober, Fink, and Bohn (SFB) [226–229] and is based on the hydrolysis of TEOS in a basic solution of water and alcohol. Particle size depends on the reactant concentration, i.e., the TEOS/alcohol ratio, water concentration, and pH (>7). This method has been extended to other metal oxide systems with similar success, particularly for TiO2 synthesis [85, 230]. The hydrous oxide particles precipitated by the hydrolysis of an alkoxide compound have the same tendency to agglomerate as that described for metal colloid systems. Different stabilizers can be used to stabilize these particles and prevent coagulation (step 2). These stabilizers control coagulation by electrostatic repulsion or by steric effects [44], similarly to the metal colloid systems. There is not only a similarity but also a fundamental difference between the approach used to control coagulation in the sol–gel process and that used for metal nanocrystal systems. As previously discussed, in metal oxide particles the surface charge is controlled by the protonation or deprotonation of their hydrous oxide surfaces (M-OH). Thus, the charge-determining ions are H+ and OH− . The ease with which protonation or deprotonation occurs will depend on the metal atoms and can be controlled by the pH. Electrostatic stabilization is most commonly employed in the water solution system, while steric stabilization can be more effective in organic media [231, 232]. A steric stabilizer can be used to control the condensation reaction during the precipitation of hydrous oxides. In this case, the stabilizer is added during the hydrolysis

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step [86, 87, 233, 234]. Peir´o and coworkers [235] recently reported on the synthesis of TiO2 anatase phase with a nanorod morphology (9 × 5 nm size) using controlled hydrolysis of tetraisopropyl orthotitanate (TIP) and tetrabutylammonium hydroxide ((TBA)OH) as a steric stabilizing agent. Finally, the crystallization process (step 3) can be considered as the critical step in the sol–gel process when a crystalline phase is desirable. If an amorphous phase is the final target, as in the case of SiO2 nanoparticle processing, the synthesis is complete in step 2. However, for crystalline materials, a heat or hydrothermal treatment is often necessary to promote the crystallization of the generally amorphous hydrous oxide which is formed during hydrolysis. Such subsequent treatments can lead to particle growth and modify the particles’ morphology. In the case of crystallization by heat treatment, the hydrous oxide colloidal suspension must be dry before the treatment. During the heat treatment, normally done in an electric furnace, crystallization occurs by a nucleation growth process into the generated nucleus and can be described by the discussed nucleation and growth theory [100, 236]. Since the amorphous phase crystallizes via the nucleation-growth process, particle size and growth can be controlled based on the separation of the nucleation phenomena from the growth process. However, during crystallization, each hydrous metal oxide particle can generate several nuclei, rendering it very difficult to control particle morphology and shape. The polynuclei process generates polycrystalline particles rather than freestanding ones. Controlling the generation of polynuclei in a single amorphous particle is the main challenge involved in obtaining crystalline metal oxide freestanding nanoparticles through the sol–gel process or by any other process that requires crystallization by heat treatment at high temperatures. The origin of the polynuclei process occurring during sol–gel amorphous precursor crystallization is assumed to be related to the preferential heterogeneous nucleation process (at the surface and interface nucleation) in detriment to homogeneous nucleation. The presence of hydroxyl groups and other defects on the particle surface can contribute to reduce the Gibbs free energy for crystallization, rendering the surface crystallization more favorable than the bulk crystallization. Since crystallization occurs in a scenario of high driving force (high temperature of heat treatment), surface crystallization must occur first, followed or not by bulk crystallization, giving rise to a particle with several nuclei. A possible way to avoid this problem is to suppress surface crystallization by using an inhibitory surface layer. If crystallization occurs at a temperature that favors bulk crystallization, a single nucleus can be generated, resulting in a freestanding particle. This approach was used recently to process freestanding lead zirconate titanate (PZT) nanoparticles. Liu and coworkers [237] used a sol–gel process based on controlled hydrolysis and a twostep heat treatment. They first applied a 12-h treatment in Ar atmosphere at 700◦ C, which formed a surface layer rich in carbonaceous materials on the nanoparticles, inhibiting surface nucleation. A second treatment was carried out at 500–600◦ C, in air, to burn out the carbon residue. Freestanding PZT nanoparticles with a mean particle size of 17 nm were reported. Freestanding particles are desirable in a variety of fundamental studies and in some technologies, particularly for ferroelectric metal oxides such as PbTiO3

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(PT), Pb(Zr,Ti)O3 (PZT), BaTiO3 (BT), among others. Freestanding and single crystallinenanorods of BT and SrTiO3 (ST) were recently obtained [238, 239]. The approach used in both these studies to obtain this type of material was the injection of a bimetallic alkoxide compound into a solvent at high temperature (100–280◦ C), in which the hydrolysis took place (injection-hydrolysis method). O’Brien et al. [238] synthesized BT nanoparticles with diameters ranging from 6–12 nm based on this approach, controlling the particle size by the ratio BaTi(OR)6 /oleic acid. Urban and coworkers [239] reported on the synthesis of BT and ST single crystalline nanorods using a similar process. The origin of nanorod morphology is not yet well understood. Nonetheless, the above-described approach appears to promote and control crystallization with no extra heat treatment, allowing for good control of particle size and morphology. Another alternative approach to avoid the heat treatment process is to promote crystallization under hydrothermal conditions, a process that is widely used in the synthesis of zeolites [240, 241]. In hydrothermal conditions, the solubility of the amorphous oxide particle is significantly enhanced, and the crystallization may occur concurrently to growth processes, i.e., redissolution and reprecipitation of the particles – but in crystalline nuclei. Ying and Wang [242] used hydrothermal treatment to promote the crystallization of anatase and rutile phases, using an alkoxide sol–gel route and achieving the crystallization of anatase TiO2 phase with a mean particle size of 10 nm at 180◦ C, as well as the synthesis of ultra fine rutile TiO2 phase obtained by hydrothermal treatment in an acidic medium. The hydrolysis of metal halides and other inorganic salts is a method widely employed to process metal oxide nanoparticles, such as TiO2 [90, 243], doped and undoped SnO2 [244–248], ZnO temeulenkamp98, meulenkamp981 , wong98, ZrO2 [245, 250], Y2 O3 [251], and others. This process is less sensitive to water content, requiring less control than the hydrolysis of metal alkoxide. In fact, the hydrolytic process normally occurs in a water solution. In solution, the metallic salt generates n+ the anion (Cl− , F− , NO− 3 , and others) and the cation (M ). The cation is normally hydrolyzed by pH changing. Hydrolysis promotes the precipitation of an insoluble amorphous hydrous metal oxide. Thus, the steps used to describe the metal alkoxide hydrolysis-based sol–gel process can also be used to describe the sol–gel process based on inorganic salts. The synthesis based on this approach requires the same control described earlier for the sol–gel method related to the hydrolysis of metal alkoxide. However, control of the atmosphere and water content in the solvents is much less demanding. The crystallinity of the formed particle is, in any case, determined by thermodynamic and kinetic parameters. Leite and coworkers [252,253] recently demonstrated that well-crystallized SnO2 nanocrystals could be produced at room temperature with no hydrothermal treatment. This process is based on the hydrolysis of SnCl2 in an ethanol solution, followed by dialysis to remove the Cl− ions. The result of this dialysis is a transparent colloidal suspension formed by near-spheric particles, as illustrated in Fig. 9 later. Zinc Oxide (ZnO) nanocrystals have also been synthesized at room temperature. The process developed by Bahnemann et al. [67] consists of hydrolyzing zinc acetate dihydrate dissolved in 2-propanol by the addition of NaOH

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Fig. 9 Tin dioxide (SnO2 ) particles synthesized by hydrolysis of SnCl2 at room temperature. The final particles (after elimination of residual chloride by dialysis) are near-spherical nanocrystals

in a 2-propanol solution. A colloidal suspension of crystalline ZnO nanoparticles is obtained without hydrothermal treatment. Similar results were obtained by Spanhel and Anderson [254] and by Meulenkamp emeulenkamp98, meulenkamp981; however, they dissolved the zinc acetate dihydrate (Zn(Ac)2 · xH2 O) in ethanol and used LiOH to promote the Zn+2 hydrolysis. Particles in the range of 3–6 nm were reportedly obtained by both these processes. However, the most common product of synthesis is amorphous, like in metal alkoxide hydrolysis and, again, the major problem of the metal salts hydrolysis approach is the crystallization step. An adequate route to obtain good crystallinity at low temperatures with minimum particle growth is the hydrothermal treatment. N¨utz and Haase [244] synthesized well-crystallized Sb-doped SnO2 nanocrystals, with particles in the range of 4–9 nm, using a hydrothermal treatment of colloidal gel. The gel was treated in an autoclave at temperatures in excess of 250◦ C. The authors used a solution of SnCl4 and SbCl3 or SbCl5 in fuming HCl as precursors and promoted hydrolysis by increasing the pH (using aqueous ammonium). Goebbert et al. [247] also reported on the synthesis of well-crystallized Sb-doped SnO2 , using the hydrothermal process. However, they used a solution of SnCl4 and SbCl3 or SbCl5 in ethanol, promoting hydrolysis by raising the pH (using aqueous ammonium). The hydrothermal treatment was carried out at 150◦ C using 10 bar of pressure. This synthesization route produced nanocrystals in the range of 5 nm.

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Once again, control of growth after nucleation is necessary to obtain desirable nanoparticles. Rusakova et al. [255] used an interesting approach to control the particle growth of hydrous metal oxide gels. They showed that the growth could be inhibited by replacing the surface hydroxyl group, before the crystallization step, with a functional group that does not condense and that can produce small secondaryphase particles, which restrict boundary mobility at high temperatures. These authors reported that fully crystalline SnO2 , TiO2 , and ZrO2 nanocrystals (ranging in size from 1.5 to 5 nm) can be obtained after heat treating the precipitate gel at 500◦ C, by replacing the hydroxyl group with the methyl siloxyl group before firing. The development of metal oxide nanocrystals by nonhydrolytic synthesization routes results in materials whose surfaces are free of OH− groups and produces nanocrystals with different properties particularly suitable for catalytic and sensor applications. Several nonhydrolytic processes have been developed to process metal oxides, and the molecular chemistry of these various methods is discussed by Vioux [256]. On the basis of the strategy used to process II-IV semiconductor nanocrystals, using the rapid decomposition of molecular precursor in the presence of strong coordinating agents, Trentler and coworkers [88] proposed an interesting route to process TiO2 nanocrystals, based on the following reactions: TiX4 + Ti(OR)4 → 2TiO2 + RX

(53)

TiX4 + 2ROR → TiO2 + 4RX

(54)

where X is a halide ion (Cl− , F− , Br− , I− ) and R an alkyl group. The synthetic route involved injecting the metal alkoxide (Ti(OR)4 ) into a titanium halide mixed with trioctylphosphine oxide (TOPO) and a solvent at high temperature (300◦ C). Nanoparticles with a mean particle size of 7.3 nm and anatase phase were obtained. Alivisatos and collaborators [257] demonstrated that transition metal oxide nanocrystals (γ -Fe2 O3 , Mn3 O4 , Cu2 O) could be prepared using a nonhydrolytic process based on the thermal decomposition of metal Cupferron complexes Mx Cupx (M = metal ion, Cup = C6 H5 N(NO)O− ) in a hot solvent with surfactant. Their results suggest that a good level of control can be achieved when this approach is used to process metal oxide nanoparticles. Camargo et al. [258–261] recently developed a new route to synthesize leadbased perovskite nanoparticles, such as PT [260], PZT [259], PbZrO3 (PZ) [258], and PbHfO3 (PH) [261]. This method, which apparently involves no hydrolytic reaction and is carbon and halide-free, is called the oxidant peroxo method (OPM) because it is based on the oxidation–reduction reaction between Pb(II) ion and water-soluble metal-peroxide complexes with high pH. This process results in an inorganic amorphous precursor that requires subsequent thermal treatment to promote crystallization of the desired phase. The low crystallization temperatures (400–450◦ C for the PT phase) of the amorphous precursor suggest that the OPM method favors the formation of a homogeneous inorganic compound. An important nonhydrolytic chemical process is the so-called Pechini process or in situ polymerizable complex (IPC) [262]. This process is based on the ability of polycarboxylic acids, particularly citric acid (CA), to form very stable water-soluble

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chelate complexes. Even cations with a high tendency to become hydrolyzed, such as Ti+4 and Nb+5 , can be chelated by CA in a water solution, preventing the hydrolysis and precipitation of hydrous metal oxide. The CA complex thus formed can be immobilized in a solid organic resin through a polyesterification reaction with ethylene glycol (EG). This process leads to the formation of a polymeric precursor with the cations of interest randomly distributed in a three-dimensional solid lattice, avoiding precipitation or phase segregation during the synthesis of the metal oxide compound [263]. This method is widely used to process titanates [264–268], niobates [269–271] and other kinds of polycationic or single cationic metal oxides [272, 273]. In the last five years, this method has also proved suitable to process oxide thin films with superior performance [273–277]. Using this process, PbTiO3 thin film [277] and nanometric powder [278], for example, can be synthesized at temperatures as low as 450◦ C, resulting in a metastable cubic PbTiO3 phase. Crystallization was observed at a temperature at which long-range diffusion had to be constrained, and the thermodynamic equilibrium configuration was kinetically suppressed [278]. The ability to form complex metal oxides at low crystallization temperatures and metastable phases is not yet well understood, but it is generally assumed to be associated with the tendency of a poly-cationic CA complex to develop during the chelation step in water solution [279], and/or the tendency to form an inorganic amorphous phase, with a local symmetry close to that of the crystalline phase, during the crystallization step [280]. The major problem with this process is maintaining control over the particle size and morphology. During the crystallization process, it is very difficult to keep the nucleation and the growth processes separate, resulting in agglomerates made up of nanocrystals. The particle growth process, which was studied in the final stage of the crystallization of nanometric powder processed by the IPC method, showed that growth occurs in two different stages [281]. At heat treatment temperatures of 800◦ C, particle growth is controlled by densification of the agglomerate formed by nanometric particles and by the neck-size-controlled growth mechanism [282]. Basically, two methodologies have been used to control the particle size of metal oxides processed by the IPC method. Quinelato et al. [272] demonstrated that the particle size and morphology of CeO2 -doped ZrO2 could be controlled by controlling the metal/CA ratio. A high concentration of CA leads to smaller particles with a soft agglomeration. Leite and collaborators [283, 284] showed that the particle size and morphology of SnO2 could be controlled by the addition of dopants such as Nb2 O5 and rare earths. The same authors [284] also showed that doped SnO2 nanocrystals are highly stable against particle growth, even at high temperatures. The technique used to achieve this high stability was to process supersaturated solid solution between the SnO2 and the dopant. Segregation of the dopant on the nanocrystal surface occurs during the heat treatment, decreasing the particle boundary mobility or the surface energy. This approach was originally developed to control the particle growth of metal nanocrystals [5, 285] and was used successfully to control the growth of metal oxide nanocrystals.

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6 Summary As one can see, several properties can be explored on a nanoscale and an introductory view of the subject was discussed here. Advances in understanding nanoparticle formation mechanisms and the nature of nanoparticle properties undoubtedly offer the best pathway for developing viable nanotechnology and for augmenting the benefits of its use. Acknowledgments The authors gratefully acknowledge the financial support of the Brazilian research funding agencies FAPESP and CNPq.

References 1. L. V. Interrante and M. J. Hampden-Smith. Chemistry of Advanced Materials. Wiley, New York, NY, 1998 2. A. P. Alivisatos. Perspectives on the physical chemistry of semiconductor nanocrystals. J. Phys. Chem., 100:13226–13239, 1996 3. S. Morup. Nanomagnetism, chapter Studies of Superparamagnetism in Samples of Ultrafine Particles, pages 93–99. Kluwer, Boston, MA, 1993 4. K. O’Grady and R. W. Chantrell. Magnetic Properties of Fine Particles, chapter Magnetic Properties: Theory and Experiments. Elsevier, Amsterdan, 1992 5. H. Gleiter. Nanostructured materials: Basic concepts and microstructure. Acta Materialia, 48:1–29, 2000 6. M. Gratzel. Photoelectrochemical cells. Nature, 414:338–344, 2001 7. P. Mulvaney. Not all that’s gold does glitter. MRS Bull., 26:1009–1014, 2001 8. M. Faraday. The bakerian lecture: Experimental relations of gold (and other metals) to light. Philos. Trans. R. Soc., 147:145–181, 1857 9. B. Oregan and M. Gratzel. A low-cost, high-efficiency solar-cell based on dye-sensitized colloidal TiO2 films. Nature, 353:737–740, 1991 10. W. J. Li, H. Osora, L. Otero, D. C. Duncan, and M. A. Fox. Photoelectrochemistry of a substituted-Ru(bpy)(3)(2+)-labeled polyimide and nanocrystalline SnO2 composite formulated. J. Phys. Chem. A, 102:5333–5340, 1998 11. I. Bedja P. V., Kamat X., Hua A., Lappin G., and Hotchandani S. Photosensitization of nanocrystalline ZnO films by bis(2, 2 -bipyridine)(2, 2 -bipyridine-4,4 -dicarboxylic acid)ruthenium(ii). Langmuir, 13:2398–2403, 1997 12. L. Kavan, K. Kratochvilova, and M. Gratzel. Study of nanocrystalline TiO2 (anatase) electrode in the accumulation regime. J. Electroanal. Chem., 394:93–102, 1995 13. F. Croce, G. B. Appetecchi, L. Persi, and B. Scrosati. Nanocomposite polymer electrolytes for lithium batteries. Nature, 394:456–458, 1998 14. U. Bach, D. Lupo, P. Comte, J. E. Moser, F. Weissortel, J. Salbeck, H. Spreitzer, and M. Gratzel. Solid-state dye-sensitized mesoporous TiO2 solar cells with high photon-toelectron conversion efficiencies. Nature, 395:583–585, 1998 15. A. Hagfeldt and M. Gratzel. Light-induced redox reactions in nanocrystalline systems. Chem. Rev., 95:49–68, 1995 16. N. Yamazoe. New approaches for improving semiconductor gas sensors. Sens. Actuators B-Chem., 5:7–19, 1991 17. D. Weller and A. Moser. Thermal effect limits in ultrahigh-density magnetic recording. IEEE Trans. Magn., 35:4423–4439, 1999

68

C. Ribeiro and E.R. Leite

18. S. H. Sun, C. B. Murray, D. Weller, L. Folks, and A. Moser. Monodisperse FePt nanoparticles and ferromagnetic FePt nanocrystal superlattices. Science, 287:1989–1992, 2000 19. J. B. Dai, J. K. Tang, S. T. Hsu, and W. Pan. Magnetic nanostructures and materials in magnetic random access memory. J. Nanosci. Nanotechnol., 2:281–291, 2002 20. W. Chen, D. Grouquist, and J. Roark. Voltage tunable electroluminescence of CdTe nanoparticle light-emitting diodes. J. Nanosci. Nanotechnol., 2:47–53, 2002 21. V. L. Colvin, M. C. Schlamp, and A. P. Alivisatos. Light-emitting-diodes made from cadmium selenide nanocrystals and a semiconducting polymer. Nature, 370:354–357, 1994 22. C. Feldmann. Preparation of nanoscale pigment particles. Adv. Mater., 13:1301–1303, 2001 23. Y. M. Chiang, D. P. Birnie III, and W. D. Kingery. Physical Ceramics. Wiley, New York, NY, 1997 24. B. Gilbert, F. Huang, H. Z. Zhang, G. A. Waychunas, and J. F. Banfield. Nanoparticles: Strained and stiff. Science, 305:651–654, 2004 25. K. K. Nanda, S. N. Sahu, and S. N. Behera. Liquid-drop model for the size-dependent melting of low-dimensional systems. Phys. Rev. A, 66:013208–1–8, 2002 26. C. J. Coombes. The melting of small particles of lead and indium. J. Phys. F: Metal. Phys., 2:441–449, 1972 27. P. Buffat and J. P. Borel. Size effect on melting temperature of gold particles. Phys. Rev. A, 13:2287–2298, 1976 28. T. Castro, R. Reifenberger, E. Choi, and R. P. Andres. Size-dependent melting temperature of individual nanometer-sized metallic clusters. Phys. Rev. B, 42:8548–8556, 1990 29. C. L. Cleveland and U. Landman. The energetics and structure of nickel clusters – size dependence. J. Chem. Phys., 94:7376–7396, 1991 30. F. Ercolessi, W. Andreoni, and E. Tosatti. Melting of small gold particles – mechanism and size effects. Phys. Rev. Lett., 66:911–914, 1991 31. A. N. Goldstein, C. M. Echer, and A. P. Alivisatos. Melting in semiconductor nanocrystals. Science, 256:1425–1427, 1992 32. T. P. Martin, U. Naher, H. Schaber, and U. Zimmermann. Evidence for a size-dependent melting of sodium clusters. J. Chem. Phys., 100:2322–2324, 1994 33. J. B. Mitchel and J. T Schwartz. Preparation of Catalysts IV: Scientific Bases for the Preparation of Heterogeneous Catalysts (Studies in Surface Science and Catalysis), volume 31, chapter Catalyst preparation science. Elsevier, Amsterdan, 1987 34. J. Turkevich and G. Kim. Palladium – preparation and catalytic properties of particles of uniform size. Science, 169:873, 1970 35. H. Hirai, Y. Nakao, and N. Toshima. Colloidal rhodium in polyvinyl-alcohol as hydrogenation catalyst of olefins. Chem. Lett., 1976:905–910, 1976 36. D. N. Furlong, A. Launikonis, W. H. F. Sasse, and J. V. Sanders. Colloidal platinum sols – preparation, characterization and stability towards salt. J. Chem. Soc.-Farad. Trans. I, 80:571, 1984 37. T. Teranishi and M. Miyake. Size control of palladium nanoparticles and their crystal structures. Chem. Mater., 10:594–600, 1998 38. R. Narayanan and M. A. El-Sayed. Catalysis with transition metal nanoparticles in colloidal solution: Nanoparticle shape dependence and stability. J. Phys. Chem. B, 109:12663–12676, 2005 39. C. Burda, X. B. Chen, R. Narayanan, and M. A. El-Sayed. Chemistry and properties of nanocrystals of different shapes. Chem. Rev., 105:1025–1102, 2005 40. R. Narayanan and M. A. El-Sayed. Shape-dependent catalytic activity of platinum nanoparticles in colloidal solution. Nano Lett., 4:1343–1348, 2004 41. T. S. Ahmadi, Z. L. Wang, T. C. Green, A. Henglein, and M. A. ElSayed. Shape-controlled synthesis of colloidal platinum nanoparticles. Science, 272:1924–1926, 1996 42. J. S. Bradley. Clusters and Colloids: From Theory to Applications, chapter The Chemistry of Transition Metal Colloids, pages 459–544. VCH, Weinheim, 1994 43. E. R. Leite. Encyclopedia of Nanoscience and Nanotechnology, chapter Nanocrystals assembled from bottom-up, pages 537–550. American Scientific Publishers, 2004

Assembly and Properties of Nanoparticles

69

44. R. J. Pugh. Surface and Colloid Chemistry in Advanced Ceramics Processing, chapter Dispersion and Stability of Ceramic Powders in Liquids, pages 127–192. Marcel Dekker, NY, New York, 1994 45. G. A. Parks. Isoelectric points of solid oxides solid hydroxides and aqueous hydroxo complex systems. Chem. Rev., 65:177, 1965 46. Y. Yin and A. P. Alivisatos. Colloidal nanocrystal synthesis and the organic-inorganic interface. Nature, 437:664–670, 2005 47. X. Wang, J. Zhuang, Q. Peng, and Y. Li. A general strategy for nanocrystal synthesis. Nature, 473:121–124, 2005 48. Z. Y. Tang, N. A. Kotov, and M. Giersig. Spontaneous organization of single CdTe nanoparticles into luminescent nanowires. Science, 297:237–240, 2002 49. Y. Volkov, S. Mitchell, N. Gaponik, Y. P. Rakovich, J. F. Donegan, D. Kelleher, and A. L. Rogach. In-situ observation of nanowire growth from luminescent cdte nanocrystal in a phosphate buffer solution. Chem. Phys. Chem., 5:1600–1602, 2004 50. K. S. Cho, D. V. Talapin, W. Gaschler, and C. B. Murray. Designing PbSe nanowires and nanorings through oriented attachment of nanoparticles. J. Am. Chem. Soc., 127:7140–7147, 2005 51. N. J. Wagner and R. Klein. The rheology and microstructure of charged colloidal suspensions. Colloid Polym. Sci., 269:295–319, 1991 52. J. N´emeth and I. D´ek´any. The effect of nanoparticle growth on rheological properties of silica and silicate dispersions. Colloid Polym Sci., 278:211–219, 2000 53. V. Tohver, A. Chan, O. Sakurada, and J. A. Lewis. Nanoparticle engineering of complex fluid behavior. Langmuir, 17:8414–8421, 2001 54. V. Tohver, J. E. Smay, A. Braem, P. V. Braun, and J. A. Lewis. Nanoparticle halos: A new colloid stabilization mechanism. Proc. Natl Acad. Sci. U S A., 98:8950–8954, 2001 55. I. N. Levine. Quantum Chem. Prentice Hall, 5th edition, 1999 56. S. Folsch, P. Hyldgaard, R. Koch, and K. H. Ploog. Quantum confinement in monatomic Cu chains on cu(111). Phys. Rev. Lett., 92:056803–1–4, 2004 57. N. Nilius, T. M. Wallis, and W. Ho. Realization of a particle-in-a-box: Electron in an atomic pd chain. J. Phys. Chem. B, 109:20657–20660, 2005 58. W. P. Halperin. Quantum size effects in metal particles. Rev. Mod. Phys., 58:533–606, 1986 59. A. Kawabata and R. Kubo. Electronic properties of fine metallic particles.2. plasma resonance absorption. J. Phys. Soc. Jpn., 21:1765, 1966 60. R. Kubo, A. Kawabata, and S. Kobayashi. Electronic-properties of small particles. Ann. Rev. Mater. Sci., 14:49–66, 1984 61. L. E. Brus. A simple-model for the ionization-potential, electron-affinity, and aqueous redox potentials of small semiconductor crystallites. J. Chem. Phys., 79:5566–5571, 1983 62. L. E. Brus. Electron electron and electron-hole interactions in small semiconductor crystallites – the size dependence of the lowest excited electronic state. J. Chem. Phys., 80:4403– 4409, 1984 63. L. Brus. Electronic wave-functions in semiconductor clusters – experiment and theory. J. Phys. Chem., 90:2555–2560, 1986 64. S. V. Gaponenko. Optical Properties of Semiconductor Nanocrystals. Cambridge University Press, Cambridge, 1998 65. R. Rossetti, S. Nakahara, and L. E. Brus. Quantum size effects in the redox potentials, resonance Raman-spectra, and electronic-spectra of cds crystallites in aqueous-solution. J. Chem. Phys., 79:1086–1088, 1983 66. R. Rossetti, J. L. Ellison, J. M. Gibson, and L. E. Brus. Size effects in the excited electronic states of small colloidal cds crystallites. J. Chem. Phys., 80:4464–4469, 1984 67. D. W. Bahnemann, C. Kormann, and M. R. Hoffmann. Preparation and characterization of quantum size zinc-oxide – a detailed spectroscopic study. J. Phys. Chem., 91:3789–3798, 1987 68. A. P. Alivisatos, A. L. Harris, N. J. Levinos, M. L. Steigerwald, and L. E. Brus. Electronic states of semiconductor clusters – homogeneous and inhomogeneous broadening of the optical-spectrum. J. Chem. Phys., 89:4001–4011, 1988

70

C. Ribeiro and E.R. Leite

69. C. B. Murray, D. J. Norris, and M. G. Bawendi. Synthesis and characterization of nearly monodisperse cde (e = s, se, te) semiconductor nanocrystallites. J. Am. Chem. Soc., 115:8706–8715, 1993 70. X. G. Peng, J. Wickham, and A. P. Alivisatos. Kinetics of II–VI and III–V colloidal semiconductor nanocrystal growth: Focusing of size distributions. J. Am. Chem. Soc., 120:5343– 5344, 1998 71. G. Oskam, Z. S. Hu, R. L. Penn, N. Pesika, and P. C. Searson. Coarsening of metal oxide nanoparticles. Phys. Rev. E, 66:011403–1–4, 2002 72. N. S. Pesika, Z. S. Hu, K. J. Stebe, and P. C. Searson. Quenching of growth of ZnO nanoparticles by adsorption of octanethiol. J. Phys. Chem. B, 106:6985–6990, 2002 73. N. Chiodini, A. Paleari, D. DiMartino, and G. Spinolo. SNO2 nanocrystals in SiO2: A wideband-gap quantum-dot system. Appl. Phys. Lett., 81:1702–1704, 2002 74. Z. S. Hu, G. Oskam, R. L. Penn, N. Pesika, and P. C. Searson. The influence of anion on the coarsening kinetics of ZnO nanoparticles. J. Phys. Chem. B, 107:3124–3130, 2003 75. Z. S. Hu, G. Oskam, and P. C. Searson. Influence of solvent on the growth of ZnO nanoparticles. J. Colloid Interface Sci., 263:454–460, 2003 76. G. Oskam, A. Nellore, R. L. Penn, and P. C. Searson. The growth kinetics of TiO2 nanoparticles from titanium(IV) alkoxide at high water/titanium ratio. J. Phys. Chem. B, 107: 1734–1738, 2003 77. N. S. Pesika, K. J. Stebe, and P. C. Searson. Determination of the particle size distribution of quantum nanocrystals from absorbance spectra. Adv. Mater., 15:1289, 2003 78. N. S. Pesika, K. J. Stebe, and P. C. Searson. Relationship between absorbance spectra and particle size distributions for quantum-sized nanocrystals. J. Phys. Chem. B, 107:10412– 10415, 2003 79. E. J. H. Lee, C. Ribeiro, T. R. Giraldi, E. Longo, E. R. Leite, and J. A. Varela. Photoluminescence in quantum-confined SnO2 nanocrystals: Evidence of free exciton decay. Appl. Phys. Lett., 84:1745–1747, 2004 80. W. E. Buhro and V. L. Colvin. Semiconductor nanocrystals – Shape matters. Nat. Mater., 2:138–139, 2003 81. A. A. Kokhanovsky and E. P. Zege. Optical properties of aerosol particles: A review of approximate analytical solutions. J. Aerosol Sci., 28:1–21, 1997 82. G. Blasse and B. C. Grabmaier. Luminescent Materials. Springer, Berlin, 1 edition, 1994 83. C. Ribeiro, E. J. H. Lee, T. R. Giraldi, E. Longo, and E. R. Leite. Internal report, Federal University of Sao Carlos, unpublished work, 2003 84. A. Navrotsky and O. J. Kleppa. Enthalpy of anatase-rutile transformation. J. Am. Ceramic Soc., 50:626, 1967 85. E. A. Barringer and H. K. Bowen. High-purity, monodisperse TiO2 powders by hydrolysis of titanium tetraethoxide.1. synthesis and physical-properties. Langmuir, 1:414–420, 1985 86. J. H. Jean and T. A. Ring. Nucleation and growth of monosized TiO2 powders from alcohol solution. Langmuir, 2:251–255, 1986 87. T. E. Mates and T. A. Ring. Steric stability of alkoxy-precipitated TiO2 in alcohol-solutions. Colloids Surf., 24:299–313, 1987 88. T. J. Trentler, T. E. Denler, J. F. Bertone, A. Agrawal, and V. L. Colvin. Synthesis of TiO2 nanocrystals by nonhydrolytic solution-based reactions. J. Am. Chem. Soc., 121:1613–1614, 1999 89. G. Garnweitner, M. Antonietti, and M. Niederberger. Nonaqueous synthesis of crystalline anatase nanoparticles in simple ketones and aldehydes as oxygen-supplying agents. Chem. Comm., 3:397–399, 2005 90. J. Ragai and W. Lotfi. Effect of preparative ph and aging media on the crystallographic transformation of amorphous TiO2 to anatase and rutile. Colloids Surf., 61:97–109, 1991 91. S. Han, S. H. Choi, S. S. Kim, M. Cho, B. Jang, D. Y. Kim, J. Yoon, and T. Hyeon. Lowtemperature synthesis of highly crystalline TiO2 nanocrystals and their application to photocatalysis. Small, 1:812–816, 2005 92. H. Z. Zhang and J. F. Banfield. Kinetics of crystallization and crystal growth of nanocrystalline anatase in nanometer-sized amorphous titania. Chem. Mater., 14:4145–4154, 2002

Assembly and Properties of Nanoparticles

71

93. M. R. Ranade, A. Navrotsky, H. Z. Zhang, J. F. Banfield, S. H. Elder, A. Zaban, P. H. Borse, S. K. Kulkarni, G. S. Doran, and H. J. Whitfield. Energetics of nanocrystalline TiO2 . Proc. Natl Acad. Sci. U S A, 99:6476–6481, 2002 94. A. Navrotsky. Energetic clues to pathways to biomineralization: Precursors, clusters, and nanoparticles. Proc. Natl Acad. Sci. U S A, 101:12096–12101, 2004 95. A. S. Barnard and P. Zapol. Predicting the energetics, phase stability, and morphology evolution of faceted and spherical anatase nanocrystals. J. Phys. Chem. B, 108:18435–18440, 2004 96. A. S. Barnard and P. Zapol. Effects of particle morphology and surface hydrogenation on the phase stability of TiO2 . Phys. Rev. B, 70:235403–1–13, 2004 97. A. Paul. Chemistry of Glasses. Chapman and Hall, London, 1982 98. B. L. Cushing, V. L. Kolesnichenko, and C. J. OConnor. Recent advances in the liquid-phase syntheses of inorganic nanoparticles. Chem. Rev., 104:3893–3946, 2004 99. S. V. Ushakov and A. Navrotsky. Direct measurements of water adsorption enthalpy on hafnia and zirconia. App. Phys. Lett., 87:164103, 2005 100. C. J. Brinker and G. W. Scherrer. Sol–Gel Science. Academic, Boston, MA, 1990 101. D. V. Talapin, A. L. Rogach, M. Haase, and H. Weller. Evolution of an ensemble of nanoparticles in a colloidal solution: Theoretical study. J. Phys. Chem. B, 105:12278–12285, 2001 102. H. Z. Zhang, F. Huang, B. Gilbert, and J. F. Banfield. Molecular dynamics simulations, thermodynamic analysis, and experimental study of phase stability of zinc sulfide nanoparticles. J. Phys. Chem. B, 107:13051–13060, 2003 103. H. Z. Zhang and J. F. Banfield. Aggregation, coarsening, and phase transformation in zns nanoparticles studied by molecular dynamics simulations. Nano Lett., 4:713–718, 2004 104. F. Huang, B. Gilbert, H. H. Zhang, and J. F. Banfield. Reversible, surface-controlled structure transformation in nanoparticles induced by an aggregation state. Phys. Rev. Lett., 92:15550– 1–4, 2004 105. F. Huang, B. Gilbert, H. Zhang, M. P. Finnegan, J. R. Rustad, C. S. Kim, G. A. Waychunas, and J. F. Banfield. Interface interactions in nanoparticle aggregates. Geochim. Cosmochim. Acta, 68:A222–A222, 2004 106. H. Z. Zhang and J. F. Banfield. Size dependence of the kinetic rate constant for phase transformation in TiO2 nanoparticles. Chem. Mater., 17:3421–3425, 2005 107. F. Huang and J. F. Banfield. Size-dependent phase transformation kinetics in nanocrystalline zns. J. Am. Chem. Soc., 127:4523–4529, 2005 108. S. Toschev. Crystal Growth – an introduction, chapter Homogeneous nucleation, pages 1–49. Elsevier, Amsterdam 1973 109. A. S. Barnard and P. Zapol. A model for the phase stability of arbitrary nanoparticles as a function of size and shape. J. Chem. Phys., 121:4276–4283, 2004 110. S. H. Tolbert and A. P. Alivisatos. Size dependence of a first-order solid-solid phasetransition – the wurtzite to rock-salt transformation in CdSe nanocrystals. Science, 265: 373–376, 1994 111. S. H. Tolbert and A. P. Alivisatos. The wurtzite to rock-salt structural transformation in CdSe nanocrystals under high-pressure. J. Chem. Phys., 102:4642–4656, 1995 112. C. Herring. Some theorems on the free energies of crystal surfaces. Phys. Rev., 82:87–93, 1951 113. A. Beltran, J. Andres, E. Longo, and E. R. Leite. Thermodynamic argument about SnO2 nanoribbon growth. Appl. Phys. Lett., 83:635–637, 2003 114. J. Oviedo and M. J. Gillan. Energetics and structure of stoichiometric SnO2 surfaces studied by first-principles calculations. Surf. Sci., 463:93–101, 2000 115. P. A. Mulheran and J. H. Harding. The stability of SnO2 surfaces. Model. Simul. Mater. Sci. Eng., 1:39–43, 1992 116. B. Slater, C. R. A. Catlow, D. H. Gay, D. E. Williams, and V. Dusastre. Study of surface segregation of antimony on SnO2 surfaces by computer simulation techniques. J. Phys. Chem. B, 103:10644–10650, 1999

72

C. Ribeiro and E.R. Leite

117. M. J. Yacaman, J. A. Ascencio, H. B. Liu, and J. Gardea-Torresdey. Structure shape and stability of nanometric sized particles. J. Vac. Sci. Technol. B-an Int. J. Devoted to Microelectron. Nanometer Struct.-Process Meas. Phenomena, 19:1091–1103, 2001 118. B. Gilbert, H. Z. Zhang, F. Huang, M. P. Finnegan, G. A. Waychunas, and J. F. Banfield. Special phase transformation and crystal growth pathways observed in nanoparticles. Geochem. Trans., 4:20–27, 2003 119. B. Gilbert, H. Z. Zhang, F. Huang, J. F. Banfield, Y. Ren, D. Haskel, J. C. Lang, G. Srajer, A. Jurgensen, and G. A. Waychunas. Analysis and simulation of the structure of nanoparticles that undergo a surface-driven structural transformation. J. Chem. Phys., 120:11785–11795, 2004 120. H. Z. Zhang, B. Gilbert, F. Huang, and J. F. Banfield. Water-driven structure transformation in nanoparticles at room temperature. Nature, 424:1025–1029, 2003 121. A. S. Barnard, P. Zapol, and L. A. Curtiss. Modeling the morphology and phase stability of TiO2 nanocrystals in water. J. Chem. Theory Comput., 1:107–116, 2005 122. P. P. von Weimarn. The precipitation laws. Chem. Rev., 2:217–242, 1925 123. M. Zurita-Gotor and D. E. Rosner. Aggregate size distribution evolution for brownian coagulation – sensitivity to an improved rate constant. J. Colloid Interface Sci., 274:502–514, 2004 124. B. Mutaftschiev. Handbook of Crystal Growth, chapter Nucleation, page 187. Elsevier Science, Amsterdam, 1993 125. B. K. Chakraverty. Crystal Growth – An Introduction, chapter Heterogeneous nucleation and condensation on substrates, pages 50–104. Elsevier, Amsterdam, 1973 126. G. H. Weiss. Overview of theoretical models for reaction rates. J. Stat. Phys., 42:3–36, 1986 127. D. P. Dinega and M. G. Bawendi. A solution-phase chemical approach to a new crystal structure of cobalt. Angewandte Chemie-international Edition, 38:1788–1791, 1999 128. P. Jensen. Growth of nanostructures by cluster deposition: Experiments and simple models. Rev. Mod. Phys., 71:1695–1735, 1999 129. M. Aoun, E. Plasari, R. David, and J. Villermaux. A simultaneous determination of nucleation and growth rates from batch spontaneous precipitation. Chem. Eng. Sci., 54:1161–1180, 1999 130. R. Zauner and A. G. Jones. Determination of nucleation, growth, agglomeration and disruption kinetics from experimental precipitation data: the calcium oxalate system. Chem. Eng. Sci., 55:4219–4232, 2000 131. S. A. Kukushkin and S. V. Nemna. The effect of pH on nucleation kinetics in solutions. Doklady Phys. Chem., 377(6):792–796, 2000 132. E. A. Meulenkamp. Size dependence of the dissolution of ZnO nanoparticles. J. Phys. Chem. B, 102:7764–7769, 1998 133. G. W. Greenwood. The growth of dispersed precipitates in solutions. Acta Metallurgica, 4:243–248, 1956 134. S. A. Kukushkin and A. V. Osipov. Crystallization of binary melts and decay of supersaturated solid solutions at the ostwald ripening stage under non-isothermal conditions. J. Phys. Chem. Solids, 56:1259–1269, 1995 135. E. M. Wong, J. E. Bonevich, and P. C. Searson. Growth kinetics of nanocrystalline ZnO particles from colloidal suspensions. J. Phys. Chem. B, 102:7770–7775, 1998 136. E. M. Wong, P. G. Hoertz, C. J. Liang, B. M. Shi, G. J. Meyer, and P. C. Searson. Influence of organic capping ligands on the growth kinetics of ZnO nanoparticles. Langmuir, 17:8362– 8367, 2001 137. F. Huang, H. Z. Zhang, and J. F. Banfield. Two-stage crystal-growth kinetics observed during hydrothermal coarsening of nanocrystalline ZnS. Nano Lett., 3:373–378, 2003 138. I. M. Lifshitz and V. V. Slyozov. The kinetics of precipitation from supersaturated solid solutions. J. Phys. Chem. Solids, 19:35–50, 1961 139. C. Wagner. Theorie der alterung von niederschlagen durch umlosen (ostwald-reifung). Z. Elektrochem., 65:581–591, 1961 140. H. Gr¨atz. Ostwald ripening: New relations betwenn particle growth and particle size distribution. Scrip. Mater., 37:9–16, 1997

Assembly and Properties of Nanoparticles

73

141. R. L. Penn, G. Oskam, T. J. Strathmann, P. C. Searson, A. T. Stone, and D. R. Veblen. Epitaxial assembly in aged colloids. J. Phys. Chem. B, 105:2177–2182, 2001 142. J. F. Banfield, S. A. Welch, H. Z. Zhang, T. T. Ebert, and R. L. Penn. Aggregation-based crystal growth and microstructure development in natural iron oxyhydroxide biomineralization products. Science, 289:751–754, 2000 143. X. G. Peng, L. Manna, W. D. Yang, J. Wickham, E. Scher, A. Kadavanich, and A. P. Alivisatos. Shape control of CdSe nanocrystals. Nature, 404:59–61, 2000 144. R. L. Penn and J. F. Banfield. Morphology development and crystal growth in nanocrystalline aggregates under hydrothermal conditions: Insights from titania. Geochim. Cosmochim. Acta, 63:1549–1557, 1999 ´ 145. E. J. H. Lee. S´ıntese e caracterizac¸a˜ o de nanopart´ıculas de Oxido de estanho obtidas a partir de suspens˜oes coloidais. Master’s thesis, Univ. Fed. S. Carlos, 2004 146. M. Nespolo and G. Ferraris. The oriented attachment mechanims in the formation of twins – a survey. Eur. J. Mineral., 16:401–406, 2004 147. M. Nespolo, G. Ferraris, S. Durovic, and Y. Takeuchi. Twins vs. modular crystal structures. Z. Kristallogr., 219:773–778, 2004 148. M. Nespolo and G. Ferraris. Applied geminography – symmetry analysis of twinned crystals and definition of twinning by reticular polyholohedry. Acta Cryst. A, 60:89–95, 2004 149. M. Nespolo and G. Ferraris. Hybrid twinning – a cooperative type of oriented crystal association. Z. Kristallogr., 220:317–323, 2005 150. R. L. Penn and J. F. Banfield. Oriented attachment and growth, twinning, polytypism, and formation of metastable phases: Insights from nanocrystalline TiO2 . Am. Mineralogist, 83: 1077–1082, 1998 151. Y. Chushkin, M. Ulmeanu, S. Luby, E. Majkova, I. Kostic, P. Klang, V. Holy, Z. Bochnicek, M. Giersig, M. Hilgendorff, and T. H. Metzger. Structural study of self-assembled Co nanoparticles. J. Appl. Phys., 94:7743–7748, 2003 152. J. Polleux, N. Pinna, M. Antonietti, and M. Niederberger. Ligand-directed assembly of preformed titania nanocrystals into highly anisotropic nanostructures. Adv. Mater., 16:436–439, 2004 153. J. Polleux, N. Pinna, M. Antonietti, C. Hess, U. Wild, R. Schlogl, and M. Niederberger. Ligand functionality as a versatile tool to control the assembly behavior of preformed titania nanocrystals. Chem.-a Europ. J., 11:3541–3551, 2005 154. E. J. H. Lee, C. Ribeiro, E. Longo, and E. R. Leite. Oriented attachment: An effective mechanism in the formation of anisotropic nanocrystals. J. Phys. Chem. B, 109:20842–20846, 2005 155. W. W. Mullins. 2-dimensional motion of idealized grain boundaries. J. Appl. Phys., 27:900– 904, 1956 156. P. Feltham. Grain growth in metals. Acta Metallurgica, 5:97–105, 1957 157. M. Hillert. On theory of normal and abnormal grain growth. Acta Metallurgica, 13:227, 1965 158. N. P. Louat. Theory of normal grain-growth. Acta Metallurgica, 22:721–724, 1974 159. G. Herrmann, H. Gleiter, and G. Baro. Investigation of low-energy grain-boundaries in metals by a sintering technique. Acta. Met., 24:353–359, 1976 160. H. Sautter, H. Gleiter, and G. Baro. Effect of solute atoms on energy and structure of grainboundaries. Acta. Met., 25:467–473, 1977 161. U. Erb and H. Gleiter. Effect of temperature on the energy and structure of grain-boundaries. Scrip. Metall., 13:61–64, 1979 162. H. Kuhn, G. Baero, and H. Gleiter. Energy-misorientation relationship of grain-boundaries. Acta. Met., 27:959–963, 1979. 163. D. Moldovan, D. Wolf, and S. R. Phillpot. Theory of diffusion-accommodated grain rotation in columnar polycrystalline microstructures. Acta Materialia, 49:3521–3532, 2001 164. D. Moldovan, V. Yamakov, D. Wolf, and S. R. Phillpot. Scaling behavior of grain-rotationinduced grain growth. Phys. Rev. Lett., 89:206101–1, 2002 165. D. Moldovan, D. Wolf, S. R. Phillpot, and A. J. Haslam. Role of grain rotation during grain growth in a columnar microstructure by mesoscale simulation. Acta Materialia, 50: 3397–3414, 2002

74

C. Ribeiro and E.R. Leite

166. A. J. Haslam, D. Moldovan, V. Yamakov, D. Wolf, S. R. Phillpot, and H. Gleiter. Stressenhanced grain growth in a nanocrystalline material by molecular-dynamics simulation. Acta Materialia, 51:2097–2112, 2003 167. H. L. Zhu and R. S. Averback. Sintering of nano-particle powders: Simulations and experiments. Mater. Manuf. Process., 11:905–923, 1996 168. H. L. Zhu and R. S. Averback. Sintering processes of two nanoparticles: A study by molecular-dynamics. Philos. Mag. Lett., 73:27–33, 1996 169. M. Yeadon, J. C. Yang, R. S. Averback, J. W. Bullard, D. L. Olynick, and J. M. Gibson. In-situ observations of classical grain growth mechanisms during sintering of copper nanoparticles on (001) copper. Appl. Phys. Lett., 71:1631–1633, 1997 170. M. Yeadon, M. Ghaly, J. C. Yang, R. S. Averback, and J. M. Gibson. Contact epitaxy observed in supported nanoparticles. Appl. Phys. Lett., 73:3208–3210, 1998 171. K. E. Harris, V. V. Singh, and A. H. King. Grain rotation in thin films of gold. Acta Materialia, 46:2623–2633, 1998 172. C. Ribeiro, E. J. H. Lee, T. R. Giraldi, R. Aguiar, E. Longo, and E. R. Leite. In situ oriented crystal growth in a ceramic nanostructured system. J. Appl. Phys., 97:024313–1–4, 2005 173. S. A. Kukushkin and A. V. Osipov. New phase formation on solid surfaces and thin film condensation. Prog. Surf. Sci., 5:1–107, 1996 174. F. Huang, H. Z. Zhang, and J. F. Banfield. The role of oriented attachment crystal growth in hydrothermal coarsening of nanocrystalline ZnS. J. Phys. Chem. B, 107:10470–10475, 2003 175. R. L. Penn. Kinetics of oriented aggregation. J. Phys. Chem. B, 108:12707–12712, 2004 176. C. Ribeiro, E. J. H. Lee, T. R. Giraldi, J. A. Varela, E. Longo, and E. R. Leite. Study of synthesis variables in the nanocrystal growth behavior of tin oxide processed by controlled hydrolysis. J. Phys. Chem. B, 108:15612–15617, 2004 177. M. von Smoluchowski. Versuch einer mathematischen theorie der koagulationkinetik kollider l¨osungen. Z. Phys. Chem., Stoechiom. Verwandtschaftsl, 29:129–168, 1917 178. D. Mozyrsky and V. Privman. Diffusional growth of colloids. J. Chem. Phys., 110:9254– 9258, 1999 179. N. J. Wagner. The smoluchowski equation for colloidal suspensions developed and analyzed through the generic formalism. J. Non-newtonian Fluid Mech., 96:177–201, 2001 180. O. A. Linnikov. Spontaneous crystallization of potassium chloride from aqueous and aqueous-ethanol solutions part 1: Kinetics and mechanism of the crystallization process. Cryst. Res. Technol., 39:516–528, 2004 181. O. A. Linnikov. Spontaneous crystallization of potassium chloride from aqueous and aqueous-ethanol solutions part 2: Mechanism of aggregation and coalescence of crystals. Cryst. Res. Technol., 39:529–539, 2004 182. T. Arita, O. Kajimoto, M. Terazima, and Y. Kimura. Experimental verification of the smoluchowski theory for a bimolecular diffusion-controlled reaction in liquid phase. J. Chem. Phys., 120:7071–7074, 2004 183. J. H. Yu, J. Joo, H. M. Park, S. I. Baik, Y. W. Kim, S. C. Kim, and T. Hyeon. Synthesis of quantum-sized cubic ZnS nanorods by the oriented attachment mechanism. J. Am. Chem. Soc., 127:5662–5670, 2005 184. D. V. Talapin, E. V. Shevchenko, C. B. Murray, A. Kornowski, S. Forster, and H. Weller. Cdse and CdSe/CdS nanorod solids. J. Am. Chem. Soc., 126:12984–12988, 2004 185. M. Adachi, Y. Murata, J. Takao, J. T. Jiu, M. Sakamoto, and F. M. Wang. Highly efficient dye-sensitized solar cells with a titania thin-film electrode composed of a network structure of single-crystal-like TiO2 nanowires made by the “oriented attachment” mechanism. J. Am. Chem. Soc., 126:14943–14949, 2004 186. L. Vayssieres, C. Chaneac, E. Tronc, and J. P. Jolivet. Size tailoring of magnetite particles formed by aqueous precipitation: An example of thermodynamic stability of nanometric oxide particles. J. Colloid Interface Sci., 205:205–212, 1998 187. L. Vayssieres, A. Hagfeldt, and S. E. Lindquist. Purpose-built metal oxide nanomaterials. The emergence of a new generation of smart materials. Pure Appl. Chem., 72:47–52, 2000 188. L. Vayssieres, K. Keis, A. Hagfeldt, and S. E. Lindquist. Three-dimensional array of highly oriented crystalline ZnO microtubes. Chem. Mater., 13:4395–4398, 2001

Assembly and Properties of Nanoparticles

75

189. L. Vayssieres, K. Keis, S. E. Lindquist, and A. Hagfeldt. Purpose-built anisotropic metal oxide material: 3D highly oriented microrod array of zno. J. Phys. Chem. B, 105:3350–3352, 2001 190. L. Vayssieres, N. Beermann, S. E. Lindquist, and A. Hagfeldt. Controlled aqueous chemical growth of oriented three-dimensional crystalline nanorod arrays: Application to iron(III) oxides. Chem. Mater., 13:233–235, 2001 191. L. Vayssieres, L. Rabenberg, and A. Manthiram. Aqueous chemical route to ferromagnetic 3-d Arrays of iron nanorods. Nano Lett., 2:1393–1395, 2002 192. L. Vayssieres and A. Manthiram. 2-d mesoparticulate arrays of alpha-Cr2 O3 . J. Phys. Chem. B, 107:2623–2625, 2003 193. L. Vayssieres. Growth of arrayed nanorods and nanowires of ZnO from aqueous solutions. Adv. Mater., 15:464–466, 2003 194. L. Vayssieres and M. Graetzel. Highly ordered SnO2 nanorod arrays from controlled aqueous growth. Angewandte Chemie-international Edition, 43:3666–3670, 2004 195. L. Vayssieres, C. Sathe, S. M. Butorin, D. K. Shuh, J. Nordgren, and J. H. Guo. Onedimensional quantum-confinement effect in alpha-Fe2 O3 ultrafine nanorod arrays. Adv. Mater., 17:2320, 2005 196. J. Turkevich, P. C. Stevenson, and J. Hillier. A study of the nucleation and growth processes in the synthesis of colloidal gold. Discuss. Farad. Soc., 11:55, 1951 197. H. Bonnemann and R. M. Richards. Nanoscopic metal particles – Synthetic methods and potential applications. Europ. J. Inorg. Chem., 10:2455–2480, 2001 198. E. Bourgeat-Lami. Organic-inorganic nanostructured colloids. J. Nanosci. Nanotechnol., 2:1–24, 2002 199. C. Sanchez, G. J. D. A. Soler-Illia, F. Ribot, T. Lalot, C. R. Mayer, and V. Cabuil. Designed hybrid organic-inorganic nanocomposites from functional nanobuilding blocks. Chem. Mater., 13:3061–3083, 2001 200. J. S. Bradley, J. M. Millar, and E. W. Hill. Surface-chemistry on colloidal metals – a highresolution nuclear-magnetic-resonance study of carbon-monoxide adsorbed on metallic palladium crystallites in colloidal suspension. J. Am. Chem. Soc., 113:4016–4017, 1991 201. M. A. Hayat. Colloidal Gold: Methods and Applications. Academic, San Diego, CA, 1989 202. C. D. Keating, M. D. Musick, M. H. Keefe, and M. J. Natan. Kinetics and thermodynamics of Au colloid monolayer self-assembly – undergraduate experiments in surface and nanomaterials chemistry. J. Chem. Education, 76:949–955, 1999 203. P. R. Vanrheenen, M. J. Mckelvy, and W. S. Glaunsinger. Synthesis and characterization of small platinum particles formed by the chemical-reduction of chloroplatinic acid. J. Solid State Chem., 67:151–169, 1987 204. T. Ould Ely, C. Amiens, B. Chaudret, E. Snoeck, M. Verelst, M. Respaud, and J. M. Broto. Synthesis of nickel nanoparticles. Influence of aggregation induced by modification of poly(vinylpyrrolidone) chain length on their magnetic properties. Chem. Mater., 11:526–+, 1999 205. F. Dassenoy, K. Philippot, T. Ould-Ely, C. Amiens, P. Lecante, E. Snoeck, A. Mosset, M. J. Casanove, and B. Chaudret. Platinum nanoparticles stabilized by CO and octanethiol ligands or polymers: FT-IR, NMR, HREM and WAXS studies. New J. Chem., 22:703–711, 1998 206. J. Osuna, D. deCaro, C. Amiens, B. Chaudret, E. Snoeck, M. Respaud, J. M. Broto, and A. Fert. Synthesis, characterization, and magnetic properties of cobalt nanoparticles from an organometallic precursor. J. Phys. Chem., 100:14571–14574, 1996 207. A. Rodriguez, C. Amiens, B. Chaudret, M. J. Casanove, P. Lecante, and J. S. Bradley. Synthesis and isolation of cuboctahedral and icosahedral platinum nanoparticles. ligand-dependent structures. Chem. Mater., 8:1978–1986, 1996 208. A. Duteil, R. Queau, B. Chaudret, R. Mazel, C. Roucau, and J. S. Bradley. Preparation of organic solutions or solid films of small particles of ruthenium, palladium, and platinum from organometallic precursors in the presence of cellulose derivatives. Chem. Mater., 5: 341–347, 1993

76

C. Ribeiro and E.R. Leite

209. T. Ould Ely, C. Pan, C. Amiens, B. Chaudret, F. Dassenoy, P. Lecante, M. J. Casanove, A. Mosset, M. Respaud, and J. M. Broto. Nanoscale bimetallic CoxPt1-x particles dispersed in poly(vinylpyrrolidone): Synthesis from organometallic precursors and characterization. J. Phys. Chem. B, 104:695–702, 2000 210. M. Figlarz. Chimie-douce – a new route for the preparation of new materials – some examples. Chemica Scripta, 28:3–7, 1988 211. G. Viau, F. Ravel, O. Acher, F. Fievetvincent, and F. Fievet. Preparation and microwave characterization of spherical and monodisperse co-ni particles. J. Magn. Magn. Mater., 140: 377–378, 1995 212. C. B. Murray, S. H. Sun, H. Doyle, and T. Betley. Monodisperse 3d transition-metal (Co, Ni, Fe) nanoparticles and their assembly into nanoparticle superlattices. MRS Bull., 26:985–991, 2001 213. J. I. Park and J. Cheon. Synthesis of “solid solution” and “core-shell” type cobalt-platinum magnetic nanoparticles via transmetalation reactions. J. Am. Chem. Soc., 123:5743–5746, 2001 214. J. R. Thomas. Preparation and magnetic properties of colloidal cobalt particles. J. Appl. Phys., 37:2914, 1966 215. S. J. Park, S. Kim, S. Lee, Z. G. Khim, K. Char, and T. Hyeon. Synthesis and magnetic studies of uniform iron nanorods and nanospheres. J. Am. Chem. Soc., 122:8581–8582, 2000 216. V. F. Puntes, K. M. Krishnan, and A. P. Alivisatos. Colloidal nanocrystal shape and size control: The case of cobalt. Science, 291:2115–2117, 2001 217. M. Chen and D. E. Nikles. Synthesis, self-assembly, and magnetic properties of FexCoyPt100-x-y nanoparticles. Nano Lett., 2:211–214, 2002 218. S. R. Whaley, D. S. English, E. L. Hu, P. F. Barbara, and A. M. Belcher. Selection of peptides with semiconductor binding specificity for directed nanocrystal assembly. Nature, 405: 665–668, 2000 219. L. O. Brown and J. E. Hutchison. Formation and electron diffraction studies of ordered 2-D and 3-D superlattices of amine-stabilized gold nanocrystals. J. Phys. Chem. B, 105: 8911–8916, 2001 220. S. H. Sun, S. Anders, H. F. Hamann, J. U. Thiele, J. E. E. Baglin, T. Thomson, E. E. Fullerton, C. B. Murray, and B. D. Terris. Polymer mediated self-assembly of magnetic nanoparticles. J. Am. Chem. Soc., 124:2884–2885, 2002 221. A. L. Roest, J. J. Kelly, D. Vanmaekelbergh, and E. A. Meulenkamp. Staircase in the electron mobility of a ZnO quantum dot assembly due to shell filling. Phys. Rev. Lett., 89:36801–1–4, 2002 222. H. Weller. Quantized semiconductor particles – a novel state of matter for materials science. Adv. Mater., 5:88–95, 1993 223. J. Y. Ying. Preface to the special issue: Sol-gel derived materials. Chem. Mater., 9:2247– 2248, 1997 224. C. Sanchez, J. Livage, M. Henry, and F. Babonneau. Chemical modification of alkoxide precursors. J. Non-Cryst. Solids, 100:65–76, 1988 225. V. K. Lamer and R. H. Dinegar. Theory, production and mechanism of formation of monodispersed hydrosols. J. Am. Chem. Soc., 72:4847–4854, 1950 226. W. Stober, A. Fink, and E. Bohn. Controlled growth of monodisperse silica spheres in micron size range. J. Colloid Interface Sci., 26:62, 1968 227. H. Boukari, J. S. Lin, and M. T. Harris. Probing the dynamics of the silica nanostructure formation and growth by saxs. Chem. Mater., 9:2376–2384, 1997 228. H. Boukari, J. S. Lin, and M. T. Harris. Small-angle x-ray scattering study of the formation of colloidal silica particles from alkoxides: Primary particles or not? J. Colloid Interface Sci., 194:311–318, 1997 229. H. Boukari, G. G. Long, and M. T. Harris. Polydispersity during the formation and growth of the stober silica particles from small-angle x-ray scattering measurements. J. Colloid Interface Sci., 229:129–139, 2000 230. M. T. Harris and C. H. Byers. Effect of solvent on the homogeneous precipitation of titania by titanium ethoxide hydrolysis. J. Non-Cryst. Solids, 103:49–64, 1988

Assembly and Properties of Nanoparticles

77

231. T. Sato and R. Ruch. Stabilization of Colloidal Dispersion by Polymer Adsorption. Marcel Dekker , New York, 1980 232. D. H. Napper. Polymer Stabilization of Colloidal Dispersion. Academic, New York, 1983 233. J. L. Look and C. F. Zukoski. Alkoxide-derived titania particles – use of electrolytes to control size and agglomeration levels. J. Am. Ceramic Soc., 75:1587–1595, 1992 234. J. L. Deiss, P. Anizan, S. ElHadigui, and C. Wecker. Steric stability of TiO2 nanoparticles in aqueous dispersions. Colloids Surf. A-physicochem. Eng. Aspects, 106:59–62, 1996 235. A. M. Peiro, J. Peral, C. Domingo, X. Domenech, and J. A. Ayllon. Low-temperature deposition of TiO2 thin films with photocatalytic activity from colloidal anatase aqueous solutions. Chem. Mater., 13:2567–2573, 2001 236. R. W. Schwartz. Chemical solution deposition of perovskite thin films. Chem. Mater., 9:2325–2340, 1997 237. C. Liu, B. S. Zou, A. J. Rondinone, and Z. J. Zhang. Sol–gel synthesis of free-standing ferroelectric lead zirconate titanate nanoparticles. J. Am. Chem. Soc., 123:4344–4345, 2001 238. S. O’Brien, L. Brus, and C. B. Murray. Synthesis of monodisperse nanoparticles of barium titanate: Toward a generalized strategy of oxide nanoparticle synthesis. J. Am. Chem. Soc., 123:12085–12086, 2001 239. J. J. Urban, W. S. Yun, Q. Gu, and H. Park. Synthesis of single-crystalline perovskite nanorods composed of barium titanate and strontium titanate. J. Am. Chem. Soc., 124: 1186–1187, 2002 240. R. M. Barrer. Hydrothermal Chemistry of Zeolites. Academic, London, 1982 241. S. Mintova, N. H. Olson, V. Valtchev, and T. Bein. Mechanism of zeolite a nanocrystal growth from colloids at room temperature. Science, 283:958–960, 1999 242. C. C. Wang and J. Y. Ying. Sol-gel synthesis and hydrothermal processing of anatase and rutile titania nanocrystals. Chem. Mater., 11:3113–3120, 1999 243. L. X. Cao, H. B. Wan, L. H. Huo, and S. Q. Xi. A novel method for preparing ordered SnO2 /TiO2 alternate nanoparticulate films. J. Colloid Interface Sci., 244:97–101, 2001 244. T. Nutz and M. Haase. Wet-chemical synthesis of doped nanoparticles: Optical properties of oxygen-deficient and antimony-doped colloidal SnO2 . J. Phys. Chem. B, 104:8430–8437, 2000 245. G. S. Pang, S. G. Chen, Y. Koltypin, A. Zaban, S. H. Feng, and A. Gedanken. Controlling the particle size of calcined SnO2 nanocrystals. Nano Lett., 1:723–726, 2001 246. R. S. Hiratsuka, S. H. Pulcinelli, and C. V. Santilli. Formation of SnO2 gels from dispersed sols in aqueous colloidal solutions. J. Non-crystalline Solids, 121:76–83, 1990 247. C. Goebbert, R. Nonninger, M. A. Aegerter, and H. Schmidt. Wet chemical deposition of ATO and ITO coatings using crystalline nanoparticles redispersable in solutions. Thin Solid Films, 351:79–84, 1999 248. A. P. Rizzato, L. Broussous, C. V. Santilli, S. H. Pulcinelli, and A. F. Craievich. Structure of SnO2 alcosols and films prepared by sol-gel dip coating. J. Non-Crystalline Solids, 284:61– 67, 2001 249. E. A. Meulenkamp. Synthesis and growth of ZnO nanoparticles. J. Phys. Chem. B, 102: 5566–5572, 1998 250. M. Z. C. Hu, R. D. Hunt, E. A. Payzant, and C. R. Hubbard. Nanocrystallization and phase transformation in monodispersed ultrafine zirconia particles from various homogeneous precipitation methods. J. Am. Ceramic Soc., 82:2313–2320, 1999 251. M. D. Fokema, E. Chiu, and J. Y. Ying. Synthesis and characterization of nanocrystalline yttrium oxide prepared with tetraalkylammonium hydroxides. Langmuir, 16:3154–3159, 2000 252. E. R. Leite, T. R. Giraldi, F. M. Pontes, E. Longo, A. Beltran, and J. Andres. Crystal growth in colloidal tin oxide nanocrystals induced by coalescence at room temperature. Appl. Phys. Lett., 83:1566–1568, 2003 253. E. R. Leite, E. J. H. Lee, T. R. Giraldi, F. M. Pontes, and E. Longo. A simple and novel method to synthesize doped and undoped SnO2 nanocrystals at room temperature. J. Nanosci. Nanotechnol., 4:774–778, 2004

78

C. Ribeiro and E.R. Leite

254. L. Spanhel and M. A. Anderson. Semiconductor clusters in the sol–gel process – quantized aggregation, gelation, and crystal-growth in concentrated zno colloids. J. Am. Chem. Soc., 113:2826–2833, 1991 255. N. L. Wu, S. Y. Wang, and I. A. Rusakova. Inhibition of crystallite growth in the sol–gel synthesis of nanocrystalline metal oxides. Science, 285:1375–1377, 1999 256. A. Vioux. Nonhydrolytic sol-gel routes to oxides. Chem. Mater., 9:2292–2299, 1997 257. J. Rockenberger, E. C. Scher, and A. P. Alivisatos. A new nonhydrolytic single-precursor approach to surfactant-capped nanocrystals of transition metal oxides. J. Am. Chem. Soc., 121:11595–11596, 1999 258. E. R. Camargo, M. Popa, J. Frantti, and M. Kakihana. Wet-chemical route for the preparation of lead zirconate: An amorphous carbon- and halide-free precursor synthesized by the hydrogen peroxide based route. Chem. Mater., 13:3943–3948, 2001 259. E. R. Camargo, J. Frantti, and M. Kakihana. Low-temperature chemical synthesis of lead zirconate titanate (PZT) powders free from halides and organics. J. Mater. Chem., 11:1875– 1879, 2001 260. E. R. Camargo and M. Kakihana. Peroxide-based route free from halides for the synthesis of lead titanate powder. Chem. Mater., 13:1181–1184, 2001 261. E. R. Camargo and M. Kakihana. Lead hafnate (PbHfO3) perovskite powders synthesized by the oxidant peroxo method. J. Am. Ceramic Soc., 85:2107–2109, 2002 262. M. Kakihana. “sol–gel” preparation of high temperature superconducting oxides. J. Sol-gel Sci. Technol., 6:7–55, 1996 263. P. A. Lessing. Mixed-cation oxide powders via polymeric precursors. Am. Ceramic Soc. Bull., 68:1002–1007, 1989 264. S. G. Cho, P. F. Johnson, and R. A. Condrate. Thermal-decomposition of (sr, ti) organic precursors during the pechini process. J. Mater. Sci., 25:4738–4744, 1990 265. E. R. Leite, C. M. G. Sousa, E. Longo, and J. A. Varela. Influence of polymerization on the synthesis of srtio3.1. characteristics of the polymeric precursors and their thermaldecomposition. Ceramics Int., 21:143–152, 1995 266. E. R. Leite, J. A. Varela, E. Longo, and C. A. Paskocimas. Influence of polymerization on the synthesis of srtio3.2. particle and agglomerate morphologies. Ceramics Int., 21:153–158, 1995 267. M. Kakihana, T. Okubo, M. Arima, O. Uchiyama, M. Yashima, M. Yoshimura, and Y. Nakamura. Polymerized complex synthesis of perovskite lead titanate at reduced temperatures: Possible formation of heterometallic (Pb,Ti)-citric acid complex. Chem. Mater, 9:451–456, 1997 268. M. Cerqueira, R. S. Nasar, E. R. Leite, E. Longo, and J. A. Varela. Synthesis and characterization of PLZT (9/65/35) by the Pechini method and partial oxalate. Mater. Lett., 35:166–171, 1998 269. H. Takahashi, M. Kakihana, Y. Yamashita, K. Yoshida, S. Ikeda, M. Hara, and K. Domen. Synthesis of NiO-loaded KTiNbO5 photocatalysts by a novel polymerizable complex method. J. Alloys Compounds, 285:77–81, 1999 270. M. A. L. Nobre, E. Longo, E. R. Leite, and J. A. Varela. Synthesis and sintering of ultra fine NaNbO3 powder by use of polymeric precursors. Mater. Lett., 28:215–220, 1996 271. E. R. Camargo, E. Longo, and E. R. Leite. Synthesis of ultra-fine columbite powder MgNb2O6 by the polymerized complex method. J. Sol–gel Sci. Technol., 17:111–121, 2000 272. A. L. Quinelato, E. Longo, E. R. Leite, and J. A. Varela. Synthesis of nanocrystalline tetragonal zirconia by a polymeric organometallic method. Appl. Organomet. Chem., 13:501–507, 1999 273. S. M. Zanetti, E. R. Leite, E. Longo, and J. A. Varela. Cracks developed during SrTiO3 thinfilm preparation from polymeric precursors. Appl. Organomet. Chem., 13:373–382, 1999 274. V. Bouquet, M. I. B. Bernardi, S. M. Zanetti, E. R. Leite, E. Longo, J. A. Varela, M. G. Viry, and A. Perrin. Epitaxially grown LiNbO3 thin films by polymeric precursor method. J. Mater. Res., 15:2446–2453, 2000

Assembly and Properties of Nanoparticles

79

275. F. M. Pontes, J. H. G. Rangel, E. R. Leite, E. Longo, J. A. Varela, E. B. Araujo, and J. A. Eiras. Low temperature synthesis and electrical properties of PbTiO3 thin films prepared by the polymeric precursor method. Thin Solid Films, 366:232–236, 2000 276. F. M. Pontes, E. R. Leite, E. Longo, J. A. Varela, E. B. Araujo, and J. A. Eiras. Effects of the postannealing atmosphere on the dielectric properties of (Ba, Sr)TiO3 capacitors: Evidence of an interfacial space charge layer. Appl. Phys. Lett., 76:2433–2435, 2000 277. F. M. Pontes, E. R. Leite, E. J. H. Lee, E. Longo, and J. A. Varela. Dielectric properties and microstructure of SrTiO3 /BaTiO3 multilayer thin films prepared by a chemical route. Thin Solid Films, 385:260–265, 2001 278. E. R. Leite, E. C. Paris, E. Longo, and J. A. Varela. Direct amorphous-to-cubic perovskite phase transformation for lead titanate. J. Am. Ceramic Soc., 83:1539–1541, 2000 279. S. M. Zanetti, E. R. Leite, E. Longo, and J. A. Varela. Preparation and characterization of SrBi2Nb2O9 thin films made by polymeric precursors. J. Mater. Res., 13:2932–2935, 1998 280. E. R. Leite, E. C. Paris, E. Longo, F. Lanciotti, C. E. M. Campos, P. S. Pizani, V. Mastelaro, C. A. Paskocimas, and J. A. Varela. Topotatic-like phase transformation of amorphous lead titanate to cubic lead titanate. J. Am. Ceramic Soc., 85:2166–2170, 2002 281. E. R. Leite, M. A. L. Nobre, M. Cerqueira, E. Longo, and J. A. Varela. Particle growth during calcination of polycation oxides synthesized by the polymeric precursors method. J. Am. Ceramic Soc., 80:2649–2657, 1997 282. C. Greskovich and K. W. Lay. Grain-growth in very porous a12o3 compacts. J. Am. Ceramic Soc., 55:142, 1972 283. E. R. Leite, I. T. Weber, E. Longo, and J. A. Varela. A new method to control particle size and particle size distribution of SnO2 nanoparticles for gas sensor applications. Adv. Mater., 12:96, 2000 284. E. R. Leite, A. P. Maciel, I. T. Weber, P. N. Lisboa, E. Longo, C. O. Paiva-Santos, A. V. C. Andrade, C. A. Pakoscimas, Y. Maniette, and W. H. Schreiner. Development of metal oxide nanoparticles with high stability against particle growth using a metastable solid solution. Adv. Mater., 14:905–908, 2002 285. J. Weissmuller. Alloy thermodynamics in nanostructures. J. Mater. Res., 9:4–7, 1994

Electrochemistry, Nanomaterials, and Nanostructures Paulo Roberto Bueno and Claude Gabrielli

Abstract This chapter deals with the development of new methods for the design of more efficient electrochemical cells destined specifically for energy conversion and storage based on synthesis and design of functional electrodes and electrolytes. The main focus of this chapter is on novel strategies that exploit nanoscale architectures to enhance the efficiency of alternative energy conversion and storage devices as well as on the basic principles of electrochemistry governing the effects of nanoscale design on electrodes and electrolytes. In addition, the chapter provides a review of fundamental electron transfer concepts of relevance to electrochemistry in general and alternative energy devices in particular.

1 Introduction An in-depth understanding of the processes involved in the operation of electrochemical cells is crucial in the development of new methods for the design of more efficient electrochemical cells destined specifically for energy conversion and storage. An indispensable aspect of this body of knowledge is a thorough grasp of the synthesis and design of functional electrodes and electrolytes with unusual and valuable properties which, today, are provided to a large extent by the nanosize effect of these cells’ functional components. Indeed, future developments in this field will necessarily depend on nanoscience and nanotechnology, as this chapter intends to demonstrate. The main focus of this chapter, therefore, is on novel strategies that exploit nanoscale architectures to enhance the efficiency of alternative energy conversion and storage devices and on the basic principles of electrochemistry governing the P.R. Bueno () Instituto de Qu´ımica, Departamento de F´ısico-Qu´ımica, Universidade Estadual Paulista, C. Postal 355, 14801-907, Araraquara, S˜ao Paulo, Brazil e-mail: [email protected] E.R. Leite (ed.), Nanostructured Materials for Electrochemical Energy Production and Storage, Nanostructure Science and Technology, DOI 10.1007/978-0-387-49323-7 3, c Springer Science+Business Media LLC 2009 

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effects of nanoscale on electrodes and electrolytes. In addition, this chapter introduces basic principles of nanotechnology to guide the reader through this incipient interdisciplinary boundary. The scope of ensembles of nanosized objects and products that have been and can be created is truly remarkable. Moreover, the potential impact of these products on basic science and applications is so great that the subject is inexhaustible, particularly in view of the enormous diversity of nanosized objects. Therefore, this chapter must perforce be limited to objects and systems that already show real promise for a variety of applications. The electrochemical manufacture of small objects ranks high in the design of new materials and systems with special properties. However, although the mechanism of formation or removal of small individual portions of solids plays a decisive role in the field of electrochemical nanotechnology, the use of electrochemistry as a tool for the preparation of nanostructures for electrode and electronic applications lies outside the scope of this chapter. In other words, the absence of this and other related topics clearly indicates, from the start, that no attempt will be made to cover the field comprehensively here.

2 Electrochemistry and Nanoscale Materials 2.1 Electrochemistry and Size Effects Electrochemistry and nanoscience (and/or nanotechnology) are interdisciplinary fields, both of which are gaining increasing importance in the development of high performance and reliable alternative energy devices (conversion or storage) [1–3]. To begin to understand how these areas are interrelated to improve the performance of such devices, a brief explanation about both areas must be given. Electrochemistry, in turn, can be understood as the interaction between chemistry and electricity, although it encompasses far more than mere knowledge of chemical systems and the physics of electric fields or potential. As the name itself suggests, electrochemistry is a field of science that deals with the relationship between electrical current or potential and chemical systems. From a more specific standpoint, electrochemistry addresses the chemical and physical transformations underlying chemical energy storage and conversion and their relationship to limitations in the performance of electrochemical systems [2–6]. Modern electrochemistry covers all phenomena in which a chemical change is the result of electric forces and vice versa, where an electric force is generated by chemical processes. It includes the properties and behavior of electrolytic conductors in liquid or solid form. Moreover, modern electrochemistry can be divided into interfacial electrochemistry (electrochemistry of heterogeneous systems) and bulk electrochemistry (electrochemistry of homogeneous systems). On the one hand, interfacial electrochemistry differs from bulk electrochemistry by dealing with topics such as the nature of an electrode–electrolyte interphase, the thermodynamics and kinetics of reactions occurring in the interphase and mass-transport effects throughout it [2–6]. On the other hand, bulk electrochem-

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istry deals with ion–solvent and ion–ion interactions, activity coefficient, ionic mobility, ionic conductivity, and so on [2–6]. Bulk electrochemistry describes the performance of electrolytes and is the key to future improvements in electrochemical components used as ionic sources and membranes in solar energy devices for electric power production, energy storage, e.g., batteries and supercapacitors, as well as advanced electroanalytical sensor devices [2–6]. Bulk electrochemistry is discussed briefly here, in the context of ionic conductivity of solid-state electrolytes. However, most of this chapter focuses on the fundaments of interfacial electrochemistry and its relationship to nanostructures, which is of vital importance in electrochemical alternative energy devices. The term nanotechnology has been defined in a variety of ways; however, we will define it here as the technology of design, manufacture and application of nanostructures and nanomaterials [7, 8]. The study of the fundamental relationships between physical and chemical phenomena and materials’ dimensions on a nanometric scale are also referred to as nanoscience. Nanotechnology involves the fabrication, characterization, and manipulation of materials with at least one dimension in the range of 1–100 nm. Thanks to their diminutive size, nanoscale objects will lead to groundbreaking discoveries and are expected to be at the forefront of technological innovation for the next decade. The interrelation between interfacial electrochemistry and nanoscience gives rise to new possibilities for designing chemical surfaces by controlling surface structures at the molecular level, leading to innovative metal or semiconductor surfaces and charge transfer lengths. Improved nanostructured devices based on nanostructured electroactive material can be designed in different ways [9–15]. For instance, the interfacial electrochemical properties of specific materials can govern the performance of charge accumulating at the interface, leading to highly efficient double layer capacitors [16–24]. In bulk electrochemistry, a proper understanding of the high performance of ionconduction properties on a nanolength scale is crucial [25–29]. Other examples will be discussed later herein. Micrometric-scale materials generally display the same physical properties as those in bulk form; however, nanometric-scale materials may exhibit physical properties that are distinctively unlike those of bulk. Materials in this size range possess remarkable specific properties deriving from the transition from atoms or molecules to bulk form that takes place in this size range. On the one hand, the interfaces in polycrystalline microstructured materials are considered as defects that influence the macroscopic properties. On the other hand, in polycrystalline nanostructured materials, the interface dominates and the bulk plays a totally different role. Numerous experimental studies have shown that, if a material’s particle size is less than the critical size of about 10 nm, its bulk properties change noticeably. A particle of about 10 nm contains 104 –105 atoms, 1–5% of which are on the surface of the particle and contribute substantially to the material’s physicochemical properties [30]. Ensembles of such nanostructures will be shown here to be important in electrochemical applications such as electrodes [8, 9, 12, 13, 31–38]. Another example of the influence of nanometric effects is on the Debye temperature, which decreases in nanocrystalline systems, and is lower when the same

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system is on a micrometric scale. Thus, the nanometric scale gives an additional contribution to the low-temperature heat capacity, and this contribution increases as the scale decreases [39]. This effect can be explained by changes in the nanocrystals’ vibrational status (an increase in the number of low frequency modes in response to a decrease in the number of high frequency modes) as the size decreases. Therefore, nanometricscale crystals have a low melting point (sometimes below 900◦ C) and reduced lattice constants, since the number of surface atoms or ions represents a significant fraction of the total number of atoms or ions. In this case, surface energy plays a significant role in the thermal stability, while bulk represents the defect in the properties. From this standpoint, nanotechnology can be considered new, but nanometer scale research is not new at all. Nanometric-scale engineering of many materials such as colloidal dispersion, metallic quantum dots and catalysts [37, 40–49] has existed for decades. Nanotechnology is therefore not a novelty; indeed, you can see it all around you if you just know where to look. Actually, nanotechnology is a combination of existing technologies, and our newfound ability to observe and manipulate on the atomic scale makes nanotechnology highly compelling from the scientific, business and political points of view. This aspect of nanotechnology was already foreseen in a conference presented by Nobel Prize winner Richard Feynman in 1959. One can visualize another example of the nanoscale effect by picturing a bulk material, e.g., a metal or n-type semiconductor metal oxide, simplistically, as consisting of charged particles, positive ions, and electrons in the first situation, and positive and negative ions in the second. In both cases, the total positive charge balances the total negative charge, so that there is no net electric charge in the material’s bulk. Now imagine reducing a piece of this material to the nanoscale by applying a top-down approach such as any lithographic technique in a vacuum medium. What electronic properties will such a small, strongly charged material have? Considering the vacuum as the environment in which these properties are embedded, there is a small degree of spillover of the electrons from the material into the vacuum, resulting in a disturbance of the former balance of electrical charge in the surface region of the materials, which in this case represents a substantial percentage of the total volume. Note that interfaces in micrometric or millimetric materials can also be electrified, but there are some differences. A totally different functionality arises on the nanoscale, because of the size range involved [30]. Indeed, changes in the electronic properties of nanoscale materials due to the size effect must be interpreted in the domain of quantum chemistry [50]. If the size of the nanocrystal is compared with the de Broglie wavelength of elementary excitations, the quantization conditions of electron energy are changed and the energy bands split into an energy system of energy level and, in this case, the pattern of the absorption spectrum becomes similar to that of the spectra of individual clusters. Semiconductor nanocrystals possessing these properties are called quantum dots [50]. The physicochemical properties of nanometric-scale materials are part of the domain of nanoscience but, in specific situations, nanomaterials can converge with electrochemistry. For instance, if our previously pictured nanomaterials (nanocrys-

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talline particles) are immersed in an appropriate solution, a colloidal system is likely to arise [51, 52]. The use of nanoparticles to form colloidal systems has a long history, as exemplified by a comprehensive study about the preparation and properties of colloidal gold, which was first published in the mid-nineteenth century [53]. The colloidal dispersion of gold prepared by Michael Faraday in 1857 [54] remained stable for almost a century, showing no sign of spontaneous chemical degradation before it was destroyed in a Word War II air raid. Colloidal properties result from the combination of the properties of an electrified surface and nanomaterials/ solution, the structure of the double layer thus formed being the most important factor. In the emerging field of nanotechnology applied to electrode design, the goal is to create nanostructures or nanoarrays with special properties unlike those of bulk or single particle nanosize elements. Thus, if nanoparticles are combined in any way under a conductor substrate and inserted into an electrolyte, the resulting properties will differ from those produced under the same conditions but without nanoparticles or nanoscale materials [10, 12, 30, 37, 47]. Nanoparticles themselves, or an electrode composed of nanoparticles, can exhibit unique chemical properties because of the limited size and high density of corner or edge surface sites [7, 30, 55, 56], but as electrode-forming components, the most important properties are those arising from the charge transfer rate, electronic and ionic transport, etc. [8, 15, 30–32, 40, 42, 47, 57, 58]. It is a known fact that, from the standpoint of materials and surface science, many of the properties of systems are controlled by interfaces and contact between different materials [7]. However, knowledge of how to control and design new contact (electrodic or electronic) properties on a nanometer scale is new and is very rapidly gaining ground. Such contacts constitute the electrodes of galvanic cells which can be used for the generation of chemical products by electric power (electrolysis), as will be discussed later herein. It is of primary importance to know how to differentiate between electrochemical responses and events that result from changes in charge transfer length relating to the functionalized surface properties of nanoscale materials and those that arise from transport properties through nanostructures. It is easy to demonstrate that chemical reactions occurring in nanostructured electrodes (electrode reactions) and mass and electrical transportation in such electrodes, and even in electrolytes based on nanocomposites or other kinds of nanomaterials, will cause a tremendous revolution in every aspect of applied electrochemistry [8, 12, 13, 15, 30, 32–34, 36, 38, 42, 43, 57, 59–70]. The main focus here is to show how these nanoscale effects resulting from the use of designed nanostructured electrodes will inevitably contribute to the development of alternative energy devices based principally on concepts of electrochemistry. We, therefore, need to know more about how to deal with and take advantage of the continuous flow of electrons across electronic nanostructures and ionic species in a nanoscale ionic conductor (electrolyte). Furthermore, it is also important to understand how charge transfer lengths are influenced on the nanoscale and how size affects electrochemical properties [8, 30]. Accordingly, we will consistently address

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the processes and factors affecting the transportation of charges across interfaces between nanostructured chemical phases. In the latter case, electrochemical reactions are involved and the transfer of electrons from the electronic phase to the ionic conducting phase is classified as an oxidation–reduction (redox) reaction. In the case of electrochemical conversion systems, it is also important to deal with charge transfers occurring from molecules to semiconducting nanoparticles [71].

2.2 Challenges of Charge Transfer It must also be emphasized that oxidation–reduction reactions always involve charge transfers, without which we can no longer exist [8]. Electron transfers are vital to our daily life. Indeed, we owe our very existence to photosynthetic and biochemical electron transfer events, and we would be unable to function properly without the myriad transistor-based electronic devices that control and amplify current flows. Electron transfer and charge storage are correlated in a series of events in our body. Another example of the importance of electron transfer reactions is photosynthesis, which photoelectrochemical systems designed for energy conversion attempt to imitate [3, 72]. In photosynthesis, a photon triggers an electrical current in the leaf, activating the leaf’s electrons to produce H2 while the holes produce O2 . Therefore, electron transfer events are basic to the understanding and development of novel generations of electrochemical energy conversion and storage systems based on the imitiation of the most efficient biological systems. Electrochemical energy conversion and storage devices form an important branch of alternative energy emerging in the twenty-first century [1] that, like nanotechnology, has crucial scientific, technological, and political implications. At this point, however, it is important to stress that despite the importance of properly grasping the charge transfer phenomenon, molecular and bulk level charge transfer processes are still not fully understood and the characterization of nanoscale (1–100 nm) processes is still incipient [8, 73]. Nanoscale charge transfer is important both to the frontiers of fundamental science and to applications in molecular electronics, including problems such as electrocatalysis [8] and solar photoconversion. Progress in the area of nanoscale charge transfer requires interdisciplinary collaboration, combining a wide range of materials synthesis and electrochemical characterization, a challenging range of experimental techniques to probe charge transfer processes, and theory for their interpretation [8]. Current interest ranges from the use of single or small groups of molecules (usually organic) as components in electronic devices to the exploitation of semiconductor and metal nanoparticles because of their high surface areas and other size-dependent properties. The nature of the attachment of such components to bulk metal and semiconductor surfaces and the control of their properties are overarching concerns [8]. The experimental measurements used to characterize nanoscale charge-transfer properties include

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rate constants, spectroscopy, and conductance/resistance measurements, depending on the nature of the system studied [30]. Predictions of the kinetics of electrons taking into account all size-dependent factors are possible only when adequate ion-molecular models of reaction layers are built. For a number of systems, this problem can be solved successfully by employing quantum-chemical methods based on quantum mechanical theory of the charge-transfer elementary act [74, 75] along with the classical effects of the cation size, which are manifested in the reduction of anions on a negatively charged surface [74, 75]. In general, the characteristic dimensions of conventional components of electrochemical systems (electrodes, electrolytes and membranes) cover 5–10 orders of magnitude and the lower boundaries of the corresponding intervals approach typical sizes of specific space regions (layers) that arise only at the electrode–electrolyte junctions, generally called Electrical Double Layer (EDL) [3–6]. According to modern notions of the interface structure, the adsorbate layers and the edges of surface atoms on electrodes are spatially separated by gaps. In electrochemical systems, the properties of this gap depend on the electrode potential (charge). The prospect of using size effects to intensify electrode processes cannot be contemplated without including nanotechnology and electrode design. The latter will be introduced in Sect. 2.3.

2.3 Nanomaterials and Nanostructured Films as Electroactive Electrodes Earlier herein we mentioned several challenges posed by nanoscience and electrochemistry. Some aspects relating to electrified surfaces in contact with electrolyte, the so-called electrified interfaces in electrodics, metal– or semiconductor– electrolyte junctions whose properties can control charge transfer length, charge transfer kinetics, and the EDL structure, have been discussed briefly. These topics will be discussed in greater detail in other sections of this chapter. Also briefly mentioned earlier is the fact that the physical properties of the interface of nanoparticles in solution/solvent or electrolytes may lead not only to colloidal behavior but also to particle–particle interaction or particle–solvent interaction. Self-supporting colloid network structures allow for the coexistence of high conductivity with mechanical stability, enabling colloidal gels to be used as electrolytes [76–78]. Despite all these aspects of electrochemistry and nanoscale discussed so far, undoubtedly the most important question to be answered is “Why is nanoscience or nanotechnology so beneficial to electrochemical energy devices?” The answer lies in understanding the fundamental principles underpinning the electrochemical generation of electricity. The conversion of energy necessarily involves some kind of energy transfer step, whereby the energy from the source is

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passed along to electrons, which constitute the electric current. This transfer occurs at a finite rate and must take place at an interface or reaction surface. Thus, the amount of electricity produced scales with the amount of reaction surface area or interfacial area available for the energy transfer. In other words, the efficiency of the reaction and the amount of reaction depend, respectively, on the features of the surface and on the extent of the surface. In this perspective, how can nanotechnology and electrochemical devices (e.g., energy conversion and storage devices) converge from a nanoscopic standpoint of electronic transfer, transport and kinetic reactions occurring in these devices? To begin answering this question, we must first offer a basic introduction to the term “electroactive materials” so popular in the electrochemical literature. Electroactive materials are materials that possess redox properties, and they play an increasingly central role in nanotechnology and electrochemistry. At present, the wide range of applications for these materials include electrodes and membranes for electrochemical energy conversion and storage, electroceramic electrode devices and sensors, organic diodes, and magnetic and optical devices [1, 7, 8, 43, 79–83]. Further along in this chapter we will discuss the concept and definition of electrodes and electrochemical cells. For now, an electrode can be considered a source or a sink of electrons to be interplayed with the ionic conductor in contact with it, while the electrochemical cell is composed of a source and a sink electrode separated by an ionic conductor (electrolyte). Therefore, all electroactive materials are potential electrodes. From the standpoint of nanotechnology, this material can be prepared on a nanoscale (to enlarge the surface area) mainly in three distinct forms (a) zerodimensional, (b) one-dimensional and (c) two-dimensional nanostructures. Therefore, it is not surprising that the desire for large surface areas has led researchers to focus on nanomaterials and electrochemistry in the search for nanosized structures for electrode applications. Nanomaterials include molecular wires, nanoparticles – both semiconducting and metallic, nanotubes, electrodes, and the connectors that link these objects together to create larger structures (Fig. 1). Other products, such as filled zeolites, aerogels, dendrites, and layered polymers, also offer enormous potential for useful electrochemical functions [8]. All these nanosized structures [from (a) to (c)] are synthesized using either one of two manufacturing concepts, i.e., top-down or bottom-up approaches. Based on these two approaches, several methods have been developed in recent years for the preparation of novel nanostructures [7]. In the case of (a), the zero-dimensional (0-D) nanostructure is composed of nanoparticles whose fabrication requires the control of more than merely their diminutive size. For any practical applications such as electroactive components in electrodes, the processing conditions must be controlled so that the resulting nanoparticles have the following characteristics (a) identical size of all particles (also referred to as monosized or quasi-monosized), (b) identical shape or morphology, and (c) identical or at least very similar chemical composition and crystal structure. Single crystalline nanoparticles are often referred to in the literature as nanocrystals. When the characteristic dimensions of nanoparticles are sufficiently small and quantum effects are observed, these nanoparticles are commonly

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Fig. 1 Nanostructured electrodes can be prepared by several methodologies, many of them based on bottom–up approaches. This figure illustrated the ordered (left) and disordered (right) preparation of brushlike structures obtained from nanowires and/or nanotubes. We are indebted to Dr. Ednan Joanni for providing some parts of this schematic representation

described as quantum dots. From the electrochemical standpoint we are interested in the redox properties of such nanoparticles, which are generally metallic, inorganic or compounds. One-dimensional (1-D) nanostructures (b) are composed mainly of nanowires, nanorods and nanobelts. Spontaneous growth, template-based synthesis and electrospinning are considered bottom-up approaches, while lithography is a top-down technique [7, 84]. Two-dimensional (2-D) nanostructures (c) involve thin films, which have been the object of intensive study for almost a century and for which many methods have been developed and improved. Insofar as the concept of electrode is concerned, it is important to stress here that most electrodes for electrochemical application in alternative energy devices are manufactured mainly by interfacing semiconducting nanostructures with conducting substrates. By combining different electrodes, one can attain a three-dimensional (3-D) integrated electrochemical cell [85–87]. Electrodes can

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also be developed based on a 3-D concept, whereby they are assembled using 0-D, 1-D, or 2-D nanostructures. 2-D-based electrodes can be fabricated as homogeneous thin films or by an assembly of 0-D and 1-D nanostructures; however, the film’s thickness must be limited to the nanoscale. 3-D electrodes can be similarly manufactured, but their thickness is not limited to nanolengths. Therefore, the assembly and synthesis of these nanostructures with multiple dimensions is common in electrochemistry. They are usually referred to as nanostructured electrodes and most of them are highly porous. The nanostructuring of electroactive materials introduces major changes in the electrochemical properties of the devices of which they are a part. For instance, dye-sensitized solar cells (DSSC) is an example of 2-D and 3-D nanometer-sized structures assembled with quasi 0-D structures or building blocks (nanoparticles). The charge transfer kinetics is often influenced and high surface areas provide greater numbers of electroactive charge transfer sites. A more specific example is the extremely large internal surface area, which is made possible by the nanocrystalline particle nature of nanostructured semiconductor electrodes. This huge surface area is crucial for the proper functioning of DSSCs for a number of reasons. Some of these reasons are (1) sufficient adsorption of the monolayer of dye molecules to achieve efficient light absorption, (2) the huge surface causes charge carrier percolation across the nanoparticulate lattice, and (3) the very rapid and highly efficient interfacial charge transfer between the oxide and each and every one of the dye molecules anchored to the particle surface. We have already shown here that large surface areas translate into enhanced electrochemical performance and, from this perspective, nanostructures are also very important for fuel cell devices [8,70,88–90], particularly as regards the catalyst part of the cell where the oxygen reduction reaction can only occur in spatially confined regions [8, 70, 88–90]. Returning to the subject of nanostructures designed and used as electrodes, it is easily observed from the electrochemical literature that 2-D or 3-D structured electrodes composed of architectures possessing high surface-to-volume ratio nanostructures, which are constituted by the arrangement of multiple dimensional nanostructures (0-D, 1-D, and 2-D), are extremely useful in energy storage or conversion device applications because they improve storage capacity and conversion [1, 8, 15, 37, 70, 86]. We will provide specific examples in this chapter, and several other examples are given in the handbook. As mentioned earlier, thin films can be considered 2-D nanostructures. In the recent past, thin film-based technologies have been responsible for the design of an enormous variety of thin film-based electrochemical devices. 2-D nanostructures [91] composed of 0-D or 1-D materials are those that are associated with the interfacial properties of electrodes. In electrochemistry they are known as porous electrodes, and they sometimes possess an effective surface more than 1,000 times greater than the geometric area expected for a compact and homogeneous 2-D structured electrode, e.g., porous thin film-related electrodes [92–96]. As can be seen, therefore, the porous effect is an important and significant aspect of nanostructures applied as electrodes. It is so important to note that, in the

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electrochemical literature, this aspect leads to the use of terms such as porous electrodes when referring to nanostructured electrodes [92–101]. Porous, or nanostructured, electrodes form an electrochemical system when in contact with an electrolyte, leading to the simultaneous transport of electronic and ionic species. Owing to the minute scale of the constituents of the porous lattice, charge ionic carriers in transit are always close to the surface, implying that transport and heterogeneous transfer processes are strongly coupled in these systems [92–101]. We will discuss porous electrode theory further along in this chapter.

2.4 Nanomaterials as Electrolytes Nanoscience and nanotechnology influence not only the design of nanoscale electrodes but also that of nanoscale electrolytes [9, 28, 102–105]. The continuous research of new materials for electrolyte applications has led to advances in the design of nanostructured materials to improve ionic conductivity [25, 28, 102]. The development of new solid materials for electrolyte applications is creating opportunities for new types of electrical power generation and storage systems. Progress to date in solid-state ionics is largely the result of fast ionic conductors [29,106]. There are several new classes of materials based on the concept of nanoionics (nanostructured materials for use primarily as electrolytes). Solid ionic materials of this kind are based on nanoceramics, polymeric compounds, and hybrid organic–inorganic nanocomposites [102]. All these materials are being investigated to improve their transport properties for the ionic species of interest, e.g., lithium, proton, or oxygen. Therefore, enhancing the ionic conductivity of nanoscale materials is of great interest, for it offers a predictable way to design a wide range of new ionic materials with practical applications. An obvious technological target is the preparation of nanoscale lithium-ion conductors to make more efficient rechargeable batteries for portable electronics [107]. Many problems still remain to be solved, such as the scale-up of laboratory techniques for mass production. Nonetheless, the results achieved so far suggest that the emerging field of nanoionics has a healthy future [28, 107]. The concept behind nanoionic materials is based on the use of nanoscale effects to improve overall ionic conductivity [28]. Overall conductivity, which is the product of defect concentration and mobility, is low in simple classic inorganic solid ionic materials such as NaCl. The electrical conductivity at the melting point is eight orders of magnitude lower than in metal, and is almost impossible to measure at room temperature. The conductivities of a few materials even approach those of aqueous electrolyte solutions. Solid state electrolyte material began to attract serious attention with the discovery of new compounds and nanocompounds with high ionic conductivities, and with the demonstration of feasible devices, particularly solid-state batteries, fuel cells, and sensors [108,109]. Fuel cells based on these materials – known as fast-ion conductors or solid electrolytes – offer a highly efficient and clean method of large-scale energy production [109].

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An example of classical solid state electrolyte is electrolytes based on zirconia polycrystalline material that conducts oxygen ions, with hydrogen as the fuel, air as the oxidant, and water as the waste product [109]. The fossil fuel crisis and the need for better energy management will lead to increased activity in this area, and interest in nanosized ionic materials continues to grow [1]. For example, the properties of electrolyte ceramic materials can be improved by the nanoscale surface properties. The surface properties of an ionic crystal create a space-charge region, in which the concentration of defects at the surface is governed by the energies of individual defects and one type of defect in a pair can dominate. As a result, the surface has an excess of one type of defect, as in the case of chemical doping, and ionic conduction in this region is enhanced accordingly [28, 110]. Some experiments and theories indicate that dramatic increases in ionic conductivity should be expected when the spacing of interfaces is comparable to, or smaller than, the space-charge layer [28, 110]. However, it is evident that lowering the length scale may lead to enhanced defect densities and, therefore, to enhanced ionic conductivities in the space charge regions, irrespective of yet unknown mobility effects. With regard to the safe storage of (sustainable) hydrogen, exciting new avenues are being opened for storage using nanosized and nanostructured materials [102]. While the quantum confinement regime has been explored for some ionic materials, it is evident that thus far only optical properties have been related to the quantum confinement regime. Electrical properties of solid electrolytes or mixed ionic–electronic conducting materials in the quantum confinement regime have not yet been described fully and represent a challenge to this field. The achieving of high ionic conductivity in nanostructure-based electrolytes requires a better understanding of the fundamentals of ion dissociation and transport in such kinds of nanosized materials [28].

2.5 Nanoscale Electronic and Ionic Transport Finally, considering what was discussed previously, when dealing with nanosized materials and nanostructured electrodes for electrochemistry, it is important to separate the different effects of interface on the electronic and ionic transport: the kinetics and mechanisms of transport along and across interfaces. The literature commonly considers transport along interfaces as grain boundary transport, corresponding to diffusion parallel to interfaces, as in grain boundaries of polycrystalline materials or in nanoscale materials, as across nanostructures limited to a thin layer of nanometric thickness. In contrast, transport across interfaces involves transport perpendicular to the interface. It is possible to show that, if one considers the correct description of ionic diffusion coefficient suction of a crystal, the value obtained for the ionic coefficient on the surface is abnormally high in the nanoscale compared with the microscale [111]. It has also been stated [72] that the coefficients of oxygen diffusion in TiO2

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nanocrystals are 5–6 orders of magnitude greater than in bulk crystals and that the coefficients of diffusion of dissolved hydrogen in palladium nanocrystals are greater than in the bulk specimen. Oxygen conductivity can also be improved in the same way for ZrO2 -based solid electrolyte [102]. The same concept can be applied to interfaces between the components of rechargeable solid-state lithium ion batteries, thereby improving the performance and reducing the resistivities of dc batteries [102].

2.6 Energy Conversion and Storage in Electrochemistry The conversion and storage of energy by electrochemical devices is a highly important technological issue of debate, for it represents an entirely new source of energy generation affecting every aspect of our daily lives, and its efficiency is tied in with the concept of free energy (the capacity to do work, in the formal physical definition), which is the most fundamental resource. With an inexhaustible supply of free energy, almost anything can be done. According to the first law of thermodynamics, energy cannot be created or destroyed, but the critical constraint lies in the second law of thermodynamics. In the way it is usually expressed, the second law states that, in an isolated system, a quantity called entropy, having units of energy/temperature, must always increase in any spontaneous process. It therefore follows that increasing entropy, in turn, implies that free energy cannot be fully recycled. Although the total energy remains unchanged, less energy is available to perform useful work. A certain amount is irretrievably lost, in practice generally as low-grade waste heat, which from Earth is ultimately radiated out into space. Hence, ongoing sources of free energy (or just energy, loosely) are required for all biological and technological activities. Sunlight is the source for the biosphere. In the case of conventional technology, a whole suite of sources is used, but nowadays the predominant source is fossil fuels. These have a considerably higher energy density than that of sunlight. However, as fossil fuel supplies are expected to become increasingly scarce, expensive, and environmentally impacting, increasing dependence on energy conservation and alternative sources of energy are expected to become the most obvious solution, especially energy from the sun, i.e., solar energy. When the sun is directly overhead and the sky is clear, radiation on a horizontal surface is about 1, 000 W m2 [1, 71]. To give an example, photovoltaics and solar cells have, in fact, provided reliable electrical power to space missions for many years. Sunlight can be used for heating, lighting, and electricity generation, and it can be concentrated to provide steam to run turbines. The principal disadvantages of solar energy are still that, at present, the conversion efficiency of sunlight to electric power is not high, and sunlight varies according to the time of day, weather conditions and seasons. Closely related to solar cells are fuel cells, which convert fuel or chemical energy directly to electric energy. The main chemical reactions involve the oxidation of CO and H2 . Although fuel cells have been operating reliably and efficiently

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in space missions for more than 40 years, they have not yet been widely used on Earth, largely because of their cost. To make this technology commercially competitive, better anode, cathode, and electrolyte materials and processes are needed [1]. However, what is the real importance of electrochemical alternative energy devices? There are several energy sources, as presented earlier. All of them involve electron transfer reactions, and their development and applications are growing rapidly [1, 71, 109, 112], especially because conventional energy supply technology is exhausting its resource base at an accelerating rate, exacerbated by the revolution of rising expectations in the less-developed world due to the global communications revolution. This rapid expansion in the study and development of electrochemical energy generation and conversion-based devices is due mainly to the fact that most of the world’s energy is supplied by fossil and nuclear sources, which face continual and increasingly severe issues of resource limitation and environmental pollution. To meet the growing global demand for energy and to compensate for the depletion of fossil fuel supplies in the coming years, alternative renewable sources of energy that do not depend on fossil fuels and that cause only marginal environmental impacts must be developed, offering low costs, safety, and higher efficiency. There is also a great demand for devices based on the concept of energy storage, i.e., on the electrochemical concept of storage of chemical energy. These devices are also required to supply mobile energy for the portable electronic devices upon which our modern lifestyle is so strongly dependent, for they are at the heart of modern mobility and convenience [107]. Indeed, electrochemical nanostructure-based devices offer an important solution to this dilemma, with the prospect of providing something approaching a sustainable standard of living for the entire world (so far enjoyed only by industrialized countries), since they provide the capability for developing more efficient devices in all areas involving electrochemical alternative energy while causing a low environmental impact (sustainable development).

3 Overview of the Principles of Operation of Energy Conversion and Storage Devices To understand the basic principles of operation of an energy conversion or storage device it is important to know what an electrochemical cell is. Basically, it is a device in which a chemical reaction either generates or is caused by an electric current. A galvanic cell is an electrochemical cell in which a spontaneous chemical reaction is used to generate an electric current. An electrolytic cell, in turn, is an electrochemical cell in which a reaction is driven in its nonspontaneous direction by an externally applied electric current. There are three types of galvanic cell: the primary, the secondary, and the fuel cell [5, 6]. Primary galvanic cells are those in which the reactants are built-in during the manufacturing process, while secondary cells are those that must be charged (i.e.,

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1.00

20.4 nM

0.75

10.2 nM

0.50

0.0 nM

0.25

0

0.25

0.50

0.75

0 1.00

μm

Fig. 2 Design of 2-D and 3-D nanostructures from 0-D nanostructures. Both 2-D and 3-D nanostructures are very commonly applied as electroactive materials in the manufacture of nanostructured porous electrodes

used as electrolytic cells) before the reactants are present for the reverse, spontaneous reaction [5, 6]. Fuel cells are the type of galvanic cells in which the reactants are supplied continuously as they produce current. An electrochemical cell comprises two electrodes in contact with an electrolyte, i.e., an ionic conductor. These electrodes are called cathodes and anodes. A cathode is the electrode that acts as a source of site for reduction reactions in the electrochemical cell, while an anode is the electrode that acts as a source of site for oxidation reactions. Therefore, the removal of electrons that occurs in the anode can be described as follows: (1) Ared → Aox + e− ,

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in which Ared is the reduced form of a site or species and Aox is the oxidized site or species in the anode. The following reaction occurs in the cathode: Cox + e− → Cred ,

(2)

in which, in turn, Cox corresponds to the oxidized form of a site or species in the cathode, while Cred is the reduced site or species in the cathode. Many oxidation and/or reduction reactions are also accompanied by the transfer of atoms or molecules. Batteries and fuel cells operate according to the same fundamental principle. In other words, under appropriate conditions, the chemical free energy associated with a particular reaction can be converted into electrical energy, often with extremely high efficiency. Considering that both are electrochemical cells, it is possible to demonstrate that during operation, electrons flow from the anode to the cathode, constituting an electrical current that can be used to drive an external device, e.g., see Figs. 3.3 and 3.5. The fuel is an inherent part of the battery; a battery, in other words, carries its fuel around with it, whereas fuel must be supplied to a fuel cell from an external source. Unlike a battery, a fuel cell cannot become depleted and so long as fuels are supplied it will generate electricity. Recharging problems are therefore peculiar to batteries [107]. These systems can therefore be understood in terms of parts, since the overall chemical reactions can be broken down into components of oxidation and reduction reactions, the former involving the transfer of electrons from one set of reactants to the anode and the latter involving the transfer of electrons from the cathode to a

CHARGE

Power supply

e−

Load

O DISCHARGE

Co

ELECTROLYTE

Li Carbon

CATHODE

ANODE

Li1-xCoO2

Graphite

Fig. 3 Schematic of a rechargeable lithium battery in discharge/charge mode. The lithium ion is intercalated in the anode during charging and in the cathodes during discharging. The layered host lattice in the cathode and anode is also illustrated, considering a cathode composed of a lithium cobalt host and an anode composed of a crystalline structure of hexagonal graphite. See Color Plates

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second set of reactants. The overall electrochemical device may be set up in such a way that electron-transfer reactions are rapid and, ideally, completely reversible in chemical terms [6].

3.1 Lithium Ion Batteries Lithium-ion rechargeable battery solid state devices rank high among the alternative energy devices in which nanostructured cathodes or anodes make a dramatic difference in improving rate capabilities [79, 81, 82, 86, 107, 113–117]. Despite its low density (0.53 g cm−3 ), low electronegativity and high electron/atom mass ratio, lithium is the preferred choice for the active element of the anode, whose discharge functions as an electron donor can be expressed as: discharge

xLi

−−−−−→ charge

−−−−−→

xLi+ (electrolyte) + xe− ,

(3)

where Li+ enters the electrolyte, and the electron exits the anode, moving to the external circuit to power the load. Other types of materials containing lithium (lithiated host materials) are also used as anodes [118–120]. The most classic example is lithiated carbon (Lix C6 ). The anode reaction for this type of material is as follows: discharge

Lix C

−−−−−→ charge

−−−−−→

C + xLi+ (electrolyte) + xe− .

(4)

The carbon host materials that have been studied include natural and synthetic graphites, carbon fibers, and mesocarbons, all of which differ in degree of crystallization and stacking order, but all of which have the characteristic structural feature of graphite, namely, planar layers of carbon atoms forming fused sixmembered rings and separated by intercalate layers, supplying an electrochemical potential close to that of metallic lithium electrodes [121]. The large number of boundaries resulting from the use of graphite nanostructures has proved useful for improving lithium intercalation capacity [102, 107, 121]. Indeed, the interfacial boundary area can accommodate lithium to form Lix C with x > 1, and hence, an increased reversible capacity [102, 121]. The following reaction generally takes place at the cathode: discharge

xLi+ (electrolyte) + xe− + MO2 −−−−−→ Lix MO2 ,

(5)

which clearly indicates that to operate effectively, Lix MO2 (which represents a lithiated transition-metal oxide usually applied in commercial cells) must conduct electronically, or at least be miscible with, an appropriate inert conducting ionic– electronic nanocomposite, in which the diffusion of Li ions must be reasonably

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facile and, ideally, highly reversible to enable the battery to be rechargeable. The latter requirement suggests that layered structures, which allow Li+ ions to diffuse easily throughout the bulk of the crystal, are likely the most effective structure. In the cathode, Lix MO2 is usually mixed with carbon black to raise the electronic conductivity. Lithium cobalt and nickel oxides are commonly used as cathodes (Li1−y CoO2 and Li1−y NiO2 ), since these oxides possess the transition metal in a highly oxidized state, allowing a high cell voltage to be developed. Considering the lithium cobalt oxide, one may have discharge

xLi+ (electrolyte) + xe− + LiCoO2 −−−−−→ Li1+x CoO2 .

(6)

Therefore, in the cathode, Li+ ions engage in an electron-transfer reaction that decreases the chemical potential of lithium in relation to its value in the anode and calls for the compensating electron. Upon discharge, the cathode functions as an electron acceptor and the previous reaction (6) can be expressed alternatively as follows: cathode (7) xCo4+ + xe− −−−−→ xCo3+ . If the battery is to be rechargeable, the reactions must be reversible. The importance of lithiated transition-metal oxides (Lix MO2 ) is that they are capable of accommodating large quantities of lithium per formula unit and have low relative molecular masses, giving rise to high power and energy densities. Materials for cathodes and anodes (insertion electrodes) for rechargeable lithium batteries are called intercalation compounds and constitute a special class of electroactive material [122]. The intercalation refers to the reversible insertion of mobile guest species into a crystalline host lattice, which contains an interconnected system of empty lattice sites of appropriate size, while the structural integrity of the host lattice is formally conserved [122]. Considering electrodes composed of nanoscale electroactive materials, high energy density and high power density (the same as rate capabilities) can be achieved simultaneously. This requires a large electrode–electrolyte interfacial area coupled with short diffusion distances within the electrodes themselves [10–13, 86, 113, 118–120]. Nanoscale materials for lithium ion storage devices are emerging as a successful solution for improving the rate capability [86, 113, 123–125]. A battery’s rate capability is its ability to deliver a large capacity when discharged at high C rates (a rate of C/1 corresponds to the current required to completely discharge an electrode in 1 h). During high-power pulses required for transmission of digitized and compressed voice data, the battery’s delivery capacity decreases to a fraction of its low rate value. It is widely believed that these limitations in the rate capabilities of Li ion batteries are caused by slow solid-state diffusion of Li+ within the electrode materials. For this reason, tremendous interest currently focuses on the research and development of nanostructured Li ion battery electrodes, whose nanostructure clearly restricts the distance that Li+ must diffuse, which may be as small as 50 nm [10–13,86,113,118–120]. Two kinds of geometry are commonly applied to achieve a faster solid-state diffusion, as depicted in Fig. 4. The first geometry is based on

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a

| jc | (for η > 0), and j < 0 for | ja | < | jc | (for η < 0). At equilibrium where j = 0, | ja | = | jc | = jeq . At low overvoltages: nF j ≈ jeq η. (24) RT I/ Ie

Ii

1.0 0.8 0.6

Ia Total current I

0.4 0.2 100 400

−300

−200

−100

Eeq

−0.2

Ieq

Ic

200

300

400

h, mV

−0.4 −0.6 −0.8

−Ii

−1.0

Fig. 7 Current–voltage curve j = f (η ) for mass transport limitation (continuous curve) and partial current densities ja = f (η ) and jc = f (η ) (dashed line), limiting diffusion current densities: jal and jcl . For comparison, the curve j = f (η ) where kinetics is the only rate-limiting step, i.e., without mass transport limitation is plotted (dotted line)

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In the linear range of the current–potential relationship, the charge transfer is equivalent to a resistance called charge transfer resistance at the equilibrium potential, (Rt )eq RT 1 (Rt )eq = . (25) nF jeq In contrast, far from the equilibrium potential (large overvoltages), one of the two exponential functions is preponderant. Hence: • For η  0, the rate of the reduction process (cathodic) is practically 0 and the oxidation process (anodic) is dominant.   cR (0,t) α nF j ≈ ja = jeq exp η . (26) c∗R RT This relationship called Tafel relationship was proposed empirically in 1905. • For η 0, on the contrary, it is the reduction process (cathodic) that is practically preponderant:   cO (0,t) (1 − α ) nF j ≈ jc = jeq exp − η . (27) c∗O RT The system is considered fast if jeq is large, i.e., a large value of k◦ and a low value of the charge transfer resistance are associated. Conversely, when jeq is low, k◦ is also low while the charge transfer resistance is large, so the system is considered slow.

4.1.2 Mass Transport Phenomena Involved in Electrochemical Processes Because electrochemical reactions are localized at the contact between the electrolyte and the electrode, an electrochemical reaction can evolve only if the electroactive species involved is present on the surface. This means that the dissolved species arrives at the electrode surface by some transport process through the electrolyte in which it is initially homogeneously distributed. Various transport modes can occur [147, 149]: • For ionic species, an electric field in the solution produces transport by ionic electromigration. • The consumption or the production of a species at the electrode surface leads to a decrease or an increase of the concentration of this species in the vicinity of the electrode. This concentration gradient produces transport by diffusion. • In liquid electrolytes, a movement of the ensemble of the electrolyte produces transport by convection (i.e., stirring or flowing of the electrolyte or electrode movement). In the permanent regime, equilibrium is established between the fluxes imposed by the various transport processes on the one hand, and the flux of the electric

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charges transferred across the interface to produce the electrode reaction on the other hand. This equilibrium is traduced by a relationship between the mass flux and the current density corresponding to the electrochemical reaction. This relationship implies that the global rate of the electrochemical process depends not only on the kinetics of the reaction occurring at the electrode but also on the mass transport kinetics. Therefore, the rate-determining step of the global process can be controlled by either the reaction kinetics or the mass transport, or both. → − Ionic electromigration in bulk electrolytes. The electric field E = −Δφ (where φ is the potential in the bulk electrolyte) is the driving force for the electric charges. Under its influence each ion gains a speed: → − → − v i = −ui ∇ φ ,

(28)

where ui is the electric mobility of the ion, positive for a cation, and negative for an anion. Because of the opposite signs of their charge, anions and cations migrate in opposite directions: anions migrate toward the anode and cations toward the cathode. This ionic movement of all the mobile ions maintains the electroneutrality of the solution. The flux density of the ion, Ji , is defined as the number of moles of the ion crossing a unit surface perpendicular to the transport direction per time unit. → − → − J i = −ui ci ∇ φ (Ji in mol cm−2 s−1 ).

(29)

The electric quantity brought by the flux of the ion i (with charge zi ) is the current density (charge flux): → − → − → − j i = Fzi J i = −Fzi ui ci ∇ φ . (30) If the migration of each ion is independent of the migration of the others, which is valid at infinite dilution, then: → − → − → − j = ∑ j i = −F ∑ (zi ui ci ) ∇ φ , i

(31)

i

→ − → − i.e., j = κ E , where κ = F ∑i zi ui ci is the conductivity of the electrolyte (S or Ω−1 ), which is the sum of the partial conductivities κi = Fzi ui ci for each species i. Transport by diffusion. The electrolytic current can be related to the mass flux densities at the electrode surface, Jid ∗. For an electrochemical reaction, one has O + ne− → R, j

= nFJOd ∗ = −nFJRd ∗ ,

(32) (33)

by counting the fluxes leaving the electrode positively and the fluxes going toward the electrode negatively.

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The flux density of species i transported by diffusion is equal to: → − → −d J i = −Di ∇ ci .

(34)

For a one-dimensional diffusion, Fick’s first law is obtained:

∂ ci → −d J i = −Di . ∂x

(35)

In the same way, if Di is independent of ci , Fick’s second law is as follows:

∂ ci ∂ 2 ci = Di 2 . ∂t ∂x

(36)

Transport by diffusion-convection. If transport by convection (natural or mechanically imposed), which imposes a speed v on the electrolyte, is taken into account, the convective diffusion law is obtained. When a diffusion gradient is superimposed on this convection regime, the density of the global flux is as follows: → − → − dc → −d → −c − v. J i = J i + J i = −Di ∇ ci + ci →

(37)

In this condition, Fick’s second law for one-dimensional transport is as follows:

∂ ci ∂ 2 ci ∂ ci = Di 2 − v . ∂t ∂x ∂x

(38)

The solution for these equations requires complete knowledge of the velocity of the liquid, which depends on the mechanical device used to impose the convection. The differential equation of the steady-state regime is obtained for ∂ ci /∂ t ≡ 0 in the general equation, which becomes as follows: Di

∂ 2 ci ∂ ci . =v ∂ x2 ∂x

(39)

A very simplified model of the convective diffusion was introduced in electrochemistry by Nernst (1904), which is based on the hypothesis of the formation, at the electrode surface, of a motionless limiting layer with a thickness δN where diffusion occurs. Hence, in the steady-state regime, the concentration gradients and the diffusion fluxes remain restricted in a layer, called the Nernst diffusion layer, close to the electrode. In this layer, Fick’s equations are easily solved:

leads to

∂ 2 ci =0 ∂ x2

(40)

c0 − c∗i ∂ ci = cte = i , ∂x δN

(41)

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where c∗i is the concentration at the external limit of the diffusion layer (x ≥ δN ), i.e., the concentration of the species in the homogeneous solution, and c0i = c(x = 0) is the concentration at the other limit, at the electrode. Hence, the steady-state flux is equal to: c0 − c∗i d Ji,stat = −Di i (42) δN (∂ ci /∂ x > 0 and Ji < 0 for a species consumed at the electrode and ∂ ci /∂ x < 0 and Ji > 0 for a species produced). The steady-state current density related to this diffusion flux is as follows:      nF d   nF d 0  stat ∗     (43) | j | =  Ji,stat  =  ki (ci − ci ) , νi νi where kid = Di /δN (cm s-1) is the diffusion transport rate across the Nernst layer. The profile of the concentration is given in Fig. 8. In reality, instead of the angular point at x = δN , the concentration profile changes progressively from a linear variation close to the electrode to c = c∗ far from the electrode.

4.1.3 The Electric Double Layer at Interfaces The accumulation of electric charges (nontransferable across the interface in the absence of electrochemical process) on each part of the interface results from the existence of mobile charge carriers in the two phases in contact with each other and an interfacial potential difference (Δφ El/sol = φ El − φ sol ) [153]. The charge accumulated on one side of the interface is counterbalanced by the charge accumulated on the other side: (44) qsol = −qEl , where q represents the charge per surface unit (C cm−2 ). The charge brought by the electrode itself (qEl ) is constituted either by an excess of electrons (negative charge) or by a shortage of electrons (positive charge), depending on the sign of Δφ . The compensating charge on the electrolytic solution side is due either to an excess of cations compared with anions, for Δφ < 0 (when the electrode is negatively charged), or to an excess of anions compared with the cations (when the electrode is positively charged). ˚ the thickness of the If the charged layer at the electrode surface is thin (< 0.1 A), layer in the solution where the ionic distribution is not electrically neutral is much larger because of the size of the solvated ions. Double-layer structure. It is generally assumed that the ions can approach the electrode only at a distance of a few angstroms. Their centers are located in a plane (called Helmholtz plane). The Helmholtz layer (or compact layer) would contain only solvent molecules oriented by the electric field.

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a C(x) Cs

(real profile)

C*

steady-state flux

δN

0

steady-state diffusion layer

x

homogeneous solution

(NERNST hypothesis)

b C(x) C*

steady-state flux

Cs

0

δN

x

Fig. 8 Concentration profile of the electroactive species dissolved in the diffusion layer. a Species consumed by the electrochemical reaction, b species produced by the electrochemical reaction. The concentration profiles are represented in the Nernst hypothesis (continuous curve), and in real values

However, this is actually more complex. The ions that are not adsorbed (generally cations) are kept at a certain distance from the electrode by their solvation shell and by a layer of solvent molecules adsorbed on the electrode. Conversely, those that are specifically adsorbed (anions) are directly in contact with the electrode surface. Therefore, there are two Helmhotz planes. On the other hand, the ions accumulated close to the electrode are under the influence of the thermal movement. They constitute the diffuse layer (or Gouy–Chapman layer).

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The ensemble Helmholtz layer/Gouy–Chapman layer constitutes the electrochemical double layer. Its thickness is in the order of a few tens of Angstroms. This layer is generally represented by the series combination of two capacitances relative to the diffuse and compact layers, Cdiff and Ccomp . The capacity of the double layer, Cd , is thus equal to: 1 1 1 = + . (45) Cd Cdiff Ccomp Capacitive current. The charging of the electrode/solution interface leads to a capacitive current when a variation of the interfacial charge occurs: jcapa =

dqEl . dt

(46)

This phenomenon occurs when the electrode potential is changed as qEl changes with E. The capacitive current shows an exponential decrease relating to the values of the double layer capacity, Cd , and the cell resistance, Rcell . The decrease is very short (lower than 1 ms) since the time constant, τ = Cd Rcell , is in the order of a few tens of microseconds. If a continuous change of the potential is imposed at the electrode, a permanent capacitive current is observed: jcapa =

dE dqEl dE = Cd . dE dt dt

(47)

If E varies like E = Ei + bt, a continuous capacitive current appears, which is proportional to the rate b.

4.2 Techniques Used for Investigating Electrode Reactions To determine the elementary processes involved in a reaction mechanism occurring at an electrode/electrolyte interface (mass transport, chemical, and/or electrochemical reactions) requires the use of techniques to control the state of the electrode and to analyze the behavior of the interface. One begins by studying the steady-state regime. Although this study sometimes suffices for simple processes, it proves inadequate as the degree of complexity of the processes and their coupling increases. Nonsteady-state techniques must then be used [148, 151, 153]. In electrochemistry, because electrical quantities are easy to use and provide information directly relating to the behavior of the interface, they are particularly useful to identify interfacial processes. Contrary to other techniques, which require a vacuum chamber [low-energy electron diffraction (LEED), Auger electron spectroscopy, etc.] or electromagnetic radiation (optical: ellipsometry, or X-rays: EXAFS), which need no alteration of the electrode surface, electrical techniques can be used in situ on any surface state of the electrode. In addition, thanks to the advances in electronics, experimentalists can use more and more sophisticated

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instrumentation. These electrical techniques will be only briefly presented, since details can be found in reference books. They can be transposed to other quantities: pressure, surface, rotation velocity of the electrode, temperature, etc., which can be used to clarify the phenomena involved at the interface between an electrode and an electrolyte. The principle of the nonsteady-state techniques (also called relaxation techniques) is based on the fact that the steady state depends on some quantities (potential, pressure, temperature). A perturbation of these quantities by the experimentalist changes the state of the system. The rate at which it tends to a new steady state depends on its characteristic parameters: reaction rate constants, diffusion coefficient, and their various couplings. Analyses of the transient regime can lead to information on these parameters and on the phenomenological equations that relate to them. However, due to the nonlinearity inherent to electronic transfer, the derivation and the exploitation of the response of the interface to a large amplitude signal are often inextricable in complex processes. Therefore, low-amplitude signals are often used in electrochemistry. However, even in this condition, the time transient response is generally very complicated. In contrast, the frequency response is usually simpler, allowing for easy exploitation of experimental results. By controlling the electrochemical reactions, the use of electrochemical quantities allows for kinetic studies whereby the various elementary phenomena can be dissociated. In this way, the monoelectronic steps of the reaction mechanisms can be distinguished and the often unstable intermediates involved in the reactions can be counted. Although these techniques do not lead to an identification of the chemical bonds or the intermediates in the chemical sense, they give information on the rates of the reactions occurring at the electrochemical interface and provide a certain characterization of the intermediates. The plot of the steady state current–voltage curve allows reliable data to be quantitatively obtained only for the slowest step in the overall reaction scheme. This may suffice for very simple systems (i.e., oxido–reduction reaction without mass transport limitation) but is largely insufficient for multistep mechanisms with or without mass transport limitation. In potential step experiments, the potential of the working electrode is changed instantaneously and the current–time response is recorded. These techniques are known as chronoamperometry and chronopotentiometry when the potential response to a current step is recorded. Sometimes it is appropriate to use chronocoulometry by plotting the total charge (determined by integration of the current) with respect to time. These techniques are restricted to pure electron transfer under mass transport limitation coupled, or not, with homogeneous chemical reactions. For more complex systems, particularly where multistep electrochemical reactions occur, one is well advised to use small signal techniques and particularly impedance spectroscopy. In some very favorable situations, several techniques can have comparable effectiveness. However, when complex heterogeneous reactions interact with mass transport, analyses of the current or potential time transients lead to poor results if a reaction mechanism has to be resolved. A frequency analysis is then more efficient. Therefore, impedance measurements, by means of a perturbation sine wave

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signal with low amplitude in a wide frequency range, have been widely developed [97,141–153]. Examples of applications of impedance analyses to various problems can be found in the special issues of Electrochimica Acta, which follow the International Symposia on Electrochemical Impedance Spectroscopy (EIS) that are held every 3 years: Electrochimica Acta 35, n◦ 10 (1990); 38, n◦ 14 (1993); 41, n◦ 7/8 (1996); 44, n◦ 24 (1999); 47, n◦ 13/14 (2002); 51, n◦ 8/9 (2006). On the other hand, a special issue devoted to impedance techniques was published by J. Electroanal. Chem. 572, n◦ 2 (2004). Among the nonsteady state techniques, impedance techniques are increasingly used in electrochemistry as well as in academic studies or industrial applications to characterize electrode processes to dissect overall electrochemical processes. These techniques are based on an analysis of the current response (or potential) to a lowamplitude perturbation, often sinusoidal, of the potential (or current). The measurement is carried out at constant polarization potential, as soon as the electrode has reached a steady state, by varying the analyzing frequency in a large-frequency domain (often from 50 kHz to 0.001 Hz). This measurement is then repeated all along the current–voltage curve in the studied potential range. The electrochemical system is polarized using a potentiostat or a galvanostat. The impedance is measured with a frequency response analyzer. The impedance gives information on the processes occurring at the interface (electrochemical and chemical reactions and diffusion) and on the structure of the interface. Plotted in the complex plane (Re[Z( f )]),-Im[Z( f )), the high-frequency limit generally gives the electrolyte resistance and the low-frequency limit – the polarization resistance (inverse of the slope of the current–voltage curve). In the high-frequency range, a capacitive loop is related to the parallel arrangement of the charge transfer resistance and the double-layer capacity. In the lower frequency range, one can observe capacitive or inductive semicircles, which represent the relaxations of the reaction intermediates, capacitive loops related to diffusion characterized by a 45◦ part with respect to the real axis, and negative resistance for passivation. Impedance is a quantity defined for a linear system. In electrochemistry, where nonlinear behavior occurs because of the reaction rate constants, which depend exponentially on the potential, the use of low-amplitude signal allows the system to be linearized. Therefore, the electrochemical nonlinear system is approximated by a linear system around the polarization point. The experimental results can be interpreted in two ways. On the one hand, one can look for an equivalent circuit having the same impedance. An example will be given in the following paragraph, using transmission lines to describe the behavior of porous electrodes. On the other hand, one can look for a model involving kinetic equations describing the reactions and mass transport and, after linearization, calculate a theoretical impedance, which can be compared with the experimental data. The latter approach will be developed later. To illustrate the various techniques, the same redox process limited by mass transport will be analyzed by three different methods, namely linear voltammetry, chronoamperometry, and impedance spectroscopy.

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If an oxido–reduction reaction occurs between species O and R, with concentrations cO and cR , such as: k1

−−− −→ O + ne− − ←− −− R, +k2

where the reaction rate constants are   nF E k1 = k10 exp −(1 − α ) RT

 nF k2 = k20 exp α E , RT 

and

(48)

the concentrations of species O and R should diffuse with coefficients DO and DR in the direction x perpendicular to the electrode surface, and their concentrations obey the following:

∂ cO (x,t) ∂ 2 cO (x,t) = DO ∂t ∂ x2 2 ∂ cR (x,t) ∂ cR (x,t) = DR . ∂t ∂ x2

(49) (50)

The initial and boundary conditions describe the experimental conditions. (a) The initial conditions, at t = 0, express the homogeneity of the electrochemical solution before switching on the current, and the concentrations of O and R species are then equal to c∗O and c∗R : for t = 0 one has cO (x, 0) = c∗O and cR (x, 0) = c∗R . (b) The boundary conditions impose, at a certain distance from the electrode surface, that the concentrations of the species are equal to those found in the bulk electrolyte, c∗O and c∗R : for t ≥ 0 and x → ∞ one has cO (x,t) → c∗O and cR (x,t) → c∗R . (c) The boundary conditions at the electrode surface are imposed by the charge and mass balance. The fluxes of the O and R species are the same and are equal to the faradaic current (Fick’s first law): for t ≥ 0 and x = 0 one has DO

∂ cO ∂ cR IF (t) (0,t) = −DR (0,t) = , ∂x ∂z nFA

(51)

where the faradaic current is given by the law of heterogeneous kinetics: IF (t) = nFA[k2 cR (0,t) − k1 cO (0,t)]. Then, at the electrode surface, (x = 0):     ∂ cR (x,t) ∂ cO (x,t) + DR = 0. DO ∂t ∂t x=0 x=0

(52)

(53)

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4.2.1 Linear Sweep Voltammetry For linear sweep potential voltammetry and chronoamperometry, a reversible electrochemical reaction, i.e., a redox process for which the reaction rate constants k1 and k2 are assumed to be very large, is considered. Thus, the potential can be written as follows: E = EO +

RT cO (0,t) ln nF cR (0,t)

(54) 

 nF cO (0,t) O or = f (t) = exp (E − E ) . cR (0,t) RT

(55)

For linear sweep voltammetry, the potential changes are expressed as follows: E(t) = Ei − vt,

(56)

where ν is the rate of the potential sweep. The flux at the electrode is proportional to the current intensity:   ∂ CO (x,t) I(t) −JO (0,t) = = DO . nFA ∂x x=0

(57)

Hence, it can be shown that [146]: CO (0,t) = CO∗ − [nFA(π DO )1/2 ]−1

 1 O

i(τ )(t − τ )dτ .

(58)

The change of the current with respect to the potential can be obtained from the numerical integration of:  σt 0

i(z)dz = (σ t − z)1/2

nFAc∗0 (π D0 σ )1/2 , 1/2 1 + DDR0 exp [σ (Ei − vt − E 0 )] 

(59)

where σ = (nF/RT ). The results of this integration are given in Fig. 9. If, for a reversible redox process limited by diffusion, linear cyclic voltammetry allows quantitative results to be obtained in a relatively short time, the interpretation of the voltammograms relative to more complicated reaction mechanisms such as processes involving adsorbed intermediates becomes much more difficult.

4.2.2 Chronoamperometry In the case of chronoamperometry, E(t) is a potential step. If E(t) is imposed on an electrochemical interface where a reversible redox reaction occurs from a potential

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Ep

ip

E1/2

0.4

Current

0.3

Ep/2 0.2

0.1

0

+100

−100

0

E-E1/2 Fig. 9 Voltamperogram with linear sweep of potential

where there is no current to a more negative potential, the current response, I(t), can be obtained by using the Laplace transform: nFAD0 c∗0 1 √ 1 + νξ πt 1/2

I(t) = where



ν = exp

nF(E − E O ) RT

(60) 

 and

ξ=

DO . DR

(61)

The limiting diffusion current, Il , obtained for E → −∞, is equal to: Il =

nFAD1/2 c∗ √O O, πt

(62)

i.e., I = Il /(1 + νξ ) and E = E1/2 + (RT /nF) ln(Il − I)/I, where the half-wave potential is equal to  DR RT E1/2 = E O + ln . (63) nF DO The concentration repartition with respect to the distance x is given by:

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 ∗ cO (x,t) = cO 1 −

x 1 erfc √ 1 + νξ 2 DOt   x ξ ∗ √ erfc , cR (x,t) = cO 1 + νξ 2 DRt

 ,

(64)

(65)

where the function erfc(z) is defined by: erfc(z) = 1 −

2

 z

π 1/2

0

  exp −y2 dy.

(66)

Therefore, the concentrations at the electrode surface are as follows:   ξ 1 cO (0,t) = c∗O 1 − . and cR (x,t) = c∗O 1 + νξ 1 + νξ The solution of nonlinear evolution equations in the time domain is known analytically only in very simple cases such as reversible redox processes limited by diffusion. For electrochemical nonlinear systems, the treatment of nonsteady-state techniques generally requires calculations that are at least partially numerical. In addition, the solutions found to express the response to a perturbing signal depend specifically on the form of the perturbation. These drawbacks are largely eliminated if the amplitude perturbation is limited to a sufficiently low value to allow the equations to be linearized. In this case, analyses in the frequency domain are very powerful.

4.2.3 Electrochemical Impedance Here, the redox process is supposed to be irreversible, i.e., the process is not considered fast (k1 and k2 are not infinite, as in the previous examples). The faradaic current associated to this process is then: IF (t) = nFA(k2 cR (0,t) − k1 cO (0,t)).

(67)

When a small amplitude perturbation ΔE exp ( jω t) is applied to the interface around the polarization potential, the corresponding current response, ΔIF exp( jω t), is obtained by differentiating the equations describing the value of the faradaic current and mass transport. By eliminating the terms in exp( jω t) on the two sides of the following relationship, one has the following when there is a transport limitation by diffusion: (1 − α )nF α nF ΔIF = k1 c¯O (0)ΔE − k1 ΔcO (0) + k2 c¯R (0)ΔE + k2 ΔcR (0), nFA RT RT ∂ 2 Δci (x) jω Δci (x) = Di , (68) ∂ x2

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where Δci represents a small variation of ci and i represents the indices O and R. c¯i (x) is the concentration of the species, at a distance x from the electrode, for a steady state polarization, such as: ci (x,t) = c¯i (x) + Δci (x)exp( jω t).

(69)

These equations lead to two important concepts: the charge transfer resistance and the Warburg impedance. It must be kept in mind that, even if simply for the sake of derivation convenience, the quantities exp( jω t) are only taken into account implicitly, the preexponential terms ΔIF and ΔCi (x) also depend on the pulsation ω . Charge transfer resistance Rt . The charge transfer resistance is defined by:   1 ∂ IF = . (70) Rt ∂ E ci The linearized expression of the faradaic current leads to: 1 n2 F 2 [(1 − α )k1 c¯O + α k2 c¯R ] , =A Rt RT

(71)

where c¯i = ci (0,t → ∞). Warburg impedance. The resulting perturbation of the concentration Δci (0,t) is deduced from the general solution of the equation: jω Δci (x) = Di

∂ 2 Δci (x) ∂ x2

obtained after the terms in exp( jω t) have been cancelled:       jω jω Δci (x) = Mi exp x + Ni exp −x . Di Di

(72)

The integration constants Mi and Ni result from the boundary conditions and depend on the hypothesis of the diffusion layer thickness. Diffusion layer of infinite thickness (e.g., motionless solution). In this case, Mi = 0; otherwise Δci → ∞ when x → ∞, and one has:    jω Δci (x) = Ni exp −x . (73) Di By putting this value in the boundary conditions at the electrode surface, one has:   jω jω ΔIF (t) = −NO nFADO exp( jω t) = NR nFADR exp( jω t). (74) DO DR After elimination of the integration constant Ni between the last two equations:

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ΔcO (x = 0) 1 √ =− , ΔIF nFA jω DO

(75)

ΔcR (x = 0) 1 √ = . ΔIF nFA jω DR

(76)

Thus, the change of the faradaic current with respect to the potential is obtained:   k1 ΔI 1 k2 √ F ΔIF = ΔE − √ +√ (77) Rt jω DO DR and, therefore, the impedance is equal to:   λ ΔE ZF (ω ) = = Rt 1 + √ , (78) ΔIF jω   √   √ where λ = kd / DOx + ki / DRed . √ In the expression of the faradaic impedance, the term Rt λ / jω is usually called the Warburg impedance. The limiting value of the impedance when the frequency tends to infinity is equal to Rt . By taking into account the double-layer capacity, Cd , and the electrolyte resistance, Re , one obtains the Randles equivalent circuit [150] (Fig. 10), where the faradaic impedance ZF is represented by the transfer resistance Rt in series with the Warburg impedance W . It can be shown that the high-frequency part of the impedance diagram plotted in the complex plane (Nyquist plane) is a semicircle representing Rt in parallel with Cd and the low-frequency part is a Warburg impedance. As Fig. 10 indicates, the extrapolation of the 45◦ straight line, which represents the Warburg impedance, intercepts the real axis at: R0 = Re + Rt − R2t λ 2Cd .

(79)

Various shapes can be obtained for the impedance diagrams, depending on the relative values of the parameters describing the charge transfer and species diffusion. Hence, obtaining the kinetic quantities from the simple extrapolation of the 45◦ straight line can be difficult, except if λ 1, since, in that case, the charge transfer and diffusion phenomena are well separated. Diffusion layer of finite thickness (diffusion + convection). We now use the Nernst hypothesis, which assumes that the concentration of the reacting species that diffuse changes linearly in a layer of thickness δN and is constant thereafter. ci (x,t) = ci (0,t) + [c∗i − ci (0,t)] ci (x,t) = c∗i

for

x ≥ δN ,

x δN

for

x < δN ,

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a

Cd

Re

W

Rc t

b

Re

Re + Rct Rct 2 λ 2 Cd

Fig. 10 Electrochemical impedance for a diffusion layer of infinite thickness. a Randles equivalent circuit; b Scheme of the impedance in the complex plane

where δN is the thickness of the Nersnt diffusion layer. Thus, the general solution of the diffusion equation leads to the following equation for the boundary condition at x = δN :       jω jω Δci (x = δN ) = Mi exp δN + Ni exp −δN = 0 for x ≥ δN Di Di    jω so Mi = −Ni exp −2δN δN       jω jω and Δci (x) = −2Ni exp −δN sinh (x − δN ) for x < δN Di Di

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.02

−Im(Z)

.03

.05 .07 .14

.11 .09

.07

.05

.18 .24 .40

.03 .02

1

.01

4 20

.002

Rt

Rt kf δN

Re (Z)

D0

Fig. 11 Faradaic impedance ZF (ω ) plotted for a finite thickness of the diffusion layer (Nernst hypothesis) (frequency in Hz). For comparison, the impedance is also plotted (dotted lines) for an infinite thickness of the diffusion layer



and

      jω jω jω exp −δN cosh δN , then Di Di Di  jω 1 1 ki tanh δN DR ΔcR (0) √ W (ω ) = = (80) ΔIF nFA δN nFA jω DR

ΔIF = 2nFANi Di

and the faradaic impedance is equal to:   ⎞ tanh δN DjωO tanh δN DjωR ⎠. ZF (ω ) = Rt ⎝1 + k1 √ + k2 √ jω DO jω DR ⎛

(81)

This impedance is represented in Fig. 11. It is noticeable that: (a) When ω → ∞, the Warburg impedance is found in the high-frequency range, as follows:  tanh δN

jω D

tanh(y) → 1 when y → ∞, therefore: √ jω D i ≈ √ j1ω D , and i i (b) When δN → ∞, the Warburg impedance is obviously found again. (c) If DO = DR , then:  ⎞ ⎛ tanh δN DjωO ⎠. ZF (ω ) = Rt ⎝1 + (k1 + k2 ) √ jω DO

(82)

Therefore, if the double-layer capacity is considered, as for the diffusion layer of infinite thickness, there is a coalescence of the 45◦ straight line and the high-

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frequency circle, and the straight line crosses the real axis at: R0 = Re + Rt − R2t λ 2Cd .

(83)

In Fig. 11, the oscillation above the Warburg straight line (at frequencies from 0.4 to 0.14 Hz)) is related to the Nernst hypothesis. A numerical calculation taking into account the convection term in the transport equation showed that the impedance diagram is below the Warburg straight line. Within the electrochemical framework of this classical example of a redox process whose rate is limited by the transport by diffusion, it was shown that, even for a reversible redox process, the derivation of the current response in the time domain is far from simple. In contrast, the impedance approach allows the more difficult case of an irreversible (finite reaction rate constants) redox process to be derived. Using the same approach, we will now examine the case of a multistep reaction, which is very difficult to investigate using techniques of potential step cyclic voltammetry.

4.2.4 Two-Step Charge Transfer with an Adsorbed Intermediate A species A in the solution should react at the electrode to give a species, C, through a reaction intermediate B, which is adsorbed at the electrode surface. Thus, the reaction mechanism follows: k

1 Bads , First step: Asol + e− −−−→

k

2 Second step: Bads + e− −−−→ Csol .

The reaction rate constants are equal to: k1 = k10 exp (−b1 E) and k2 = k20 exp (−b2 E) , where the Tafel coefficients, b1 and b2 , are positive. The kinetic parameter whose evolution governs the impedance is the concentration of the intermediate Bads in the adsorbed phase. If θ is the fraction of the electrode surface covered by this adsorbate and β is the superficial concentration for a complete coverage by Bads , by assuming a Langmuir adsorption isotherm, the surface concentration of Bads is cB = β θ . • The evolution equation describes the balance of β θ and expresses the mass conservation:

β (dθ /dt) = formation rate – consumption rate. The formation rate of Bads is equal to k1 cA for a first order reaction in A. By taking into account the available area fraction, Bads becomes (1 − θ )k1 cA . The consumption rate of Bads is equal to k2 β . By taking into account the area fraction occupied by Bads , then Bads becomes β θ k2 .

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The evolution equation for β θ is then:

β

dθ = (1 − θ )k1 cA − β θ k2 . dt

The potential E, which is perturbed, does not explicitly appear in this equation but is implicitly involved through k1 and k2 . Steady-state solution of the evolution equation. The steady-state solution, θs , of the evolution equation at a polarization point Es , is obtained by putting d/dt ≡ 0, which leads to: (1 − θ )k1 cA − β θ k2 = 0, i.e., θs = k1 cA /(k1 cA + k2 β ). Solution of the linearized nonsteady-state equation. The small amplitude changes of the quantities θ , E, and I will be denoted by Δ. Thus, the linearized evolution equation is written as:

β

dΔθ = ((1 − θs )b1 k1 cA − β θs b2 k2 )ΔE − (k1 cA + k2 β )Δθ , dt

(84)

where the values of the rate constants k1 and k2 are taken at the potential Es . The solution of this equation for a sinewave potential perturbation of ΔE = |ΔE| exp( jω t) centered on Es is as follows: Δθ (1 − θs )b1 k1 cA − β θs b2 k2 = . ΔE jωβ + k1 cA + k2 β

(85)

For frequencies much greater than the rate constants, the kinetics of the variations of θ , imposed by its evolution equation, does not allow the perturbation of the potential to be followed, which means that Δθ /ΔE → 0. At these high frequencies, the coverage is said to be frozen. The coverage rate θ is not usually directly measurable. The impedance is the observable quantity, and will be calculated from the electrochemical current I. The faradaic current I is the sum of the elementary currents of each step: I = −F((1 − θ )k1 cA + β θ k2 ). By considering θ = θs in this equation, the steady-state current is obtained: IF = 2F β θs k2 , i.e., by taking into account the steady-state value of θ Is = −2F

β k1 k2 cA . k1 cA + β k2

The differentiation of I around the polarization point (θs , Es ) gives: ΔI = F{((1 − θs )b1 k1 cA + β b2 k2 θs )ΔE + (−k1 cA + k2 β )Δθ }.

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Then, by substituting Δθ /ΔE and θs for their values, one obtains: 1 β k1 k2 cA (b1 + b2 ) β k1 k2 cA (b1 − b2 ) . = + (−k1 cA + k2 β ) FZF k1 cA + k2 β (k1 cA + k2 β )( jωβ + k1 cA + k2 β ) When ω → ∞ ZF = (k1 cA + k2 β )/[F β k1 k2 cA (b1 + b2 )], which is the charge transfer resistance. When ω → 0 ZF (0) = Rp , which is the polarization resistance (i.e., the slope of the current–voltage curve). The variations with the frequency of the faradaic impedance are determined by the sign of the numerator of the fraction coming from Δθ /ΔE. This sign depends on the relative rate of the two steps of the total reaction. Figure 12 shows the current–voltage curve and the impedance for b1 > b2 . For potentials lower than Ec , the impedance has an inductive loop, whereas there is a capacitive loop for potentials greater than Ec . Ec is defined when the two steps have equal rates. At this particular potential, where θs = 0.5, the impedance is reduced to the charge transfer resistance Rt . It is possible to ascertain that the polarization resistance, Rp , which is the limit of ZF when ω → 0, always remains positive and equal to the slope of the current–voltage curve. For a two-step monoelectronic reaction mechanism, the Rt Is product is a constant equal to: 2 Rt Is = . b1 + b2 θs 1

0.5 0

log I

E>Ec

−Im[Z] ω=∞

−Im[Z] ω=∞

E<Ec

ω=0 Rt =Rp

Rt

ω=0 Re[Z] Rp

Re[Z]

−Im[Z] ω=∞

Rp ω=0

Rt

Re[Z] Ec

E

Fig. 12 Scheme in the Tafel plane (log I, E) of the steady state behavior and the impedance of the two-step reaction mechanism when b1 > b2 . I: total current. I1 and I2 : partial currents of the first and second steps. Ec is the potential where I1 = I2 and θ = 0.5. Upper part: variation of θ with respect to E

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5 Porous (Nanostructured) Electrode Geometry As the use of nanotechnology in design electrodes and cells for energy conversion and storage devices continues to grow, it is important to take into account the porous effect and how to characterize the electrode’s response to such porous and nanostructured architectures. The porosity and nanostructures are very important in energy conversion and storage devices. Therefore, important aspects involving porous electrode theory will be presented and discussed in this section. The transport and reaction processes occurring in nanostructured electrode can be understood by considering the electrochemical theory of porous electrodes. Although the subject of porous theory has been extensively examined in the literature [92, 95, 96, 98–101, 154–184], it continues to be of permanent interest, particularly now that nanostructured electrodes are so widely applied and the capability to design different porous materials and electrodes for electrochemical applications continues to grow. The porous electrode theory is based on the fact that electrodes operate in contact with an electrolyte by simultaneous transport of electronic and ionic species in the solid and liquid phase, respectively. The solid phase in contact with the conducting substrate provides a continuous path for the transport of electrons (or holes, or polarons), but the dimension of the structural elements is extremely small, i.e., on the nanometric scale. The electrolyte penetrates the voids in the solid phase up to the substrate, and again the dimension of the liquid channel is very small. Therefore, the system is characterized by the existence of two closely mixed phases in the electroactive nanostructured layer, with narrow channels for transport, displaying a large degree of disorder. The transport of charge carriers in both phases is believed to be influenced by complex mechanisms. Note that, to apply the model, one might deal with the ability of the electrolyte to penetrate the pores; thus, contact with the very high surface area of the semiconductor is critical. The porous electrode theory was developed by several authors for dc conditions [185–188], but the theory is usually applied in the ac regime [92,100,101,189–199], where mainly small signal frequency-resolved techniques are used, the best example of which are ac theory and impedance spectra representation, introduced in the previous section. The porous theory was first described by de Levi [92], who assumed that the interfacial impedance is independent of the distance within the pores to obtain an analytical solution. Because the dc potential decreases as a function of depth, this corresponds to the assumption that the faradaic impedance is independent of potential or that the porous model may only be applied in the absence of dc current. In such a context, the effect of the transport and reaction phenomena and the capacitance effects on the pores of nanostructured electrodes are equally important, i.e., the effects associated with the capacitance of the ionic double layer at the electrode/electrolyte-solution interface. For instance, with regard to energy storage devices, the desirable specifications for energy density and power density, etc., are related to capacitance effects. It is a known fact that energy density decreases as the power density increases. This is true for EDLC or supercapacitors as well as for secondary batteries and fuel cells, particularly due to the distributed nature of the pores

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in nanostructured electrodes. The usable energy stored in EDLCs or Li-ion batteries diminishes as it is extracted at higher discharge rates. Therefore, it is important to understand not only the porous effect but also the distribution characteristics involved and to grasp their rationale to maximize the energy density at desired power densities in such devices. In addition, it has already been proven than nanostructured lithium-ion battery electrodes based on nanofibers or nanotubes of the electrode material protruding from an underlying current-collector surface like the bristles of a brush, for example, or nanoparticles (see Fig. 4a) are able to dramatically improve the rate capabilities because, in nanostructured electrodes, the distance that Li+ must traverse to diffuse through the solid state (the current- and power-limiting step in Li-ion battery electrodes) is significantly smaller [86, 91, 113, 123–125, 200]. Two kinds of geometry are commonly employed to improve rate capabilities and achieve a faster solid-state diffusion, as depicted in Fig. 4. The first geometry is based on connected spherical-like nanoparticles and the second on nanofibers that protrude, brushlike, from the current collector [113]. With regard to energy conversion devices, as discussed earlier herein, porous nanocrystalline materials for electrodes possess extraordinary physical and chemical properties thanks to their ultrafine structure (i.e., grain size < 50 nm), resulting in very important surface effects that render them appropriate for use as electrodes in DSSC devices. The role of the pores is to increase the screening of the electrons in the electrode, via adsorbed ionic solution species, increasing the rate of charge transfer between the oxide and each of the dye molecules adsorbed on the particle surface. The nanostructured electrode also provides sufficient monolayer adsorption of dye molecules to increase the efficiency of light adsorption [201, 202]. Although this picture of the operation of such films is generally accepted, a consensus has not yet been reached regarding the description of the transport and recombination mechanisms of electrons inside the porous matrix, nor is the origin of photopotential in DSSC completely understood. Impedance spectroscopy is one of the techniques exploited to increase knowledge in processes that occurs in DSSC devices [22].

5.1 Transmission Line Description of Porous Electrodes To help elucidate some of the aspects involved in the boundary conditions of nanostructured electrodes, a proper grasp of the theory of ac porous impedance is important to extract relevant information on the kinetics of specially designed nanostructured electrodes. For a general view of this subject, the features expected in a homogeneous electrode are compared, later, with those of a porous electrode in which two phases, liquid and solid, become mixed inside the electrode region. A homogeneous electrode with a macroscopically flat surface is shown schematically in Fig. 13. The impedance porous model is adequately represented by the transmission line approach, according to Fig. 14. In general, the transmission line method is strictly one-dimensional; the equipotential surfaces are planes, and such models

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129

flat electrode

Zc

Zi

Ze electrolyte

conducting substrate

Fig. 13 Schematic of a cross section of a macroscopically flat surface electrode, indicating the impedance elements. Three different impedances are represented: Zc is the impedance of the contact between the current collector (conduction substrate) and the electrode, Zi is interfacial impedance of the electrode–electrolyte interface, and Ze is the impedance corresponding to the properties of the electrolyte, which is generally given by a pure resistance element such as the one indicated in Fig. 10 (Re ) and (14) (Rs ) or as Rcell in (15), representing the ohmic drop in the electrolyte

ϕ1

ϕ1 ζ

conducting substrate

0

electroactive nanostructured electrode ϕ1 ϕ1

ζ

ζ

ϕ2

ϕ2

ζ

Rs

ζ ϕ2

electrolyte

L

x 0

L

Fig. 14 Scheme of a porous electrode with the equivalent general circuit model according to the theory explained earlier. Note that in this picture Rs is the electrolyte resistance, which in the previous section was Rcell

can hardly represent special types of pores. The different models based on the transmission line approach differ from each other by the choice of these elements and partly by the possible addition of further discrete elements of the transmission line. Therefore, in this kind of approach of porous electrode representation, basic electrical properties such as capacitance, resistance, and inductance are defined independently of frequency, for idealized cases. Also, their impedances have well-defined frequency behaviors and the majority of methods usually presuppose that all the

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elements throughout the layer are the same. As can be seen, the equivalent circuit modeling of the cell impedance involves the connection of a series of elements describing the division of the applied small-signal ac voltage in three parts: one at the bulk of the layer, another at the solid/liquid interface, and the third, which includes the potential drop at the bulk electrolyte and metal contacts (see Fig. 14). It is well known from studies of the interfacial impedance Zi of planar semiconductor electrodes that several effects occur at the semiconductor/liquid interface, including the capacitance and resistance of the space-charge region, the effect of surface states, the capacity and charge transfer resistance across the Helmholtz layer, and the diffusion of reacting species (details were given previously in Sect. 4). Therefore, the form of Zi may become quite complex, but nonetheless, the various processes involved in Zi are localized in the sense that the potential difference driving these processes obeys two conditions: it resides essentially at the semiconductor/electrolyte interface, and it is essentially independent on the position on the surface. Or, to put it another way, the flux of carriers is always normal to the plane of the surface, and the current density is the same at any point in the surface. Consequently, Zi can be described by the series and/or parallel combinations of resistive and capacitive components. Figure 14 schematically illustrates the cases in which the two phases are closely mixed in space because the layer is porous on a small scale. Both media are considered as effectively homogeneous and continuously connected phases. A standard equivalent circuit model also is represented in Fig. 14, describing the essential features of electrical transport along each phase and the exchange of charge through the inner surface. This model assumes that the predominant contribution to the current is electrical field-driven rather than diffusive, but different situations arise according to the systems to be considered. Now the porous structure gives rise to the spread of electrical current in various directions. First, electrical charge can flow along each medium; the resulting ac currents are termed here i˜1 and i˜2 (the subscripts 1 and 2 denote the liquid and solid phase, respectively) and they follow the x direction in the scheme of Fig. 14, i.e., both i˜1 and i˜2 are parallel to the inner surface shown in the figure. Moreover, current can flow in the normal direction to the inner surface due to electrochemical reactions and/or capacitive charging. Therefore, at a given location, i˜1 may decrease (increase) with a corresponding increase (decrease) of i˜2 , the constraint being obeyed that i˜T = i˜1 + i˜2 (the total current flowing through the external circuit) is independent of position. In agreement with this description of electrical current distribution, the equivalent circuit branches at each point in each medium into an element that continues in the same medium, ϕ1 or ϕ2 , and another impedance element ζ that crosses the interface. The impedance elements ϕ1 and ϕ2 describe a local ohmic drop at each point of the transport channels, depending on media conductivity and more generally on transport properties, whereas the element ζ describes an exchange of electrical charge at the interface, owing to faradaic currents and polarization at the pore surface. (Obviously, the interfacial impedance ζ itself might consist of a complex equivalent circuit, as mentioned earlier with regard to Zi ). The branching in the equivalent circuit model is intended to occur continuously.

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The classical model for porous or mixed-phase electrodes is therefore formulated in terms of equations that describe the local variation of electric current and potential in each phase in the layer of thickness L by the following equations: 1 ∂ φ1 , ϕ1 ∂ x 1 ∂ φ2 i2 = − , ϕ2 ∂ x ∂ i1 1 = − (φ1 − φ2 ), ∂x ζ ∂ i2 1 = (φ1 − φ2 ). ∂x ζ i1 = −

(86) (87) (88) (89)

The quantities or elements ϕ1 and ϕ2 are impedances per unit length (Ω cm−1 ) corresponding to the whole electrode area A, and ζ is an impedance length (Ω cm−1 ). The overall impedance is isomorphous to that of a transmission line. Regarding the electrical potential distribution, the simple assumption is made that an ac potential can be defined in each phase φ˜1 and φ˜2 which is, at each frequency, a unique function of position x; no radial distribution of potential into the pores or solid particles is considered. It follows that the ac potential difference between the two phases at a point x, i.e., the overvoltage in interfacial reactions, is φ˜2 − φ˜1 . In addition to the differential equations, the boundary conditions must also be taken into account. For this case, the ionic current is usually assumed to vanish at the end of the liquid channel, whereas the electronic current vanishes at the outer edge of the electrode, so that i1 (L) = 0 and i2 (0) = 0. For such boundary conditions, the generalized solution of the model leads to the following impedance function [92, 95, 97, 160, 190]:   ϕ 2 + ϕ22 ϕ1 ϕ2 2λ Z= coth(L/δ ), (90) L+ +δ 1 ϕ1 + ϕ2 sinh(L/λ ) ϕ1 + ϕ2 in which



δ=

ζ ϕ1 + ϕ2

1/2 ,

(91)

and L represents the thickness of layered electroactive material over the current collector. Or, in other words, L stands for the porous thickness length.

5.2 Macrohomogeneous Concept (Two-Phase Model) It is important to emphasize that there are different types of assumptions regarding geometry and microstructure that lead to (5). One arrives at this result by considering the original perfect cylinder geometry described in de Levi’s original

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proposal of porous electrode geometry, which is normally used provided that pore is long compared with its diameter, or from an effective macrohomogeneous description of two closely mixed phases, as described by Paasch et al., who considered an effective macrohomogeneous mixture of two phases in the electrode region [101]. Keiser et al. also extended the transmission line model to a noncylindrical pore [14]. The models that consider this approach are largely based on the assumption of effectively homogeneous local relaxation processes related to transport in each of the phases and electrical charge exchange between them. Thus, the complex problem of an uneven distribution of electrical current and potential inside the electrode can be described analytically, and impedances can be calculated. Furthermore the models may be conveniently pictured as a double-channel transmission line (Fig. 3.5). In several papers, the theory of the impedance of porous electrodes has been extended to cover those cases in which a complex frequency response arises in the transport processes [100] or at the inner surface [194, 203]. Therefore, if the electrode’s nanostructure composed of two mixed phases is of a macrohomogeneous nature, (5) can be used even if the pores have a noncylindrical geometry. In this case, one can consider a solid phase having the form of connected channels of spherical-like particles or nanofibers that protrude from the current collector substrate and a liquid phase consisting of a penetrating electrolyte that reaches the current collector substrate. In specific cases in which a solid electrolyte is used, this macrohomogeneous medium can be seen as a mixture of two solid phases without compromising the result of the analysis. It should be noted that if the percolating phase emerging from the current collector substrate is primarily a mixed ionic and electronic conductor, the other phase (such as a liquid) that emerges from the electrolyte (which can be seen as an ion collector penetrating up to the current collector substrate) must be a purely ionic conductor. Furthermore, because of the previous picture, the transmission line approach is easily used to envision a physical model based on frequency-dependent phenomena. A macrohomogeneous electrode can be established in different dimensional structures and the resulting models, which can present analytical or numerical solutions, could relate the global performance of the cathodic or anodic layer to unmeasurable local distributions of reactants, electrode potential, and reaction rates. These unmeasurable local distributions define a penetration depth of the active zone and suggest an optimum range of current density and electroactive layer thickness with minimal performance losses and highest electroactive effectiveness. In addition, the macrohomogeneous theory can be extended to include concepts of percolation theory. As the macrohomogeneous electrode theory has proven its worth in electrode diagnostics and design, so the finer details of electroactive layer structure and electrocatalytic mechanisms are moving to the fore. A useful concept is to consider agglomerates as structural units of the electroactive layer. Ideal locations of electroactive particles are at the true two- or even three-phase boundary. This approach is capable of and vital for showing that micropores inside agglomerates are filled with liquid water to keep the particles active. Even for well defined and extensively

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studied electrode geometry, the essentials of the kinetic mechanisms are not totally settled. Each of the key steps (adsorption, surface mobility, charge transfer, and desorption) still constitutes a huge scientific problem involving the application of the macrohomogeneous concept. Therefore, the macrohomogeneous concept can also be adequately extended to the whole cell. For instance, a framework for macrohomogeneous modeling of porous SOFC electrodes is possible by taking into account multicomponent diffusion, multiple electrochemical and chemical reactions, and electronic and ionic conduction. The concept applies to both porous anodes and cathodes. The derivation of the model is illustrated by considering different chemical and electrochemical reaction schemes. The framework is general enough so that additional chemical and electrochemical reactions can be accounted for. Moreover, recent studies have revealed drastic differences in the kinetics of nanoparticle surfaces. Generally, small particle sizes and highly dispersed electroactive sites lead to high specific activities (per total mass of electroactive sites such as Pt in the catalytic layer of fuel cells). Considering fuel cell applications, it is important to know the real effect of nanoparticles on the kinetics because extremely small particle sizes (below ∼3 nm) affect the electronic structure of the system and render the catalyst surface rather heterogeneous. This begs several questions: What is the optimum nanoparticle size? What are the best properties of nanoparticle arrays? Which substrate is the best? Ultimately, the following questions should be addressed: What is the benefit of nanoparticles? Is it an intrinsic size effect or an effect of surface heterogeneity? What is the role of the substrate? All of these questions can be addressed in the future by the use of the macrohomogeneous concept of electrodes and cells.

5.3 Transport in the Solid and Electrolyte Phases ϕ1 , ϕ2 and ζ elements must be specified in the context of (90) to be used as impedance measurements in a defined kinetic model. Independently of the specific systems, the general basic models can be obtained considering some reasonable and generally valid assumptions about the basic elements in the general transmission line, featuring the transport characteristics in each of the phases and their interfacial behavior. For instance, the solid phase impedance ϕ1 can be simply treated as possessing an ohmic behavior (Ohm’s law). Therefore, the solid channel (channel 1) consists of distributed resistances such as:   1 ϕ1 = r1 = , (92) Aσe where A is the geometric surface of the phase and σe is its electronic conductivity. Assuming that the Nernst–Einstein relation is obeyed, the conductivity is related to the diffusion coefficient, De , by the equation:

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σe =

q2 n¯ De , kB T

(93)

where n¯ stands for the dc concentration of electronic charge carriers, q is the elementary charge, kB is Boltzmann’s constant, and T is the temperature. In this simple model for electronic conductivity in the solid phase channel of the porous electrode, the conductivity is merely a function of the local concentration of the carriers and the diffusion coefficient of the material. Therefore, the total resistance can be calculated easily based on the distributed resistance by R1 = r1 L. This means that the dc behavior of the charge transport processes is independent of frequency, which is useful mainly for very high conductive solid phases. The impedance of the liquid phase or electrolyte can similarly be described by a resistive element and, therefore, the impedance-related element takes the form of ϕ2 = r2 = 1/Aσl , in which A is now the geometric area of the liquid or electrolyte and σl is the ionic conductivity. ¯ B T )Dl , where c¯ is the concentraFurthermore, similar to (8), we obtain σl = (q2 c/k tion of ionic charge carriers and Dl is the diffusion coefficient of the ionic species in the liquid phase or electrolyte. In the same way, the total resistance in the electrolyte contained inside the pores (electrolyte channel) can be given by R2 = r2 L.

5.4 Polarization and Charge Transfer at the Porous Interface The interfacial impedance element, ζ , offers many possibilities. This is the region of transition between the solid phase (electroactive material or electrode) and the electrolyte. Therefore, in this region, charge transfer and double-layer effects are evidenced. Potential differences may sustain charge storage and charge transfer kinetics in this region. For an ideally polarizable interface, the differential relationship between the charge at the boundary and the electrical potential is the interfacial capacitance. An ideally polarizable distributed interface can be described by a capacitance, ci , the distributed interfacial capacitance, whose interfacial impedance is described by: 1 ζ= . (94) jci ω The total capacitance in the walls of the pores is given by Ci = ci L. This capacitance is attributed to double-layer effects, so it is usually a function of the potential. It can also be used to describe the space-charge polarization at the semiconductor–liquid junction if the spatial distribution of electrical charge as a function of potential is known. An ideally polarizable interface with charge transfer can be described by considering the charge transfer as a resistance, rct , which goes in parallel to the capacitance so that the ζ impedance element yields an impedance such as:

ζ=

rct , 1 + jω /ωi

(95)

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with the characteristic frequency of charge transfer defined as ζ = 1/RctCi = 1/rct ci , with Rct = rct /L being the total wall charge transfer resistance. It is not easy to interpret rct , but among a variety of situations, it could be the concentration of reactant species in the electrolyte, characteristic reaction rates, etc. In any case, the reaction or rct resistance originates the faradaic currents at the surface of the electrode.

5.5 Distributed Features and Dispersion Ideally, the polarizable interface is the exception rather than the rule. In many types of interfaces the capacitance of the interface has been found to be a function of the frequency, which is known as capacitive dispersion. In other words, the electrical properties of real circuit elements only approach the ideal within a limited frequency range. For instance, EDLCs show frequency-dependent capacitance even though a capacitance should be independent of frequency. This abnormal frequency dependency is called a distributed characteristic or frequency dispersion of electrical properties. A circuit element with distributed characteristics (distributed element) cannot be exactly expressed as a combination of a finite number of ideal circuit elements except in certain limited cases. Distributed characteristics result from two origins [204]. First, they appear nonlocally when a dimension of a system under study (e.g., electrode thickness or pore length) is longer than a characteristic length (e.g., diffusion length or penetration depth), which is a function of frequency. This type of distributed characteristic exists even when all system properties are homogeneous and space-invariant. This category includes diffusion in a diffusion-limited system [189, 190], double-layer charging of a porous electrode [92], and sluggish processes such as adsorption of anions, surface reconstruction, and transformation in the layer. Secondly, a distributed characteristic is attributed to various heterogeneities: geometric heterogeneity such as roughness or distribution of pore size [205] and crystallographic heterogeneity such as anisotropic surface metal structure and a surface disorder of polycrystalline platinum or gold [192]. Porous material with deep pores is an extreme example of the influence of geometry on frequency dispersion, unlike rough surfaces (with shallow pores) [192]. This is especially true when other heterogeneities are suppressed by careful experimental conditions. The frequency dispersion of porous electrodes can be described based on the finding that a transmission line equivalent circuit can simulate the frequency response in a pore. The assumptions of de Levi’s model (transmission line model) include cylindrical pore shape, equal radius and length for all pores, electrolyte conductivity, and interfacial impedance, which are not the function of the location in a pore, and no curvature of the equipotential surface in a pore is considered to exist. The latter assumption is not applicable to a rough surface with shallow pores. It has been shown that the impedance of a porous electrode in the absence of faradaic reactions follows the linear line with the phase angle of 45◦ at high frequency and then

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a vertical line at low frequency in the Nyquist plot [190,206]. Several particularized examples of blocking interface or nonblocking dispersive boundary conditions are studied in detail in different papers [190, 207]. These models all state that, for idealized interfaces, the phase angle approaches 90◦ at low frequencies. In the Nyquist plot, a vertical line is shown at low frequencies. However, many experimental data of impedance for porous materials show that the phase angle is not 90◦ even at very low frequencies, which is shown as an inclined line in the Nyquist plot. In this case, the dispersive capacitance can be described by another interfacial element capable of dealing with such low-frequency dispersion. A blocking capacitive interface response that takes into account a frequency dependency can generally be modeled by an interfacial impedance element such as:

ζ=

1 ( jω )βi , qi

(96)

which is known as constant phase element (CPE), with a prefactor for the whole interface given by Qi = qi L. In contrast with the voltage dependence of the interfacial capacitance, it is extremely difficult to justify the observed frequency dependence on a theoretical basis. For instance, with regard to dispersive behavior, the porous carbon electrodes widely used in EDLCs have two types of distributed characteristics mentioned previously; one from pore lengths longer than the penetration depth of the ac signal and the other from the pore size distribution. Therefore, the microstructure (represented as pore size distribution) of the porous electrode should be optimized to obtain the desirable energy and power density. With the introduction of a CPE (96) into the porous model represented by (5), it is possible to simulate the nonvertical behavior of impedance at low frequencies [93,94,189,190,208]. Various origins of CPE behavior have been discussed, depending on different systems [189, 195–199, 207, 209–212]. Some authors believe that the inclined line of impedance at low frequencies comes from the pore size distribution of porous materials [171, 182], and a few attempts have been made to consider the effect of pore size distributions (PSD) on the impedance of a porous electrode [171, 182], although the PSD must contribute considerably to the distributed characteristics [171, 182]. The impedance curve in the Nyquist plot is observed to change with the shape of a pore in the intermediate frequency region, despite its similarity to a cylindrical pore at extremely low or high frequencies. Some authors have reported that the real part of the reduced impedance (the ratio of impedance of a pore to electrolyte resistance in a pore) approached one-third at low frequency, irrespective of the shape of a pore [171, 182]. The PSD effect is difficult to take into account, particularly because of the timeconsuming calculations required by this method, while a parametric study is difficult because of too many parameters (sizes of different pores), but some analytical solutions are being used to represent the pore size distribution of a porous electrode [171, 182]. In other words, the pore size distribution considers that the elements of the impedance of the layer are not constant along the length. Thus, both porosity and resistivities can vary in the course of the preparation. In other experimental situations,

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during the preparation of a nanostructured porous layer, the dependence of the potential sweep (electrochemically prepared nanostructured porous layer) causes variation in the degree of oxidation, and this degree of oxidation can vary throughout the layer, or variations in the composition may lead to gradients of resistivities, etc. Such problems have been considered in several cases, e.g., in [189, 190, 213] by using a CPE description. Another way of dealing with such problems is by using transfer matrix methods [167, 193], which allow for their solution. Eloot et al. [214, 215] developed the matrix method to calculate the impedance of a noncylindrical pore by extending Keiser’s model [206]. According to these authors, it appears that the limit of the real part of the reduced impedance depends on the geometry of a pore. The matrix model was used recently as the basis for considering the elements in the channels dependent on the frequency, and they can also vary across the layer [167, 193]. The examples show clearly that, independently of the parameters of the system, inhomogeneity can lead to qualitative modifications of the impedance response, the most important of which is the influence on the low-frequency pseudocapacitive behavior of the impedance, which is transformed into a CPE-like form (which, as discussed previously here, is usually introduced only phenomenologically by replacing j(ω /ωc ) to j(ω /ωc )β with β < 1). Some of the dependencies demonstrated by the authors resemble those already obtained with simpler equivalent circuits (but including the phenomenological CPE). Therefore, as discussed earlier and as is well known for simpler models, the use of transfer matrix methods and porous theory for data fitting and microscopic characterization requires further experimental information (e.g., on porosity, changing composition) as well as the impedance data itself. Therefore, experimental support is still needed to validate the model and show what the influence of porous distribution is.

5.6 Charge Transport in Nanostructured Electrodes The electrical response of nanostructured electrodes has been extensively studied, as discussed earlier here. We know, from solid-state semiconductor physics, that disordered structures in polycrystalline film electrodes, for instance, normally perform poorly compared with electrodes made of highly ordered materials such as single crystals, a fact that raises several questions. How can electrons be collected and transported efficiently through a poor and disordered structure such as a nanostructured film electrode? What are the mechanisms of charge transport? Although extensive work has been done, there are still questions to be answered and the mechanism of charge transport in mesoporous electrodes or disordered systems is currently under intense debate in the literature [201, 202, 216–220]. Nanostructured compound electrolytes or ionically conductive electrodes for lithium ion batteries may also present nonpattern charge transport [210, 221, 222]. Furthermore, with regard to the ac electrical response, it is a well-established fact that the conductivity in many solid materials displays a universal pattern consisting

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of a power-law domain at high frequencies and a constant conductivity in the lowfrequency wing. The possible consequences of such behavior on the impedance response of porous electrodes have been explored [223, 224]. Therefore, a description of the anomalous transport effect is readily incorporated into the standard doublechannel transmission line model for porous electrodes, on the basis of a macroscopic phenomenological theory for transport in disordered solids [223,224]. The influence of the power-law behavior in the solid network gives rise to such familiar features as a curvature in the Warburg part of the spectra, or to an arc at high frequency, depending on the relative magnitudes of the conductivities in both solid and liquid or electrolyte phases. It was suggested that a similar description could be attempted for the ionic transport through fine pores, so the transport in solid and electrolyte phase exemplified previously by (92) and (93) must be reviewed to consider the disorder effects [24, 83, 222, 225–251]. Another aspect that should be taken into account in the interpretation of experiments is the fact that the diffusion mechanism need not be unique at all the scales of frequency–time. It has been observed that the normal behavior in many disordered systems consists in an anomalous diffusion mechanism at high frequencies and short times, which changes to ordinary diffusion as the frequency decreases or the time scale increases [221]. So the resulting diffusion would be either anomalous or ordinary, depending on whether the distance traveled by the random walker during the observation time was shorter or longer than the cutoff scale of the structure [252]. These situations could be treated by introducing a characteristic crossover time or frequency that separates the diffusion regimes. Such an analysis was presented for impedance of porous electrodes [223]. Example of the uses of porous model approach in energy conversion porous electrode is given by the use of general transmission line model of DSSC. From this model it is possible to calculate, for instance, charge-transfer resistance of the charge recombination process between electrons in the mesoporous TiO2 film, the chemical capacitance of the electroactive film, transport resistance of the electrons in the TiO2 film, and Nernst diffusion in the electrolyte among other parameters. By using such approach it is possible to understand characteristics of high efficiency of DSSC to conclude, at this moment, that the high efficiency of the DSSC cells can be ascribed to the high transport and low recombination rate of the electrons in TiO2 -electrolyte interface [253].

6 Future Prospects The development of alternative storage and conversion energy devices was shown to be strongly correlated to and in some aspects dependent on nanotechnology. Therefore, new components for these devices will continue to be designed in the coming years, especially aiming for better performance and scale mass production. The future economic development of our modern society will depend to a great extent on such development, since the era of fossil fuel is coming to an end.

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Conversion and storage of energy requires efficient energy capture, charge separation and transport, and, finally, efficient utilization or storage by chemical or electrochemical means. The high surface area of nanostructures has been proven to enhance efficiency tremendously. In addition, to improve the performance of these devices, the role of interfaces is crucial for highly efficient nanostructured electrodes. The efficiencies of catalytic sequences for utilization and storage are also enhanced by the high surface area. Thus, nanoscale systems are expected to advance conversion, and any headway made in understanding the relevant charge transfer process and the strongly related energy transfer will be central to this progress. To produce materials and systems with improved properties we must be able to modify the amount of interface and its properties in a controlled manner. The engineering of nanostructured electrodes depends on a more in-depth understanding of the nanoscale size effect properties of compounds and on the characterization and assembly of 2-D and/or 3-D nanostructured electrodes or cells. Any strategy for modifying these nanostructured electrodes in a specific way should involve the design of nanostructured electrodes with controlled electrochemical properties. Despite recent technological successes through the clever incorporation of the use of nanosized materials in electrodes (nanostructured electrodes) in alternative energy devices, we are still far away from possessing a solid scientific understanding of what really goes on at the nanoscale. Many critical questions remain to be answered. For instance, what are the characteristic dimensions over which energy transfer or charge transfer reactions can effectively occur in devices? How does the nanosize material surface influence this dimension? How exactly do kinetic properties scale in small dimension? Is there more than simple surface area scaling at work? Because of these and other questions that are still open, the study of the kinetic scaling behavior of nanostructured systems is quite complex and must be the focus of further development of appropriate nanostructured electrodes.

References 1. Dresselhaus, M.S. and I.L. Thomas, Alternative energy technologies. Nature, 2001. 414: pp. 332–337 2. Goodisman, J., Electrochemistry: Theoretical Foundation. 1987, Chichester: Wiley 3. Schmickler, W., Interfacial Electrochemistry. 1995, Oxford: Oxford University Press 4. Bard, A.J. and L.R. Faulkner, Electrochemical Methods: Fundamentals and Applications. 2000, Chichester: Wiley 5. Bockris, J.O.M. and S.U.M. Khan, Surface Electrochemistry: A Molecular Level Approach. 1993, New York: Springer 6. Bockris, J.O.M. and A.K.N. Reddy, Modern Electrochemistry. Vol.1. 1973, New York: A Plenum/Rosetta Edition 7. Cao, G., Nanostructures and Nanomaterials: Synthesis, Properties and Applications. 2004, Singapore: Imperial College Press 8. Adams, D.M., L. Brus, C.E.D. Chidsey, S. Creager, C. Creutz, C.R. Kagan, P.V. Kamat, M. Lieberman, S. Lindsay, R.A. Marcus, R.M. Metzger, M.E. Michel-Beyerle, J.R. Miller,

140

9.

10. 11.

12. 13.

14. 15. 16.

17. 18.

19.

20.

21.

22. 23. 24.

25. 26. 27. 28. 29.

30.

P.R. Bueno and C. Gabrielli M.D. Newton, D.R. Rolison, O. Sankey, K.S. Schanze, J. Yardley, and X.Y. Zhu, Charge transfer on the nanoscale: Current status. Journal of Physical Chemistry B, 2003. 107(28): pp. 6668–6697 Zukalova, M., A. Zukal, L. Kavan, M.K. Nazeeruddin, P. Liska, and M. Gratzel, Organized mesoporous TiO2 films exhibiting greatly enhanced performance in dye-sensitized solar cells. Nano Letters, 2005. 5(9): pp. 1789–1792 Li, N.C., C.R. Martin, and B. Scrosati, Nanomaterial-based Li-ion battery electrodes. Journal of Power Sources, 2001. 97–98: pp. 240–243 Liu, Y., C. Compson, and M.L. Liu, Nanostructured and functionally graded cathodes for intermediate temperature solid oxide fuel cells. Journal of Power Sources, 2004. 138(1–2): pp. 194–198 Sides, C.R., N.C. Li, C.J. Patrissi, B. Scrosati, and C.R. Martin, Nanoscale materials for lithium-ion batteries. Mrs Bulletin, 2002. 27(8): pp. 604–607 Singhal, A., G. Skandan, G. Amatucci, F. Badway, N. Ye, A. Manthiram, H. Ye, and J.J. Xu, Nanostructured electrodes for next generation rechargeable electrochemical devices. Journal of Power Sources, 2004. 129(1): pp. 38–44 Bishop, D., Nanotechnology and the end of Moore’s Law? Bell Labs Technical Journal, 2005. 10(3): pp. 23–28 Lai, L.B., D.H. Chen, and T.C. Huang, Preparation and electrocatalytic activity of Pt/Ti nanostructured electrodes. Journal of Materials Chemistry, 2001. 11(5): pp. 1491–1494 An, K.H., K.K. Jeon, J.K. Heo, S.C. Lim, D.J. Bae, and Y.H. Lee, High-capacitance supercapacitor using a nanocomposite electrode of single-walled carbon nanotube and polypyrrole. Journal of the Electrochemical Society, 2002. 149(8): pp. A1058–A1062 Frackowiak, E. and F. B´eguin, Carbon materials for the electrochemical storage of energy in capacitors. Carbon, 2001. 39: pp. 937–950 Fuertes, A.B., F. Pico, and J.M. Rojo, Influence of pore structure on electric double-layer capacitance of template mesoporous carbons. Journal of Power Sources, 2004. 133(2): pp. 329–336 Kim, I.H., J.H. Kim, Y.H. Lee, and K.B. Kim, Synthesis and characterization of electrochemically prepared ruthenium oxide on carbon nanotube film substrate for supercapacitor applications. Journal of the Electrochemical Society, 2005. 152(11): pp. A2170–A2178 Kim, I.H., J.H. Kim, and K.B. Kim, Electrochemical characterization of electrochemically prepared ruthenium oxide/carbon nanotube electrode for supercapacitor application. Electrochemical and Solid State Letters, 2005. 8(7): pp. A369–A372 Liu, C.G., M. Liu, M.Z. Wang, and H.M. Cheng, Research and development of carbon materials for electrochemical capacitors – II – The carbon electrode. New Carbon Materials, 2002. 17(2): pp. 64–72 Wang, Q., J.E. Moser, and M. Gratzel, Electrochemical impedance spectroscopic analysis of dye-sensitized solar cells. Journal of Physical Chemistry B, 2005. 109(31): pp. 14945–14953 Xiao, Q.F. and X. Zhou, The study of multiwalled carbon nanotube deposited with conducting polymer for supercapacitor. Electrochimica Acta, 2003. 48(5): pp. 575–580 Lee, K., R. Menon, C.O. Yoon, and A.J. Heeger, Reflectance of conducting polypyrrole: Observation of the metal insulator transition driven by disorder. Physical Review B, 1995. 52: pp. 4779 Gray, F.M., Polymer Electrolytes. 1997, Cambridge: Royal Society of Chemistry Bujdak, J., E. Hackett, and E.P. Giannelis, Chemical Materials, 2000. 12: pp. 2168 Solomon, M.J., A.S. Almusallam, K.F. Seefeldt, A. Somwangthanaroj, and P. Varadan, Macromolecules, 2001. 34: p. 7219 Maier, J., Prog. Solid State Chem., 1995. 23: pp. 171–265 Rhodes, C.P., J.W. Long, M.S. Doescher, J.J. Fontanella, and D.R. Rolison, Nanoscale polymer electrolytes: Ultrathin electrodeposited poly(phenylene oxide) with solid-state ionic conductivity. Journal of Physical Chemistry B, 2004. 108(35): pp. 13079–13087 Petrii, O.A. and G.A. Tsirlina, Size effects in electrochemistry. Uspekhi Khimii, 2001. 70(4): pp. 330–344

Electrochemistry, Nanomaterials, and Nanostructures

141

31. Hagfeldt, A., G. Boschloo, H. Lindstrom, E. Figgemeier, A. Holmberg, V. Aranyos, E. Magnusson, and L. Malmqvist, A system approach to molecular solar cells. Coordination Chemistry Reviews, 2004. 248(13–14): pp. 1501–1509 32. Li, N.C., C.J. Patrissi, G.L. Che, and C.R. Martin, Rate capabilities of nanostructured LiMn2O4 electrodes in aqueous electrolyte. Journal of the Electrochemical Society, 2000. 147(6): pp. 2044–2049 33. Schultze, J.W., A. Heidelberg, C. Rosenkranz, T. Schapers, and G. Staikov, Principles of electrochemical nanotechnology and their application for materials and systems. Electrochimica Acta, 2005. 51(5): pp. 775–786 34. Davies, T.J., M.E. Hyde, and R.G. Compton, Nanotrench arrays reveal insight into graphite electrochemistry. Angewandte Chemie International Edition, 2005. 44(32): pp. 5121–5126 35. Waje, M., C. Wang, J. Tang, and Y.S. Yan, Nanostructured electrodes for hydrogen fuel cells. Abstracts of Papers of the American Chemical Society, 2004. 227: pp. U1082–U1082 36. Cai, C.D., J.Z. Zhou, L. Qi, Y.Y. Xi, B.B. Lan, L.L. Wu, and Z.H. Lin, Conductance of a single conducting polyaniline nanowire. Acta Physico-Chimica Sinica, 2005. 21(4): pp. 343–346 37. Park, S., Y. Xie, and M.J. Weaver, Electrocatalytic pathways on carbon-supported platinum nanoparticles: Comparison of particle-size-dependent rates of methanol, formic acid, and formaldehyde electrooxidation. Langmuir, 2002. 18(15): pp. 5792–5798 38. Vinodgopal, K., M. Haria, D. Meisel, and P. Kamat, Fullerene-based carbon nanostructures for methanol oxidation. Nano Letters, 2004. 4(3): pp. 415–418 39. Sun, N.X. and K. Lu, Physical Review B, 1997. 54: pp. 6058 40. Park, S., P.X. Yang, P. Corredor, and M.J. Weaver, Transition metal-coated nanoparticle films: Vibrational characterization with surface-enhanced Raman scattering. Journal of the American Chemical Society, 2002. 124(11): pp. 2428–2429 41. Park, S., A. Wieckowski, and M.J. Weaver, Electrochemical infrared characterization of CO domains on ruthenium-decorated platinum nanoparticles. Journal of the American Chemical Society, 2003. 125(8): pp. 2282–2290 42. Park, S. and M.J. Weaver, A versatile surface modification scheme for attaching metal nanoparticles onto gold: Characterization by electrochemical infrared spectroscopy. Journal of Physical Chemistry B, 2002. 106(34): pp. 8667–8670 43. Park, S., S.A. Wasileski, and M.J. Weaver, Some interpretations of surface vibrational spectroscopy pertinent to fuel-cell electrocatalysis. Electrochimica Acta, 2002. 47(22–23): pp. 3611–3620 44. Park, S., Y.T. Tong, A. Wieckowski, and M.J. Weaver, Infrared spectral comparison of electrochemical carbon monoxide adlayers formed by direct chemisorption and methanol dissociation on carbon-supported platinum nanoparticles. Langmuir, 2002. 18(8): pp. 3233–3240 45. Park, S., Y. Tong, A. Wieckowski, and M.J. Weaver, Infrared reflection-absorption properties of platinum nanoparticle films on metal electrode substrates: control of anomalous opticaleffects. Electrochemistry Communications, 2001. 3(9): pp. 509–513 46. Park, S., P.K. Babu, A. Wieckowski, and M.J. Weaver, Electrochemical infrared characterization of CO domains on ruthenium decorated platinum nanoparticles. Abstracts of Papers of the American Chemical Society, 2003. 225: pp. U619–U619 47. Weaver, M.J. and S.H. Park, Vibrational and electrocatalytic characterization of Pt-group nanoparticle films. Abstracts of Papers of the American Chemical Society, 2002. 223: pp. U387–U387 48. Weaver, M.J., Surface-enhanced Raman spectroscopy as a versatile in situ probe of chemisorption in catalytic electrochemical and gaseous environments. Journal of Raman Spectroscopy, 2002. 33(5): pp. 309–317 49. Brinker, C.J. and C.W. Scherer, Sol–Gel Science: The Physics and Chemistry of Sol-Gel Processing. 1990, San Diego: Academic 50. Alivisatos, A.P., Science, 1996. 271: p. 933 51. Tamashiro, M.N., V.B. Henriques, and M.T. Lamy, Aqueous suspensions of charged spherical colloids: Dependence of the surface charge on ionic strength, acidity, and colloid concentration. Langmuir, 2005. 21(24): pp. 11005–11016

142

P.R. Bueno and C. Gabrielli

52. Manciu, M. and E. Ruckenstein, The polarization model for hydration/double layer interactions: the role of the electrolyte ions. Advances in Colloid and Interface Science, 2004. 112(1–3): pp. 109–128 53. Turkevish, J., Gold Bull., 1985. 18: p. 86. 54. Faraday, M., Philos. Trans., 1857. 147: p. 145. 55. Grabar, K.C., P.C. Smith, M.D. Musik, J.A. Davis, D.G. Walter, M.A. Jackson, A.P. Guthrie, and M.J. Natan, Journal of American Chemical Society, 1996. 118: p. 1148 56. Hodes, G., Electrochemistry of Nanomaterials. 2001, Weinheim: Wiley 57. Agrios, A.G. and P. Pichat, State of the art and perspectives on materials and applications of photocatalysis over TiO2 . Journal of Applied Electrochemistry, 2005. 35(7): pp. 655–663 58. Wallace, J.M., B.M. Dening, K.B. Eden, R.M. Stroud, J.W. Long, and D.R. Rolison, Silvercolloid-nucleated cytochrome c superstructures encapsulated in silica nanoarchitectures. Langmuir, 2004. 20(21): pp. 9276–9281 59. Xiang, J., B. Liu, S.T. Wu, B. Ren, F.Z. Yang, B.W. Mao, Y.L. Chow, and Z.Q. Tian, A controllable electrochemical fabrication of metallic electrodes with a nanometer/angstrom-sized gap using an electric double layer as feedback. Angewandte Chemie International Edition, 2005. 44(8): pp. 1265–1268 60. Wasileski, S.A. and M.J. Weaver, Influence of solvent co-adsorption on the bonding and vibrational behavior of carbon monoxide on Pt(111) electrodes. Abstracts of Papers of the American Chemical Society, 2003. 225: p. U682 61. Schindler, W., M. Hugelmann, and P. Hugelmann, In situ scanning probe spectroscopy at nanoscale solid/liquid interfaces. Electrochimica Acta, 2005. 50(15): pp. 3077–3083 62. Han, D.H. and S.M. Park, Electrochemistry of conductive polymers. 32. Nanoscopic examination of conductivities of polyaniline films. Journal of Physical Chemistry B, 2004. 108(37): pp. 13921–13927 63. Gutierrez-Tauste, D., I. Zumeta, E. Vigil, M.A. Hernandez-Fenollosa, X. Domenech, and J.A. Ayllon, New low-temperature preparation method of the TiO2 porous photoelectrode for dye-sensitized solar cells using UV irradiation. Journal of Photochemistry and Photobiology Chemistry, 2005. 175(2–3): pp. 165–171 64. Altair, Hosokawa, Rutgers work on nanostructured electrodes. American Ceramic Society Bulletin, 2004. 83(10): pp. 3–3 65. Gomez, R. and P. Salvador, Photovoltage dependence on film thickness and type of illumination in nanoporous thin film electrodes according to a simple diffusion model. Solar Energy Materials and Solar Cells, 2005. 88(4): pp. 377–388 66. Gomez, R., J. Solla-Gullon, J.M. Perez, and A. Aldaz, Nanoparticles-on-electrode approach for in situ surface-enhanced Raman spectroscopy studies with platinum-group metals: examples and prospects. Journal of Raman Spectroscopy, 2005. 36(6–7): pp. 613–622 67. Lakard, B., J.C. Jeannot, M. Spajer, G. Herlem, M. de Labachelerie, P. Blind, and B. Fahys, Fabrication of a miniaturized cell using microsystern technologies for electrochemical applications. Electrochimica Acta, 2005. 50(9): pp. 1863–1869 68. Jang, S.Y., M. Marquez, and G.A. Sotzing, Writing of conducting polymers using nanoelectrochemistry. Synthetic Metals, 2005. 152(1–3): pp. 345–348 69. Sides, C.R. and C.R. Martin, Nanostructured electrodes and the low-temperature performance of Li-ion batteries. Advanced Materials, 2005. 17(1): pp. 125–128 70. Xu, Q. and M.A. Anderson, J. Am. Ceram. Soc., 1994. 77: p. 1939. 71. Gr¨atzel, M., Photoelectrochemical cells. Nature, 2001. 414: pp. 338–344 72. Uvarov, N.F. and V.V. Boldyrev, Size effects in chemistry of heterogeneous systems. Russian Chemical Review, 2001. 70(4): pp. 265–284 73. Rhodes, C.P., J.W. Long, M.S. Doescher, B.M. Dening, and D.R. Rolison, Charge insertion into hybrid nanoarchitectures: mesoporous manganese oxide coated with ultrathin poly(phenylene oxide). Journal of Non-Crystalline Solids, 2004. 350: pp. 73–79 74. Kuznetsov, A.M. and J. Ulstrup, Electrochemica Acta, 2000. 45: p. 2339 75. Fawcett, W.R., J. Lipkowski and P.N. Ross, Editors. Electrocatalysis 1998, Wiley: New York. p. 323

Electrochemistry, Nanomaterials, and Nanostructures

143

76. Aral, B.K. and D.M. Kalyon, Effects of temperature and surface roughness on timedependent development of wall slip in torsional flow of concentrated suspensions. Journal of Rheology, 1994. 38: p. 957–972 77. Roberts, G.P. and H.A. Barnes, New measurements of the flow-curves for Carbopol dispersions without slip artifacts. Rheological Acta, 2001. 40: p. 499 78. Leger, L., H. Hervert, G. Massey, and E. Durlist, Journal of Physics: Condensed Matter, 1997. 9: p. 7719 79. Arico, A.S., P. Bruce, B. Scrosati, J.M. Tarascon, and W. Van Schalkwijk, Nanostructured materials for advanced energy conversion and storage devices. Nature Materials, 2005. 4(5): pp. 366–377 80. Nanu, M., J. Schoonman, and A. Goossens, Solar-energy conversion in TiO2/CuInS2 nanocomposites. Advanced Functional Materials, 2005. 15(1): pp. 95–100 81. Sides, C.R., F. Croce, V.Y. Young, C.R. Martin, and B. Scrosati, A high-rate, nanocomposite LiFePO4/carbon cathode. Electrochemical and Solid State Letters, 2005. 8(9): pp. A484– A487 82. Finke, A., P. Poizot, C. Guery, and J.M. Tarascon, Characterization and Li reactivity of electrodeposited copper–tin nanoalloys prepared under spontaneous current oscillations. Journal of the Electrochemical Society, 2005. 152(12): pp. A2364–A2368 83. Zuppiroli, L., M.N. Bussac, S. Paschem, O. Chauvet, and L. Forro, Hopping in disordered conducting polymers. Physical Review B, 1994. 50: p. 5196 84. Xia, Y., P. Yang, Y. Sun, Y. Wu, B. Mayers, B. Gates, Y. Yin, F. Kim, and H. Yan, Advanced Materials, 2003. 15: p. 353 85. Hart, R.W., H.S. White, B. Dunn, and D.R. Rolison, 3-D microbatteries. Electrochemistry Communications, 2003. 5(2): pp. 120–123 86. Bueno, P.R., E.R. Leite, T.R. Giraldi, L.O.S. Bulh˜oes, and E. Longo, Nanostructured Li ion insertion electrodes. 2. Tin dioxide nanocrystalline layers and discussion on Nanoscale Effect. Journal of Physical Chemistry B, 2003. 107: pp. 8878–8883 87. Nanu, M., J. Schoonman, and A. Goossens, Nanocomposite three-dimensional solar cells obtained by chemical spray deposition. Nano Letters, 2005. 5(9): pp. 1716–1719 88. Pietron, J.J., R.M. Stroud, and D.R. Rolison, Using three dimensions in catalytic mesoporous nanoarchitectures. Nano Letters, 2002. 2(5): pp. 545–549 89. Rolison, D.R., Catalytic nanoarchitectures – The importance of nothing and the unimportance of periodicity. Science, 2003. 299(5613): pp. 1698–1701 90. L¨offler, M.-S., H. Natter, R. Hempelmann, and K. Wippermann, Electrochemica Acta, 2003. 48: p. 3047 91. Li, N., L. Shi, W. Lu, X. Huang, and L. Chen, Journal of Electrochemical Society, 2001. 147: p. A915 92. de Levie, R., On porous electrodes in electrolyte solutions. Electrochimica Acta, 1963. 8: pp. 751–780 93. Gabrielli, C., O. Haas, and H. Takenoutti, Impedance analysis of electrodes modified with a reversible redox polymer film. Journal of Applied Electrochemistry, 1987. 17: p. 82 94. Gabrielli, C., H. Takenoutti, O. Haas, and A. Tsukada, Impedance investigation of the charge transport in film-modified electrodes. Journal of Electroanalytical Chemistry, 1991. 302: pp. 59–89 95. Gassa, L.M., J.R. Vilche, M. Ebert, K. J¨uttner, and W.J. Lorenz, Electrochemical impedance spectroscopy on porous electrodes. Journal of Applied Electrochemistry, 1990. 20: pp. 677–685 96. Lasia, A., Hydrogen evolution/oxidation reactions on porous electrodes. Journal of Electroanalytical Chemistry, 1998. 454: pp. 115–121 97. Macdonald, J.R., Impedance Spectroscopy. 1987, New York: Wiley 98. Ohmori, T., T. Kimura, and H. Masuda, Impedance measurements of a platinum cylindrical porous electrode replicated from anodic porous alumina. Journal of the Electrochemical Society, 1997. 144: p. 1286 99. Rangarajan, S.K., Theory of flooded porous electrodes. Journal of Electroanalytical Chemistry, 1969. 22: pp. 89–104

144

P.R. Bueno and C. Gabrielli

100. Raistrick, I.D., Impedance studies of porous electrodes. Electrochimica Acta, 1990. 35: pp. 1579–1586 101. Paasch, G., K. Micka, and P. Gersdorf, Theory of the electrochemical impedance of macrohomogeneous porous electrodes. Electrochimica Acta, 1993. 38(18): pp. 2653–2662 102. Schoonman, J., Nanoionics. Solid State Ionics, 2003. 157: pp. 319–326 103. Guo, Y.G., J.S. Lee, and J. Maier, AgI nanoplates with mesoscopic superionic conductivity at room temperature. Advanced Materials, 2005. 17(23): p. 2815–2819 104. Bhattacharyya, A.J., J. Fleig, Y.G. Guo, and J. Maier, Local conductivity effects in polymer electrolytes. Advanced Materials, 2005. 17(21): p. 2630 105. Snaith, H.J., S.M. Zakeeruddin, L. Schmidt-Mende, C. Klein, and M. Gratzel, Ioncoordinating sensitizer in solid-state hybrid solar cells. Angewandte Chemie International Edition, 2005. 44(39): pp. 6413–6417 106. Rhodes, C.P., J.W. Long, and D.R. Rolison, Direct electrodeposition of nanoscale solid polymer electrolytes via electropolymerization of sulfonated phenols. Electrochemical and Solid State Letters, 2005. 8(11): pp. A579–A584 107. Tarascon, J.-M. and M. Armand, Issues and challenges facing rechargeable lithium batteries. Nature, 2001. 414: pp. 359–367 108. Chadwick, A.V., Solid progress in ion conduction. Nature, 2000. 408: pp. 925–926 109. Steele, B.C.H. and A. Heinzel, Material for fuel-cell technologies. Nature, 2001. 414: pp. 345–352 110. Sata, N., K. Eeberman, K. Eberl, and J. Maier, Nature, 2000. 408: pp. 946–949 111. Hoffler, H.J., R.S. Averback, H. Hahn, and H. Gleiter, Journal of Applied Physics, 1993. 74: p. 3832 112. Schlapbach, L. and A. Z¨uttel, Hydrogen-storage materials for mobile applications. Nature, 2001. 414: pp. 353–358 113. Bueno, P.R. and E.R. Leite, Nanostructured Li ion insertion electrodes. 1. Discussion on fast transport and short path for ion diffusion. Journal of Physical Chemistry B, 2003. 107: pp. 8868–8877 114. Grugeon, S., S. Laruelle, L. Dupont, F. Chevallier, P.L. Taberna, P. Simon, L. Gireaud, S. Lascaud, E. Vidal, B. Yrieix, and J.M. Tarascon, Combining electrochemistry and metallurgy for new electrode designs in Li-ion batteries. Chemistry of Materials, 2005. 17(20): pp. 5041–5047 115. Delacourt, C., L. Laffont, R. Bouchet, C. Wurm, J.B. Leriche, M. Morcrette, J.M. Tarascon, and C. Masquelier, Toward understanding of electrical limitations (electronic, ionic) in LiMPO4 (M=Fe, Mn) electrode materials. Journal of the Electrochemical Society, 2005. 152(5): pp. A913–A921 116. Scrosati, B., Power sources for portable electronics and hybrid cars: Lithium batteries and fuel cells. Chemical Record, 2005. 5(5): pp. 286–297 117. Thackeray, M.M., C.S. Johnson, J.T. Vaughey, N. Li, and S.A. Hackney, Advances in manganese-oxide ‘composite’ electrodes for lithium-ion batteries. Journal of Materials Chemistry, 2005. 15(23): pp. 2257–2267 118. Courtney, I.A. and J.R. Dahn, Journal of Power Sources, 1997. 144: p. 2045 119. Besenhard, J.O., J. Yang, and M. Winter, Journal of Power Sources, 1997. 68: p. 87 120. Idota, Y., T. Kubota, A. Matsufuji, Y. Maekawa, and T. Miyasaki, Tin-based amorphous oxide: A high capacity lithium-ion storage material. Science, 1997. 276: p. 1395 121. Huang, H., Anode materials for lithium-ion batteries. 1999, Delft University of Technology 122. Winter, M., J.O. Besenhard, M.E. Spahr, and P. Nov´ak, Insertion electrode materials for rechargeable lithium batteries. Advanced Materials, 1998. 10(10): pp. 725–763 123. Li, N., C.R. Martin, and B. Scrosati, Electrochem. Solid-State Letters, 2000. 3: p. 316 124. Li, N. and C.R. Martin, Journal of Electrochemical Society, 2001: p. A164 125. Martin, C.R., N. Li, and B. Scrosati, Nanomaterial-based Li-ion battery electrodes. Journal of Power Sources, 2001. 97–98: pp. 240–243 126. Long, J.W., B. Dunn, D.R. Rolison, and H.S. White, Three-dimensional battery architectures. Chemical Reviews, 2004. 104(10): pp. 4463–4492

Electrochemistry, Nanomaterials, and Nanostructures

145

127. Liu, Y., S.W. Zha, and M.L. Liu, Novel nanostructured electrodes for solid oxide fuel cells fabricated by combustion chemical vapor deposition (CVD). Advanced Materials, 2004. 16(3): p. 256–260 128. Gratzel, M., Solar energy conversion by dye-sensitized photovoltaic cells. Inorganic Chemistry, 2005. 44(20): pp. 6841–6851 129. Miyake, M., T. Torimoto, T. Sakata, H. Mori, and H. Yoneyama, Photoelectrochemical characterization of nearly monodisperse CdS nanoparticles-immobilized gold electrodes. Langmuir, 1999. 15: pp. 1503–1507 130. Drouard, S., S.G. Hickey, and D.J. Riley, CdS nanoparticle-modified electrodes for photochemical studies. Chemical Communications, 1: 1999: p. 67 131. Conway, B.E., Electrochemical Supercapacitors. 1999, New York: Kluwer/Prenum 132. Endo, M., T. Maeda, T. Takeda, Y.J. Kim, K. Koshiba, H. Hara, and M.S. Dresselhaus, Capacitance and pore-size distribution in aqueous and nonaqueous electrolytes using various activated carbon electrodes. Journal of Electrochemical Society, 2001. 148: pp. A910–A914 133. Qu, D. and H. Shi, Studies of activated carbon used in double-layer capacitors. Journal of Power Sources, 1998. 74: pp. 99–107 134. Salitra, G., A. Soffer, L. Eliad, Y. Cohen, and D. Aurbach, Carbon electrodes for doublelayer capacitors. I. Relations between ion and pore dimensions. Journal of Electrochemical Society, 2000. 147: pp. 2486–2493 135. Shiraishi, S., H. Kurihara, H. Tsubota, A. Oya, Y. Soneda, and Y. Yamada, Electrochem. and Solid State Letters, 2001. 4: pp. A5–A8 136. Endo, M., Y.J. Kim, T. Takeda, T. Maeda, T. Hayashi, K. Kashiba, H. Hara, and M.S. Dresselhaus, Journal of Electrochemical Society, 2001. 148: pp. A1135–A1140 137. Weng, T.-C. and H. Teng, Journal of Electrochemical Society, 2001. 148: pp. A368–A373 138. Schmitt, C., H. Pr¨obstle, and J. Fricke, Journal of Non-Crystalline Solids, 2001. 285: pp. 277–282 139. Niu, C., E.K. Sichel, R. Hoch, D. Moy, and H. Tennent, Applied Physics Letters, 1997. 70: pp. 1480–1482 140. Diederich, L., E. Barborini, P. Piseri, A. Podest`a, P. Milani, A. Schneuly, and R. Gallay, Applied Physics Letters. 75: pp. 2662–2664 141. Instrumental Method in Electrochemistry, Ed. Southampton Electrochemistry Group. 1985, Chichester: Ellis Horwood Ltd 142. Epelboin, I. and M. Keddam, Journal of Electrochemical Society. 1970. 117: p. 1052 143. Gabrielli, G., Identification of Electrochemical Processes by Frequency Response Analysis. 1980, Farnborough U. K.: Solartron 144. Gabrielli, G., Use and Applications of Electrochemical Impedance Techniques. 1990, Farnborough U. K.: Solartron 145. Gerisher, H. and W. Mehl, Z. Elektrochem, 1955 59: p. 1049 146. Girault, H.H., Electrochimie physique et analytique. 2001, Presses Polytechniques et Universitaires Romandes: Lausanne, Suisse 147. Levich, V.D., Physicochemical Hydrodynamics. 1962, Englewood Cliffs, NJ: Prentice Hall 148. Macdonald, D.D., Transient Techniques in Electrochemistry. 1977, New York: Plenum 149. Newman, J., Electrochemical Systems. 1973, Englewood Cliffs, NJ: Prentice Hall 150. Randles, J.E.B., Transactions of Faraday Society, 1948. 44: p. 327 151. Rubinstein, I., Physical electrochemistry. 1995, New York: Marcel Dekker 152. Sluyters-Rembach, M. and J.H. Sluyters, in Electroanalytical Chemistry, A.J. Bard, Editor. 1970, Marcel Dekker: New York 153. Yeager, E., J. O’M. Bockris, B.E. Conway, and S. Sarangapani, Comprehensive treatise of Electrochemistry. 1984, New York: Plenum 154. Bisquert, J., G. Garcia Belmonte, and F. Fabregat Santiago. Coupled ion-electron transport in illuminated TiO2 nanoporous electrodes. in 12th International Conference on Photoelectrochemical Conversion and Storage of Solar Energy. 1998. Berlin 155. Bisquert, J., G. Garcia-Belmonte, F. Fabregat-Santiago, and A. Compte, Anomalous transport effects in the impedance of porous electrodes. Electrochemistry Communications, 1999. 1: pp. 429–435

146

P.R. Bueno and C. Gabrielli

156. Candy, J.-P., P. Fouilloux, M. Keddam, and H. Takenouti, The characterization of porous electrodes by impedance mesurements. Electrochimica Acta, 1981. 26: p. 1029 157. Fievet, P., M. Mullet, and J. Pagetti, Impedance measurements for determination of pore texture of a carbon membrane. Journal of Membrane Science, 1998. 149: pp. 143–150 158. Keddam, M., C. Rakotomavo, and H. Takenoutti, Impedance of a porous electrode with an axial gradient of concentration. Journal of Applied Electrochemistry, 1984. 14: p. 437 159. Kramer, M. and M. Tomkiewicz, Porous electrodes. I. Numerical simulation using random network and single-pore models. Journal of the Electrochemical Society, 1984. 131: pp. 1283–1288 160. Lasia, A., Impedance of porous electrodes. Journal of Electroanalytical Chemistry, 1995. 397: pp. 27–33 161. Lasia, A., Porous electrodes in the presence of a concentration gradient. Journal of Electroanalytical Chemistry, 1997. 428: pp. 155–164 162. Lasia, A., Nature of two semicircles observed on the complex plane plots on porous electrodes in the presence of a concentration gradient. MMM, Journal of Electroanalytical Chemistry 163. Liu, M. and Z. Wu, Significance of interfaces in solid-state cells with porous electrodes of mixed ionic–electronic conductors. Solid State Ionics, 1998. 107: pp. 105–110 164. McHardy, J., J.M. Baris, and P. Stonehart, Investigation of hydrophobic porous electrodes. I. Differential capacitance by a low frequency a. c. impedance technique. Journal of Applied Electrochemistry, 1976. 6: pp. 371–376 165. Meyers, J.P., M. Doyle, R.M. Darling, and J. Newman, The impedance response of a porous electrode composed of intercalation particles. Journal of the Electrochemical Society, 2000. 147: pp. 2930–2940 166. Newman, J.S. and C.W. Tobias, Theoretical analysis of current distribution in porous electrodes. Journal of the Electrochemical Society, 1962. 1962: p. 1183 167. Nguyen, P.H. and G. Paasch, Transfer matrix method for the electrochemical impedance of inhomogeneous porous electrodes and membranes. Journal of Electroanalytical Chemistry, 1999. 460(18): pp. 63–79 168. Posey, F.A. and T. Morozumi, Theory of potentiostatic and galvanostatic charging of the double layer in porous electrodes. Journal of the Electrochemical Society, 1966. 113: pp. 176–184 169. Prins-Jansen, J.A., G.A.J.M. Plevier, K. Hemmes, and J.H.W. Wit, An ac-impedance study of dense and porous electrodes in molten-carbonated fuel cells. Electrochimica Acta, 1996. 41: pp. 1323–1329 170. Rossberg, K., G. Paasch, L. Dunsch, and S. Ludwig, The influence of porosity and the nature of the charge storage capacitance on the impedance behaviour of electropolymerized polyaniline films. Journal of Electroanalytical Chemistry, 1998. 443: p. 49 171. Song, H.-K., Y.-H. Jung, K.-H. Lee, and L.H. Dao, Electrochemical impedance spectroscopy of porous electrodes: the effect of pore size distribution. Electrochimica Acta, 1999. 44: pp. 3513–3519 172. Bisang, J.M., K. J¨uttner, and G. Kreysa, Potential and current distribution in porous electrodes under charge-transfer kinetic control. Electrochimica Acta, 1994. 39(8/9): pp. 1297– 1302 173. Bisquert, J., Influence of the boundaries in the impedance of porous film electrodes. Physical Chemistry Chemical Physics, 2000. 2: pp. 4185–4192 174. Choi, Y.-M. and S.-I. Pyun, Effects of intercalation-induced stress on lithium transport through porous LiCoO2 electrode. Solid State Ionics, 1997. 99: pp. 173–183 175. Hitz, C. and A. Lasia, Experimental study and modeling of impedance of the her on porous Ni electrodes. Journal of Electroanalytical Chemistry, 2001. 500: pp. 213–222 176. Lasia, A., Nature of the two semi-circles observed on the complex plane plots on porous electrodes in the presence of a concentration gradient. Journal of Electroanalytical Chemistry, 2001. 500: pp. 30–35 177. Lindbergh, G., Experimental determination of the effective electrolyte conductivity in porous lead electrodes in the lead-acid battery. Electrochimica Acta, 1997. 42(8): pp. 1239–1246

Electrochemistry, Nanomaterials, and Nanostructures

147

178. Liu, C., J.E. Szecsody, J.M. Zachara, and W.P. Ball, Use of the generalized integral transform method for solving equations of solute transport in porous media. Advances in Water Resourses, 2000. 23: pp. 483–492 179. Lundqvist, A. and G. Lindbergh, Kinetic study of a porous metal hydride electrode. Electrochimica Acta, 1999. 44: pp. 2523–2542 180. Pell, W.G. and B.E. Conway, Analysis of power limitations at porous supercapacitor electrodes under cyclic voltammetry modulation and dc charge. Journal of Power Sources, 2001. 96: pp. 57–67 181. Perez, J., E.R. Gonzalez, and E.A. Ticianelli, Oxygen electrocatalysis on thin porous coating rotating platinum electrodes. Electrochimica Acta, 1998. 44: pp. 1329–1339 182. Song, H.-K., H.-Y. Hwang, K.-H. Lee, and L.H. Dao, The effect of pore size distribution on the frequency dispersion of porous electrodes. Electrochimica Acta, 2000. 45: pp. 2241–2257 183. Srikumar, A., T.G. Stanford, and J.W. Weidner, Linear sweep voltammetry in flooded porous electrodes at low sweep rates. Journal of Electroanalytical Chemistry, 1998. 458: pp. 161– 173 184. Yang, T.-H. and S.I. Pyun, A study of the hydrogen absorption reaction into alfa- and betaLaNi5Hx porous electrodes by using electrochemical impedance spectroscopy. Journal of Power Sources, 1996. 62: pp. 175–178 185. Bisang, J.M., K. J¨uttnerr, and G. Kreysa, Electrochemica Acta, 1994. 39: p. 1297 186. Posey, F.A., Journal of Electrochemical Society, 1964. 111: p. 1173 187. Scott, K., Journal of Applied Electrochemistry, 1983. 13: p. 709 188. Tilak, B.V., S. Vankatesh, and S.K. Rangarajan, Journal of Electrochemical Society, 1989. 136: p. 1977 189. Bisquert, J., G. Garcia-Belmonte, P.R. Bueno, E. Longo, and L.O.S. Bulh˜oes, Impedance of constant phase element (CPE) -blocked diffusion in film electrodes. Journal of Electroanalytical Chemistry, 1998. 452: pp. 229–234 190. Bisquert, J., G. Garcia-Belmonte, F. Fabregat-Santiago, and P.R. Bueno, Theoretical models for ac impedance of diffusion layers exhibiting low frequency dispersion. Journal of Electroanalytical Chemistry, 1999. 475: p. 152 191. de Levie, R., in Advances in Electrochemistry and Electrochemical Engineering, P. Delahay, Editor. 1967, Interscience: New York 192. Grebenkov, Transport Laplacien Aux Interfaces Irregulieres: Etude Theorique, Numerique ´ Et Experimentale. 2004, Ecole Polytechnique: Paris 193. Paasch, G. and P.H. Nguyen, Electrochem. Appl., 1997. 1: p. 7 194. Pakossy, T., Solid State Ionics, 1997. 94: p. 123 195. Presa, M.J.R., R.I. Tucceri, M.I. Florit, and D. Posadas, Constant phase element behavior in the poly(o-toluidine) impedance response. Journal of Electroanalytical Chemistry, 2001. 502: pp. 82–90 196. Sadkowski, A., On the ideal polarisability of electrode displaying CPE-type capacitance dispersion. Journal of Electroanalytical Chemistry, 2000. 481: pp. 222–226 197. Sadkowski, A., Response to the ‘Comments on the ideal polarisability of electrodes displaying CPE-type capacitance’ by G. L´ang, K. E. Heusler. Journal of Electroanalytical Chemistry, 2000. 481: pp. 232–236 198. Zoltowski, P., On the electrical capacitance of interfaces exhibiting constant phase element behaviour. Journal of Electroanalytical Chemistry, 1998. 443: pp. 149–154 199. Zoltowski, P., Comments on the paper ‘On the ideal polarisability of electrodes displaying CPE-type capacitance’ by A. Sadkowski. Journal of Electroanalytical Chemistry, 2000. 481: pp. 230–231 200. Beaulieu, L.Y., D. Larcher, R.A. Dunlap, and J.R. Dahn, Journal of Electrochemical Society, 2000. 147: p. 3206 201. Peter, L.M., E.A. Ponomarev, G. Franco, and N.J. Shaw, Electrochemica Acta, 1999. 45: pp. 549–560 202. Peter, L.M. and J. Vanmaekelbergh, in Advances in Electrochemical Science and Engineering, R.C. Alkire and D.M. Kolb, Editors. 1999, New York: Wiley

148

P.R. Bueno and C. Gabrielli

203. Motheo, A.J., A. Sadkowski, and R.S. Neves, Journal of Electroanalytical Chemistry, 1998. 455: p. 107 204. Macdonald, J.R. and D.R. Franceschetti, in Impedance Spectroscopy, J.R. Macdonald, Editor. 1987, Wiley: New York. pp. 84–132 205. Sapoval, B., J.-N. Chazalviel, and J. Peyri`ere, Electrical response of fractal and porous interfaces. Physical Review A, 1988. 38(11): pp. 5867–5887 206. Keiser, H., K.D. Beccu, and M.A. Gutjahr, Electrochimica Acta, 1976. 21: p. 539 207. Diard, J.P., B. Le Gorrec, and C. Montella, Linear diffusion impedance. General expression and applications. Journal of Electroanalytical Chemistry, 1999. 471: pp. 126–131 208. Deslouis, C., C. Gabrielli, M. Keddam, A. Khalil, R. Rosset, B. Tribollet, and M. Zidoune, Impedance techniques at partially blocked electrodes by scale deposition. Electrochimica Acta, 1997. 42(8): pp. 1219–1233 209. L´ang, G. and K.L. Heusler, Comments on the ideal polarisability of electrodes displaying CPE-type capacitance dispersion. Journal of Electroanalytical Chemistry, 2000. 481: pp. 227–229 210. Kerner, Z. and T. Pajkossy, Impedance of rough capacitive electrodes: the role of surface disorder. Journal of Electroanalytical Chemistry, 1998. 448: pp. 139–142 211. L´ang, G. and K.E. Heusler, Remarks of the energetics of interfaces exhibiting constant phase element behaviour. Journal of Electroanalytical Chemistry, 1998. 457: pp. 257–260 212. Liu, S.H., Fractal model for the ac response of a rough interface. Physical Review Letters, 1985. 55: pp. 529–532 213. G¨ohr, H. and C.A. Schiller, Electrochimica Acta, 1993. 38: p. 1961 214. Eloot, K., F. Debuyck, M. Moors, and A.P. van Peterghem, Journal of Applied Electrochemistry, 1995. 25: p. 334 215. Eloot, K., F. Debuyck, M. Moors, and A.P. van Peterghem, Journal of Applied Electrochemistry, 1995. 25: p. 326 216. S¨odergren, S., A. Hagfeldt, J. Olsson, and S.E. Lindquist, Journal of Physical Chemistry B, 1998. 98: pp. 5552–5556 217. Cao, F., G. Oskam, and P.C. Searson, Journal of Physical Chemistry B, 1996. 100: pp. 17021– 17027 218. Vanmaekelbergh, J. and P.E. de Jongh, Journal of Physical Chemistry B, 1999. 103: pp. 747–750 219. de Jongh, P.E. and J. Vanmaekelbergh, Journal of Physical Chemistry B, 1997. 101: pp. 2716–2722 220. de Jongh, P.E. and J. Vanmaekelbergh, Physical Review Letters, 1996. 77: pp. 3427–3440 221. Sidebottom, D.L., P.F. Green, and R.K. Brow, Anomalous-diffusion model of ionic transport in oxide glasses. Physical Review B, 1995. 51: p. 2770 222. Maass, P., J. Petersen, A. Bunde, W. Dieterich, and H.E. Roman, Non-Debye relaxation in structurally disordered ionic conductors: Effect of Coulombic interaction. Physical Review Letters, 1991. 66: p. 52 223. Bisquert, J., G. Garcia-Belmonte, F. Fabregat-Santiago, and A. Compte, Anomalous transport effects in the impedance of porous film electrodes. Electrochemistry Communications, 1999. 1: pp. 429–435 224. Garcia-Belmonte, G., J. Bisquert, E.C. Pereira, and F. Fabregat-Santiago, Anomalous transport on polymeric porous film electrodes in the dopant-induced insulator-to-conductor tansition analyzed by electrochemical impedance. Applied Physics Letters, 2001. 78(13): pp. 1885–1887 225. B¨assler, H., Charge transport in disordered organic photoconductors. Physics Status Solidii (b), 1993. 175: pp. 15–56 226. B¨assler, H., P.M. Borsenberger, and R.J. Perry, Charge transport in poly(methylphenylsilane): the case of superimposed disorder and polaron effects. Journal of Polymer Science: Part B: Polymer Physics, 1994. 32: pp. 1677–1685 227. Bernasconi, J., H.U. Beyeler, S. Str¨assler, and S. Alexander, Anomalous frequency-dependent conductivity in disordered one-dimensional systems. Physical Review Letters, 1979. 42: p. 819

Electrochemistry, Nanomaterials, and Nanostructures

149

228. Bisquert, J. and G. Garcia-Belmonte, Scaling properties of thermally stimulated currents in disordered systems. Journal of Non-Crystalline Solids, 1999. 260: pp. 109–115 229. Borsenberger, P.M., L. Pautmeier, and H. B¨assler, Charge transport in disordered molecular solids. The Journal of Chemical Physics, 1991. 94: pp. 5447–5454 230. Bouchaud, J.P. and A. Georges, Anomalous diffusion in disordered media: statistical mechanismis, models and physical applications. Physics Reports, 1990. 195: pp. 127–293 231. Brown, R. and B. Esser, Kinetic networks and order-statistics for hopping in disordered systems. Philosophical Magazine B, 1995. 72: pp. 125–148 232. Bunde, A. and P. Maass, Diffusion in disordered systems: non-Debye relaxation due to longrange interactions. Journal of Non-Crystalline Solids, 1991. 131–133: p. 1022 233. Dieterich, W., D. Kn¨odler, and P. Pendzig, Relaxation of charged particles in disordered systems. Journal of Non-Crystalline Solids, 1994. 172: p. 1237 234. Dyre, J.C., A simple model of a.c. conductivity in disordered solids. Physics Letters, 1985. 108A: p. 457 235. Dyre, J.C., The random free-energy barrier model for ac conductivity in disordered solids. Journal of Applied Physics, 1988. 64: p. 2456 236. Dyre, J.C. and T.B. Schroder, Universality of ac conduction in disordered solids. Reviews of Modern Physics, 2000. 72: p. 873 237. Dyre, J.C. and T.B. Schroder, Effective one-dimensionality of universal ac hopping condution in the extreme disorder limit. Physical Review B, 1996. 54: pp. 14884–14887 238. Dyre, J.C. and J.M. Jacobsen, Universality of anomalous diffusion in extremely disordered systems. Chemical Physics, 1996. 212: p. 61 239. Dyre, J.C., Universal low-temperature ac conductivity of macrossopially disordered nonmetals. Physical Review B, 1993. 48: pp. 12511–12526 240. Dyre, J., Univeral ac conductivity in nonmetallic disordered solids at low temperatures. Physical Review B, 1993. 47: p. 9128 241. Dyre, J.C., Some remarks on ac conduction in disordered solids. Journal of Non-Crystalline Solids, 1991. 135: p. 219 242. Lee, P.A. and T.V. Ramakrishnan, Disordered electronic systems. Reviews of Modern Physics, 1985. 57: pp. 287–337 243. Macdonald, J.R., Analysis of ac conduction in disordered solids. Journal of Applied Physics, 1989. 65: pp. 4845–4853 244. Mott, N.F., Electrons in disordered structures. Advances in Physics, 1967. 16: p. 49 245. Moura, F.A.B.F. and M.L. Lyra, Delocalization in the 1D Anderson model with long-range correlated disorder. Physical Review Letters, 1998. 81: p. 3735 246. Scher, H. and M. Lax, Stochastic transport in a disordered solid. I. Theory. Physical Review B, 1973. 7: pp. 4491–4502 247. Scher, H. and M. Lax, Stochastic transport in a disordered solid. II. Impuruty conduction. Physical Review B, 1973. 7: pp. 4502–4519 248. Ziman, J.M., Models of Disorder. 1979, Cambridge: Cambridge University. Press. pp. 370– 385 249. Sheng, P. and J. Klafter, Hopping conductivity in granular disordered systems. Physical Review B, 1983. 27: pp. 2583–2586 250. Schroder, T.B. and J.C. Dyre, Scaling and universality of ac conduction in disordered solids. Physical Review Letters, 2000. 84: p. 310 251. Schirmacher, W., Anomalous diffusion in disordered systems: an effective medium description. Berichte der Bunsengesellschaft fur Physical Chemie, 1991. 95: pp. 368–376 252. Gefen, Y., A. Aharony, and S. Alexander, Anomalous diffusion on percolating clusters. Physical Review Letters, 1983. 50: pp. 77–80 253. Wang, Q., S. Ito, M. Gratzel, F. Fabregat Santiago, I. Mora-Ser´o, J. Bisquert, T. Bessho, and H. Imai

Nanotechnology for Fuel Cells Angelika Heinzel and Uwe K¨onig

Abstract There are noteworthy developments in nanotechnology and its relevance to the energy field. Fuel cells especially benefit from electrodes and membrane electrolytes with nanostructured and therefore enlarged surfaces. Fuel cells also derive benefits from the development of nanoparticles and nanotubes for catalytic application, allowing also study of the molecular electrochemical behaviour. In this chapter we describe the impact of nanotechnology in the performance of the different components of the fuel cell as well as the impact of nanotechnology in the electrochemistry process.

1 Introduction 1.1 What Relevance Has Nanotechnology for Fuel Cell Systems [1]? Energy research is becoming increasingly important, particularly as regards the role it plays in support of a wide range of key policies (e.g. security and diversification of energy supply, energy market liberalization, sustainable development). Nanotechnology shows promising potential in all segments of the energy sector: production, storage, distribution and conversion. There are noteworthy developments in nanotechnology and its relevance to the energy field. Fuel cells especially benefit from electrodes and membrane electrolytes with nanostructured and therefore enlarged surfaces. Fuel cells also derive benefits from the development of nanoparticles and nanotubes for catalytic application, allowing also study of the molecular electrochemical behaviour. A. Heinzel () Fachgebiet Energietechnik, Universit¨at Duisburg, Lotharstr. 1-21, 47057 Duisburg, Germany e-mail: [email protected] E.R. Leite (ed.), Nanostructured Materials for Electrochemical Energy Production and Storage, Nanostructure Science and Technology, DOI 10.1007/978-0-387-49323-7 4, c Springer Science+Business Media LLC 2009 

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However, the fuel cell catalysts have drawbacks; they are both expensive and have limited efficiency. To solve this issue, research work is being done in nanostructuring the carbon electrodes to avoid the deactivation of catalysts by e.g. agglomeration and therefore reduce the amount of noble metals and increase the catalyst performance. In spite of the promising potentials of fuel cells, most analysts do not believe that fuel cells will be widely used in the coming 20 years [1]. Fuel cells for portable applications are appraised as most promising. Although the detailed problems depend on the type of fuel cell the main obstacles are the same: • The central problem inhibiting a wider market penetration of fuel cells is the high manufacturing costs. The costs of fuel cells were approximately 20,000 Euro per kilowatt power in 2002 [2]. • The problems are mainly caused by expensive materials used in fuel cell technology. • Technical challenges such as thermal as well as mechanical expansion, seals, lifetime and reproducible properties have also to be solved. However, a growing number of companies are confident that they are now on the verge of bringing prices for fuel cells down to levels where they can compete with conventional electric-power generating equipment. The most prominent nanostructured materials in fuel cells are the electrocatalysts of low- and medium-temperature fuel cells, which consist of carbon-supported precious metal particles in the range of 1–5 nm. This structure is necessary to increase the surface to volume ratio of the noble metals, thus reducing the costs of the material. A further approach to nanostructured materials is the introduction of nanoscale hydrophilic (high affinity to water) inorganic materials such as silica into the polymer membranes being used as electrolyte to improve water retention of the membrane at elevated temperatures. The functioning of the cell using sulfonated membranes such as NafionTM is related to the hydrogen ion conductivity of the membrane, which decreases strongly if water content is not sufficient. Thus, alternative membranes with defined properties in the nanometer range are intensively under development.

1.2 Fuel Cell Technology and Nanotechnology Fuel cells as efficient energy conversion devices are one of the present R&D subjects in energy technology. Hydrogen and oxygen from air may be converted directly by an electrochemical process into electrical energy and heat. High efficiency values are achievable even in the lower power range. As fuel cells can be operated continuously as long as fuel is available, various applications are interesting. These range from combined heat and power supply systems in the 100 kW to the 1-kW power segment, to mobile (electric traction) or even portable applications. The main obstacle – the use of hydrogen as fuel – might be overcome by gas processing technologies, converting fossil or biogenic fuels into a hydrogen-rich gas mixture.

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e−

H2 H2O

AFC PEFC PAFC MCFC SOFC

O2

100 ⬚C

H'

O2 H 2O

80 ⬚C 200 ⬚C

H2 H2O

CO22−

O2 CO2

650 ⬚C

H2 H2O

O2−

H2 CO2

OH−

O2

fuel gas

1000 ⬚C

oxygen anode elektrolyte cathode

Fig. 1 Operation principle of the various types of fuel cells: PEMFC polymer electrolyte membrane fuel cell, AFC alkaline fuel cell, PAFC phosphoric acid fuel cell, MCFC molten carbonate fuel cell, SOFC solid oxide fuel cell

Different material combinations for practical realization of fuel cells have been developed in the past few decades [3]; comprehensive overviews about the technology have been published [4]. Possible operation temperatures of fuel cells range from ambient temperature to 1,000◦ C. The operation principle of the different fuel cells is depicted in Fig. 1. The main components are the same for all types of fuel cells and comprise an electrolyte, catalytically active electrodes, and a cell frame for gas distribution and current collection. Regular nanostructures are not typically used until now, but nanomaterials for preparation of layers are frequently the best base materials. Some examples will be given in the description of the five types of fuel cells in this introductory chapter. The main electrochemical reactions for hydrogen-fed fuel cells are as follows: Anode: H2 → 2H+ + 2e− 1 Cathode: O2 + 2e− → O2− 2 1 H2 + O2 → H2 O 2 This reaction should theoretically lead to a cell voltage of 1.23 V, practically, cell voltages of 1 V at zero current (open circuit voltage) and 0.5 V during operation are achieved. These low-voltage values per cell lead to the requirement of series connection of various single cells to form a so-called cell stack. For most of the cell types, a layered bipolar construction is state of the art, shown in Fig. 2, for the example of a polymer electrolyte membrane fuel cell.

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Fig. 2 Components of a membrane fuel cell

The functions of the different layers are as follows: • Cell frames contain a system of gas channels integrated in the bipolar plate, the so-called flow field for the distribution of fuel and air evenly over the entire active electrode area of the anode and the cathode; the dimensions of channels and ribs are usually in the millimetre range. The cell frames act as well as current collectors, and thus a good electrical conductivity is required. In addition, the cell frames can contain cooling channels, either for air cooling or for liquid cooling. Various cooling concepts have already been realised. • The second layer is a gas diffusion layer (GDL), typically a carbon paper or carbon cloth. This GDL protects the membrane from mechanical damages, ensures spatial electrical contact, and is important for gas distribution to the electrode parts under the ribs of the flow field and for removal of product water. GDLs are a porous system formed by hydrophobic and hydrophilic pores in the submillimeter range. Its compressibility is important for stack construction, because small deviations in thickness of sealings and bipolar plates can be compensated. • The third layer is the electrode, a thin catalyst layer that might be coated onto the GDL or in most cases onto the membrane, then forming a so-called membrane/electrode assembly MEA. For operation at low (ambient) temperatures, noble metals are required as catalyst. The goal of cost reduction led to the development of catalyst systems consisting of a carbon carrier material with a noble metal loading of about 0.4 mg cm−2 ; lower loadings are envisaged for future electrode materials. A large electro-catalytically active surface area is important for achieving high current densities, thus preparation processes are used leading to nanoparticles of noble metals on the larger carbon particles (see Fig. 3). Another issue is CO tolerance of the electrocatalyst, if the fuel cell shall be operated with reformate generated from fossil fuels instead of pure hydrogen. • The fourth layer is the polymer membrane itself. The membrane is the electrolyte. Proton conductivity is its most important property besides the safe separation of the fuel in the anode compartment of the cell and the air in the cathode compartment. Chemical stability is achieved by using a fluorinated polymer

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Fig. 3 Electrocatalyst as prepared for use in PEMFC (source: MPI M¨ulheim)

backbone. Proton conductivity is realised by sulfonic acid groups attached to side chains of this backbone. The first polymer electrolyte of this type was developed in the early seventies [5]. The hydrophobic backbone and the hydrophilic acid groups lead to a structure, showing hydrophilic channels in a hydrophobic matrix. Proton conductivity additionally requires the presence of a sufficient amount of liquid water [6] (see Fig. 4). Thus, for membrane fuels cells, water management in the different layers is important to be properly controlled, ensuring a good humidity of the membrane but avoiding flooding of the porous GDL. Another important aspect is the structure of the so-called three-phase boundary in a gas diffusion electrode. The electrodes in PEMFC operating with gaseous fuel in fact constitute a four-phase boundary, even more complicating the facts. The first phase is the gaseous phase, containing either the hydrogen or the oxygen, which shall be transported to the reaction zone. The second phase is liquid water being generated as product and contributing to the ionic conductivity of the membrane. Part of the water is necessary to conduct hydrated protons from the anode to the cathode side; part of the water has to be removed in order to avoid flooding of the gas diffusion structure. The third phase is the solid electrolyte material, necessarily being hydrated with liquid water and also being in close contact with the sites, where ions are generated. The fourth phase finally is the electrocatalyst, also in close contact with the fuels in order to catalyse the electron transfer reaction and to conduct the electrons to the outer circuits. This interface is a unique structure of the membrane fuel cell, and much effort was undertaken to optimize it [7].

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Specific conductivity [S /cm]

0,12

0,1

0,08

0,06

0,04

0,02

0 0

5

10

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30

water content = NH2O / NSO3H Fig. 4 Specific conductivity of NafionTM 117 as function of water content

The same type of membrane fuel cell can be fed with a liquid solution of methanol in water instead of hydrogen or reformate as fuel. The electrochemical reactions are as follows: Anode: CH3 OH + H2 O → CO2 + 6H+ + 6e− 3 Cathode: O2 + 6H+ + 6e− → 3H2 O 2 3 O2 + CH3 OH → CO2 + H2 O 2 For methanol as fuel, the cell voltage calculated from thermodynamic data is 1.215 V, but here in practice open circuit voltages of about 0.7 V are achieved and 0.4–0.3 V is achieved during operation. Because of the formation of the poisoning intermediate adsorbate CO, the achievable current densities are limited, and higher noble metal catalyst loadings are required, and CO tolerance also is an important issue. Special MEAs have been developed for direct methanol fuel cells (DMFC). A polymer membrane in contact with methanol shows significant transfer of methanol and water from the anode side to the cathode side of the fuel cell, leading to losses due to formation of a mixed potential at the air electrode. Typical MEAs are shown in Fig. 5, where the variety of nanostructures is also pointed out. But the advantageous simplicity of the fuel cell system and the high energy density of the liquid fuel make the DMFC attractive despite these mentioned drawbacks. For a liquid-fed DMFC, the requirements for the structure of the interfacial catalyst layer are different than for gaseous hydrogen as fuel, which is thus also a matter for optimisation [8].

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Fig. 5 Scanning electron microscopy (SEM) pictures of DMFC electrodes: upper – E-Tek electrode, lower – electrode made by DLR

In addition to the earlier described state of the art, nanotechnology plays a role in the development of micro fuel cells; the realisation of special properties of surfaces and the enhancement of functionalities by nanostructures, nanolayers as coatings and nanoparticles raise increasing interest. Nanostructured electrolytes, carbon supports or coatings for bipolar plates are examples. The alkaline fuel cell (AFC) with its liquid alkaline electrolyte KOH uses gas diffusion electrodes with a hydrophobic porous part, which is not flooded by the alkaline electrolyte, and a hydrophilic part containing electrolyte and thus leading to a three-dimensional three-phase boundary layer. As the electrode potentials in alkaline electrolyte are shifted towards more negative values, corrosion is less problematic. Raney Nickel and silver are the state-of-the-art catalysts. The practical use

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of alkaline fuel cells is limited due to the sensitivity of the electrolyte towards CO2 , which leads to potassium carbonate precipitation. The phosphoric acid fuel cell (PAFC) has a quite similar construction and components as the PEMFC; the electrolyte is liquid phosphoric acid in an inert matrix. The operation temperature of 200◦ C avoids formation of liquid water and improves CO tolerance of the electrocatalyst. For the catalyst properties, the same requirements are valid as for the PEMFC – nanoparticles with a high surface area and a good dispersion on the carbon carrier material are required. The application of PAFC typically is the combined heat and power supply in the 200-kW power range. The molten carbonate fuel cell (MCFC) with its operation temperature of 650◦ C is developed since the sixties. Corrosion of the metallic cell frames in contact with the molten salt electrolyte and electrolyte loss during operation still limit the lifetime of the stacks. The materials used mainly have structures in the micrometer range; the anode is made of Ni/Cr or Ni/Al with a mean pore size of 6 μm; the cathode is NiO, which is formed from Ni by in-situ oxidation of a porous Ni plate with pores of a size of 8 μm, and the liquid electrolyte is contained in a matrix (LiAlO2 ) and must be held there by capillary forces. The pore size of the matrix must therefore be carefully controlled and be smaller than the mean pore size of the electrodes. Changes of pore diameters during lifetime have to be avoided. Thus, submicron LiAlO2 is a nanomaterial used in MCFC, and the particle growth during tens of thousands of operational hours is well investigated [9]. The solid oxide fuel cell (SOFC) consists of solid components, usually the three layers, namely, anode, electrolyte and cathode, which are manufactured as MEA as it is the case for the membrane fuel cell. Because of the high operation temperature, mechanical stress due to different thermal expansion coefficients of the materials used is a major challenge. Material development for adopted physical properties and for electrolytes with high conductivity at reduced temperatures of about 500–700◦ C is the focus. To achieve a good performance, the anodes of SOFC are a well-defined micro-structural layer of Ni/YZS (Yttria-stabilised Zirconia). Operation at high current densities and at high fuel utilisation leads to a significant increase of anode resistance, and a structural change of the cermet can be observed [10], mainly sintering of the small Ni particles. For realizing a long-term stable high surface area cathode, a special preparation method was recently examined [11]. Single YSZ particles are sintered onto the electrolyte, resulting in a high surface area. The surface then is covered by a thin layer (approximately 100 nm) of (La, Sr)CoO3 by metalorganic deposition. An increase in power density and in long-term thermal cycling stability was observed. Another approach to improve the anode using nanolayers was recently reported [12]. A better long-term stability was achieved with a channelled anode produced directly by solidification of a NiO–YSZ eutectic mixture, by laser zone melting of rods or plates and subsequent reduction of NiO. A lamellar thickness between 200 nm and 1 μm could be realised. Summarising the activities using nanotechnology for fuel cells, the membrane fuel cell is the most promising type. Thus, the focus of the subsequent chapters will be on this type of fuel cell and will give more details on new approaches using nanostructured electrocatalysts and membranes.

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2 Nanostructures 2.1 General Properties of Electrolyte Membranes The membrane in a membrane fuel cell fulfils several important functions as stated in the introduction. NafionTM was the first commercially available membrane, which lead to a breakthrough in fuel cell technology. Today, various companies are engaged in membrane development especially for this purpose, aiming at improved material properties. The goals are less sensitivity towards elevated temperature and dry operation, better chemical and mechanical stability and reduced methanol crossover for DMFC operation. A significant improvement of the mechanical stability was achieved by incorporation of a PTFE porous sheet as mechanical support for the membrane material [13, 14]. Another approach was the synthesis of inorganic/organic composite materials to influence the properties of the membrane. An overview on the state of the art of composite perflourinated membranes is given in [15]. Infiltration of a polymer carrier material with various inorganic proton conductors is subject of a patent [16]. For operation at elevated temperature, several materials have been considered. In an early work, NafionTM /H3 PO4 showed better conductivity at temperatures above 100◦ C compared with blank NafionTM and also reduced methanol permeability [17]. New types of polymers are also under development for better temperature stability; one of the most advanced examples is the high-temperature material polybenzimidazole, which usually is doped with phosphoric acid [18]. The use of low-cost basic polymers instead of NafionTM is an interesting alternative [19, 20].The development of new polymers for ionomer membranes including perfluorinated ionomers, partially fluorinated ionomers, nonfluorinated ionomers, high-molecular/low-molecular composite membranes as well as novel polymer modification processes and novel membrane materials is summarised in [21]. The microstructure of NafionTM and sulfonated polyetherketones also was a matter of recent investigations [22]. For NafionTM , the nanoseparation into hydrophobic and hydrophilic domains is well known, with the hydrophilic domain being responsible for the transport of protons and the hydrophobic backbone providing the morphological stability and preventing the membrane from dissolving (Fig. 6). The sulfonated polyetherketones showed a less pronounced nanoseparation due to the less hydrophobic backbone and the less acidic sulfonic groups. Nanomaterials come into consideration for various composite materials, in which different materials contribute to specific advantageous properties.

2.2 Alternative Membranes There are tremendous efforts in developing alternative polymeric membranes for PEFC. The main challenge for new membranes is the realisation of high proton

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F (CF2)n

C O

-

SO3-

SO3 H2O

CF O

Na+

CF2 CF2 SO3-

H2O

O

Na+ SO3O

H2O

B

SO3-

H2O

H2O

A

O

H2O

O

CF2 F3C

O

O

(CF 2) n

C

O O

Fig. 6 Structure of a NafionTM membrane according to H. Yeager, A. Eisenberg in Perfluorinated Ionomer Membranes, A. Eisenberg, H. Yeager, Eds., ACS Symp. Series No. 180 (American Chemical Society, Washington DC, 1982) pp 1–6, 41–63/ (source: http://www.psrc. usm.edu/mauritz/nafion.html). A: hydrophobic fluorocarbon region, B: interfacial region, C: hydrophilic region with ionic exchange groups, counter ions (Na+ in this picture instead of H+) and water

mobility in a robust polymer matrix; a defined nanostructure often is a key issue. Especially the transport properties of the protons and the water content have to be taken into account. Furthermore, the contact to the catalysts is important. Nanotechnological approaches will lead to defined structures on the molecular level by implementing active side groups or isolated particles as well as by crosslinking via side chains. Specially designed chemicals such as ionic liquids (ILs) allow the immobilisation and as a consequence the defined distribution of active particles such as catalysts. These kinds of chemicals can also be used to functionalise inorganic structures such as zeolites or molecular sieves. Nanoparticles will be incorporated into the membranes to enhance the in-situ generation of hydrogen from e.g. methanol as well as to increase the basic fuel cell reaction. Moreover, the proton conductivity can be improved by the incorporation of nanoparticles.

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Several types of other proton conducting membranes that incorporate quaternary nitrogen atoms are presently under investigation: • Polymer blends leading to high-end polymers, e.g. from sulfonated polymers (sPEEK – sulfonated polyether-etherketone, sPPSU – sulfonated polyphenylsulfone) combined with alkaline components (amine, imidazole, polybenzimidazole): The combination results in ionic cross-linked phases. Commercially available polymers can be modified by different sulfonation reagents. Another possibility is to combine different monomers based on block co-polymers. The conductivity can be controlled by the number of SO3H groups due to the dependence of the water uptake from the number of groups ([23] and references cited therein). Novel side-chain polymers with heterocycles such as imidazole attached to appropriate polymer backbones are used as proton-solvating moieties and for achieving high proton mobility at high temperatures (>100◦ C), where poisoning effects of the used electrocatalysts are drastically reduced. As opposed to the conventional membranes, these systems are aprotic; the high proton conductance does not rely on the presence of water. Advantages: High thermal stability, high conductivity and lower permeability of methanol. Disadvantages: Problems may arise from oxidation of aliphatic bonds; often difficult to synthesise and expensive; swellable by water uptake. • Dendrimer PTFE copolymers combining hydrophilic dendrimers with hydrophobic linear polymers Advantages: High thermal stability and high conductivity. Disadvantages: Problems may arise from oxidation of aliphatic bonds; often difficult to synthesize and expensive; swellable by water uptake. • Composite membranes formed by incorporation of inorganic nanoparticles or polyacids Solvated proton conducting polymers and composite membranes should govern the transport of protons and water by micro structural control. The objective of this attempt is to take advantage of the high proton conductance in watery systems and to control the proton conductivity by a sophisticated water management. Nevertheless, the conductivity is strongly dependent on the water content, which also influences the mechanical properties by e.g. swelling. Advantage: High variety of properties possible; humidity systems also to temperatures above T > 100◦ C possible. Disadvantage: Agglomeration of particles possible; often difficult to synthesize and expensive; swellable by water uptake. More details are given in Sect. 2.3.

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Novel Brønstedt acid–base ionic liquids [24, 25], e.g. from organic amines with (trifluoromethanesulfonyl) amide (HTFSI); electroactive for H2 oxidation and O2 reduction at a Pt electrode under non-humidifying conditions at moderate temperatures (ca. 130◦C). Advantages: High variety of properties possible; operation at temperatures above T > 100◦C possible; no water content; no swelling; high conductivity. Disadvantages: Ionic liquids have to be supported by e.g. ceramic systems; often difficult to synthesize; presently expensive due to scientific state. • Ionic liquid mixtures such as a 4:6 mixture of methyl and dimethyl ammonium nitrate: The incorporation of imidazol derivates results in a better stability up to T = 180◦ C with a conductivity of 0.1 S cm−1 [26]. The stabilisation of the ionic liquids is possible by introducing the substances into a porous silica matrix [27,28]. A typical liquid is the 1-butyl-3-methyldiazonium derivate with addition of BF− 4 and H3 PO4 to fit the acidity. The system shows a thermal stability up to T = 300◦C with a conductivity up to 80 mScm−1 [29]. Functional monomers are added to an adequate backbone, e.g. the addition of alkylimidazilium to a vinyl- or allyl backbone. The resulting polymer form a cationic structure where the anions can move at (Fig. 7). Advantages: High variety of properties possible; operation at temperatures above T > 100◦ C possible; no water content; no swelling; high conductivity; high chemical and mechanical stability. Disadvantages: Ionic liquids have to be supported by e.g. ceramic systems; often difficult to synthesize; presently expensive due to scientific state. In all cases disadvantages arise from the possibility of oxidation of the aliphatic bonds and the fact that the systems are often difficult to synthesise and the costs are high. Detailed information about the state of the art of ionic liquids is given in Sect. 2.5.

R N

N

+

N

R N X

RX R N

N

+

N

−

Kat. R⬘

N X

−

+

N

N (CH2)n X

R

−

R⬘

+

N

N (CH2)n X

−

n = 0 und 1 Fig. 7 Cationic polymerisation of IL

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2.3 Nanoparticles for Improved Membrane Properties – Composite Membranes The modification of membrane properties by inorganic materials raised increased interest in the past few years. Facilitating the water management especially for low-humidity operation conditions and improving the mechanical and thermal properties usually is the goal; a reduced methanol crossover could also be a desired result. The homogeneous dispersion of small particles in the polymer matrix is of outstanding importance for good membrane properties. Thus, manufacturing procedures leading to nanoparticles are typically used. Two main preparation procedures are known [30]: the in-situ growth of inorganic materials and the polymer in-situ sol/gel reaction. The incorporation of inorganic nanoparticles with a high affinity to water into the electrolyte polymers, such as for example silica, improves the water retention of the membrane. Different approaches have been pursued in the past. The incorporation of hydrophilic compounds into recast NafionTM films was intensively investigated. Zirconium phosphate is one of the most prominent inorganic compounds that exhibit proton conductivity and a layered structure. Hybrid membranes can be produced [31]. It is important to maintain the nanoscale platelet structure of the inorganic particles. For example in [32], layered phosphates of titanium and zirconium were prepared and investigated with respect to proton conductivity. The inorganic additive was reported to increase the stiffness of the membrane and reduce the methanol transfer. It finally leads to a slightly reduced proton conductivity but at the same time to a smaller influence of temperature on conductivity so that the conductivity values for 130◦ C are nearly the same for the composite membrane and blank NafionTM , due to reduced conductivity of the latter at elevated temperature caused by drying out of the NafionTM membrane. Tailor-made layered structures of various zirconium phosphates and zirconium-sulfophenyl phosphates as oriented lamellar structures were also investigated [33]. As membranes, NafionTM and sulfonated polytherketones were used as polymer materials, and it was found that the improvement of membrane properties for polyetherketones was less pronounced than for composites with NafionTM . The performance of Nafion-composite membranes at an elevated temperature of 110◦ C could significantly be improved, as hydration of the composite could be maintained at a high level. Nanocomposite membranes consisting of SiO2 /polyethlenoxide (PEO) have been synthesised [34]. The molecular design of the nanocomposites was achieved by nanosized interfusion among organic, inorganic and acidic molecules. The organic and inorganic components were hydrolysed at a nanoscale. The resulting hybrid materials can have quite different properties than a linear combination of the individual bulk properties. The hybrids can be structurally and chemically modified to form nanosized interconnecting networks. An increasing interest exists in adding heteropoly acids (HPA) as protonconducting components to the sulfonated polymers [35]. The addition will enhance the proton conductivity and the acceptance of CO. Because of their structural

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diversity these materials can be incorporated into a wide variety of membrane materials. The HPA have interesting redox and catalytic properties, which are not fully understood yet. The addition of superacid metal (IV) phosphonates is particularly suitable for the preparation of hybrid membranes. The proton conductivity in some cases reaches values even higher than 0.1 S cm−1 . The presence of nanoparticles of metal phosphonates in the electrode interface Nafion/Pt already improves the electrochemical characteristics of fuel cells in the temperature range 80–130◦ C [36]. With monodecylphosphate and phosphotungstic acid, flexible, transparent and homogeneous hybrid membrane materials could be synthesised. The temperature stability reached 250◦ C, and the conductivity of the humidified membrane reached ∼1 × 10−3 S cm−1 at 80◦ C. Nanosized ceramic powders with good adsorption capacity for acids together with a polymer binder – not an ionomer – were also reported to be developed by Tel Aviv University [37]: silicon dioxide (150 nm), alumina (50 nm) and titanium dioxide (21 nm) were used as nanopowders. With PVDF as polymer binder, membranes with nanosized pores were cast, the pore diameter mainly being below 2 nm. The use of such a membrane consisting of PVDF, SiO2 and triflic acid in a DMFC led to high power densities of up to 500 mW cm−2 [38]. The membrane material had 10– 20 times higher water permeation than NafionTM , and it was expected that this high permeation leads to a high back-diffusion of water to the anode side, thus avoiding the flooding of the cathode catalyst and GDL. All these membranes still have to prove their practical applicability.

2.4 Nanostructured Membranes A first attempt to use an array of nanochannels as an electrolyte is described in [39]. The effect of the enhancement of proton conductivity by overlapping electrical double layers was intended to be used to fabricate an improved micro fuel cell. First experiments with micro channels of depth between 50 nm and 50 μm were investigated using diluted aqueous HClO4 as electrolyte. Normalising the experimental results showed an increase in apparent proton conductivity for the low values of channel depth and being higher than the bulk proton conductivity. The effect was even observed with channels of depth 1–2 μm, which is one order of magnitude larger than the thickness of the electrical double layer. A concise scientific explanation of the observed results still is lacking. During fuel cell operation the membranes are stressed mainly by mechanical interference. Differences in the local gas and water distribution would lead to different processes in chemical reactions, shrinkage or expansion. The mechanical stress can induce changes in the distribution of the catalytic nanoparticles by e.g. agglomeration at fissures. Intensive efforts are made in the field of gas separation of industrial gas mixtures. Membranes with a porosity of less than 1 nm allow the uncomplicated separation of propylene/propane, benzene/cyclohexane and high-pressure CO2 /CH4 mixtures

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[40]. The reaction takes place via a solution-diffusion mechanism, which requires a well-defined modification of the membrane in the nanometer range. The application of these types of membrane is also useful for fuel cells since they allow a molecular transport of the fuel gas and water [41].

2.5 Ionic Liquids (ILs) The use of ionic liquids in fuel cells is a further attempt to develop new types of membranes. Because of the current development in the field of ionic liquids, this material class is a promising alternative to the other attempts of polymer materials. The general advantage of the ionic liquids is that the conductivity is independent of the water content. The main nanotechnological approach of the ionic liquids is the opportunity to immobilise the catalysts by covering the nanoparticles with a liquid phase onto a solid surface. Huang et al. immobilised Pd nanoparticles on molecular sieves by ionic liquids [42]. The catalytic system was used for solvent-free hydrogenation. The combination of nanoparticles, ionic liquids and solid surface showed excellent synergistic effects to enhance the activity and durability of the catalyst. In fuel cell systems, this approach can be used to enhance the catalytic oxidation of hydrogen by improved immobilisation. Another approach is related to the functionalisation of nafion membranes by replacement of water by ionic liquid used to realise a sufficient proton conductivity of NafionTM membranes. The main advantage is that such a system is independent of the water content formed during the fuel cell reaction. A first approach was published [43] in which NafionTM was swollen in ionic liquids instead of water. These membranes using 1-butyl,3-methyl imidazolium triflate (BMITf) and BMI tetraflouroborate (BMIBF4 ) as ionic liquids show excellent conductivity at elevated temperatures up to 200◦ C. BMITf-imbibed membrane samples (Nafion, Dow) even show higher conductivity values in a temperature range from 40 to 180◦ C. The first evaluation of ILs as electrolytes for fuel cells has just been done [25]. This appears to have been the first attempt to apply ILs under aprotic conditions. Adequate hydrophobic properties of the ionic liquids are necessary to realize the three-phase boundary necessary for the fuel cell operation. Furthermore, the transport of water throughout the membrane will be hindered. The water produced during the reaction will not diffuse through the membrane, and a sophisticated water management is not necessary. Ionic liquids are considered more and more as alternatives for conventional electrolytes [44]. The reported ionic conductivity is sufficient enough, even though the values of 100 mS cm−1 are based on the IL itself; they do not include the target ions such as protons and the primary charge carriers are still not known yet and are under discussion. The systems are intensively studied for proton transfer towards fuel cell applications under water-free conditions ([44] and references therein). These ILs are known as Brønstedt acid–base ILs and require certain conditions in preparation.

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One of the most interesting systems is the class of imidazoles. They are selfdissociation compounds with high proton conductivity (>100 mS cm−1 ) without any acid doping. Further enhancement of the conductivity and also the thermal stability of the system can be realised by the addition of acidic components [45]. This is due to the proton transfer via the Grotthuss mechanism. Two other types of ionic liquids are very promising candidates for conducting polymers. They are ionic liquids based on choline chloride, which have already shown superior properties in electrochemical processes (e.g. metal finishing) [46], and single-ended or double-ended diallylammonium ionic liquids, which are protic compounds with a high potential for excellent proton conductivity [47]. Furthermore, the solubility of the fuel gas oxygen and hydrogen has to be as small as possible but not completely insoluble. In general, the experimental results indicate a very small solubility [44,48]. Nevertheless, it is possible that the solubility of the gases influences each other [49]. It is important to realise a low pH value to enhance the proton conductivity. This can be done by an adequate anion such as PO4 3− . The challenge in preparing the adequate ionic liquid is the realisation of the Grotthuss mechanism in the proton transport. For example it is shown by Kerr et al. that the linkage of aliphatic chains to the imidazole molecule results in a decrease in conductivity [50]. This is explained by the hindering of the N-substituted imidiazole to participate in the Grotthuss mechanism by a structural effect. Kerr et al. also indicate that due to possible volatility the IL must be fixed to a matrix. Current models developed using Hole theory [51] will be used to design the compounds with optimum conductivity and viscosity. The requirements of an adequate liquid are as follows: • • • • • • •

Broad electrochemical window Thermal stability up to 300◦ C Stable against hydrolysis Hydrophobic Free of halogen Recyclable Cheaper than NafionTM

For structuring, the IL has to be immobilised. This can be done using i.e. zeolitic structures or molecular sieves. It is obvious that with increasing surface area of the solid phase, the motion of the liquid and the proton transport will be hindered. From polymerisation experiments it is known that the stiffening of polymers by crosslinking can be compared with the polymer–surface interaction. Electrode surfaces and solids such as silica, carbon black or cathode powder also stiffen the polymer [52]. This can be explained by different transport properties at the interfaces. As a consequence it must be expected that at the surface of the added particles the ionic liquid will behave in a different way than in the immobilised liquid phase. Studies of the use of molecular sieve exhibit that Pd nanoparticles can be immobilised by the combination of molecular sieves and ionic liquids. The results indicate that the nanoparticles immobilised onto the molecular sieve by ionic liquids were very active and were stable catalysts for the solvent-free hydrogenation of olefins [42, 53, 54].

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Another nanotechnological approach is the use of a metalorganic chemical vapor deposition (MOCVD) process. This process will be used for producing highly nanodispersed platinum particles on GDL allowing the decrease of overpotential resistance of oxygen reduction reaction. The interest of the MOCVD process is linked with vapour penetration inside the first ten μm of the substrate (carbon layer for example) allowing a 3D repartition of the catalytic element inside the carbon network. MOCVD process brings then a rational approach of the platinum loading inside the active layer in terms of platinum accessibility and electroactivity. This MOCVD process will be developed on a range of catalysts in order to immobilise the catalytic phase on electrode (carbon support) or on membrane support, and to select a highly stable catalyst in contact with the ionic liquid [55]. Table 1 compares the relevant properties of various alternative materials. Table 1 Comparison of conductivity data and values of glass transition temperature for various membrane materials Material

Aqueous systems FS-PEEK [56] BPSH [56] F-PES [56] F-PES [57] HPA – Nafion [56] Nafion 117 [57] Nafion 1100 [58] 3M [56] – perfluorinated sulfonic acid Dupont [56] Ionic liquids Nafion [26] 3-methyl imidazolium BF4 PBI [58] (polybenzimidazol) EMImBF4 [59] – 1-ethyl-3methylimidazolium BF4 BMImBF4 [59] – 1-butyl-3methylimidazolium BF4 BMIm [29] – 1-butyl-3methylimidazolium BF4/H3PO4 BMPBETI [59] – 1-butyl-3pyrazolium BETI Gel-type membranes [60], various polyether Silica gel stabilised [27] – imidazolium (IONOGEL)

Test conditions Conductivity Glass transition T (˚C) RH (%) mS cm1 temperature T (˚C)

>140 135 140 90 90 90

Remarks RH = relative humidity/water content

κ κ κ κ κ κ κ

= = = = = = =

f (RH) f (RH) f (RH) f (RH) f (RH) f (RH) f (RH)

120 120 120 120 120 120 120 120

50 50 50 50 50 50 50 0

30 55 20 3–30 30 30 30 40

120

50

>150

180

0

100

200

200 120

30