Solid State Proton Conductors: Properties and Applications in Fuel Cells

By Philippe Knauth and Maria Luisa Di Vona

Proton conduction can be found in many different solid materials, from organic polymers at room temperature to inorganic oxides at high temperature. Solid state proton conductors are of central interest for many technological innovations, including hydrogen and humidity sensors, membranes for water electrolyzers and, most importantly, for high-efficiency electrochemical energy conversion in fuel cells.

Focusing on fundamentals and physico-chemical properties of solid state proton conductors, topics covered include:

• Morphology and Structure of Solid Acids
• Diffusion in Solid Proton Conductors by Nuclear Magnetic Resonance Spectroscopy
• Structure and Diffusivity by Quasielastic Neutron Scattering
• Broadband Dielectric Spectroscopy
• Mechanical and Dynamic Mechanical Analysis of Proton-Conducting Polymers
• Ab initio Modeling of Transport and Structure
• Perfluorinated Sulfonic Acids
• Proton-Conducting Aromatic Polymers
• Inorganic Solid Proton Conductors

Uniquely combining both organic (polymeric) and inorganic proton conductors, Solid State Proton Conductors: Properties and Applications in Fuel Cells provides a complete treatment of research on proton-conducting materials.

• Language: English
• Publisher: Wiley
• Release date: Jan 18, 2012
• ISBN: 9781119963004

Book preview

Preface

Solid state proton conductors are of central interest for many technological innovations and, most importantly, for high-efficiency electrochemical energy conversion in fuel cells working at low or intermediate temperature.

The most recent textbook on all aspects of solid state proton conductors was published in 1992. Although some excellent review papers have been published since then, an updated textbook summarizing the current knowledge on solid state proton conductors seemed worthwhile.

This book presents review chapters on selected characterization techniques, modelling and properties of solid state proton conductors written by us and some of the leading experts in the field. It focuses on fundamentals and physico-chemical properties; synthesis procedures are only marginally addressed. Most chapters discuss first and foremost the basics that require a decent level of abstraction, before presenting detailed descriptions of solid state proton conductors.

We are confident that this book will close a gap in recent textbook literature.

Writing and editing a book are difficult and time-consuming tasks, but they also comprise a rewarding adventure and we hope the readers will consider their journey through the pages of this book a gratifying experience as well.

We want to thank all authors and friends, who contributed their knowledge in a timely manner. Without their commitment and hard work, this book would not have been possible.

We also gratefully acknowledge the financial support by many institutions which helped to finance our research in the field of solid state proton conductors over the years, including the European Hydrogen and Fuel Cell Technology Platform (FP7 JTI-FCH), the Italian Ministry of Education, Universities and Research (MIUR) and the Franco-Italian University.

Philippe Knauth and M. Luisa Di Vona

Marseille and Roma, June 2011

About the Editors

Philippe Knauth was the recipient of a doctorate in sciences (Doctor Rerum Naturalium) in 1987 and the Habilitation à diriger des recherches in 1996. He has been a professor of materials chemistry at Aix-Marseille University since 1999. Awarded the CNRS Bronze Medal in 1994, he was an Invited Scientist at the Massachusetts Instuitute of Technology, United States from 1997--1998 and an Invited Professor at the National Institute of Materials Science (NIMS), Tsukuba, Japan in both 2007 and 2010. He is currently director of the Laboratoire Chimie Provence (UMR 6264), which includes 130 academic staff working in all fields of chemistry. He has been an elected member of France's Conseil National des Universités for materials chemistry since 2003 and president of the Provence-Alpes-Côte d'Azur regional section of the Société Chimique de France since 2010. His principal research topics are ionic conduction at interfaces, electrochemistry at the nanoscale and materials for energy and the environment. He is currently mainly working on solid state proton conductors for fuel cells and micro-electrodes for lithium-ion batteries, and he is a member of the editorial board of the Journal of Electroceramics.

Maria Luisa Di Vona obtained a doctorate in chemistry cum laude in 1984. In 1987 she became a researcher in organic chemistry at the Faculty of Science of the University of Rome Tor Vergata. She was visiting professor at the Laboratoire Chimie Provence, Université de Provence, Marseille, France, in 2007 and 2009, and at the National Institute for Materials Science (NIMS), Tsukuba, Japan in 2010. She is the author of about 100 papers in international journals on materials synthesis and characterization, multifunctional `inorganic and organic–inorganic materials, the formation and study of nanocomposite materials and characterization by means of multinuclear NMR (nuclear magnetic resonance) spectroscopy. Her current research interest is in the field of proton exchange membranes. She is a project leader and recipient of research grants from the ASI, Italian Ministry, Franco-Italian University (Vinci program) and European Union (the European Hydrogen and Fuel Cell Technology Platform, or FP7 JTI-FCH). She is a member of the organizing and scientific committees of several conferences and was the principal organizer of the 2009 European Materials Research Society (E-MRS) symposium Materials for Polymer Electrolyte Membrane Fuel Cells as well as the 2011 Materials Research Society (MRS) symposium Advanced Materials for Fuel Cells.

Contributing Authors

Giulio Alberti, Department of Chemistry, University of Perugia, Via Elce di Sotto 8, I-06123 Perugia, Italy

Jean-François Chailan, Laboratoire MAPIEM, Université du Sud Toulon-Var, F-83957 La Garde, France

Jeffrey K. Clark II, Department of Chemical and Biomolecular Engineering, University of Tennessee, Knoxville, TN 37996, USA

Vito Di Noto, Department of Chemical Sciences, University of Padua, Via F. Marzolo 1, I-35131 Padova, Italy

Maria Luisa Di Vona, Dipartimento di Scienze e Tecnologie Chimiche, University of Rome Tor Vergata, Via della Ricerca Scientifica, I-00133 Roma, Italy

Guinevere A. Giffin, Department of Chemical Sciences, University of Padua, Via F. Marzolo 1, I-35131 Padova, Italy

Michael D. Guiver, National Research Council Canada, Institute for Chemical Process and Environmental Technology Ottawa, ON, K1A 0R6, Canada and WCU, Department of Energy Engineering, Hanyang University, Seoul 133–791, Republic of Korea

Rolf Hempelmann, Physical Chemistry, Saarland University, D-66123 Saarbrücken, Germany

Mustapha Khadhraoui, Laboratoire Chimie Provence-Madirel, Aix-Marseille University - CNRS, Centre St Jérôme, F-13397 Marseille, France

Philippe Knauth, Laboratoire Chimie Provence-Madirel, Aix-Marseille University - CNRS, F-13397 Marseille, France

Sandra Lavina, Department of Chemical Sciences, University of Padua, Via F. Marzolo 1, I-35131 Padova, Italy

Baijun Liu, Alan G. MacDiarmid Institute, Jilin University, Changchun 130012, P.R. China

Riccardo Narducci, Department of Chemistry, University of Perugia, Via Elce di Sotto 8, I-06123 Perugia, Italy

Stephen J. Paddison, Department of Chemical and Biomolecular Engineering, University of Tennessee, Knoxville, TN 37996, USA

Matteo Piga, Department of Chemical Sciences, University of Padua, Via F. Marzolo 1, I-35131 Padova, Italy

Oliver Schäf, Laboratoire Chimie Provence-Madirel, Aix-Marseille University, Centre St Jérôme, F-13397 Marseille, France

Emanuela Sgreccia, Dipartimento di Scienze e Tecnologie Chimiche, University of Rome Tor Vergata, Via della Ricerca Scientifica, I-00133 Roma, Italy

Sebastiano Tosto, ENEA Centro Ricerche Casaccia, Via Anguillarese 301, I-00123 Roma, Italy

Keti Vezzù, Department of Chemistry, University of Venice, Via Dorsoduro, 2137, I-30123 Venice, Italy

Chapter 1

Introduction and Overview: Protons, the Nonconformist Ions

Maria Luisa Di Vona and Philippe Knauth

The Nonconformist Ion is the title of a review article on proton-conducting solids by Ernsberger in 1983 [1]. Indeed, many proton properties are peculiar. First of all, the very particular electronic structure is unique: its only valence electron lost, the proton is exceptionally small and light and polarizes its surroundings very strongly. In condensed matter, this will lead to strong interactions with the immediate environment and very strong solvation in solution.

Second, two very particular proton migration mechanisms are well established. In vehicular motion, a protonated solvent molecule is used as a vehicle. This mechanism is typically characterized by higher activation energy and lower proton mobility. In structural motion, the so-called Grotthuss mechanism involves site-to-site hopping between proton donor and proton acceptor sites with local reconstruction of the environment around the moving proton. This mechanism is related to lower values of activation energy and higher proton mobility.

Proton conduction can be found in many very different solid materials, from soft organic polymers at room temperature to hard inorganic oxides at high temperature. The importance of atmospheric humidity for the existence and stability of proton conduction is another common point, which goes with experimental difficulties for measuring proton conductivity in solids.

Proton-conducting solids are the core of many technological innovations, including hydrogen and humidity sensors, hydrogen permeation membranes, membranes for water electrolyzers, and most importantly high-efficiency electrochemical energy conversion in fuel cells working at low temperature (polymer electrolyte membrane or proton exchange membrane fuel cells, PEMFC) or intermediate temperature (proton-conducting ceramic fuel cells, PCFC).

1.1 Brief History of the Field

Proton mobility is a special case in the field of ion transport. In early textbooks on the electrochemistry of solids, proton-conducting solids are not even mentioned [2], except ice [3].

Historically, the existence of protons in aqueous solutions had already been conjectured by de Grotthuss in 1806 [4]. The study of proton-conducting solids started at the end of the nineteenth century, when it was noticed that ice conducts electricity, with the investigation of the electrical conductivity of ice single crystals [5]. A first mention of vagabond ions in an inorganic compound, hydrogen uranyl phosphate (HUP), was due to Beintema in 1938 [6]. However, it was not until the 1950s that the study of solid proton conductors started in earnest: Bjerrum's fundamental study on ice conductivity led the way in 1952 [7], and Eigen and coworkers discussed the proton conductivity of ice crystals in 1964 [8]. Nevertheless, these investigations were fundamental studies and the materials could still be considered only laboratory curiosities.

The first proton-conducting material applied in practice was a perfluorinated sulfonated polymer, Nafion, adapted by DuPont in the 1960s as a proton-conducting membrane for PEMFC, used in the Gemini and Apollo space programs. This gave important momentum to the domain of solid proton conductors. Several inorganic solid proton conductors were then reported in the 1970s and 1980s. The rediscovery of HUP was followed by the discovery by Russian groups of several acid sulfates showing structural phase transitions, such as CsHSO4 [9] and zirconium hydrogenphosphate (ZrP), by Alberti and coworkers [10]. Furthermore, oxide gels containing water show nearly always some proton conductivity [11]. However, with the exception of ZrP, the proton conductivity of these materials is limited to about 200 °C.

An important discovery was, therefore, the report by Iwahara and coworkers in the 1980s of high-temperature proton conduction in perovskite-type oxides in humidity- or hydrogen-containing atmosphere [12], where the maximum of proton conductivity is typically observed at temperatures above 400 °C.

Nowadays the main fields of development are proton-conducting polymer membranes for low-temperature applications and proton-conducting oxide ceramics for intermediate- and high-temperature devices. Given the current interest for the possible future hydrogen economy, the fuel cell field is mentioned in most articles of this book.

1.2 Structure of This Book

The most recent textbook on all aspects of solid state proton conductors was published in 1992 [13]. Excellent review papers have been published afterward, for example by Norby in 1999; [14] Alberti and Casciola in 2001 [15]; and Kreuer, Paddison, Spohr, and Schuster in 2004 [16], but an updated textbook summarizing the current knowledge on solid state proton conductors seemed worthwhile.

In the following chapters, some of the leading experts in the field have written authoritative review chapters on the characterization techniques, modeling, and properties of solid state proton conductors.

The chapter Morphology and Structure of Solid Acids shows an overview of structural analysis of some important solid acids by scanning electron microscopy. This beautifully illustrated chapter is an aesthetic pleasure, and the micrographs are complemented by polyhedral representations and a short introduction on the technique.

The chapter Diffusion in Solid Proton Conductors: Theoretical Aspects and Nuclear Magnetic Resonance Analysis starts with an overview on fundamentals of diffusion. Then, principles of nuclear magnetic resonance (NMR) spectroscopy are introduced. Nuclear magnetic resonance is a very powerful technique for investigation of structure and diffusion in solid proton conductors; NMR imaging is a newer development, and is also addressed on a basic level in this chapter.

The chapter Structure and Diffusivity in Proton-Conducting Membranes Studied by Quasi-elastic Neutron Scattering introduces the basics of neutron scattering, which is obviously of particular importance for the field. Analysis of diffusional processes in inorganic as well as organic solid proton conductors is presented and discussed.

The chapter Broadband Dielectric Spectroscopy: A Powerful Tool for the Determination of Charge Transfer Mechanisms in Ion Conductors is devoted to the electrical properties of ion-conducting solids, especially macromolecular systems. This chapter describes fundamentals and examples of dielectric measurements in a broad frequency domain, which can be used for a wide range of materials from insulators to super-protonic conductors.

The chapter Mechanical and Dynamic Mechanical Analysis of Proton-Conducting Polymers introduces first some basic principles of the mechanics of materials: elastic and plastic deformation, creep and relaxation, and dynamic mechanical analysis. Then, the mechanical properties of proton-conducting polymers and their durability are discussed.

The chapter Ab Initio Modeling of Transport and Structure of Solid Proton Conductors presents a rapid introduction on the theoretical methods of choice. Significant examples of solid proton conductors are discussed, including proton-conducting polymers; solid acids, such as CsHSO4; and proton-conducting perovskite oxides.

Two chapters are devoted to polymeric proton conductors. The chapter Perfluorinated Sulfonic Acids as Proton Conductor Membranes introduces the field and presents recent progress for the improvement of the oldest but still leading ionomer, Nafion. This chapter reviews a physicochemical approach and strategies for future enhancement of the durability of Nafion membranes.

The chapter Proton Conductivity of Aromatic Polymers discusses a main family of alternative ionomers based on fully aromatic polymers. Their synthesis and electrical properties and further possibilities for improvement, such as hybrid organic–inorganic ionomers and cross-linked systems, are discussed.

The last chapter reviews Inorganic Solid Proton Conductors. The chapter recalls fundamentals of ionic conduction in inorganic solids and presents the main classes of proton-conducting materials, including layered and porous solids, quasi-liquid structures, and defect solids, especially perovskite oxides.

References

1. Ernsberger, F.M. (1983) The nonconformist ion. Journal of the American Ceramic Society, 66, 747.

2. Rickert, H. (1982) Electrochemistry of Solids, Springer, Berlin.

3. Kröger, F.A. (1974) The Chemistry of Imperfect Crystals, North-Holland, Amsterdam.

4. Grotthuss, C.J.T.d. (1806) Mémoire sur la décomposition de l'eau et des corps qu'elle tient en dissolution à l'aide de l'électricité galvanique. Annales de Chimie, LVII, 54.

5. Ayrton, W.E. and Perry, J. (1877) Ice as an electrolyte. Proceedings of the Physical Society, 2, 171.

6. Beintema, J. (1938) On the composition and the crystallography of autunite and the meta-autunites. Recueil des Travaux Chimiques des Pays-Bas, 57, 155.

7. Bjerrum, N. (1952) Structure and properties of ice. Science, 115, 385.

8. Eigen, M., Maeyer, L.D. and Spatz, H.C. (1964) Kinetic behavior of protons and deuterons in ice crystals. Berichte der Bunsengesellschaft für Physikalische Chemie, 68, 19.

9. Baranov, A.I., Shuvalov, L.A. and Shchagina, N.M. (1982) Superion conductivity and phase-transitions in CsHSO4 and CsHSeO4 crystals. Jetp Letters, 36, 459.

10. Alberti, G. and Torracca, E. (1968) Electrical conductance of amorphous zirconium phosphate in various salt forms. Journal of Inorganic and Nuclear Chemistry, 30, 1093.

11. Livage, J. (1992) Sol-gel ionics. Solid State Ionics, 50, 307.

12. Takahashi, T. and Iwahara, H. (1980) Protonic conduction in perovskite type oxide solid solutions. Revue Chimie Minérale, 17, 243.

13. Colomban, P. (1992) Proton Conductors: Solids, Membranes and Gels - Materials and Devices, Cambridge University Press, Cambridge.

14. Norby, T. (1999) Solid-state protonic conductors: principles, properties, progress and prospects. Solid State Ionics, 125, 1.

15. Alberti, G. and Casciola, M. (2001) Solid state protonic conductors, present main applications and future prospects. Solid State Ionics, 145, 3.

16. Kreuer, K., Paddison, S., Spohr, E. and Schuster, M. (2004) Transport in proton conductors for fuel-cell applications: simulations, elementary reactions, and phenomenology. Chemical Reviews, 104, 4637.

Chapter 2

Morphology and Structure of Solid Acids¹

Habib Ghobarkar, Philippe Knauth and Oliver Schäf

2.1 Introduction

The objective of this chapter is to introduce some important solid acids from a structural, and also morphological, point of view. The micrographs were obtained by scanning electron microscopy (SEM) on samples prepared in situ, according to the techniques described in the following section.

2.1.1 Preparation Technique of Solid Acids

Almost all solid acids were prepared by rapid evaporation of highly concentrated aqueous solutions from open stainless-steel containers heated either by a gas flame or by an induction furnace. Different evaporation speeds could be obtained in this way, but over-heating had to be strictly avoided. During the cooling process, the samples were placed in the sputtering unit (low-pressure Ar-plasma atmosphere) in order to cover them with a protective gold layer (necessary for subsequent SEM observations) before rehydration occurred.

High-pressure hydrothermal processing at temperatures below 200 °C and at 100 MPa pressure as described in detail in reference [1] could be used only for the synthesis of the complex transition – metal phosphoric acids, presented in Sections 2.2.3.1 and 2.2.3.3.

Samples from both synthesis pathways were immediately transferred to the SEM in order to avoid any further degradation.

2.1.2 Imaging Technique with the Scanning Electron Microscope

X-ray diffraction is the first and standard method commonly used for the identification of crystalline phases. Ghobarkar [2, 3] developed a new method for the identification of microcrystals that allows the optical identification of crystals observed by the SEM. In contrast to the optical reflection goniometer, this method allows the measurement of crystal faces even in the micrometre range applying the crystallographic principle that the face normal angles of crystals keep constant independent from size. The face normal angles of an idiomorphous crystal phase, however, are characteristic for each crystallographic system while the axis ratios are determined. Furthermore, the calculated axis ratios can be compared to X-ray diffraction data.

The differences in depth created by object points appearing in different spherical distances with respect to the eyes are called parallaxes. Ghobarkar could show that these parallaxes can be used to quantify the relative position of a plane of a microcrystal's face relative to the next. This is done in order to obtain all angles between the appearing faces (represented by their face normal angles).

By using SEM, crystals can be indexed and their crystallographic grouping determined. Furthermore, the energy-dispersive X-ray (EDS) method allows the measurement of the chemical composition in a semiquantitative way. The two different results are based on standard measurements in chemical composition and face angles.

The stereo comparator method can be subdivided into different parts. In the electron-microscopic part, the crystalline phase under investigation is analysed by stereo imaging. The specimen containing the microcrystals is installed on the goniometer specimen stage of the SEM. In a first approximation, the SEM delivers parallel projection images of the observed objects.

Different perspectives for stereo-comparator processing are created by taking two different images, the first at a position of 0° and the second after an inclination of 12° (Figure 2.1). To get useful results, the inclination has to be done precisely in the same crystallographic zone. Two different image pairs are taken in order to reduce systematic errors introduced by mechanical movement of the specimen stage. It is important that the images are taken at the same value of magnification. Generally, the method is useful for crystals which need magnification higher than 500 times as crystals bigger in size can be analysed by other methods. The smaller the crystals are, the higher the precision of the final phase angle measurements.

Figure 2.1 Position of crystal images after inclination: L: −12° inclination, M: 0°, R: +12° (two pairs for control and accuracy purposes) [1]. Reprinted with permission from The Reconstruction of Natural Zeolites by H. Ghobarkar, O. Schäf, Y. Massiani, P. Knauth, Copyright (2003) Kluwer Academic.

1.2.1 The Calculation of x,y,z from Measured x,y, Px and Py

The calculation of the face angles is done by the determination of x,y as well as the parallaxes Px and Py for a respective point on a crystal face. Four points (three points to define a plane, plus one control point) are measured per crystal face. The co-ordinates x and y can be directly taken, while Py has to be kept constant carefully during the measurement in order to guarantee accuracy. The z value for the respective point is calculated by:

(2.1) equation

given that Px for both directions of inclination (−12°, 0°, 12°) gives the same value (control of accuracy).

By doing this for three points (one supplementary point for control), a plane is clearly defined; the common form of the equation of a plane is:

(2.2) equation

The angle between planes 1 and 2 (crystal faces) is then given by:

(2.3)

equation

The calculation is simplified by using the vector form of the plane equation. This has the big advantage that the angle between two crystal faces is identical to the angle between their normal vectors. The determination of the angle between two faces, therefore, covers two steps.

The first step is the determination of the normal vectors of both planes: the determined three points of a plane permit one to calculate two vectors which pass within the plane. The normal vector of these planes is placed perpendicular to the plane and is the complementary angle to 180°.

Second is the determination of the angles between the normal vectors: these are the angles between the crystal faces (Figure 2.2) obtained by the cross product of the two vectors.

Figure 2.2 Angles between crystal faces are obtained by determining the face normal angles from the respective plane vectors for each face [1]. Reprinted with permission from The Reconstruction of Natural Zeolites by H. Ghobarkar, O. Schäf, Y. Massiani, P. Knauth, Copyright (2003) Kluwer Academic.

2.1.2.2 Crystal Indexing

In order to confirm the results on the face normal angles obtained by the stereo-comparator with respect to the crystal habit (crystal morphology), the values are written in the stereographic projection. At last, the stereographic projection has to be turned in such a way that a standard set-up is achieved. The final indexing has to be accomplished by trial and error, while theoretical values can be taken into account once the crystal axis ratios and the crystal axis angles have been determined. More details on this SEM observation technique of microcrystals can be found in references [4, 5].

2.2 Crystal Morphology and Structure of Solid Acids

This chapter presents acid morphologies in the crystalline state, while the respective crystal structures are directly correlated to these morphologies.

The reader may use corresponding crystal visualization software to obtain complementary three-dimensional orientations of the respective crystal lattices. Crystal structure references are indicated to facilitate this approach.

2.2.1 Hydrohalic Acids

2.2.1.1 Hydrofluoric Acid

Chemical formula: HF

Crystal morphology (Figure 2.3)

Figure 2.3 Orthorhombic (class: mmm) hydrofluoric acid (SEM, magnification: 2000×).

Crystal structure (Figure 2.4)

Figure 2.4 Polyhedral representation of orthorhombic hydrofluoric acid (space group: Bmmb). Data from Reference [6].

2.2.1.2 Hydrochloric Acid

Chemical formula: HCl

Crystal morphology (Figure 2.5)

Figure 2.5 Orthorhombic (class: mmm) hydrochloric acid (SEM, magnification: 1290×).

Crystal structure (Figure 2.6)

Figure 2.6 Polyhedral representation of orthorhombic hydrochloric acid (space group: Fmmm) [7].

2.2.1.3 Hydrobromic Acid

Chemical formula: HBr

Crystal morphology (Figure 2.7)

Figure 2.7 Orthorhombic (class: mmm) hydrobromic acid (SEM, magnification: 5000×).

Crystal structure (Figure 2.8)

Figure 2.8 Polyhedral representation of orthorhombic hydrobromic acid (space group: Fmmm). Data from Reference [7].

2.2.2 Main Group Element Oxoacids

2.2.2.1 Boric Acid

Chemical formula: H3BO3

Crystal morphology (Figure 2.9)

Figure 2.9 Triclinic (class: P ) boric acid (SEM, magnification: 1290×).

Crystal structure (Figure 2.10)

Figure 2.10 Polyhedral representation of triclinic boric acid (space group: P ). Data from Reference [8].

2.2.2.2 Isocyanic Acid

Chemical formula: HNCO

Crystal morphology (Figure 2.11)

Figure 2.11 Orthorhombic (class: mmm) isocyanic acid (SEM, magnification: 2000×).

Crystal structure (Figure 2.12)

Figure 2.12 Polyhedral representation of orthorhombic isocyanic acid (space group: Pnma). Data from Reference [9].

2.2.2.3 Nitric Acid

Chemical formula: HNO3

Crystal morphology (Figure 2.13)

Figure 2.13 Monoclinic (class: 2/m) nitric acid (SEM, magnification: 1590×).

Crystal structure (Figure 2.14)

Figure 2.14 Polyhedral representation of monoclinic nitric acid (space group: P121/a1). Data from Reference [10].

2.2.2.4 Phosphoric Acid

Chemical formula: H3PO4

Crystal morphology: modification 1 (Figure 2.15)

Figure 2.15 Monoclinic (class: 2/m) phosphoric acid (SEM, magnification: 2940×).

Crystal structure: modification 1 (Figure 2.16)

Figure 2.16 Polyhedral representation of monoclinic phosphoric acid (space group: P121/c1). Data from References [11, 12].

Crystal morphology: modification 2 (Figure 2.17)

Figure 2.17 Orthorhombic (class: 2/m) phosphoric acid (SEM, magnification: 2000×).

Crystal structure: modification 2 (Figure 2.18)

Figure 2.18 Polyhedral representation of orthorhombic phosphoric acid (space group: Pna21). Data from Reference [13].

2.2.2.5 Triarsenic Acid

Chemical formula: H5As3O10

Crystal morphology (Figure 2.19)

Figure 2.19 Triclinic (class: ) triarsenic acid (SEM, magnification: 733×).

Crystal structure (Figure 2.20)

Figure 2.20 Polyhedral representation of triclinic triarsenic acid (space group: P ). Data from Reference [14].

2.2.2.6 Antimonic Acid

Chemical formula: H2Sb2O6

Crystal morphology (Figure 2.21)

Figure 2.21 Cubic (class: m m) antimonic acid (SEM, magnification: 1000×).

Crystal structure (Figure 2.22)

Figure 2.22 Polyhedral representation of cubic antimonic acid (space group: Fd mz). Data from Reference [15].

2.2.2.7 Sulphuric Acid

Chemical formula: H2SO4

Crystal morphology (Figure 2.23)

Figure 2.23 Monoclinic (class: 2/m) sulphuric acid (SEM, magnification: 2150×).

Crystal structure (Figure 2.24)

Figure 2.24 Polyhedral representation of monoclinic sulphuric acid (space group: A1a1). Data from Reference [16].

2.2.2.8 Selenic Acids

Selenic(VI) Acid

Chemical formula: H2SeO4

Crystal morphology (Figure 2.25)

Figure 2.25 Orthorhombic (class: 222) selenic (VI) acid (SEM, magnification: 667×).

Crystal structure (Figure 2.26)

Figure 2.26 Polyhedral representation of orthorhombic selenic (VI) acid (space group: 212121). Data from Reference [17].

Selenic(IV) Acid – Selenous Acid

Chemical formula: H2SeO3

Crystal morphology (Figure 2.27)

Figure 2.27 Orthorhombic (class: 222) selenic(IV) acid (SEM, magnification: 3340×).

Crystal structure (Figure 2.28)

Figure 2.28 Polyhedral representation of orthorhombic selenic(IV) acid (space group: P212121). Data from Reference [18].

2.2.2.9 Chloric Acids

Chloric(VII) Acid

Chemical formula: HClO4

Crystal morphology (Figure 2.29)

Figure 2.29 Orthorhombic (class: mm2) perchloric acid (SEM, magnification: 4900×).

Crystal structure (Figure 2.30)

Figure 2.30 Polyhedral representation of orthorhombic perchloric acid (space group: Pca21). Data from Reference [19].

Chloric(VII) Acid Trihydrate – Oxonium Perchlorate

Chemical formula: HClO4·3 H2O (see also Chapter 10)

Crystal morphology (Figure 2.31)

Figure 2.31 Orthorhombic (class: mmm) perchloric acid trihydrate (SEM, magnification: 2000×).

Crystal structure (Figure 2.32)

Figure 2.32 Polyhedral representation of orthorhombic perchloric acid trihydrate (space group: Pbca). Data from Reference [20].

2.2.2.10 Iodic Acids

Iodic(VII) Acid

Chemical formula: H5IO6

Crystal morphology (Figure 2.33)

Figure 2.33 Monoclinic (class: 2/m) iodic(V) acid (SEM, magnification: 2000×).

Crystal structure (Figure 2.34)

Figure 2.34 Polyhedral representation of monoclinic iodic(VII) acid (space group: P121/n1). Data from Reference [21].

Iodic(V) Acid

Chemical formula: HIO3

Crystal morphology (Figure 2.35)

Figure 2.35 Orthorhombic (class: 222) iodic(V) acid (SEM, magnification: 2000×).

Crystal structure (Figure 2.36)

Figure 2.36 Polyhedral representation of orthorhombic iodic(V) acid (space group: P212121). Data from Reference [22].

2.2.3 Transition Metal Oxoacids

2.2.3.1 Dodecamolybdophosphoric Acid Hexahydrate

Chemical formula: H3(PMo12O40) (H2O)6

Crystal morphology (Figure 2.37)

Figure 2.37 Cubic (class: m3m) dodecamolybdophosphoric acid hexahydrate (SEM, magnification: 5040×).

Crystal structure (Figure 2.38)

Figure 2.38 Polyhedral representation of cubic (class: m3m) dodecamolybdophosphoric acid hexahydrate (space group: Fd mz). Data from Reference [23].

2.2.3.2 Tungstic Acid

Chemical formula: H2WO4

Crystal morphology (Figure 2.39)

Figure 2.39 Orthorhombic (class: mmm) tungstic acid (SEM, magnification: 2000×).

Crystal structure (Figure 2.40)

Figure 2.40 Polyhedral representation of orthorhombic tungstic acid (space group: Pnmb). Data from Reference [24].

2.2.3.3 Dodecatungstophosphoric Acid 21 Hydrate

Chemical formula: H3PW12O40·21H2O (see also Chapter 10)

Crystal morphology (Figure 2.41)

Figure 2.41 Orthorhombic (class: mmm) dodecatungstophosphoric acid 21 hydrate (SEM, magnification: 2000×).

Crystal structure (Figure 2.42)

Figure 2.42 Polyhedral representation of orthorhombic dodecatungstophosphoric acid 21 hydrate (space group: Pcca). Data from Reference [25].

2.2.4 Carboxylic Acids

2.2.4.1 Formic Acid

Chemical formula: HCOOH

Crystal morphology (Figure 2.43)

Figure 2.43 Orthorhombic (class: mm2) formic acid (SEM, magnification: 2000×).

Crystal structure (Figure 2.44)

Figure 2.44 Polyhedral representation of orthorhombic formic acid (space group: Pna21). Data from Reference [26].

2.2.4.2 Acetic Acid

Chemical formula: CH3COOH

Crystal morphology (Figure 2.45)

Figure 2.45 Orthorhombic (class: mm2) acetic acid (SEM, magnification: 6440×).

Crystal structure (Figure 2.46)

Figure 2.46 Polyhedral representation of orthorhombic acetic acid (space group: Pna21). Data from Reference [27].

Note

1. This chapter is dedicated to the memory of Dr. Habib Ghobarkar († 2010).

References

1. Ghobarkar, H., Schäf, O., Massiani, Y. and Knauth, P. (2003) The Reconstruction of Natural Zeolites, Kluwer Academic, Dordrecht.

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14. Jost, K.H., Worzala, H. and Thilo, E. (1966) Acta Crystallographica, 21, 808–813.

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16. Pascard-Billy, C. (1965) Acta Crystallographica, 18, 827–829.

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18. Larsen, F.K., Lehmann, M.S. and Sotofte, I. (1971) Acta Chemica Scandinavia, 25, 1233–1240.

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21. Feikema, Y.D. (1966) Acta Crystallographica, 20, 765–769.

22. Rogers, M.T. and Helmholz, L. (1941) Journal of the American Chemical Society, 63, 278–284.

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24. Szymanski, J.T. and Roberts, A.C. (1984) Canadian Mineralogist, 232, 681–688.

25. Spirlett, M.R. and Busing, W.R. (1978) Acta Crystallographica. Section B, Structural Science, 34, 907–910.

26. Albinati, A., Rouse, K.D. and Thomas, M.W. (1978) Acta Crystallographica. Section B, Structural Science, 34, 2188–2190.

27. Jones, R.E. and Templeton, D.H. (1958) Acta Crystallographica, 11, 484–487.

Chapter 3

Diffusion in Solid Proton Conductors: Theoretical Aspects and Nuclear Magnetic Resonance Analysis

Maria Luisa Di Vona, Emanuela Sgreccia and Sebastiano Tosto

Water behavior in solid proton conductors is a considerably complex phenomenon. However, the knowledge of transport and diffusivity inside electrolytes is an important requirement for many applications. Extensive efforts have been made in terms of modeling water transport and its management. Accurate measurements of diffusion are required to validate these models and to optimize the performance of solid proton conductors.

The focus of this chapter is the theoretical approach together with the use of nuclear magnetic resonance (NMR) techniques for the understanding of diffusion phenomena in solid proton conductors. The basic principles and the main NMR methods will be also discussed.

3.1 Fundamentals of Diffusion

Diffusion is the transport of matter activated by thermal motion of atoms or molecules in gas, liquid and solid phases [1]. The complexity of the microscopic kinetic mechanisms underlying these phenomena is due to the variety of driving forces and interaction forces that control the displacement rate of atoms, ions and molecules. The International Union of Pure and Applied Chemistry (IUPAC) defines self-diffusion as the transport of matter under vanishing chemical potential gradient. Equation 3.1 recalls the definition of the chemical potential μi, of species i, where Ni is the number of particles of species i, U is the internal energy, also simply called energy [2], and entropy S, volume V and a number of other particles of the system are constant.

(3.1) equation

In practice, this definition is often replaced by that using the Gibbs free energy G at constant temperature T and pressure p:

(3.2) equation

Self-diffusion involves a spontaneous mixing of atoms, molecules or ions in a chemically homogeneous phase under steady conditions of dynamical equilibrium and without net flow of matter. It can be evidenced replacing part of the diffusing species with isotopic tracers (tracer diffusion). More often, however, diffusion phenomena describe a transition from a situation out of equilibrium towards thermodynamic equilibrium; this is typically the case of chemical diffusion, which occurs with entropy increase due to net flow of matter, for example between two different phases. This kind of process is irreversible. As will be shortly sketched in the next section, these processes are described by appropriate generally different diffusion coefficients, D. In the former case, D concerns one species only, apart from isotopic usually negligible effects; in the latter case, D describes instead in general a multi-element system with correlation and interaction effects between different diffusing species. In general, D also depends on the activity of the diffusing species, that is, on its concentration. The quantum nature of the system is to be taken into account when the number of atoms, molecules and ions is so small that it prevents any statistical approach based on macroscopic average properties like temperature or pressure. When instead the number of species is sufficiently large to be described through statistical formalism (i.e. in terms of concentrations and concentration gradients regarded as properties of a continuum medium characterized by smooth changes of its thermodynamic properties), D characterizes the evolution of an unstable system towards its maximum entropy. The continuity condition and the Fick equations are the fundamental tools that account adequately for a huge amount of experimental data related to a wide variety of physico-chemical processes. These preliminary notes give an idea of the complexity of this topic, which controls however fundamental processes like microstructural changes, recrystallization, the nucleation of one phase into a parent phase, ionic conduction in electrolytes and so on. Despite the vastness and complexity of this topic, the present section aims to introduce in a deliberately intuitive and elementary way some basic concepts underlying the mass and charge transport; with this aim in mind, the mathematical difficulty that characterizes the modern theories of diffusion is intentionally waived to emphasize instead the conceptual link between diffusion physics and solid state ionics, with particular reference to the interest of the experimentalists on the essential concepts of the charge transport phenomena.

3.1.1 Phenomenology of Diffusion

The transport mechanisms differ, of course, depending on the nature of both diffusing species and the diffusion medium. Despite the inherent conceptual complexity, it is possible to identify some points that are common to the possible experimental situations. For instance, a general rule is that the transport occurs at decreasing rates in gases, liquids and solids. Also, from a phenomenological point of view, the most intuitive way to describe the displacement of matter is to define a flux having physical dimensions of matter per unit time and surface given by:

(3.3) equation

where c and v are the concentration and average displacement velocity of the diffusing species. This equation, although being a mere definition of flux J of matter rather than a physical law, introduces the basic ingredient to formulate the diffusion theory; see below a sketch of the random walk approach (i.e. the concentration); this way of defining the flux regards the amount of mass and charge actually transferred within a system of other atoms, ions and molecules not involved in the displacement.

The first formulation of diffusion law was due to Fick, who assumed a concentration gradient-driven effect between two contiguous volumes of a sample:

(3.4) equation

where ∇c is the concentration gradient and D is a proportionality factor. The minus sign means that the mass flow vector J is oriented against the concentration gradient, that is, the prospective effect of diffusion is a spontaneous flow of matter from a high-concentration region to a low-concentration region that tends to flatten the initial gradient. In turn, having tacitly assumed that diffusion is allowed to occur in an isolated system, this has a clear connection with the Second Law of Thermodynamics, about the spontaneous evolution of an isolated system towards the most probable and disordered state. Merging together Equations 3.3 and 3.4 yields:

(3.5a) equation

At the right-hand side, the chemical potential is expressed as a function of the concentration gradient . Regarding the gradient of this potential as the driving force of diffusion and recalling that the mobility of the diffusing species times is defined as , then:

(3.5b) equation

as is well known. A further refinement of Fick's law involves the activity rather than the concentration; assuming a linear relationship between these quantities, one finds:

(3.6) equation

where is a proper proportionality coefficient called the activity coefficient. Thus one expects that these laws can be reformulated according to a more general thermodynamic point of view. Note in this respect that combining Equation 3.5 with , analogous to Equation 3.3, yields:

(3.7) equation

At the right-hand side appears the chemical potential of the diffusing species; the constant is the activity of the diffusing species in its standard state. The corresponding standard chemical potential is taken here as zero. Since D is linked to the driving thermodynamic force that triggers the diffusion, the most general way of defining the mass flow is

(3.8) equation

where L is a new proportionality factor having physical dimensions of mobility times concentration, sometimes also called diffusivity. The last way to define explicitly the mass flow through its thermodynamic driving force has an important consequence. Since Equation 3.8 reads also , Equation 3.4 and the second Equation 3.6 yield:

(3.9) equation

This equation holds for the chemical diffusion in a homogeneous body of matter, for instance in the case of displacement of an isotope in a matrix of the same element. L being the product of mobility and concentration, from this equation one infers:

(3.10) equation

The former equation is the Darken equation, and the right-hand side of the first equation is also called the thermodynamic or Wagner factor. Moreover, the second equation, which agrees with that previously found, links the diffusion coefficient to the mobility of the particles; when extended to the case of charged particles, replacing the general value of with that of the amount of charge carried by the particle (i.e. with ), one finds:

(3.11) equation

Relevant interest also has the relationship that links the diffusion coefficient to the electrical conductivity . An elementary way to find the link between and D exploits the second Equation 3.7, simply specifying the force as that due to an electric field E acting on the charge ; so, assuming a one-dimensional (1D) case for simplicity of explanation, the equation reads , with being the electric potential. Multiply now both sides by and note that we obtain at the left-hand side a charge flow ; recalling that according to Ohm's law, the result is:

(3.12) equation

A link also exists between D and the mean squared displacement traveled by any number of non-interacting particles in the absence of a net driving force. An elementary derivation of this link is carried out here considering an ideal reference plane crossed by any particles randomly moving in the presence of a concentration gradient along the x-axis; this assumption reduces for simplicity the problem to the 1D motion perpendicularly to an arbitrary section of the plane. Consider on the reference plane and the concentration difference defined on two arbitrary points apart at the opposite sides of the plane with . Write , and multiply both sides of the equation by the diffusion rate defined as ; that is, is the distance traveled by the particles diffusing during the time range , both arbitrary and fixed once for all so that is constant. One finds , being the net flux of matter crossing the plane. Take the average of both sides of the equation defining , and calculate the average concentration on the plane: at the right-hand side, one finds the term