Physico chemistry of solid gas interfaces
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Physical Chemistry of Solid-Gas Interfaces
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Physical Chemistry of
Solid-Gas Interfaces
Concepts and Methodology for Gas Sensor Development
René Lalauze
Series Editor
Dominique Placko
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First published in France in 2006 by Hermes Science/Lavoisier entitled “Physico-chimie des interfaces
solide-gaz 1 et 2”
First published in Great Britain and the United States in 2008 by ISTE Ltd and John Wiley & Sons, Inc.
Translated from the French by Zineb Es-Skali and Matthieu Bourdrel.
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as
permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced,
stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers,
or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA.
Enquiries concerning reproduction outside these terms should be sent to the publishers at the
undermentioned address:
ISTE Ltd
6 Fitzroy Square
London W1T 5DX
UK
John Wiley & Sons, Inc.
111 River Street
Hoboken, NJ 07030
USA
www.iste.co.uk
www.wiley.com
© ISTE Ltd, 2008
© LAVOISIER, 2006
The rights of René Lalauze to be identified as the author of this work have been asserted by him in
accordance with the Copyright, Designs and Patents Act 1988.
Library of Congress Cataloging-in-Publication Data
Lalauze, René.
[Physico-chimie des interfaces solide-gaz. English]
Physical chemistry of solid-gas interfaces : concepts and methodology for gas sensors development /
René Lalauze.
p. cm.
Includes bibliographical references and index.
ISBN 978-1-84821-041-7
1. Gas-solid interfaces. 2. Gas detectors. I. Title.
QD509.G37L3513 2008
681'.2--dc22
2008022737
British Library Cataloguing-in-Publication Data
A CIP record for this book is available from the British Library
ISBN: 978-1-84821-041-7
Printed and bound in Great Britain by Antony Rowe Ltd, Chippenham, Wiltshire.
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Table of Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
Chapter 1. Adsorption Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . .
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1.1. The surface of solids: general points . . . . . . . . . . . . . . . . . . . .
1.2. Illustration of adsorption . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1. The volumetric method or manometry . . . . . . . . . . . . . . . .
1.2.2. The gravimetric method or thermogravimetry. . . . . . . . . . . .
1.3. Acting forces between a gas molecule and the surface of a solid. . . .
1.3.1. Van der Waals forces . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.2. Expression of the potential between a molecule and a solid. . . .
1.3.3. Chemical forces between a gas species and the surface of a solid
1.3.4. Distinction between physical and chemical adsorption . . . . . .
1.4. Thermodynamic study of physical adsorption . . . . . . . . . . . . . . .
1.4.1. The different models of adsorption . . . . . . . . . . . . . . . . . .
1.4.2. The Hill model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.3. The Hill-Everett model . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.4. Thermodynamics of the adsorption equilibrium in Hill’s model .
1.4.4.1. Formulating the equilibrium . . . . . . . . . . . . . . . . . . .
1.4.4.2. Isotherm equation . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.5. Thermodynamics of adsorption equilibrium in the Hill-Everett
model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5. Physical adsorption isotherms . . . . . . . . . . . . . . . . . . . . . . . .
1.5.1. General points. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5.2. Adsorption isotherms of mobile monolayers . . . . . . . . . . . .
1.5.3. Adsorption isotherms of localized monolayers . . . . . . . . . . .
1.5.3.1. Thermodynamic method . . . . . . . . . . . . . . . . . . . . .
1.5.3.2. The kinetic model . . . . . . . . . . . . . . . . . . . . . . . . .
1.5.4. Multilayer adsorption isotherms . . . . . . . . . . . . . . . . . . . .
1.5.4.1. Isotherm equation . . . . . . . . . . . . . . . . . . . . . . . . .
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Physical Chemistry of Solid-Gas Interfaces
1.6. Chemical adsorption isotherms . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.7. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Chapter 2. Structure of Solids: Physico-chemical Aspects . . . . . . . . . . . . 29
2.1. The concept of phases . . . . . . . . . . . . . . . . . . . .
2.2. Solid solutions . . . . . . . . . . . . . . . . . . . . . . . .
2.3. Point defects in solids . . . . . . . . . . . . . . . . . . . .
2.4. Denotation of structural members of a crystal lattice. .
2.5. Formation of structural point defects . . . . . . . . . . .
2.5.1. Formation of defects in a solid matrix . . . . . . .
2.5.2. Formation of defects involving surface elements .
2.5.3. Concept of elementary hopping step . . . . . . . .
2.6. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . .
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Chapter 3. Gas-Solid Interactions: Electronic Aspects . . . . . . . . . . . . . . 39
3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2. Electronic properties of gases . . . . . . . . . . . . . . . . . . . . . .
3.3. Electronic properties of solids . . . . . . . . . . . . . . . . . . . . . .
3.3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2. Energy spectrum of a crystal lattice electron. . . . . . . . . . .
3.3.2.1. Reminder about quantum mechanics principles . . . . . .
3.3.2.2. Band diagrams of solids . . . . . . . . . . . . . . . . . . . .
3.3.2.3. Effective mass of an electron . . . . . . . . . . . . . . . . .
3.4. Electrical conductivity in solids . . . . . . . . . . . . . . . . . . . . .
3.4.1. Full bands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.2. Partially occupied bands . . . . . . . . . . . . . . . . . . . . . .
3.5. Influence of temperature on the electric behavior of solids . . . . .
3.5.1. Band diagram and Fermi level of conductors . . . . . . . . . .
3.5.2. Case of intrinsic semiconductors . . . . . . . . . . . . . . . . .
3.5.3. Case of extrinsic semiconductors . . . . . . . . . . . . . . . . .
3.5.4. Case of materials with point defects. . . . . . . . . . . . . . . .
3.5.4.1. Metal oxides with anion defects, denoted by MO1x . . .
3.5.4.2. Metal oxides with cation vacancies, denoted by M1xO .
3.5.4.3. Metal oxides with interstitial cations, denoted by M1+xO
3.5.4.4. Metal oxides with interstitial anions, denoted by MO1+x .
3.6. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Chapter 4. Interfacial Thermodynamic Equilibrium Studies . . . . . . . . . . 69
4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2. Interfacial phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3. Solid-gas equilibriums involving electron transfers or electron holes .
4.3.1. Concept of surface states . . . . . . . . . . . . . . . . . . . . . . . .
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4.3.2. Space-charge region (SCR) . . . . . . . . . . . . . . . . . . . . . . .
4.3.3. Electronic work function . . . . . . . . . . . . . . . . . . . . . . . .
4.3.3.1. Case of a semiconductor in the absence of surface states . .
4.3.3.2. Case of a semiconductor in the presence of surface states . .
4.3.3.3. Physicists’ and electrochemists’ denotation systems . . . . .
4.3.4. Influence of adsorption on the electron work functions . . . . . .
4.3.4.1. Influence of adsorption on the surface barrier VS . . . . . . .
4.3.4.2. Influence of adsorption on the dipole component VD. . . . .
4.4. Solid-gas equilibriums involving mass and charge transfers . . . . . .
4.4.1. Solids with anion vacancies . . . . . . . . . . . . . . . . . . . . . .
4.4.2. Solids with interstitial cations . . . . . . . . . . . . . . . . . . . . .
4.4.3. Solids with interstitial anions. . . . . . . . . . . . . . . . . . . . . .
4.4.4. Solids with cation vacancies . . . . . . . . . . . . . . . . . . . . . .
4.5. Homogenous semiconductor interfaces. . . . . . . . . . . . . . . . . . .
4.5.1. The electrostatic potential is associated with the intrinsic energy
level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.2. Electrochemical aspect . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.3. Polarization of the junction . . . . . . . . . . . . . . . . . . . . . . .
4.6. Heterogenous junction of semiconductor metals . . . . . . . . . . . . .
4.7. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Chapter 5. Model Development for Interfacial Phenomena . . . . . . . . . . . 109
5.1. General points on process kinetics. . . . . . . . . . . . . . . . . . . .
5.1.1. Linear chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.1.1. Pure kinetic case hypothesis . . . . . . . . . . . . . . . . .
5.1.1.2. Bodenstein’s stationary state hypothesis . . . . . . . . . .
5.1.1.3. Evolution of the rate according to time and gas pressure
5.1.1.4. Diffusion in a homogenous solid phase. . . . . . . . . . .
5.1.2. Branched processes . . . . . . . . . . . . . . . . . . . . . . . . .
5.2. Electrochemical aspect of kinetic processes . . . . . . . . . . . . . .
5.3. Expression of mixed potential . . . . . . . . . . . . . . . . . . . . . .
5.4. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Chapter 6. Apparatus for Experimental Studies: Examples of
Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
6.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2. Calorimetry . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.1. General points. . . . . . . . . . . . . . . . . . . . . . .
6.2.1.1. Theoretical aspect of Tian-Calvet calorimeters
6.2.1.2. Seebeck effect. . . . . . . . . . . . . . . . . . . .
6.2.1.3. Peltier effect . . . . . . . . . . . . . . . . . . . . .
6.2.1.4. Tian equation . . . . . . . . . . . . . . . . . . . .
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Physical Chemistry of Solid-Gas Interfaces
6.2.1.5. Description of a Tian-Calvet device. . . . . . . . . . . . . . . .
6.2.1.6. Thermogram profile . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.1.7. Examples of applications . . . . . . . . . . . . . . . . . . . . . .
6.3. Thermodesorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.2. Theoretical aspect . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.3. Display of results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.3.1. Tin dioxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.3.2. Nickel oxide. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4. Vibrating capacitor methods . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.1. Contact potential difference . . . . . . . . . . . . . . . . . . . . . . .
6.4.2. Working principle of the vibrating capacitor method . . . . . . . .
6.4.2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.2.2. Theoretical study of the vibrating capacitor method . . . . . .
6.4.3. Advantages of using the vibrating capacitor technique . . . . . . .
6.4.3.1. The materials studied . . . . . . . . . . . . . . . . . . . . . . . .
6.4.3.2. Temperature conditions . . . . . . . . . . . . . . . . . . . . . . .
6.4.3.3. Pressure conditions. . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.4. The constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.4.1. The reference electrode . . . . . . . . . . . . . . . . . . . . . . .
6.4.4.2. Capacitance modulation . . . . . . . . . . . . . . . . . . . . . . .
6.4.5. Display of experimental results . . . . . . . . . . . . . . . . . . . . .
6.4.5.1. Study of interactions between oxygen and tin dioxide . . . . .
6.4.5.2. Study of interactions between oxygen and beta-alumina . . .
6.5. Electrical interface characterization . . . . . . . . . . . . . . . . . . . . . .
6.5.1. General points. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5.2. Direct-current measurement . . . . . . . . . . . . . . . . . . . . . . .
6.5.3. Alternating-current measurement . . . . . . . . . . . . . . . . . . . .
6.5.3.1. General points. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5.3.2. Principle of the impedance spectroscopy technique . . . . . .
6.5.4. Application of impedance spectroscopy – experimental results . .
6.5.4.1. Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5.4.2. Experimental results: characteristics specific to each material
6.5.5. Evolution of electrical parameters according to temperature . . . .
6.5.6. Evolution of electrical parameters according to pressure . . . . . .
6.6. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Chapter 7. Material Elaboration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
7.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2. Tin dioxide . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.1. The compression of powders . . . . . . . . . . . . .
7.2.1.1. Elaboration process and structural properties
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Table of Contents
7.2.1.2. Influence of the morphological parameters on the electric
properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.2. Reactive evaporation. . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.2.1. Experimental device . . . . . . . . . . . . . . . . . . . . . . . .
7.2.2.2. Measure of the source temperature . . . . . . . . . . . . . . .
7.2.2.3. Thickness measure . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.2.4. Experimental process . . . . . . . . . . . . . . . . . . . . . . .
7.2.2.5. Structure and properties of the films . . . . . . . . . . . . . .
7.2.3. Chemical vapor deposition: deposit contained between 50 and
300 Å. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.3.1. General points. . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.3.2. Device description . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.3.3. Structural characterization of the material . . . . . . . . . . .
7.2.3.4. Influence of the experimental parameters
on the physico-chemical properties of the films. . . . . . . . . . . . .
7.2.3.5. Influence of the structure parameters on the electric
properties of the films . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.4. Elaboration of thick films using serigraphy . . . . . . . . . . . . .
7.2.4.1. Method description. . . . . . . . . . . . . . . . . . . . . . . . .
7.2.4.2. Ink elaboration . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.4.3. Structural characterization of thick films made with
tin dioxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3. Beta-alumina . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3.1. General properties . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3.2. Material elaboration . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3.3. Material shaping . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3.3.1. Mono-axial compression . . . . . . . . . . . . . . . . . . . . .
7.3.3.2. Serigraphic process. . . . . . . . . . . . . . . . . . . . . . . . .
7.3.4. Characterization of materials . . . . . . . . . . . . . . . . . . . . . .
7.3.4.1. Physico-chemical characterization of the sintered materials
7.3.4.2. Physico-chemical treatment of the thick films. . . . . . . . .
7.3.5. Electric characterization. . . . . . . . . . . . . . . . . . . . . . . . .
7.4. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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255
255
257
261
261
262
263
263
266
273
275
Chapter 8. Influence of the Metallic Components on the Electrical
Response of the Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
8.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2. General points. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2.1. Methods to deposit the metallic parts on the sensitive element .
8.2.2. Role of the metallic elements on the sensors’ response . . . . .
8.2.3. Role of the metal: catalytic aspects . . . . . . . . . . . . . . . . .
8.2.3.1. Spill-over mechanism . . . . . . . . . . . . . . . . . . . . . .
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278
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Physical Chemistry of Solid-Gas Interfaces
8.2.3.2. Reverse spill-over mechanism . . . . . . . . . . . . . . . . . . .
8.2.3.3. Electronic effect mechanism . . . . . . . . . . . . . . . . . . . .
8.2.3.4. Influence of the metal nature on the involved mechanism. . .
8.3. Case study: tin dioxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.3.1. Choice of the samples . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.3.2. Description of the reactor . . . . . . . . . . . . . . . . . . . . . . . . .
8.3.3. Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.3.3.1. Influence of the oxygen pressure on the electric conductivity
8.3.3.2. Influence of the reducing gas on the electric conductions . . .
8.4. Case study: beta-alumina . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.4.1. Device and experimental process . . . . . . . . . . . . . . . . . . . .
8.4.2. Influence of the nature of the electrodes on the measured voltage .
8.4.2.1. Study of the different couples of metallic electrodes . . . . . .
8.4.2.2. Electric response to polluting gases . . . . . . . . . . . . . . . .
8.4.3. Influence of the electrode size . . . . . . . . . . . . . . . . . . . . . .
8.4.3.1. Description of the studied devices . . . . . . . . . . . . . . . . .
8.4.3.2. Study of the electric response according to the experimental
conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.5. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.6. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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284
284
286
288
288
289
291
291
295
296
297
298
299
301
303
303
. 304
. 306
. 307
Chapter 9. Development and Use of Different Gas Sensors . . . . . . . . . . . 309
9.1. General points on development and use . . . . . . . . . . . . . . . . . .
9.2. Examples of gas sensor development . . . . . . . . . . . . . . . . . . . .
9.2.1. Sensors elaborated using sintered materials . . . . . . . . . . . . .
9.2.2. Sensors produced with serigraphed sensitive materials . . . . . .
9.3. Device designed for the laboratory assessment of sensitive elements
and/or sensors to gas action . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.3.1. Measure cell for sensitive materials . . . . . . . . . . . . . . . . . .
9.3.2. Test bench for complete sensors . . . . . . . . . . . . . . . . . . . .
9.3.3. Measure of the signal . . . . . . . . . . . . . . . . . . . . . . . . . .
9.3.3.1. Measure of the electric conductance . . . . . . . . . . . . . .
9.3.3.2. Measure of the potential. . . . . . . . . . . . . . . . . . . . . .
9.4. Assessment of performance in the laboratory . . . . . . . . . . . . . . .
9.4.1. Assessment of the performances of tin dioxide in the presence
of gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.4.2. Assessment of beta-alumina in the presence of oxygen . . . . . .
9.4.2.1. Device and experimental process . . . . . . . . . . . . . . . .
9.4.2.2. Electric response to the action of oxygen. . . . . . . . . . . .
9.4.3. Assessment of the performances of beta-alumina in the presence
of carbon monoxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.4.3.1. Measurement device . . . . . . . . . . . . . . . . . . . . . . . .
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310
310
312
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317
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319
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322
322
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327
327
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Table of Contents
9.4.3.2. Electric results . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.5. Assessment of the sensor working for an industrial application . . . . .
9.5.1. Detection of hydrogen leaks on a cryogenic engine . . . . . . . . .
9.5.1.1. Context of the study . . . . . . . . . . . . . . . . . . . . . . . . .
9.5.1.2. Study of performances in the presence of hydrogen . . . . . .
9.5.1.3. Test carried out in an industrial environment . . . . . . . . . .
9.5.2. Application of the resistant sensor to atmospheric pollutants
in an urban environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.5.2.1. Measurement campaign conducted at Lyon in 1988 . . . . . .
9.5.2.2. Measurement campaign conducted at Saint Etienne in 1998 .
9.5.3. Application of the potentiometric sensor to the control
of car exhaust gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.5.3.1. Strategy implemented to control the emission
of nitrogen oxides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.5.3.2. Strategy implemented to control nitrogen oxide traps . . . . .
9.5.3.3. Results relative to the nitrogen oxides traps . . . . . . . . . . .
9.6. Amelioration of the selectivity properties . . . . . . . . . . . . . . . . . .
9.6.1. Amelioration of the selective detection properties of SnO2 sensors
using metallic filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.6.1.1. Development of a sensor using a rhodium filter. . . . . . . . .
9.6.1.2. Development of a sensor using a platinum filter . . . . . . . .
9.6.2. Development of mechanical filters . . . . . . . . . . . . . . . . . . .
9.6.2.1. Development of a sensor detecting hydrogen . . . . . . . . . .
9.6.2.2. Development of a protective film for potentiometric sensors .
9.7. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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333
333
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350
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352
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354
356
356
356
359
Chapter 10. Models and Interpretation of Experimental Results . . . . . . . 361
10.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.2. Nickel oxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.2.1. Kinetic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.2.2. Simulation of a kinetic model using analog electric circuits. . . .
10.2.2.1. Simulation of the curves displaying a maximum . . . . . . .
10.2.2.2. Simulation of the curves displaying a plateau . . . . . . . . .
10.2.3. Physical significance of the measured electric conductivity . . . .
10.3. Beta-alumina . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.3.1. Physico-chemical and physical aspects of a phenomenon taking
place at the electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.3.1.1. Oxygen species present at the surface of the device. . . . . .
10.3.1.2. Origin of the electric potential . . . . . . . . . . . . . . . . . .
10.3.2. Expression of the model . . . . . . . . . . . . . . . . . . . . . . . . .
10.3.2.1. The electrode potential. . . . . . . . . . . . . . . . . . . . . . .
10.3.2.2. Expression of the coverage degree . . . . . . . . . . . . . . . .
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10.3.2.3. Expression of the theoretical potential difference at the poles
of the device. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.3.3. Simulation of the results obtained with oxygen . . . . . . . . . . . .
10.3.3.1. Behavior as a function of temperature and pressure. . . . . . .
10.3.3.2. Behavior as a function of electrode size. . . . . . . . . . . . . .
10.3.3.3. Evolution of the surface potential . . . . . . . . . . . . . . . . .
10.3.4. Simulation of the phenomenon in the presence of CO . . . . . . . .
10.3.4.1. Description of the mechanisms considered . . . . . . . . . . . .
10.3.4.2. Oxidation mechanisms of carbon monoxide . . . . . . . . . . .
10.3.4.3. Results of the simulation. . . . . . . . . . . . . . . . . . . . . . .
10.4. Tin dioxide. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.4.2. Proposition for a physico-chemical model . . . . . . . . . . . . . . .
10.4.3. Phenomenon at the electrodes and role of the thickness
of the sensitive film . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.4.3.1. Calculation of the conductance G as a function
of the thickness of the film . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.4.3.2. Mathematical simulation. . . . . . . . . . . . . . . . . . . . . . .
10.5. Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
394
395
395
397
399
401
401
402
405
409
409
410
415
416
423
428
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431
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Preface
Produced with the collaboration of Christophe Pijolat and Jean Paul Viricelle,
this book is the fruit of research carried out over a long period of time by the
Microsystems, Instrumentation and Chemical Sensors department at the Ecole des
Mines, Saint Etienne, France.
The abilities of this laboratory on the subject of modeling and instrumentation on
heterogenous systems have enabled us to develop and study different devices for the
detection of gas.
The theoretical models based on kinetic concepts constitute the course of
reflection and progress in a scientific area that is still little understood.
A large part of this book refers to PhD and scientific reports. My thanks go out to
all the authors.
I would also like to thank the translators of this book from French, Zineb EsSkali and Matthieu Bourdrel.
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Chapter 1
Adsorption Phenomena1
1.1. The surface of solids: general points
The concept of form, which can be associated with that of surface, is
characteristic of a solid.
On a crystallographic level, every solid can be identified by its atomic or
molecular arrangement. This arrangement, which is specific to each solid,
constitutes a solid phase.
Generally, the identification of such a structure (atomic positions, cohesive
energy) is defined in the hypothesis of an infinite crystal, which implies a similar
environment for all atoms. Near the surface, this is no longer true and it is important
to imagine a new local structure of atoms or electrically charged species.
In the particular case of ionic species, to submit to the local electroneutrality, it
will often be necessary to take the solid’s environment into account. The material
and the different phases in contact with it will thus reach equilibrium.
Thus appears the concept of interface: a privileged area of the solid, from which
all interactions likely to occur between a solid and different surrounding compounds
upon its contact will start and develop.
Depending on the nature of these compounds, there will be talk of solid-solid,
solid-liquid or gas-solid reactions.
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Physical Chemistry of Solid-Gas Interfaces
To conceptualize the solid-gas reactions on which we will concentrate, it is
essential to start by simply picturing a molecule of gas bonding with a solid. The
bonded molecule could remain independent from its support or react with it.
In the first hypothesis, the reversible process at work is one of adsorption, which
then constitutes the overall reaction. It is called the adsorption-desorption
phenomenon (see Figure 1.1a).
In the second hypothesis, adsorption will be the first step of a more complex
process. It has, in this case, a non-reversible character due to which a new
compound, GS for instance, will form.
The nature of the observed phenomenon will depend on the thermodynamic
conditions (pressure, temperature) as well as on the chemical affinity of the present
species.
It is also possible in adsorption phenomena to distinguish between physical and
chemical adsorption. Chemical adsorption or chemisorption is characterized by a
simple electron transfer between the gas in physisorbed state and the solid. This
transfer results in the forming of a reversible chemical bond between the two
compounds (see Figure 1.1b). Once again, the appearance of the chemisorption
process is directly related to the environment’s thermodynamic conditions.
Figure 1.1. The different interaction modes between a gas and a solid:
a) physical adsorption, b) chemisorption, c) non-reversible reaction
1.2. Illustration of adsorption
Volumetric and gravimetric methods are the most explicit and common methods
used to display and quantify adsorption.
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Adsorption Phenomena
3
1.2.1. The volumetric method or manometry
In a closed system, the bonding of a gas molecule with a solid contributes to
lowering the partial pressure of the gas and measuring the variation of this pressure
is enough to access the necessary information.
To conduct an experiment, one uses two containing vessels A and B (see Figure
1.2) are used. Vessel A is connected to a device that measures pressure in it or in
vessel A+B if A and B are joined by a valve V1. Gas is introduced in vessel A using
valve V2 under pressure Pa . The solid sample is put in vessel B. A simple gas
expansion in vessel A+B is enough to allow us to measure pressure Pa b .
Figure 1.2. Adsorption-measuring device using the volumetric method
Generally, the number of gas molecules introduced, n, is given, either by:
n1
PaVa
when vessel A is isolated from vessel B, or by:
n2
Pa b (Va Vb )
after the expansion of the gas in vessel A+B.
Va and Vb are, respectively, the volumes of vessel A and B.
If there is no solid sample in vessel B, we naturally find that:
n1 = n2
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Physical Chemistry of Solid-Gas Interfaces
If there is a solid sample, we generally note that:
n1 > n2
The difference n1-n2 is the amount of gas bonded to the solid.
This experiment, if conducted under different gas pressure conditions, gives us
adsorption isotherms, which plot n against P at a given temperature.
1.2.2. The gravimetric method or thermogravimetry
When a molecule of gas bonds with a solid, it changes the mass of the solid and
simply weighing the solid gives us information about the bonded amount given the
system’s parameters. This method allows us to easily verify that the process is
reversible (see Figure 1.3).
Figure 1.3. Evolution of a solid sample’s mass gain ǻm under changing pressure:
if t < t0: P = P0 if t0 < t < t1: P = P1 > P0 if t > t1: P = P0
a) reversible process; b) non-reversible process
1.3. Acting forces between a gas molecule and the surface of a solid
1.3.1. Van der Waals forces
By analogy with molecular interactions, we can use forces known as Van der
Waals forces to interpret the source of the physical adsorption processes which are
G
favored by very low temperatures. These forces, denoted by F for instance, are
associated with a scalar potential ij:
G
F
grad M
The scalar potentials are additive and the global scalar potential is the sum of the
potential of attraction M a and the potential of repulsion M r :
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Adsorption Phenomena
M
5
Ma Mr
where:
C
r6
Ma
Mr
B
rn
and:
r represents the intermolecular distance, while the constant C consists of three
contributions:
– the Keesom interaction or Keesom force, which only applies to polar
molecules and originates from the attraction between several molecules’ permanent
dipoles;
– the induction interaction or Debye force, which originates from a molecule’s
polarizability. It is caused by the attraction between permanent dipoles and other
dipoles that are induced by the permanent dipoles;
– London’s dispersion force, which originates from the attraction between
molecules’ instantaneous dipoles. This is generally the most powerful attraction.
As for the expression of M r , this is an empirical expression for which we
generally choose n = 12.
The global scalar potential M between two molecules is thus given by:
M
B C
r 12 r 6
If we take into account the fact that the potential reaches a minimal value, M 0 , at
equilibrium, meaning for an intermolecular distance r0, we then obtain:
ê Đ r0 Ã 6 Đ r0 Ã12
á ă á ằ
ôơ â r ạ â r ạ ằẳ
M M 0 ô2ă
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Physical Chemistry of Solid-Gas Interfaces
1.3.2. Expression of the potential between a molecule and a solid
In the hypothesis that all of the supposed semi-infinite crystal’s n molecules
interact with the gas molecule, and that the potentials are additive, the global
potential ĭ can be expressed as follows:
)a
¦M
a
for the attraction potential
)r
¦M
r
for the repulsion potential
n
and:
n
These summations can be replaced with integrals:
)a
³ M dn
)r
³ M dn
a
and:
r
where dn = N dv, and N represents the number of molecules per volume unit.
The volume element used in the integrals is the volume between the spherical
caps of radius r and r+dr, (see Figure 1.4), so:
dV
Sdr
:r 2 dr
ȍ is the solid angle, and if Į is the maximum angle formed by the sphere’s radius
and the solid’s surface normal, then:
:
2S (1 cos D )
where cos Į = Z / r , and Z is the distance between the molecule G and the solid.
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Adsorption Phenomena
7
Figure 1.4. Domain of integration in solid
The potential of attraction then becomes:
)a
SNC
6Z 3
and the potential of repulsion now is:
)r
SBN
45Z 9
Thus, in the case of a gas molecule interacting with a solid, the 1/r3 Van der
Waals potential becomes a 1/r6 potential of attraction, and a 1/r12 potential becomes a
1/r9 potential of repulsion. The solid seems to be a thousand times more attractive or
repulsive than a simple molecule.
1.3.3. Chemical forces between a gas species and the surface of a solid
In an upcoming chapter, we will go into more detail about this physico-chemical
aspect, which is crucial in explaining the workings of chemical sensors.
For now, we will merely point out that if a gas atom has free electrons, a
chemical bond between the gas and the solid becomes a possibility, and there are
two extreme polarization possibilities that can be observed, either:
G e G
or:
G G e
-
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Physical Chemistry of Solid-Gas Interfaces
1.3.4. Distinction between physical and chemical adsorption
The difference between physical and chemical adsorption is due to the difference
between the natures of forces that keep the gas molecules on the solid’s surface.
Let us analyze the ĭ = f ® curve: it goes through a minimum defined by ĭ0 and
r0. In physical adsorption (see Figure 1.5), the value of ĭ0 is so much smaller than
that observed for chemical adsorption (1 instead of 5 or 6 Joules per mole); r0, on the
contrary, is lower for chemical adsorption.
At last, physical adsorption can be represented as a non-activated and therefore
spontaneous process that is likely to take place at very low temperatures.
On the contrary, chemisorption is an activated process and the ĭ = f ® curve
goes first through a maximum marked by the activation energy value EA.
The necessity of activation is related to the fact that electron transfer, from the
gas or the solid, requires an energy input; this implies the existence of a kinetic
process.
Figure 1.5. Plot aspect of ĭ = f ® in case of a): physisorption; b): chemisorption
1.4. Thermodynamic study of physical adsorption
1.4.1. The different models of adsorption
In order to build a thermodynamic model of physical adsorption, it is important
to take note of a few experimental results. The adsorption isotherms acquired
through the volumetric or the gravimetric method allow us to make sure that the
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Adsorption Phenomena
9
quantity n of bonded molecules is a function of gas pressure and temperature. These
results involve a divariant system. Thereby, at the very least, all proposed models
will have to meet this condition.
It is important to note that the adsorption process can in no case whatsoever be
identified with a simple condensation process. Indeed, condensation is a
monovariant process that owes its origin to gas saturation. Saturation is achieved at a
pressure P greater than or equal to the saturation vapor pressure P0, which varies
with temperature only. On the other hand, adsorption is observed at gas pressure
values that are lower than P0.
The various thermodynamic models that have been proposed are grounded on
such considerations.
1.4.2. The Hill model
To take into account a system’s divariance, Hill deems it necessary to take
surface effects into consideration. With this aim in mind, he supposes that the
adsorption film, that is to say the adsorbent + adsorbed block, is easily assimilated to
a solution where the adsorbent is formed by the free sites on the solid’s surface, and
the adsorbed species are the gas molecules that have settled on those sites.
In this case, the possible variables are pressure, temperature and the quantities of
matter for the adsorbent (ns) and the adsorbed (na) species.
There are 2 independent components (adsorbent + adsorbed + gas – an
equilibrium relation between these three components).
There are 2 exterior parameters (P and T) and there are 2 phases (solid and
gaseous).
Thus, the variance v is:
v 1 3 2
2
We can therefore plot:
– isotherms na = f (P) where T = constant;
– isobars na = f (P) where P = constant;
– isosters P = f (T) where na = constant.
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