Adsorption and Diffusion in Nanoporous Materials, Second Edition PDF
Preview Adsorption and Diffusion in Nanoporous Materials, Second Edition
Adsorption and Diffusion in Nanoporous Materials Second Edition Adsorption and Diffusion in Nanoporous Materials Second Edition Rolando M.A. Roque-Malherbe Adsorption and Diffusion in Nanoporous Materials Second Edition Rolando M.A. Roque-Malherbe CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2018 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed on acid-free paper International Standard Book Number-13: 978-1-1383-0509-0 (Hardback) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmit- ted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright. com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging‑in‑Publication Data Names: Roque-Malherbe, Rolando M.A., author. Title: Adsorption and diffusion in nanoporous materials / Rolando M.A. Roque Malherbe. Description: Second edition. | Boca Raton : Taylor & Francis, 2018. | “A CRC title, part of the Taylor & Francis imprint, a member of the Taylor & Francis Group, the academic division of T&F Informa plc.” | Includes bibliographical references. Identifiers: LCCN 2017034428 | ISBN 9781138305090 (hardback : alk. paper) Subjects: LCSH: Porous materials. | Nanostructured materials. | Diffusion. | Adsorption. Classification: LCC TA418.9.P6 R67 2018 | DDC 620.1/16--dc23 LC record available at https://lccn.loc.gov/2017034428 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2018 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business Dedication No claim to original U.S. Government works Printed on acid-free paper International Standard Book Number-13: 978-1-1383-0509-0 (Hardback) This book is dedicated to my wife Teresa Fernandez-Mardones, This book contains information obtained from authentic and highly regarded sources. Reasonable efforts my parents Silvia Malherbe Peña and Rolando Roque-Fernandez, have been made to publish reliable data and information, but the author and publisher cannot assume our sons Daniel Dorr-Fernandez, Edelin Roque-Mesa, Rolando responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to Roque-Mesa and Ruben Alcides Perez-Fernandez, our grandsons copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. and all my Pets very specially to Zeolita and Trosia. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmit- ted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright. com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging‑in‑Publication Data Names: Roque-Malherbe, Rolando M.A., author. Title: Adsorption and diffusion in nanoporous materials / Rolando M.A. Roque Malherbe. Description: Second edition. | Boca Raton : Taylor & Francis, 2018. | “A CRC title, part of the Taylor & Francis imprint, a member of the Taylor & Francis Group, the academic division of T&F Informa plc.” | Includes bibliographical references. Identifiers: LCCN 2017034428 | ISBN 9781138305090 (hardback : alk. paper) Subjects: LCSH: Porous materials. | Nanostructured materials. | Diffusion. | Adsorption. Classification: LCC TA418.9.P6 R67 2018 | DDC 620.1/16--dc23 LC record available at https://lccn.loc.gov/2017034428 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com Contents Preface......................................................................................................................xv Author .....................................................................................................................xix Chapter 1 Statistical Physics .................................................................................1 1.1 Introduction .............................................................................1 1.1.1 Thermodynamic Functions and Their Relationships ..........................................................1 1.2 Definition of Quantum State–Microstate and Thermodynamic State–Macrostate .........................................3 1.3 Definition of Ensemble ............................................................4 1.4 The Canonical Ensemble ........................................................5 1.5 Evaluation of α and β for the Canonical Ensemble ................7 1.6 The Grand Canonical Ensemble .............................................9 1.7 Evaluation of α, β, and γ for the Grand Canonical Ensemble ...............................................................................10 1.8 Canonical Partition Function for a System of Noninteracting Particles ........................................................12 1.9 Factorization of the Molecular Partition Function ................14 1.10 Density Functional Theory ...................................................16 1.11 Thermodynamics of Irreversible Processes ..........................19 1.12 Statistical Mechanics of Irreversible Processes ....................22 1.12.1 Correlation Functions and Generalized Susceptibilities .......................................................22 1.12.2 Calculation of the Mean Square Displacement and the Self-Diffusion Coefficient .........................24 1.12.2.1 Calculation of the Mean Square Displacement with the Help of the Velocity Autocorrelation Function .....24 1.12.3 Brownian Motion Model Langevin Approach ......25 1.12.3.1 Diffusion Equation ..............................26 Appendix 1.1 Legendre Transformations ........................................29 Appendix 1.2 The Lagrange Multipliers .........................................30 Appendix 1.3 Methods of Counting ................................................31 Appendix 1.4 Calculus of Variations ................................................32 References ..........................................................................................33 vii viii Contents Chapter 2 Adsorption in Solid Surfaces .............................................................35 2.1 Introduction .............................................................................35 2.1.1 What Is the Meaning of the Term Adsorption ..........35 2.1.2 Phases along with Components Involved in the Adsorption Process ....................................................35 2.1.3 Porous Materials ........................................................36 2.2 Interfacial Layer, Gibbs Dividing Surface and Gibbs Adsorption ...............................................................................37 2.3 Gas–Solid Adsorption Thermodynamics................................39 2.3.1 Adsorption Interaction Fields ....................................39 2.3.2 Isosteric and Differential Heats of Adsorption .........40 2.3.3 Some Relations between Adsorption Macroscopic and Microscopic Parameters ................41 2.4 Adsorption in Porous Materials ..............................................42 2.4.1 Measurement of Adsorption Isotherms by the Volumetric Method ....................................................42 2.4.2 Characterization of Porous Materials by Adsorption Methods ..................................................43 2.5 Some Examples of the Application of the Volumetric Method ....................................................................................44 2.5.1 Volumetric Automatic Surface Area and Porosity Measurement Systems .................................44 2.5.2 Adsorption Isotherms of Nitrogen at 77 K in Zeolites ......................................................................45 2.5.3 Calorimetry of Adsorption of NH in AlPO -5 3 4 and FAPO-5 Molecular Sieves ..................................47 References ..........................................................................................48 Chapter 3 Assessment of Adsorption in Porous Adsorbents ..............................51 3.1 Introduction .............................................................................51 3.2 Dubinin Adsorption Isotherm .................................................51 3.3 Osmotic Adsorption Isotherm .................................................54 3.4 Langmuir and Fowler–Guggenheim-Type Adsorption Isotherm Equations .................................................................56 3.4.1 Application of the Grand Canonical Ensemble Methodology to Describe Adsorption in Zeolites .....56 3.4.2 Some Remarks in Relation with the Langmuir Type and Fowler–Guggenheim-Type Adsorption Isotherm Equations ....................................................60 3.5 The t-Plot Method ...................................................................63 3.6 Comments about Dubinin, Osmotic, Langmuir Type, Fowler–Guggenheim Type Isotherms, and the t-Plot Method ..................................................................................65 Contents ix 3.7 The Brunauer–Emmett–Teller Method ...................................68 3.8 Horvath–Kawazoe Method .....................................................72 References ..........................................................................................75 Chapter 4 Pore Size Distributions .......................................................................79 4.1 Introduction .............................................................................79 4.2 Capillary Condensation ...........................................................79 4.3 Macroscopic Theories to Describe Pore Condensation ...........82 4.3.1 The Kelvin–Cohan Equation .....................................82 4.3.2 The Derjaguin–Broekhoff-de Boer Theory ..............87 4.3.3 Some Concluding Remarks about the Macroscopic Theories to Describe Pore Condensation .............................................................89 4.4 Density Functional Theory .....................................................89 4.4.1 The Density Functional Theory Methodology in General ......................................................................89 4.4.2 Calculation of the Pore Size Distribution ..................90 4.4.3 The Nonlocal Density Functional Theory for the Description of Adsorption in Slit Pores, Cylindrical Pores, and Spherical Cavities .................91 4.4.4 Some Concluding Remarks about the Molecular Models to Describe Adsorption .................................98 References ........................................................................................100 Chapter 5 Molecular Transport in Porous Media .............................................103 5.1 Introduction ...........................................................................103 5.2 Fick’s Laws ............................................................................103 5.3 Transport, Self, and Corrected Diffusion Coefficients .........105 5.3.1 Transport Diffusion and Self Diffusion ..................105 5.3.2 Interdiffusion and the Frame of Reference for Porous Materials ......................................................105 5.3.3 Transport D, Corrected D , Diffusion 0 Coefficients along with Their Relations ..................106 5.3.4 Transport D, Corrected D , Self-Coefficients in 0 Zeolites along with Their Relations ........................107 5.4 Mean Square Displacement, the Random Walker, and Gaseous Diffusion .................................................................108 5.4.1 The Mean Square Displacement .............................108 5.4.2 Gaseous Diffusion and the Random Walker ...........109 5.5 Transport Mechanisms in Porous Media ..............................110 5.6 Viscous, Knudsen, and Transition Flows ..............................112 5.7 Viscous and Knudsen Flows in Model Porous Systems .......114 5.7.1 Viscous Flow in a Straight Cylindrical Pore ...........114 5.7.2 Knudsen Flow in a Straight Cylindrical Pore .........114
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