Powder Surface Area and Porosity
Powder Technology Series EDITED BY BRIAN SCARLETI Delft University of Technology The Netherlands Many materials exist in the form of a disperse system, for example powders, pastes, slurries, emulsions and aerosols. The study of such systems necessarily arises in many technologies but may alternatively be regarded as a separate subject which is concerned with the manufacture, characterization and manipulation of such systems. Chapman and Hall were one of the first publishers to recognize the basic importance of the subject, going on to instigate this series of books. The series does not aspire to define and confine the subject without duplication, but rather to provide a good home for any book which has a contribution to make to the record of both the theory and the application of the subject. We hope that all engineers and scientists who concern themselves with disperse systems will use these books and that those who become expert will contribute further to the series. Particle Size Measurement T. Allen 4th edn, hardback (041235070 X), 832 pages Powder Surface Area and Porosity S. Lowell and Joan E. Shields 3rd edn, hardback (0412396904), 256 pages Pneumatic Conveying of Solids R.D. Marcus, L.S. Leung, G.E. Klinzing and F. Rizk Hardback (0 412 21490 3), 592 pages Particle Technology Hans Rumpf Translated by F.A. Bull Hardback (0 412 35230 3), 216 pages
Powder Surface Area and Porosity S. LOWELL Quantachrome Corporation, USA JOAN E. SHIELDS c. w. Post Campus of Long Island University, USA THIRD EDITION Springer-Science+Business Media, B.V.
First edition 1979 published as Introduction to Powder Surface Area by John Wiley & Sons Inc., New York Second edition 1984 published as Powder Surface Area and Porosity by Chapman and Hall Ltd Third edition 1991 1984,1991 S. Lowell and J.E. Shields Originally published by Chapman and Hall in 1991. Softcover reprint of the hardcover 1 st edition 1991 Typeset in 1O/12pt Times by Best-set Typesetter Ltd, Hong Kong ISBN 978-90-481-4005-3 ISBN 978-94-015-7955-1 (ebook) DOI 10.1007/978-94-015-7955-1 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the UK Copyright Designs and Patents Act, 1988, this publication may not be reproduced, stored or transmitted, in any form or by any means, without the prior permission in writing of the publishers, or in the case of repro graphic reproduction only in accordance with the terms of the licences issued by the Copyright Licensing Agency in the UK, or in accordance with the terms of licences issued by the appropriate Reproduction Rights Organization outside the UK. Enquiries concerning reproduction outside the terms stated here should be sent to the publishers at the UK address printed on this page. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. British Library Cataloguing in Publication Data Lowell, S. (Seymour) -1931- An introduction to powder characterization. 1. Powders I. Title 620.43 Library of Congress Cataloging-in-Publication Data available
Contents Preface Symbols x xi PART 1 THEORETICAL 1 1 Introduction 3 1.1 Real surfaces 3 1.2 Factors affecting surface area 3 1.3 Surface area from particle size distributions 5 2 Gas adsorption 7 2.1 Introduction 7 2.2 Physical and chemical adsorption 8 2.3 Physical adsorption forces 9 3 Adsorption isotherms 11 4 Langmuir and BET theories (kinetic isotherms) 14 4.1 The Langmuir isotherm, Type I 14 4.2 The Brunauer, Emmett, and Teller (BET) theory 17 4.3 Surface areas from the BET equation 22 4.4 The meaning of monolayer coverage 23 4.5 The BET constant and site occupancy 24 4.6 Applicability of the BET theory 25 4.7 Some criticism of the BET theory 27 5 The single point BET method 30 5.1 Derivation of the single point method 30 5.2 Comparison of the single point and multipoint methods 31 5.3 Further comparisons of the multi- and single point methods 32 6 Adsorbate cross-sectional areas 35 6.1 Cross-sectional areas from the liquid molar volume 35 6.2 Nitrogen as the standard adsorbate 38 6.3 Some adsorbate cross-sectional areas 41
vi Contents 7 Other surface area methods 42 7.1 Harkins and Jura relative method 42 7.2 Harkins and Jura absolute method 44 7.3 Permeametry 46 8 Pore analysis by adsorption 52 8.1 The Kelvin equation 52 8.2 Adsorption hysteresis 55 8.3 Types of hysteresis 56 8.4 Total pore volume 58 8.5 Pore size distributions 59 8.6 Modelless pore size analysis 65 8.7 V-tcurves 68 9 Microporosity 72 9.1 Introduction 72 9.2 Langmuir plots for microporous surface area 72 9.3 Extensions of Polanyi's theory for micropore volume and area 73 9.4 The t-method 77 9.5 The as-method 84 9.6 The micropore analysis method 85 9.7 Total micropore volume and surface area 88 10 Theory of wetting and capillarity for mercury porosimetry 90 10.1 Introduction 90 10.2 Young and Laplace equation 91 10.3 Wetting or contact angles 93 10.4 Capillarity 94 10.5 Washburn equation 96 11 Interpretation of mercury porosimetry data 99 11.1 Applications of the Washburn equation 99 11.2 Intrusion-extrusion curves 100 11.3 Common features of porosimetry curves 103 11.4 Solid compressibility 104 11.5 Surface area from intrusion curves 105 11.6 Pore size distribution 107 11.7 Volume In radius distribution 110 11.8 Pore surface area distribution 110 11.9 Pore length distribution 111 11.10 Pore population 111 11.11 Plots of porosimetry functions 112 11.12 Comparisons of porosimetry and gas adsorption 119
Contents vii 12 12.1 12.2 12.3 12.4 12.5 12.6 12.7 Hysteresis, entrapment and contact angle Introduction Contact angle changes Porosimetric work Theory of porosimetry hysteresis Pore potential Other hysteresis theories Equivalency of mercury porosimetry and gas adsorption 121 121 123 124 126 127 130 131 13 13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9 13.10 Particle size Introduction Stokes'law X-ray absorption Particle size distributions Reynolds number Particle porosity and density Wall effects Particle concentration Diffusion effects Terminal velocity 135 135 135 137 138 141 142 142 143 144 150 PART 2 EXPERIMENTAL 153 14 14.1 14.2 14.3 14.4 Adsorption measurements - preliminaries Reference standards Other preliminary precautions Representative samples Sample conditioning 155 155 156 156 160 15 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9 15.10 Vacuum volumetric measurements Nitrogen adsorption Deviations from ideality Sample cells Evacuation and degassing Temperature control Isotherms Low surface areas Saturated vapor pressure Automated instrumentation Quasi-equilibrium systems 162 162 165 165 165 166 166 168 170 171 171 16 16.1 Dynamic methods Influence of helium 174 174
viii Contents 16.2 Nelson and Eggertsen continuous flow method 175 16.3 Carrier gas and detector sensitivity 177 16.4 Design parameters for continuous flow apparatus 180 16.5 Signals and signal calibration 185 16.6 Adsorption and desorption isotherms by continuous flow 188 16.7 Low surface area measurements 189 16.8 Data reduction - continuous flow 193 16.9 Single point method 194 17 Other flow methods 197 17.1 Pressure jump method 197 17.2 Continuous isotherms 198 17.3 Frontal analysis 198 18 Gravimetric method 202 18.1 Electronic micro balances 202 18.2 Buoyancy corrections 202 18.3 Thermal transpiration 204 18.4 Other gravimetric methods 204 19 Comparison of experimental adsorption methods 206 20 Chemisorption 210 20.1 Introduction 210 20.2 Chemisorption equilibrium and kinetics 210 20.3 Chemisorption isotherms 212 20.4 Surface titrations 215 21 Mercury porosimetry 217 21.1 Introduction 217 21.2 Pressure generators 217 21.3 Dilatometer 218 21.4 Continuous scan porosimetry 218 21.5 Logarithmic signals from continuous scan porosimetry 221 21.6 Low-pressure intrusion-extrusion scans 222 21.7 Contact angle for mercury porosimetry 223 22 Density measurement 227 22.1 True density 227 22.2 Apparent density 230 22.3 Bulk density 230 22.4 Tap density 231 22.5 Effective density 231 22.6 Density by Mercury porosimetry 232
23 23.1 23.2 23.3 23.4 23.5 Particle size analysis Introduction Sample preparation Sedimentation fluid Dispersion Data reduction Contents ix 235 235 235 238 238 239 References Index 243 248
Preface The rapid growth of interest in powders and their surface properties in many diverse industries prompted the writing of this book for those who have the need to make meaningful measurements without the benefit of years of experience. It is intended as an introduction to some of the elementary theory and experimental methods used to study the surface area, porosity, density, and particle size of powders. It may be found useful by those with little or no training in solid surfaces who have the need to learn quickly the rudiments of surface area, density, pore size, and particle size measurements. S. Lowell J.E. Shields
Symbols Use of symbols for purposes other than those indicated in the following table are so defined in the text. Some symbols not shown in the table are also defined in the text. d A C c D E f F g G G S h H Hi Hsv k K C L M M MPa n N N.AI" P Po P PSIA adsorbate cross-sectional area area; condensation coefficient; collision frequency BET constant concentration diameter; coefficient of thermal diffusion adsorption potential permeability aspect factor flow rate; force; feed rate gravitational constant Gibbs free energy free surface energy heat of immersion per unit area; height enthalpy heat of immersion heat of adsorption BET intercept; filament current thermal conductivity; specific reaction rate Harkins-Jura constant length heat of liquefaction mass molecular weight megapascals number of moles number of molecules; number of particles Avogadro's num'ber molecular collisions per square cm per second pressure saturated vapor pressure porosity pounds per square inch absolute
xii Symbols PSIG pounds per square inch gauge, radius 'k core radius 'p pore radius 'h hydraulic radius R gas constant; resistance s BET slope S specific surface area; entropy St total surface area t time; statistical depth T absolute temperature U pore potential v linear flow velocity; settling velocity V volume V molar volume Vp pore volume W work; weight W m monolayer weight X mole fraction a temperature coefficient ~ affinity coefficient, nonideality correction; compressibility y surface tension 11 viscosity e contact angle eo fraction of surface unoccupied by adsorbate en fraction of surface covered by n layers of adsorbate ~m micrometers (10-6 m) v vibrational frequency n surface pressure p density 1: monolayer depth; time per revolution; time for one cycle 'I' change in particle diameter per collector per revolution