Powder Surface Area and Porosity

Transcription

1 Powder Surface Area and Porosity

2 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 ( X), 832 pages Powder Surface Area and Porosity S. Lowell and Joan E. Shields 3rd edn, hardback ( ), 256 pages Pneumatic Conveying of Solids R.D. Marcus, L.S. Leung, G.E. Klinzing and F. Rizk Hardback ( ), 592 pages Particle Technology Hans Rumpf Translated by F.A. Bull Hardback ( ), 216 pages

3 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.

4 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 S. Lowell and J.E. Shields Originally published by Chapman and Hall in Softcover reprint of the hardcover 1 st edition 1991 Typeset in 1O/12pt Times by Best-set Typesetter Ltd, Hong Kong ISBN ISBN (ebook) DOI / 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) An introduction to powder characterization. 1. Powders I. Title Library of Congress Cataloging-in-Publication Data available

5 Contents Preface Symbols x xi PART 1 THEORETICAL 1 1 Introduction Real surfaces Factors affecting surface area Surface area from particle size distributions 5 2 Gas adsorption Introduction Physical and chemical adsorption Physical adsorption forces 9 3 Adsorption isotherms 11 4 Langmuir and BET theories (kinetic isotherms) The Langmuir isotherm, Type I The Brunauer, Emmett, and Teller (BET) theory Surface areas from the BET equation The meaning of monolayer coverage The BET constant and site occupancy Applicability of the BET theory Some criticism of the BET theory 27 5 The single point BET method Derivation of the single point method Comparison of the single point and multipoint methods Further comparisons of the multi- and single point methods 32 6 Adsorbate cross-sectional areas Cross-sectional areas from the liquid molar volume Nitrogen as the standard adsorbate Some adsorbate cross-sectional areas 41

6 vi Contents 7 Other surface area methods Harkins and Jura relative method Harkins and Jura absolute method Permeametry 46 8 Pore analysis by adsorption The Kelvin equation Adsorption hysteresis Types of hysteresis Total pore volume Pore size distributions Modelless pore size analysis V-tcurves 68 9 Microporosity Introduction Langmuir plots for microporous surface area Extensions of Polanyi's theory for micropore volume and area The t-method The as-method The micropore analysis method Total micropore volume and surface area Theory of wetting and capillarity for mercury porosimetry Introduction Young and Laplace equation Wetting or contact angles Capillarity Washburn equation Interpretation of mercury porosimetry data Applications of the Washburn equation Intrusion-extrusion curves Common features of porosimetry curves Solid compressibility Surface area from intrusion curves Pore size distribution Volume In radius distribution Pore surface area distribution Pore length distribution Pore population Plots of porosimetry functions Comparisons of porosimetry and gas adsorption 119

7 Contents vii 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 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 PART 2 EXPERIMENTAL Adsorption measurements - preliminaries Reference standards Other preliminary precautions Representative samples Sample conditioning 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 Dynamic methods Influence of helium

8 viii Contents 16.2 Nelson and Eggertsen continuous flow method Carrier gas and detector sensitivity Design parameters for continuous flow apparatus Signals and signal calibration Adsorption and desorption isotherms by continuous flow Low surface area measurements Data reduction - continuous flow Single point method Other flow methods Pressure jump method Continuous isotherms Frontal analysis Gravimetric method Electronic micro balances Buoyancy corrections Thermal transpiration Other gravimetric methods Comparison of experimental adsorption methods Chemisorption Introduction Chemisorption equilibrium and kinetics Chemisorption isotherms Surface titrations Mercury porosimetry Introduction Pressure generators Dilatometer Continuous scan porosimetry Logarithmic signals from continuous scan porosimetry Low-pressure intrusion-extrusion scans Contact angle for mercury porosimetry Density measurement True density Apparent density Bulk density Tap density Effective density Density by Mercury porosimetry 232

9 Particle size analysis Introduction Sample preparation Sedimentation fluid Dispersion Data reduction Contents ix References Index

10 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

11 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

12 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