Powder Surface Area and Porosity

Transcription

1 Powder Surface Area and Porosity

2 Powder Technology Series Edited by B. Scarlett Department of Chemical Engineering University of Technology Loughborough

3 Powder Surface Area and Porosity S. Lowell PhD Quantachrome Corporation, USA Joan E. Shields PhD C. w. Post Center of Long Island University and Quantachrome Corporation, USA Second Edition LONDON NEW YORK CHAPMAN AN D HALL

4 First published 1979 as Introduction to Powder Surface Area by John Wiley & Sons, Inc., New York Second edition 1984 published by Chapman and Hall Ltd 11 New Fetter Lane, London EC4P 4EE Published in the USA by Chapman and Hall 733 Third Avenue, New York NYlOOl S. Lowell and J. E. Shields Softcover reprint of the hardcover 2nd edition 1984 ISBN-13: e-isbn-13: DOl: / All rights reserved. No part of this book may be reprinted, or reproduced or utilized in any form or by any electronic, mechanical or other means, now known or hereafter invented, including photocopying and recording, or in any information storage and retrieval system, without permission in writing from the Publisher. British Library Cataloguing in Publication Data Lowell, S. Powder surface area and porosity.-2nd ed. (Powder technology series) 1. Powders-Surfaces 2. Surfaces-Areas and volumes 1. Title II. Shields, Joan E. III. Lowell, S. Introduction to powder surface area IV. Series 620'.43 TA Library of Congress Cataloging in Publication Data Lowell, S. (Seymour), Powder surface area and porosity. (powder technology series) Rev. ed. of: Introduction to powder surface area Bibliography: p. Includes index. 1. Powders. 2. Surfaces-Areas and volumes. 3. Porosity. 1. Shields, Joan E. II. Lowell, S. (Seymour), Introduction to powder surface area. III. Title. IV. Series. TA L '

5 Contents Preface List of symbols xi xii PART I THEORETICAL 1 1 Introduction Real surfaces Factors affecting surface area Surface area from size distributions 5 2 Gas adsorption Introduction Physical and chemical adsorption Physical adsorption forces 10 3 Adsorption isotherms 11 4 Langmuir and BET theories 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 28 5 The single point BET method Derivation of the single-point method 30 v

6 vi Contents 5.2 Comparison of the single-point and multipoint methods Further comparisons of the multi- and single-point methods 32 6 Adsorbate cross-sectional areas 36 6.l Cross-sectional areas from the liquid molar volume Nitrogen as the standard adsorbate Some adsorbate cross-sectional areas 42 7 Other surface area methods 44 7.l Harkins and Jura relative method Harkins and Jura absolute method Permeametry 48 8 Pore analysis by adsorption The Kelvin equation Adsorption hysteresis Types of hysteresis Total pore volume Pore-size distributions Modelless pore-size analysis V-t curves 71 9 Microporosity 75 9.l Introduction Langmuir plots for microporous surface area Extensions of Polanyi's theory for micropore volume and area The t-method The MP method Total micropore volume and surface area Theory of wetting and capillarity for mercury porosimetry Introduction Young and Laplace equation 89

7 10.3 Wetting or contact angles Capillarity Washburn equation Interpretation of mercury porosimetry data Application 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 function Pore surface area distribution Pore length distribution Pore population Plots of porosimetry functions Comparisons of porosimetry and gas adsorption 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 132 PART II EXPERIMENTAL Adsorption measurements - Preliminaries Reference standards Other preliminary precautions Representative samples Sample conditioning Vacuum volumetric measurements Nitrogen adsorption 147

8 viii Contents 14.2 Deviation from ideality Sample cells Evacuation and outgassing Temperature control Isotherms Low surface areas Saturated vapor pressure, Po of nitrogen Dynamic methods Influence of helium 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 203

9 Contents 20 Mercury porosimetry Introduction Pressure generators Dilatometer Continuous-scan porosimetry Logarithmic signals from continuous-scan porosimetry Low pressure intrusion-extrusion scans Scanning porosimetry data reduction Contact angle for mercury porosimetry Density measurement True density Apparent density Bulk density Tap density Effective density Density by mercury porosimetry 221 References 225 Index 232 ix

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 and density of powders. It may be found useful by those with little or no training in solid surfaces who have the need to quickly learn the rudiments of surface area, density and pore-size measurements. Syosset, New York May, 1983 S. Lowell J. E. Shields Xl

11 List of symbols Use of symbols for purposes other than those indicated in the following list are so defined in the text. Some symbols not shown in this list are defined in the text. d adsorbate cross-sectional area A area; condensation coefficient; collision frequency C BET constant c concentration D diameter; coefficient of thermal diffusion E adsorption potential f permeability aspect factor F flow rate; force; feed rate 9 gravitational constant G Gibbs free energy GS free surface energy h heat of immersion per unit area; height H enthalpy Hi heat of immersion Hsv heat of adsorption BET intercept; filament current k thermal conductivity; specific reaction rate K Harkins-Jura constant I length L heat of liquefaction M mass M molecular weight n number of moles N number of molecules; number of particles N Avagadro's number.ai molecular collisions per square cm per sec xii

12 List of symbols P pressure Po saturated vapor pressure p porosity psla pounds per square inch absolute pslg pounds per square inch gauge r radius r k core radius r p pore radius r 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 Wm monolayer weight X mole fraction r:x temperature coefficient {3 affinity coefficient, nonideality correction; compressibility y surface tension r[ viscosity e contact angle eo fraction of surface unoccupied by adsorbate en fraction of surface covered by n layers of adsorbate fj.m micrometers (1O-6m) v vibrational frequency n surface pressure p density 1: monolayer depth; time per revolution; time for one cycle '" change in particle diameter per collector per revolution xiii