Surface Area and Porosity Determinations by Physisorption: Measurements and Theory

297 Pages·2006·2.92 MB·English

by  James B. Condon

Surface Area and Porosity
Determinations by Physisorption
Measurements and Theory
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Surface Area and Porosity
Determinations by Physisorption
Measurements and Theory
James B. Condon
Professor of Chemistry
Roane State Community College
Harriman, TN 37748-5011
USA
Amsterdam ● Boston ● Heidelberg ● London ● New York ● Oxford
Paris ● San Diego ● San Francisco ● Singapore ● Sydney ● Tokyo
iii
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First edition 2006
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Library of Congress Cataloging-in-Publication Data
Condon,James B.
Surface area and porosity determinations by physisorption :measurements and theory /
James B. Condon. – 1st ed.
p. cm.
Includes bibliographical references and index.
Includes index.
ISBN-13:978-0-444-51964-1
ISBN-10:0-444-51964-5
1. Physisorption. 2. Porosity. 3. Surfaces,Isothermic. 4. Density functionals. 5. Adsorption. I. Title.
QD547.C65 2006
541’.335-dc22 2006043711
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
For information on all Elsevier publications
visit our website at books.elsevier.com
Printed and bound in The Netherlands
06 07 08 09 10 10 9 8 7 6 5 4 3 2 1
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Table of Contents
Foreword..............................................................................................................xi
Acknowledgments..............................................................................................xv
Symbol List......................................................................................................xvii
CHAPTER 1:AN OVERVIEW OF PHYSISORPTION
Introduction Scope and Terminology ..................................................................1
General Description of Physisorption ................................................................1
Measuring the Surface Area by Physisorption ....................................................4
Preliminary Analysis ..........................................................................................6
The Adsorption Isotherm Types ......................................................................6
Characterization of Hysteresis Loops ............................................................11
Measuring the Surface Area from the Isotherm ................................................14
Determining Porosity by Physical Adsorption ..................................................16
Micropores ....................................................................................................16
Mesopores ......................................................................................................18
Obtaining Pore Radius from the Two Slopes ............................................19
The Use of the Kelvin Equation Value of r for Mesopores ....................21
p
Macropores ................................................................................................21
Statistical Treatment of Isotherms ....................................................................21
Adsorption Types in Standard Isotherm Transformations ................................23
References..........................................................................................................26
v
vi Table of Contents
CHAPTER 2:MEASURING THE PHYSISORPTION ISOTHERM
Introduction: Equipment Requirements ............................................................29
The Volumetric Method ....................................................................................30
Equipment Description ..................................................................................30
Determination Method ..................................................................................32
Error Analysis for the Volumetric Method ....................................................34
Design Errors ............................................................................................34
Poor Calibration of V ..............................................................................35
1
Molecular Flow Versus Viscous Flow ......................................................35
Equation of State Errors ............................................................................37
Temperature Control of the Sample ..........................................................37
Limit of Detection ....................................................................................37
Advantages and Disadvantages of the Volumetric Technique ......................38
The Gravimetric Method ..................................................................................38
Equipment Description ..................................................................................38
Determination Method ..................................................................................41
Error Analysis for the Gravimetric Technique ..............................................42
Advantages and Disadvantages of the Gravimetric Technique ....................43
General Error Analysis – Common to both Volumetric and Gravimetric ........44
Pressure and Temperature Measurements ....................................................44
Kinetic Problems ..........................................................................................46
Sample Density Problems ..............................................................................46
Calorimetric Techniques ....................................................................................47
Adiabatic Calorimetry ..................................................................................47
Measuring the Isosteric Heat of Adsorption ..................................................48
The Thermal “Absolute” Method ..................................................................49
Differential Scanning Calorimetry ................................................................50
Flow Method or Carrier Gas Method ................................................................51
References..........................................................................................................52
CHAPTER 3:INTERPRETING THE PHYSISORPTION ISOTHERM
Objectives in Interpreting Isotherms ................................................................55
Determination of Surface Area from Isotherms ................................................59
The BET Analysis ........................................................................................60
Table of Contents vii
(cid:1) Plot Analysis ..............................................................................................62
The Method of Determining Surface Area by Dubinin et al. ........................63
Tóth T-Equation Isotherm ............................................................................63
The Harkins–Jura Absolute/Relative Method ..............................................64
Porosity Determinations from the Isotherm ......................................................65
Micropore Analysis ......................................................................................66
Mesoporosity Analysis ..................................................................................68
Isotherm Fits which Yield Relative Numbers for the Surface Area ..................72
Langmuir Isotherm ........................................................................................72
Freundlich Isotherm ......................................................................................74
Polanyi Formulations ....................................................................................75
deBoer–Zwikker Formulation ......................................................................76
The Frenkel, Halsey, Hill (FHH) Isotherm ..................................................76
Analysis Using Standard Isotherms ..............................................................77
Standard Isotherms ........................................................................................78
The (cid:1)-Curve Standard (see Sing, Everett and Ottewill [6]) ..................78
s
The t-Curve ..............................................................................................78
IUPAC Standards on Silica and Carbon ................................................80
RMBM Carbon Standard ........................................................................82
KFG Segmented Standard Carbon Curve ..............................................84
Cranston and Inkley Standard for Pore Analysis ....................................84
Thoria Standard Curves ..........................................................................85
Standard Curves for Lunar Soil ..............................................................86
References..........................................................................................................89
CHAPTER 4:THEORIES BEHIND THE CHI PLOT
Introduction: Historical Background ................................................................91
Theory Behind (cid:1) Plots ......................................................................................91
The Disjoining Pressure Derivation ..............................................................91
The Meaning of Γ in the Hard Sphere Model ..............................................93
m
The Quantum Mechanical Derivation of the “Simple” (cid:1) Equation ..............95
The Meaning of a – the Perfect Adsorption Equation for
ex
Hard Spheres ............................................................................................98
The Energy Correction ..................................................................................99
Simultaneous Physisorption and Chemisorption ............................................102
viii Table of Contents
Heterogeneous Surfaces ..................................................................................104
Additivity of (cid:1) Plots ....................................................................................104
Insensitivity for (cid:1) (cid:1) max (cid:1) ........................................................................107
c
Reformulation for a Distribution of E Values ............................................107
a
Heats of Adsorption ........................................................................................108
Isosteric Heat of Adsorption, q ..................................................................108
st
The Integral Heats of Adsorption ................................................................109
Adsorption of more than One Adsorbate ........................................................111
Binary Adsorption on a Flat Surface ..........................................................112
Depth Profiles and (cid:1)Theory ..........................................................................116
The Thermodynamics of the Spreading Pressure ............................................119
Gibbs’Phase Rule in Systems with Surfaces ..............................................119
Derivation of the Spreading Pressure ..........................................................120
Is the (cid:1) Plot Compatible with the Freundlich and Dubinin
Isotherms? ..............................................................................................123
References........................................................................................................125
CHAPTER 5:COMPARISON OF THE CHI EQUATION TO
MEASUREMENTS
Comparsion to Standard Isotherms ................................................................127
The (cid:1)–s Standard Plots ................................................................................127
Cranston and Inkley Standard t Curve ......................................................128
deBoer’s Standard t-Plots ............................................................................129
Standard Thoria Plots ..................................................................................130
Standard Curves for Lunar Soils ................................................................134
Isotherms by Nicolan and Teichner ............................................................136
Isotherms Quoted by Bradley ......................................................................136
Conclusion and some Comments about Carbon ........................................138
The Observation of (cid:1) ......................................................................................140
c
Observations of the Energy Implications of (cid:1) ..........................................141
c
Direct Observation of (cid:1) ..............................................................................143
c
Conclusion Concerning (cid:1) ..........................................................................148
c
Multiplane Adsorption ....................................................................................149
Examples of Two Plane Adsorption ............................................................149
Table of Contents ix
The Freundlich, Dubinin-Polanyi and Tóth Isotherms ................................150
Conclusion Concerning Multiple Energies ................................................154
Heat of Adsorption ..........................................................................................154
Adsorption of more than One Adsorbate ........................................................156
Adsorption on Non-Porous Surface ............................................................156
Binary Adsorption in Micropores ................................................................158
Lewis Rule Assumption ........................................................................158
Binary Adsorption at a Constant Pressure ............................................160
Comparison to Experiments ..................................................................161
Conclusions Regarding Binary Adsorption ................................................165
Statistical Comparisons of other Isotherms to the (cid:1) Plot ................................165
General Conclusions ........................................................................................167
References........................................................................................................168
CHAPTER 6:POROSITY CALCULATIONS
Introduction ....................................................................................................171
Micropore Analysis ........................................................................................172
The BDDT Equation ....................................................................................172
The DR and DA Equations ..........................................................................174
Standard Curve Analysis using Distributions – Uninterpreted ..................175
Chi Theory Interpretation of the Distribution Fit ........................................180
Surface Areas and Pore Volume Calculations ......................................180
Calculation of Pore Size Assuming a Geometry ..................................181
Calculating r from (cid:2)(cid:1) ........................................................................181
p p
Examples of Results ..............................................................................182
Analysis of Mesoporosity ................................................................................186
Some Comments about the Standard Plot of Determining Mesoporosity ..187
The Broekhoff—deBoer Theory ................................................................189
Is it Microporous or Mesoporous and Does it Matter? ..................................196
Combined Mesopore/Micropore Equation ..................................................196
The Interpretation of Mesopore Equation using Standard Curve ..............197
The Boundary between Mesopores and Micropores ..................................198