Surface Area and Porosity Determinations by Physisorption: Measurement, Classical Theories and Quantum Theory

437 Pages·2019·17.799 MB·English

by  James B. Condon

Surface Area
and Porosity
Determinations by
Physisorption
Surface Area
and Porosity
Determinations by
Physisorption
Measurement, Classical Theories
and Quantum Theory
Second Edition
James B. Condon
Elsevier
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README first—Organization
of this book
Thisbookisorganizedwiththemostrudimentarymaterialatthebeginningandcon-
tinueswiththemoresophisticatedmaterialattheend.Inthissenseitcouldbecon-
sidered a textbook, and in fact it was originally designed to be such. As with all
textbooks, it is not recommended to start reading in the middle, or to use material
atthebeginningtodocomplexanalysisthatisdescribedlaterinthebook.Forexam-
ple,itwouldbeill-advisedtotrytodoporesizedistributioncalculationsbysimply
skipping to Chapter 6 without the background information about the quantum
mechanically (QM) derived χ (ESW) theory.1 It would also not be very accurate
to use only the standard curve method to determine porosity, although this might
be useful.(This would be taking advantage of the fact that the χ theory breaks the
dependenceofthestandardcurvemethoduponamatchingnon-porousstandard,thus
gettingaroundtheproblemthatitisnearlyimpossibletofindamatchingnon-porous
sample.)Thus,ifyouonlyreadenoughofthisbooktousetheχtheoryinthestandard
curve method, then this will not be sufficient today to publish your analysis in the
open literature.
Myadvice,ifyouonlywanttousetheQMderivedχtheory,istoskiptheportions
ofthebookthatdealwiththeoldertheoriesandjuststudytherelevantχtheorysec-
tions. Furthermore, if you are uneasy regarding QM, then simply trust the final χ
equationthatisderivedandskiptheQMportion.(Whenyougettothispoint,there
is a note telling you todo this.)
1Theχtheory(inafewreportslistedas“CFS”),theAutoShieldingPhysisorption(ASP)theory,the
DisjoiningPressureTheory,andtheExcessSurfaceWork(ESW)theoryareallfundamentallythe
sametheory,andwillusuallybereferredtoassimplyχtheory.Eachhasapproachedtheproblemfrom
adifferentviewpointbutendsupwiththesameisothermequation.Thismakesitproblematicifone
searchesusingkeywords,andonethereforeneedstousealloftheseterms.
xi
List of figures
Fig.1.1 Amodelofadsorptionofthe“in-register”type—e.g.
chemisorption,epitaxy. 6
Fig.1.2 Modelsoftwotypesofphysisorption:(A)gas-likeand
(B)liquid-like.●beforeencounter,(cid:1)afterencounter,
hatchedisduringencounter. 7
Fig.1.3 TypeIisotherm(asharperandb). 11
Fig.1.4 TypeIIisotherm(a!,boffset ). 11
Fig.1.5 TypeIIIisotherm. 12
Fig.1.6 TypeIVisotherm(anoloopandb). 12
Fig.1.7 TypeVisothermwithdesorptionnearlyvertical. 13
Fig.1.8 TypeVI(a)isotherm. 13
Fig.1.9 Anillustrationofwhythe“B”pointmethodisnot
reliable.Thepositionofthe“B”pointdependsupon
theabscissascaleused. 15
Fig.1.10 Asimulationillustratingtheinflectionpointmethod. 17
Fig.1.11 TypeH1hysteresisloop. 19
Fig.1.12 TypeH2hysteresisloop. 19
Fig.1.13 TypeH3hysteresisloop. 20
Fig.1.14 TypeH4hysteresisloop. 20
Fig.1.15 TypeIisothermexpressedasastandardplotoraχ
plot.AsimulationofanEadistributionhasbeenadded
here. 22
Fig.1.16 TypeIIisothermexpressedasastandardplotofaχ
plot.Noenergydistributionisassumed. 22
Fig.1.17 TypeIIIisothermexpressedasastandardplotorχ
plot.AsimulationofanEadistributionhasbeenadded
here. 23
Fig.1.18 TypeIVisothermexpressedasastandardplotorχ
plot. 23
Fig.1.19 TypeVisothermexpressedasastandardplotorχplot. 24
Fig.1.20 AstandardplotofanalternateVIAisotherm.Thisis
theresultoftwosurfaceswithdifferingEas. 24
Fig.1.21 NormalTypeVIisothermexpressedasastandardplot
orχ plot. 26
Fig.1.22 ThenormalisothermforthealternateTypeVI
isotherm(VIA).StepsduetodifferentEas. 27
Fig.1.23 Aχ plotorstandardplotofatypeIisotherm. 44
xiii
xiv List of figures
Fig.1.24 Databy(S-A,S-A,LR-R)illustratingthe“Log-Law,”
whichisoftenobserved. 47
Fig.1.25 Aχ plotorastandardplotofeitheraTypeIVorV
isotherm. 48
Fig.1.26 IllustrationofthedefinitionsorA areaofpore
o
opening,A outside“wall”areaexcludingA ,r pore
w o p
radius,lporelength,andA surfaceareaofthesides
p
ofthepores. 50
Fig.2.1 Schematicofthevolumetricsystem. 61
Fig.2.2 Adrawingofthegravimetricmethodsamplearea
showingthebafflearrangement. 70
Fig.2.3 Anoverviewofthesystemusedforthegravimetric
method. 71
Fig.2.4 Consequencesoferrorsintemperature
measurement/controlintheisotherm. 76
Fig.2.5 Aschematicofaliquidnitrogencooledadiabatic
calorimeter. 78
Fig.2.6 AschematicoftheHarkinandJuracalorimeterto
measurethesurfaceareaofapowder. 80
Fig.2.7 Aschematicofhowtheadsorbedfilmisdestroyed
whenthepowderisimmersedintheliquidphasethus
releasingitssurfaceenergy. 80
Fig.2.8 SchematicofthedifferentialcalorimeterbyRouquerol
etal. 82
Fig.2.9 ThevacuumflowsystemdevelopedbyArnold. 83
Fig.2.10 Suggestedarrangementforasamplechamber. 85
Fig.2.11 Schematicofthesignalobservedfortheflowsystem. 86
Fig.2.12 Thediffusion-sinksituationthatoneexpectsfromthe
isothermtypeshownontheright.Slabs1,2,3,etc.
arefilledcompletelyupton.beforethefrontmoves
f
on. 88
Fig.2.13 ThecontrastofaTypeIIIisothermwiththeTypeII.
Theunitstepfunctionisnotallowedbutrathersmall
incrementsofincreasehappensatthesametimethat
diffusionispresent. 89
Fig.3.1 Sometypicaladsorptionisothermfornon-porous
materialsillustratingtheproblemofidentifyingthe
“knee”duetoscaling. 96
Fig.3.2 ThetransformedBETplottodeterminesurfacearea
typicalofsilicamaterial.Linearrangeisassumedtobe
0.05to0.35ofP . 98
vap
List of figures xv
Fig.3.3 ThetransformedBETplotforanorganicmaterial.The
0.05–0.35rangeyieldsaverypoorlinearfit,thusa
highrangeshouldbeselected. 98
Fig.3.4 AlinearfittotheDRKrepresentationoftheadsorption
isothermforanon-poroussurface.Thefitcovers
about2/3oftheln2range. 99
Fig.3.5 Simulated2energyχ-plotandthemeaningoftheSs
andIs. 102
Fig.3.6 AschematicofthemethodusedforDFT(NLDFTand
QSDFT). 104
Fig.3.7 Modeloftheχ methodofanalysisforphysical
adsorptionisotherm. 105
Fig.3.8 AtypicaltypeIadsorptionofpossiblymicroporosity
isotherm. 110
Fig.3.9 Thetransformedplotusingastandardcurveto
changethexaxis. 110
Fig.3.10 Preliminaryparametersobtainedfromtheisothermto
analyzesurfaceareaandporosity. 113
Fig.3.11 ExamplesofLangmuirisothermsandtheposition
ofthe“knee”asitvarieswithadsorption
energy. 119
Fig.3.12 DatabyYahiaetal.ofCH onMgOat87.4Kasa
4
χ-plot. 139
Fig.4.1 Illustrationoftheerrormadebyassuminganinfinite
potentialwelldepthversusafinitepotentialwell
depth. 151
Fig.4.2 Diagramofthesurfacepotentialwellandtheenergy
definitions. 151
Fig.4.3 ASchematicofthelayeringoftheadsorbatemolecule
andthevacancies,v,demonstratinghowthe
adsorbedliquidstatedimensionsareexpandedinthe
planeoftheadsorbentbutnotinthenormaldirection. 166
Fig.4.4 Thearrangementofanadsorbatemolecule“rolling
over”anotherandthedistancesdefinedforthe
treatmentoftheenergycorrection. 167
Fig.4.5 Thefunctionalityofsurfaceexcessenergy,Φ(Γ),with
coverage,Γ. 172
Fig.4.6 Adsorbatemoleculesbetweentwoplatestoaccount
forthesizeoftheforcebetweenthem. 175
Fig.4.7 Adsorbatemoleculesbetweentwoplatestoaccount
forthesizeoftheforcebetweenthem. 175
xvi List of figures
Fig.4.8 χplotofN adsorbedonVulcanCwithtwoE straight
2 a
linefits. 178
Fig.4.9 χ plotN adsorbedonSterlingFTCwithtwoE
2 a
straightlinefits. 179
Fig.4.10 Chiplotofnitrogenadsorbedonhighfiredthoria
indicatingtwoenergiesofadsorptionandanother
featurebythemultiplestraightlinefits. 179
Fig.4.11 DependenceofcalculatedisostericheatfromtheBET
equationforvariousinputenergies. 184
Fig.4.12 Theindividualmonolayercoveragesforlayers1
through5. 191
Fig.4.13 Argondepthprofilesagainstahard-wallofan
unlimitedsurfacefilm. 192
Fig.4.14 Theprofilesoftheadsorbate“layers”asafunctionof
Δχ. 192
Fig.4.15 Simulatedprofilefittedtoanequation(insideline). 193
Fig.4.16 Densityprofileinaslitporewallsseparatedby10nm
at3Δχs 194
.
Fig.4.17 Densityprofileinacylindricalporewithr¼5nmat
3Δχs 195
.
Fig.4.18 Denistyprofileinacylindricalporewithr¼2nmat
3Δχs 195
.
Fig.4.19 Amplitudeofthefirstpeakasafunctionofthe
calculated. 196
Fig.4.20 Arnold’sadsoptivemixtureonanataseofO :
2
N ¼15%:85% 202
2 .
Fig.4.21 Arnold’sadsoptivemixtureonanataseofO :
2
N ¼30%:70% 202
2 .
Fig.4.22 Arnold’sadsoptivemixtureonanataseofO :
2
N ¼50%:50% 203
2 .
Fig.4.23 Arnold’sadsoptivemixtureonanataseofO :
2
N ¼30%:70% 203
2 .
Fig.4.24 Arnold’sadsoptivemixtureonanataseofO :
2
N ¼85%:15% 204
2 .
Fig.4.25 χ-plotsfortheadsorptionofpureN ,n,andO ,×,on
2 2
anatasebyArnold. 204
Fig.4.26 Acomparisonoftheχ theoryenergydistributionand
Dubinin-Polanyi(DP)distribution.DPkvaluesused
were,startingfromtheoutside,1,1.5,and2. 210
Fig.5.1 StandardtcurveconstructedbyCranstonandInkley.
Thedatapointbytheauthors.Thelineistheleast
squaresχ fit. 218
List of figures xvii
Fig.5.2 Standardt-curvedatabydeBoeretal.Thedataare
thecirclesandthelineistheχ plotleastsquaresfit. 219
Fig.5.3 AdsorptionofI onCaF showingtheχplotaccording
2 2
todeBoer. 219
Fig.5.4 AdsorptionofAronSnOaccordingtodeBoerand
Zwikker.Theroundoffintheupperportionisprobably
duetosomeporosity. 220
Fig.5.5 N onMgOaerosilaccordingtodeBoeretal. 220
2
Fig.5.6 N onNiantigoriteaccordingtodeBoeretal. 221
2
Fig.5.7 AronSiO dataα-splotasaχ plot.—istheleast
2
squaresfittoχ plot. 222
Fig.5.8 N onSiO dataα-splotasaχ plot.—istheleast
2 2
squaresfittoχ plot. 222
Fig.5.9 N adsorptiononthorianormalizedto0.4P/P . 224
2 vap
Fig.5.10 Aradsorptiononthorianormalizedto0.4P/P . 224
vap
Fig.5.11 Adsorptionofwaterat25°Cafterseveralprior
adsorptioncycles.Dataisnormalizedto0.4P/P . 225
vap
Fig.5.12 N adsorptiononlunarsoil. 226
2
Fig.5.13 Aradsorptiononlunarsoil. 226
Fig.5.14 COadsorptiononlunarsoil. 226
Fig.5.15 O adsorptiononlunarsoil. 227
2
Fig.5.16 N adsorptiononSiO byNicolanandTeichner. 228
2 2
Fig.5.17 AradsorptiononSiO byNicolanandTeichner. 228
2
Fig.5.18 N adsorptiononNiObyNicolanandTeichner. 229
2
Fig.5.19 AdsorptionofAronCuSO accordingtoBradley.Inset
4
isdataset#1. 229
Fig.5.20 AdsorptionofAronAl (SO ) accordingtoBradley.
2 43
Insetisdataset#1 230
Fig.5.21 GraphofBradley-derivedvan-Hoffplotto
determineq 231
st.
Fig.5.22 TheχplotrepresentationoftheadsorptionofSO on
2
SiO gelaccordingtoMcGavackandPatrick.Three
2
successiverunswithidenticalconditionsbutwith
differentsamples. 232
Fig.5.23 TheeffectwatercontaminationoftheSO atthree
2
levels.ItappearsthatthehighertheH Olevelthe
2
higheristheapparentE . 233
a
Fig.5.24 TheRMBMstandardα-scarboncurve. 234
Fig.5.25 E versustheenthalpyofformationofvariousoxides. 237
a
Fig.5.26 PcobservationfromdatabyGPGwithmicroporous
carbon. 238
xviii List of figures
Fig.5.27 DRplotoftheGPGdatashowingthedifference
betweeneithertheDRfitorthelog-lawfittothedata. 238
Fig.5.28 N onTakedaACFcarbonbyNguyenandDo.The
2
"dog-leg"isnotevidentbeforethethresholdpressure. 239
Fig.5.29 Aradsorptiononpolytetrafluoroethylene(Teflon®)
withthenormalP/P axisbyThompson.Inthis
vap
experimentthethresholdpressureisevidenteven
withouttransformingtoaχ plot. 241
Fig.5.30 χ plotofAradsorptiononpolytetrafluoroethylene
(Teflon®)byThompson.Theχ plotmakesthe
thresholdpressuremoreobvious. 242
Fig.5.31 Variousadsorptionisothermson
polytetrafluoroethylene(Teflon®)withN ,Ar,andO . 242
2 2
Fig.5.32 χplotofargonadsorptiononH cleaneddiamondby
2
Thompson. 243
Fig.5.33 NitrogenadsorptiononH cleanedalumina. 244
2
Fig.5.34 High-resolutionN adsorptionisothermsat77.4Kan
2
activatedcarbonLMA233onalogarithmicscale. 245
Fig.5.35 High-resolutionN adsorptionisothermsat77.4Kan
2
activatedcarbonDD52onalogarithmicscale. 245
Fig.5.36 χplotofIUPAClab“H”adsorptionofN onSterlingFT
2
carbon. 247
Fig.5.37 ComparingDPisothermwithχ-plotwithσ¼1and
r ¼1(Henry’sLaw). 248
F
Fig.5.38 ComparingDPisothermwithχ-plotwithσ¼1and
r ¼0.5(Freundlich). 249
F
Fig.5.39 ComparingDRisothermwithχ-plot. 249
Fig.5.40 ComparingTo´thT-equationwithArχ-plot. 249
Fig.5.41 ComparingTo´thT-equationwithN χ-plot. 250
2
Fig.5.42 Theenergyofadsorptionwithamountadsorbed. 257
Fig.5.43 χ-plotoftheH OadsorptionisothermbyHJto
2
Fig.5.42. 257
Fig.5.44 χ plotofdatabyBerg.Parametersobtainhereare
constantstocalculatethelinesinFig.5.45. 259
Fig.5.45 TheEofadsorptionwithamountadsorbedfrom
thedatabyBerg.Linesarefromtheχ-plotanalysis. 259
Fig.5.46 χplotandheatofadsorptionKradsorbedonrutileat
126KbyDennis. 260
Fig.5.47 HeatsofadsorptionbyKingtonetal.Thelinesarethe
leastsquaresfits. 261
Fig.5.48 χplotofthepurenitrogenandpureoxygenadsorption
onanatasebyArnold. 262