108S.Haoetal./ColloidsandSurfacesA:Physicochem.Eng.Aspects444 (2014) 104–113

Fig.2.Characteristiccurvesformethaneon(a)Xingq-1–5#,(b)Qingh-2–3#,(c)Xujd-1#,and(d)Leiy-1#.ThepswascalculatedbyextrapolationofAntoine’sequation.

equationi.e.Eq.(11)fromtheD–Aequationtoexpressthecharac-teristiccurve.

W=W0exp

t

A

(11)

whereW0,E,andtareparameterstobedeterminedbyregressionanalysis.TheinputdatafortheregressionanalysiswereW,andA.Theregressedadsorptionparameters(W0,E,andt)arereportedinTableS1.ThesolidlinesinFig.2representarethecharacteristiccurvescalculatedfromtheEq.(11)usingtheregressedadsorptionparameters(W0,E,andt).AgarwalandSchwarz[43]de nedthemaximumdeviationofadsorbedphasevolumeataparticularvalueofAdividedbythemaximumadsorptionvolume(×100)asdevia-tion.However,therearescarcelytwodiscretedatapointsofwhichtheAvaluesaresame.Consequently,thedeviationofadsorbedvol-umeataparticularvalueofAisnoteasytodetermineaccurately.Inthispaper,weusethedeterminationcoef cient,R2,toindicatethedeviationofthedata.Obviously,theclosertoonethevalueofR2,thelessdiscretethedata.ThemaximumofR2is0.9888forLeiy-1#,whiletheminimumofR2is0.9811forQingh-2–3#andXujd-1#s.

consideredempirical.Dubinin’sempiricalmethodi.e.Eq.(9)waswidelyusedtocalculatethepseudo-saturationvaporpressureingas-solidadsorptionsystem[26,31,36,44,45].

Fig.3showsthecharacteristicplotsforthecoals.ThesolidlinesinFig.3representthecharacteristiccurvescalculatedfromtheEq.(11)usingtheregressedadsorptionparameters(W0,E,andt)thatarelistedinTableS2.Thepseudo-saturationvaporpressurepswascalculatedbyEq.(9).ThemaximumofR2is0.9936forXujd-1#,whiletheminimumofR2is0.9920forXingq-1–5#.ThisindicatesthatcharacteristiccurvesusingtheDubininmethodforpseudo-saturationvaporpressuredisplaysmallerdevi-ationsthantheAntoineequationextrapolationtechniques(seeFig.S3).

3.3.2.Dubinin’smethod

ExtrapolationAntoineequationresultsinhighpswhichare40.1840MPafor303.15K,45.3881MPafor313.15K,and50.9029MPafor323.15Krespectively.Flood[43]hasproposedthatintheabsenceofanydirectexperimentalinformationontheadsorbedphase,estimationofpsasthevaporpressureshouldbe

3.3.3.Schwarz’smethod

Theinteractionbetweenanadsorbateandaparticularadsor-bentwouldbeuniquetotheadsorptionsystemstudied.AmankwahandSchwarz[26]proposedEq.(10)toestimatepseudo-saturationvaporpressuresinapplicationoftheD–Aequation.Tocalculatetheadsorptionpotential,A,thevalueofkinEq.(10)shouldbeknown.However,thevalueofkisnotknownapriori.AmankwahandSchwarz[26]usedthefollowingmethodtodeterminethevalueofk.WhenEq.(10)isusedinconjunctionwithEq.(5)(i.e.D–Aequation),afourparameterequationisobtained:

k t

pcT/TcRTW

=exp ln

(12)