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

109

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

Eq.(12)whenwrittenintermsofamountadsorbed(mmol/g)is[22,31,36]:

nabsolute

k t

pcT/TcRT

=exp ln

(13)

theparametersn0,E,t,andkareobtainedfromtheregressionanal-ysis.Theinputdatafortheregressionanalysisarenabsolute,T,and

p.

Fig.S4.showsSchwarzcurve ts.Theadsorptionparameters(n0,E,t,andk)obtainedfromtheregressionanalysisarelistedinTable4.Itcanbeobservedthatn0,E,t,andkarefunctionsoftemperature.

Table4

AdsorptionparametersoftheD–AmodelusingSchwarz’smethodtoestimatekforcalculationpseudo-saturationvaporpressure.

Sample

T

n0(mmol/g)

E(kJ/mol)

t

k

Xingq-1–5#

Qingh-2–3#

Xujd-1#

Leiy-1#

303313323303313323303313323303313323

0.59670.52410.55890.48810.51760.39510.40440.37060.41161.59701.54581.6213

4.46424.08454.00706.06435.72274.18564.68644.23993.78547.99128.45158.0852

1.29041.17361.321.56611.63601.20331.33981.21641.34852.09332.14542.4872

1.771.231.772.342.921.121.811.422.093.513.294.47

This ndingisinconsistentwithSchwarz’sresults[26].Theparam-eterEinD–Amodelischaracteristicenergywhichisameasureofthestrengthofinteractionbetweenadsorbateandadsorbent[22].Theadsorptionofmethaneoncoalisphysicaladsorption[46].TheinteractionofmethanemoleculestocoalsurfaceismainlyLon-dondispersionforceswhichareindependentoftemperature[46].Consequently,theparameterEshouldnotvarywithtemperature[22].ThevariationsofEwithtemperaturecouldcomefromthereciprocalin uencebetweentheparameterskandtinEq.(13).ThekvaluesshowninTable4canbeinsertedintoEq.(10)todeterminethepseudo-saturationvaporpressure,ps,whichisusedtocalculatetheadsorptionpotentials,A.Andthencharacteristiccurvescouldbeobtained.ThesecharacteristiccurvesareshowninFig.4.ThesolidlinesinFig.4representthecharacteristiccurvescal-culatedbyusingtheregressedadsorptionparameters(W0,E,andt)thatarelistedinTableS3.ThemaximumofR2is0.9455forXujd-1#,whiletheminimumofR2is0.6914forQingh-2–3#.Thisindi-catesthatusingtheSchwarz’smethodforpseudo-saturationvaporpressureresultsindatapointofcharacteristiccurvesbeingmoredispersethantheAntoineequationextrapolationandDubinin’sempiricalmethods.

3.3.4.Modi edSchwarz’smethod

ItwasobservedthatSchwarz’smethoddidnotresultinsin-glecharacteristiccurvefromFig.4.Inthepresentwork,weimprovedtheSchwarz’smethod.Inthemodi edmethod,thepseudo-saturationvaporpressureisstillcalculatedusingtheEq.(10)proposedbyAmankwahandSchwarz.However,kwhichisusedtocalculatepsisdeterminedbythefollowingprocedure: