110S.Haoetal./ColloidsandSurfacesA:Physicochem.Eng.Aspects444 (2014) 104–113

Fig.4.Characteristiccurvesfor(a)Xingq-1–5#,(b)Qingh-2–3#,(c)Xujd-1#,and(d)Leiy-1#.ThepswascalculatedbySchwarz’smethod.

(1)Letkbeequalto1.6,2.0,2.4,...,and4.0respectivelyanda

seriesofpseudo-saturationvaporpressure,ps,whichareusedtocalculatetheadsorptionpotential,A,areobtained;

(2)PlottherelationshipbetweenWandA,andthecharacteristic

curvescorrespondingtodifferentkcouldbeobtained;

(3)FitthecharacteristiccurveswithEq.(11),andthedetermina-tioncoef cientR2couldbeobtained;

(4)PlottherelationshipbetweenR2andk,anddoregressionanal-ysisforthecurves.Then,theoptimizedkwhichthemaximumR2correspondstowouldbeobtained.

Table5

RegressionparametersforthecharacteristiccurvesusingEq.(11)asregressionequationandpsbeingcalculatedbythemodi edSchwarz’smethod.

Sample

W0(cm3/g)

E(kJ/mol)

t

R2

Xingq-1–5#Qingh-2–3#Xujd-1#Leiy-1#

0.04860.03480.03110.1090

5.03845.04764.58376.9336

1.44901.47891.37791.9258

0.99430.99420.99460.9948

Theadsorptionforce eldofvariousadsorbentswilluniquelyimpactadsorbate[26].

Fig.S5showstherelationshipbetweenkandR2.Thedatawereregressedusingthequadraticpolynomial.ThesolidlinesinFig.S5representthe ttingcurvesusingtheregressedparameters(a0,a1,anda2)thatarelistedinTableS4.Consequently,theoptimizedvalueofkis2.69forXingq-1–5#,2.24forQingh-2–3#,2.26forXujd-1#,and2.7forLeiy-1#.

Fig.5showsthecharacteristiccurvesofthesamplesforwhichkistakentheoptimizedvalue.ThesolidlinesinFig.5arethe ttingcurves(theblacklinebeingEq.(11) ttingcurveandtheredlinebeingthecubicpolynomial ttingcurverespectively).The ttingparametersbasedontheEq.(11)areshowninTable5.Thecubicpolynomial ttingparametersareshowninTable6.

AsshowninFig.5,Table5and6,themodi edSchwarz’smethodtoevaluatethepseudo-saturationvaporpressureresultsinmuch-improvedsinglecharacteristiccurvesforthesamples.Thevalueofoptimizedkisnotsameforthesamples.Thisisbecausetheadsorbate-adsorbentinteractionisnotsameforthefoursamples.

3.4.Determinationofthecharacteristiccurveformtobeutilized

Theformofcharacteristiccurvetobeutilizedisoneoftheimportantproblemsassociatedwiththeapplicationofpotentialtheories[11].Thecharacteristiccurveisusually ttedbypoly-nomial[40–42,47].Althoughthepolynomial ttingissimple,theparametersobtainedbyregressionanalysishavenophysical

Table6

Cubicpolynomialregressionparametersforthecharacteristiccurves(pswascalcu-latedbythemodi edSchwarz’smethod).

Sample

a0

a1

a2

a3

R2

Xingq-1–5#Qingh-2–3#Xujd-1#Leiy-1#

0.05130.03590.03320.1119

0.0067 0.0038 0.0056 0.0024

2.4305×10 4 4.8588×10 49.7957×10 5 0.00214

4.9921×10 56.1986×10 51.8119×10 51.4417×10 4

0.99430.99470.99460.9958