Onephaseandtwophaseregionsofcolloidstability

ProgrColloidPolymSci(1994)97:59-64©Steinkopff-Verlag1994M.V.SmalleyOne-phaseandtwo.phaseregionsofcolloidstabilityReceived:15September1993Accepted:20December1993M.V.SmalleyPolymerPhasingProjectERATO,JRDCKeihannaPlaza1-7Hikari-daiSeika,Kyoto619-02,JapanAbstractTheCoulombicattractiontheoryofcolloidstability,firstproposedbySogamiin1983,isshowntobewelladaptedtoexplaintheexistenceandextentofboththeone-phase(suspension)andtwo-phase(gel)regionsofcolloidstabilitywhichareobservedinclayswelling.ThecentralpredictionoftheSogamitheoryisthatthereisaweakattractivetailinthethermodynamicelectrostaticinteractionpotentialbetweencolloidalparticlesinelectrolytesolutions.Thepositionoftheminimuminthepairpotentialbetweenparallelclayplatesisgivenasafunctionoftheplatethicknessandtheelectrolyteconcentration(c)andisusedtoestimatehowmuchsolventtheclaywillabsorbasafunctionofitsinitialvolumefraction(r).Thisyieldsapredictionforthepositionofther-cphaseboundary,whosecurvatureisinexcellentagreementwithrecentstudiesofvermiculiteswelling.Thestandardtheoryofcolloidstability,theDLVOtheory,isalimitingcaseoftheCoulombicattractiontheory,intheone-phaseregion.Inthetwo-phaseregion,SogamitheorycombinedwiththeDirichletboundarycondition(constantsurfacepotential)predictsthattheratio(s)ofthesaltconcentrationinthesupernatantfluidtotheaveragesaltconcentrationinthegelphasewillbeconstant.Forasurfacepotentialof70mV,sisequalto2.8,inexcellentagreementwiththeexperimentalresultsonn-butylammoniumvermiculitegels.KeywordsClayswelling-colloidstability-Sogamipotential-DLVOtheory-saltfractionationIntroductionTheinteractionbetweenthechargedparticlesinioniccolloidalsolutionsisusuallytreatedintermsoftheDLVOtheory,whichwasdevelopedindependentlyinthe1940sbyDerjaguinandLandau[1]andVerweyandOverbeek[2].Accordingtothistheory,thethermodynamicpairpotentialthatdescribestheCoulombicinteractionbe-tweenthechargedparticlesisapurerepulsion.Thestabi-lityoflyophobiccolloidsisthenattributedtothevanderWaalsforce.TheDLVOtheoryhaslongbeenoneofthefoundationsofcolloidchemistry,butthebasicintuitiveconceptonwhichitisbased,namelytherepulsivenatureoftheCoulombicinteractionbetweenthelikechargedmacro-ions,hasbeenquestionedbyIseandco-workers[3,forarecentreview].TheyhavearguedthattheorderingobservedinhighlychargedmacroionicsolutionsisduetoCoulombicattractionbetweenthelikechargedparticlesthroughtheintermediatecounterions.ThisnewconceptwasfirstgiventheoreticalexpressionbySogamiin1983[4]andgeneralizedbySogamiandIsein1984[5].TheCoulombicattractiontheoryfirstreceivedattentioninthe60M.V.SmalleyOne-phaseandtwo-phaseregionsofcolloidstabilityWestwhenOverbeekdisputeditin1987[6].IthasalreadybeenshownthatOverbeek'scriticismofthenewtheoryisfundamentallyflawedandthattheCoulombicattractiontheoryprovidesalogicalandself-consistentbasisforde-scribingtheinterparticleinteractionsincolloidalsystems[7].TheCoulombicattractiontheoryhassincebeenplacedonarigorousbasisbycalculationsoftheHelmholtzfreeenergyforthecaseoftheinteractionoftwoflatdoublelayers[8,9].Inref.[8]theone-dimensionalcolloidproblemwassolvedatthemeanfieldtheorylevelsubjecttothehypothesisofcounteriondominanceandinref.[9]theexactmeanfieldtheorysolutiontotheproblemwasgiven.Thelatterpaperhasprovedrigorouslytheexistenceofeffectivelong-rangeattractionbetweenhighlychargedplatesinanelectrolytesolutionandpro-videsanewbasisfortheanalysisofavarietyofphe-nomenainmacroionicsolutions.Theworkinrefs.[7-9]ontheinteractionofhighlychargedplatesinanelectrolytehasbeencriticizedbyLevineandHall[10]andbyOverbeek[11].Whichofusturnsouttoberightwill,ofcourse,bedecidedbyexperi-ment.ThethreecomponeMsy~emWeshallstudyathree-componentsystemofamono-dispersecolloid,electrolyteandsolvent.Thebestchar-acterizedoftheone-dimensionalcolloids,then-butylammoniumvermiculitesystem[12-16],willbeusedasanexample.Therearefourconstituentsinthemacroionicsolution,thenegativelychargedclayplates,n-butylammoniumions(counterions),chlorideions(co-ions)andwater,butthesemaynotvaryindependentlybecausetheyaresubjecttotherestrictionthat[n-Bu+]=[Plate-]+[C1-]inanobviousnotation.Hence,thenumberofcompo-nentsis4-1=3.Inthefollowingweshallrefertothesolventaswaterandtotheelectrolyteassalt.Therawphenomenonoftheclayswellinginthen-butylammoniumvermiculitesystemisrepresentedsche-maticallyinFig.1.Inthecasesstudiedinrefs.[12-16]1I*wasalwaysmuchgreaterthanV,thevolumeoccupiedbythemacro-ions.WenowdefineVmtobethevolumeoccupiedbythemacroionsinthecoagulatedstate,asinFig.l(a)inthevermiculitesystem.Thisisanexperimentallycontrolledvariable.Wedefinethesolconcentrationrbyr=Vm/V*,whereV*isthetotalvolumeofthecondensedmattersystem.InthecaseofswellingillustratedbyFig.l(a)andL3f'~~tti~c¢3]I~lVoM..~AVm(a)(b)(c)(d)Fig.1Schematicillustrationoftheswellingofn-butylammoniumvermiculite,a)showstheunexpandedcrystalina1.0molarn-butylammoniumchloridesolution,b),c)andd)showthegelsformedin0.1,0.01,and0.001Msolutions,respectively(b)V*decreasesbyapproximately0.1%[16].Thisisaverysmallfractionalvolumechangecomparedtothatobserved.inV,sointhefollowingweignoretheelectro-s