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1、ARTICLEpubs.acs.org/MacromoleculesPolyelectrolyteBrushes:DebyeApproximationandMean-FieldTheory†,†,‡†,§,†‡LongChen,HolgerMerlitz,*Su-zhenHe,Chen-XuWu,*andJens-UweSommer†DepartmentofPhysicsandITPA,XiamenUniversity,Xiamen361005,P.R.China‡Leibniz-Institutf€urPolymerforschung
2、Dresden,01069Dresden,Germany§DepartmentofElectronicEngineering,PutianUniversity,Putian351100,P.R.ChinaABSTRACT:Off-latticecomputersimulationsofpolyelectrolytebrushesarecarriedoutusingtheDebyeapproximationwithexplicitcounterionsbutimplicitsalt.Theresultsarecomparedwithexpl
3、icitsaltionsimulationsandself-consistentfieldtheory.Wedemonstratethatthedatageneratedwiththesedifferenttechniquesareinexcellentagreement,therebyconfirmingthevalidityoftheDebyeapproximationinthecontextofpolyelectrolytebrushes.TheefficiencyoftheDebyeapproximationisverifiedthroug
4、hbenchmarkcomputations.Furtheron,wedevelopanimprovedFlory-typemean-fieldmodel,basedontheoriginalargumentbyPincus,buttakingintoaccountboththeexcludedvolumeandfiniteextensibilityofchains.Onthebasisofthismodel,wedemonstratehowtheinterplayofcounterionpressureandexcludedvolumer
5、epulsionexplainstheobservedeffectofsaltontheswellingofthebrushundergoodsolventconditions.Thebrushheightasafunctionofgraftingdensityisinvestigated,anditisarguedthattheresultingpowerlawscalingof-1/3isincapableofdistinguishingbetweenexcludedvolumeandelectrostaticeffects.I.INT
6、RODUCTIONapproximation,featuringanimplicitsaltmodel.Theevaluationofthisquestionwasamongtheprimarytasksofthepresentwork.Polyelectrolytebrushesconsistofchargedmacromolecules17,18Aseriesofstudiesinwhichtheelectrostaticinteractionwasthatareend-graftedtoasolidinterface.Theyar
7、eofimportanceinimplementedintermsoftheDebyeapproximationhavebeenvarioustechnicalapplicationssuchassurfacemodification,19presentedinthepast.Amongothers,Mickaetal.haveanalyzedcolloidalstabilizationandlubrication,andabundantinbiologicalthedependenceofthepersistencelengthofwe
8、aklychargedsystems.Therefore,polyelectrolytebrusheshavereceiveda1-5polyelectrolytesontheDebyescreeningl
