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Liquidsolidinterfaces

Relevance

HPLC Ships Sensors Microfluidics Colloids

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Adsorp9onisotherm

Langmuir,TypeI

Linearform

isaconstant

Adsorp9onofsoluteBfromsolu9on

Adsorp9onisotherm

Freundlichisotherm

Linearform

andareconstants

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Isotherms

!Levelingoutoftheisothermisnotbecauseofcompletelayer

!Compe99onforsurfacewiththesolvent

Adsorp9onindifferentsolvents

Moreinterac9onofsolventresultsinlessadsorp9onofsolute

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Amphiphilicsolutes

Onnonpolarsubstrate

Amphiphilicsolutes

Onpolarsubstrate

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Adsorp9onofionsChargedsurfaces

Surfaceincontactwithsolu9onofelectrolyte(e.g.waterwith

fewions)usuallycarriesanelectriccharge

chargedensity,chargeperarea[C/m 2]

0electricalpoten9alatthesurface[V]

!Differencesbetweenchargeandpoten9al!

Poten9alistheenergyperunitchargeJ/C=V

Helmholzmodel

Oppositelychargedions

adsorbonthesurface

Poten9alrapidlyfallstozero

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Helmholz

So,atconstants0,y(x)dropslinearlywithx

d

!Validforstronglyadsorbingions,orathighionicstrength

GouyChapmanmodel

Distribu9onofionsnearthe

chargedsurface

Gradualdecayofthepoten9al

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GouyChapman

1/iscalledtheDebyelength(doublelayerthickness)

Whenx=Debyelength,thepoten9alhasdroppedto36.8%(1/

e)of0

1/

1/e

Debyelength

Ionicstrength[molm3]

Largerionicstrength(moreions)meanssmallerDebyelength(1/)

permi_vityliquid

eelectroniccharge

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Exercise

Whatisthedoublelayerthicknessof: 0,1MKNO3solu9on 0,001MKNO3solu9on

permi_vityliquid(7.081010Fm1)

eelectroniccharge(1.60101C)

kBoltzmanconstant(1.381023JK1)

Sternmodel

Tworegions:

Helmholzregion

GouyChapmanregion

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SternModel

xh

h

xhiscalledtheSternofHelmholzlayer

Exercise

Aglasscapillarywallhasasurfacepoten9alof80mV.TheDebyelayerthicknessis20nanometer.

a.Calculatethepoten9alforthissystemat1nanometerfromthewallassumingtheGouyChapmanmodel.

b.Saltisaddedsotheionicstrengthisincreasedbyafactorof10.Calculatethezetapoten9al(=poten9alatsurfaceofshear,assume1nanometer)forthisnewsitua9on.

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Answer

1/

1/e

A.

B.

Electrokine9cs

Almostiden9caltotheSternpoten9alisthezetapoten9al

Itisthepoten9alatthesurfaceofshear

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Electrophoresis

Movingchargedpar9cles

Alsoproteins,DNA,etc.

Electroosmosis

EOFformovingliquidsinmicrofluidics

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Electroosmo9cflow

U

Anelectricfieldalongthesurface

ofachargedwallinducesthe

chargeintheEDLtomigrate

Itcarriestherestofthefluidbytheac9onofviscouscoupling

!Notethelengthscaleinxaxis

Stability:DLVOtheory

Stabilityisactualmetastability

Energybarrierforcoagula9onmakessuspensionappearstable

Arac9veforce:vanderWaals

Repulsiveforce:overlappingsimilarchargeddoublelayers

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Kine9csofcoagula9on

Rateofchangeinthenumberofpar9clesNp

Diffusioncoefficient

Diffusioncontrolledcoalescence

WhenenergybarrierVmax

Poten9alenergy

Arac9ve Repulsive

rpar9cleradius

ssepara9ondistance

HHamakerconstant

m,pformediumandpar9cle

0Surfacepoten9al

risra9opar9clesizeto

doublelayerthickness

r1

r1

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Overallpoten9alenergy

Repulsiveenergy

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Metastability

Effectofionicstrength

Metastability

Effectofsurfacepoten9al

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Kine9csofcoagula9on

Rateofchangeinthenumberofpar9clesNp

Diffusioncoefficient

Diffusioncontrolledcoalescence

WhenenergybarrierVmax

Exercise

Fordilutedispersions,therateofaggrega9oncanbeapproximatedby

secondorderkine9cs;

WhereNisthenumberofkine9cpar9clesperunitvolume.

a.DerivetheexpressionforN(t).

b.Thehalf9meforaggrega9ont1/2

,isdefinedasthe9meittakestoreduce

Nbyafactoroftwo.Givetheexpressionforthehalf9me.

c.Calculatethehalf9meatroomtemperatureforarateconstantof

ina1%dispersionwith100nmradius.Theviscosityofthemediumis1,5

mPas.(kB,Boltzmanconstant,1,38.1023JK1).

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a.

b.Whent=t1/2thenNt=N0/2

Inser9ngintheformulaabovegives:

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c.

inser9ngthevaluesintheformulafork:

Astheunitofkism3s1,N0mustbegivenasthenumberofpar9clespercubic

meterdispersion(ofwhich1%consistsofpar9cles):

N.B.Thisisthehalf9mebasedontheprobabilityofcollisiononly.

Everycollisionresultsincoalescenceofthepar9cles.Inreality,thereis

oenanenergybarriertoovercomebeforepar9clescollide(duetotherepulsivepoten9al).Whenanenergybarrierispresent,anaddi9onal

termisincorporatedinthekine9csequa9on(exp(Vmax/kT)).

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Exercise

Adispersionconsistsofpar9clesof2nmdiameter.TheDebyelayerthicknessis20nm.TheHamakerconstantforthissystemis1018J.Thesurfacepoten9alofthepar9clesis100mV.permi_vitywater()=7.11010Fm1

a.Calculatetherepulsivepoten9alandthearac9vepoten9alwhenthepar9clesareseparatedby10nm.

b.Saltconcentra9onisincreasedsuchthattheionicstrengthis109meshigher.Whatisthetotalinterac9onpoten9alenergynow?

c.Explainhowthestabilityofadispersionisaffectedwhensaltisadded.

d.Explainwhatwillhappenwhenneutralpolymersadsorbsonthepar9cles.

Answers

r1A.

B.

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Exercise

9.1.Calculateandcomparecurvesforthedoublelayer

interac9onenergyortherela9veenergyasa

func9onofsusingthetwoapproxima9onsofEq.

[.23].

.1

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Exercise

9.2Iden9calsphericalpar9clesofradius80nmaredispersedinanaqueousmediumcontainingsodiumchlorideataconcentra9onof3mmoldm3.Thetemperatureis28K.Theeffec9veHamakerconstantis110 1Jandthedielectricconstantofthemediumis80.10.Thepermi_vityoffreespaceis8.851012Fm1.CalculatetheDebyelengthforthediffusedoublelayeraroundeachpar9cle.Electrophore9cmeasurementsgiveavalueof45mVforthepoten9al.Calculatetheenergyofinterac9onoftwopar9clesata

separa9onof10nm.Dothesepar9clesexperienceamutualrepulsionorarac9onatthisdistance?

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