Charged colloidal suspensions in confined geometries [Elektronische Ressource] / submitted by Ana Barreira Fontecha

ChargedColloidalSuspensions
inConfinedGeometries



DissertationThesis
toobtainthedegree
“DoktorderNaturwissenschaften”
attheFachbereich08,
Physik,MathematikundInformatik
oftheJohannesGutenbergUniversität,Mainz


Submittedby


AnaBarreiraFontecha
borninValencia,Spain


Mainz,March2009





































AFerxu







































Abstract



Thebehaviourofchargedcolloidalsuspensionsundergeometricalconfinementhasbeenstudied.
We used different wedgelike geometries which allow a continuous variation of the distance
betweentheplates.Atlowsaltconcentrationstheconfinementofsuspensionsinfluidphasecells
revealed that the particles accumulate in the cusp of the wedge forming crystalline ordered
structures. We present systematic experiments to understand the accumulation effect in the
narrow part of the cell. We conclude that the effect is due to electrostatic trapping, which is
confirmedbyasimpletheoreticalmodelproposedbyLöwenetal..Crystallinestructuresappear
formingacharacteristicsequencewithincreasingplateseparation.Thisstructuralsequencehas
beenalreadyobservedpreviouslyinconfinementatwedgegeometries,however,thesmallwedge
anglesachievedinourexperimentsallowedtheobservationofnewstructures.Someofthesenew
structuresshowexoticarrangementsandhavenoatomiccounterpart.Wealsoproposedifferent
transition mechanism models between the different structures based in the experimental
observations. For that we assume that the particles behave as hard spheres subject to a high
pressure.Finally,acellwithvariableheightwasdesignedinordertostudythecompletephase
behaviour of charged spheres confined between parallel plates. The preliminary results are
comparedwiththeoreticalpredictions.































Index
Pag.
Listofterms .................................................................................................................................. 1
1 Introduction.......................................................................................................................... 3
2 ChargedSphereSystems..................................................................................................... 7
2.1 Particleinteractionsinchargedspheresystems ............................................................ 7
2.1.1Interactionpotentialbetweenchargedparticles ................................................... 8
2.1.2Phasediagramofchargedcolloidsinthebulk................................................... 10
2.2Colloidalcrystals ........................................................................................................... 12
2.2.1Crystallinestructuresinconfinement................................................................. 15
3 Formerresultsingeometricalconfinement..................................................................... 17
3.1Firstevidences:Thestructuralsequence. ...................................................................... 18
3.2Modelofhardspheresinthehighpressurelimit .......................................................... 21
3.3Thehexagonalandsquarestructuresinthestructuralsequence ................................... 22
3.4Otherstructures.............................................................................................................. 24
3.4.1Fromthemonolayertothebilayer ..................................................................... 25
3.4.1.1TheBucklingPhase .............................................................................. 27
3.4.1.2.TheRhombicphase.............................................................................. 29
3.4.2Highernumberoflayers:Theprismphases....................................................... 31
3.5Thecompletephasediagramforabilayersystemofchargedspheres.......................... 33
3.6Finalremarks ................................................................................................................. 35
4 Experimentaltechniques................................................................................................... 37
4.1BightFieldMicroscopy................................................................................................. 38
4.2Fouriermicroscopy........................................................................................................ 47
4.2.1FundamentalConceptsinLightScattering ........................................................ 47
4.2.2.LightscatteringintheRayleighGansDebyeapproximation........................... 50
4.2.3StaticLightScattering........................................................................................ 50
4.2.4.Lightscatteringfromperiodicstructures:diffractionincrystals...................... 52
4.2.5.Workingwiththemicroscopeinconoscopicmode .......................................... 59
4.3Othertechniques ............................................................................................................ 62
4.3.1AtomicForceMicroscope(AFM)...................................................................... 63
4.3.2ScanningElectronMicroscope(SEM)............................................................... 64
5 Samplespreparationandconfinementcelldesigns........................................................ 67
5.1Preparationandcharacterizationofthestocksuspensions............................................ 68
5.2Pumpingsetup ............................................................................................................... 71
5.3Cellsusedintheexperiments ........................................................................................ 75
5.3.1Wedgegeometrycells ....................................................................................... 75
5.3.1.1Rectangularcells................................................................................... 76
5.3.2Sphericalgeometrycells.................................................................................... 79
5.3.3Cellwithvariableheight.................................................................................... 81
5.3.3.1Experimentalproceeding...................................................................... 84
6 Effectofconfiningchargedparticlesinwedge-likegeometries .................................... 93
6.1Generaleffect ................................................................................................................ 94
6.2Testingevaporationcurrents ......................................................................................... 96
6.3Testingthegravitystrength ......................................................................................... 101
6.4Testingtheinfluenceofthechargeatthecellplates................................................... 104
6.5Testingtheinfluenceofsaltgradients......................................................................... 106
6.6Discusion ..................................................................................................................... 107
7 Experimentalphasediagrams ........................................................................................ 111
7.1Comparisonbetweenthetheoreticalandexperimentalphasebehaviourin.............. 112
closedwedgecells. ...................................................................................................... 112
7.2Resultsobtainedwiththecellwithparallelplates. ..................................................... 115
7.3Comparisonanddiscussionoftheexperimentalphasediagrams ............................... 118
8 Structuralsequenceofcolloidalcrystalsinconfinement............................................. 121
8.1Introduction:Thestructuralsequence ......................................................................... 122
8.2Then→(n+1)transition .................................................................................... 127
8.2.1Thebucklingstructure ..................................................................................... 129
8.2.2Thehcp⊥structure........................................................................................... 130
8.2.3Thehexagonalprismstructure......................................................................... 139
8.2.4Squareprismstructure,P A.......................................................................... 148

8.3Then→ntransition ............................................................................................ 153
8.3.1Therhombicphase,nR. ................................................................................. 158
8.3.2Thesquareprismphase,nP B ..................................................................... 162

8.3.3The(101)hcpphase,nhcp—............................................................................ 165
8.3.4Otherarrangementsinthen→ntransition .............................................. 167
8.3.5Transitionmodelforhardspheresysteminthehighpressurelimit.....