colloids under mrs bulletin2 external control€¦ · self-organization in desired directions. we...

IntroductionIn 1926, Jean Perrin received the Nobel

Prize in physics for putting “a definite endto the long struggle regarding the real exis-tence of molecules” (committee report). Inhis experiments, which he started about ahundred years ago, Perrin pioneered theuse of colloidal particles as a model systemwhen he applied Einstein’s insights on howto describe colloids using statistical me-chanics to determine Avogadro’s number(NA). Basically, Einstein realized that col-loids have a well-defined thermodynamictemperature. Amazingly, Perrin’s experi-mental approach1 was hardly differentfrom what is described in the rest of thisarticle. First, Perrin realized that he neededa monodisperse dispersion of model par-ticles and therefore went to great lengthsto patiently fractionate a dispersion of resinparticles he had precipitated by repeatedcentrifugation over a period of severalmonths. For his first determination of NA,he determined the equilibrium height dis-tribution of a low concentration of colloidsby counting particles using a microscope.This so-called barometric height distribu-tion is exactly analogous to that of the dis-tribution of molecules in the atmospherein the gravitational field of the earth, exceptthat the characteristic gravitational length,which is proportional to the particle’s massand is the height at which the potential en-ergy of a particle equals kT, is not measuredin kilometers but in centimeters or milli-

meters (or even micrometers, as will bediscussed). In another determination, healso used a microscope, this time to deter-mine the diffusion constant of colloids.Einstein calculated this diffusion constanton the one hand by taking into account thefact that the erratic diffusive or Brownianmotion the particles exhibit is caused bythe continuous bombardment of the col-loid by solvent molecules, giving rise toforces that do not exactly cancel, while onthe other hand calculating the Stokesiandrag on the particles (the friction coeffi-cient of the particles in the liquid) using acontinuum hydrodynamic description.This Brownian motion of the colloidsensures that a dispersion of such particlescan lower its free energy and by doing soself-organize.

During the past hundred years, mono-disperse colloids have possibly even in-creased their role as important modelsystems. Nowadays, they are used to testtheories on strongly interacting systemssuch as liquids and phenomena importantto condensed-matter physics such as melt-ing, freezing, and the glass transition. Thelast decade has also shown that by usingadvanced microscopy techniques, quanti-tative measurements of both structure anddynamics can be made on the single-particle level inside concentrated disper-sions. The understanding gained of theself-organization of colloids is starting to

be used to create new materials such asphotonic crystals (for example, see theAugust 2001 issue of MRS Bulletin2).

The focus of this review is on how exter-nal fields can guide and manipulate thisself-organization in desired directions. Wehave limited this review to papers fromthe last five years, in order to preventoverlap with a previous issue on colloidspublished in MRS Bulletin in 1998.3 Evenwith this restriction, space constraintsmake it impossible to be complete.

Very important to the realization of newmaterials and model systems are recentadvances in synthesis. For instance, core–shell morphologies of particles with similaroutside shell materials but different corescan have similar interparticle interactionsbut can be made to respond to externalfields differently.4–5 Moreover, control overmore complex shapes in monodisperseform (see Figure 1 and the article byManoharan and Pine in this issue) is be-coming possible, even for particles in thenanometer size range.6 This is not, how-ever, the focus of this review.

External FieldsWalls and Confinement

Although some may argue that walls orconfining boundaries are not exactly anexternal field, the presence of such a struc-ture can lead to all kinds of phenomena(e.g., wetting, pre-freezing, capillary con-densation) that modify the thermodynamicbehavior. As such, the wall acts as an ex-ternal field that modifies bulk behaviorand can therefore be used as a relativelysimple means of control. In addition,knowledge about the interactions of liquidsand solids with a wall of a different mate-rial is both of fundamental and applied in-terest. For instance, in the case of nematicliquid crystals, an understanding on themicroscopic scale is still lacking, despite

MRS BULLETIN/FEBRUARY 2004 85

Colloids underExternal Control

Alfons van Blaaderen

AbstractThe ability of colloids to self-organize through a minimization of their free energy is a

direct consequence of their well-defined thermodynamic temperature that manifestsitself through the Brownian motion they perform. In this article, it will be shown thatthrough the use of external fields such as electric and magnetic fields, gravity, structuredor confining walls, and shear, this self-organization can be directed to make new advancedmaterials. Moreover, a start has been made toward colloidal model systems to studyfundamental questions relating to materials science such as defect structure anddynamics, grain boundaries, wall and confinement effects, and tribology. Finally, wepredict that the enhanced insights on how to use external fields will also lead to “smart”materials with properties that can be changed dynamically.

Keywords: colloids, model systems, self-organization.

Figure 1. Scanning electron microscopy(SEM) image of colloidal dumbbells ofsilica particles created by controlledaggregation of silica spheres (radius,86 nm) and separated in pure form, bysedimentation, after the method of Perrin.

www.mrs.org/publications/bulletin

the importance for display applications ofaligning these molecules on substrates in acontrolled way.

Only recently have theoretical predic-tions been made in combination withcomputer simulations for the simplerhard-sphere system at a structured or pat-terned wall.7 One of the surprising out-comes is that the first layer of spheres stuckto a wall with the symmetry and spacingof close-packed crystals can induce crys-tallization against the wall at 30% belowthe bulk freezing volume fraction. On cer-tain crystalline patterns attached to thewall, the crystal that formed on this tem-plate was found to wet the structured wall.This implies that there is a logarithmic di-vergence in the number of crystalline layersapproaching the bulk freezing transition—the crystalline layer induced by the wallgrows in thickness according to a powerlaw, and becomes infinitely thick at thebulk freezing transition point. It alsomeans that sizable crystals can be grownon the container wall well before the bulkfreezes and that the structured wall causesan appreciable lowering of the free energyof the particles next to it. This is much lessthe case for an unstructured or unpatternedwall, which will induce freezing, at most,at a volume fraction a few percent belowthe bulk freezing volume fraction.7 Thispartially explains the experimental reali-zation of the growth of hcp crystals on awall templated with a crystal plane thatwould allow only the growth of thesemetastable (from a bulk point of view)crystals.8 As a matter of fact, it was shownthat any stacking sequence resulting inclose-packed crystals and, by stretchingcertain directions, also non-close-packedcrystals can be grown by using this ap-proach of “colloidal epitaxy.”8 The com-parison with theory is not one-to-one, asthe experiments were performed by havingthe colloidal crystals grow on the templatein a gravitational field, where the gravita-tional length was on the order of the par-ticle size. In the case of long-range repulsivepotentials, the density of the spheres wasmatched to that of the liquid; in this case,it was shown that crystal growth could bedirected by a 2D pattern of charged lines.9Here as well, crystals that were not thebulk equilibrium phase could be nucleatedagainst the structured wall. Crystals werealso grown on a template in the presenceof attractions induced by polymers.10 Itwould be interesting to find out whichinterparticle interaction potential will givethe highest-quality crystals.

Another popular and simple methodfor growing large colloidal crystals, be-sides growth in a gravitational field, is bydrying dilute dispersions slowly on a flat

surface drawn out of the dispersion. It isactually not even necessary to move thesurface up, as the evaporating liquid sur-face is moving down by itself.11 Particlessticking up through the surface of the dry-ing liquid are forced together by strongcapillary forces, and if the process goesslowly enough, a crystal with a thicknesscontrolled by the particle volume fractionresults. We have shown that this processof “controlled drying” still works in thelimit of crystals just one layer thick, where,without a template, a close-packed hex-agonal arrangement forms. In this modeof layer-by-layer growth, one can alternateparticles of different size or composition.In this way, �5 layers of binary crystalscan be grown.12 With size ratios close to0.5, crystals with stoichiometry LS2 (whereL represents large spheres and S smallspheres) were grown that have also beenfound in bulk crystallization. Unexpectedcrystal symmetries were deposited, bothat higher (LS3) and lower (LS1) volumefractions of the small spheres. The LS1structure is especially intriguing, as it fillsthe hexagonal array of crevices of the layerof larger spheres in every other hole. Thismeans that the drying liquid film can exertan influence over relatively large dis-tances, probably because the regular struc-ture formed at the lower volume fractionsminimizes the surface area in this way.Figure 2 demonstrates that this openstructure at lower volume fractions alsoforms on an arrangement of the first layerwith a square symmetry. The first layer inthe figure was deposited on a structured

wall with a square symmetry and demon-strates that despite the large drying forces,this process can be directed by a templateas well, as long as the number of layers de-posited is not too large.13 For size ratios ofsmall to large spheres of �0.225, it hasbeen shown that a binary crystal layer canbe deposited as a mixture of large and smallspheres.14 Surface patterns with larger di-mensions have also been used to orient col-loidal crystals for photonic applications.15

Bringing walls close together not onlyleads to phenomena such as capillary con-densation but also can lead to differentpacking arrangements that fill the confin-ing spaces more efficiently than crystalsfound in bulk.16 A different approach wastaken in Reference 17, which also involvespacking colloids in confining geometries.Here, 2D arrays of holes in a polymer layerare used to pack the colloids, also by meansof drying forces. In this way, small amountsof identical particles with more complexshapes can be designed.

In general, it can be concluded that withthe ever-increasing need to make devices—and structures on these devices—smallerand smaller, applied and fundamental re-search into the effects of walls and confine-ment will only increase in the near future.

Low-Frequency Electric andMagnetic Fields

Electromagnetic (EM) radiation withfrequencies well below the visible range issomewhat arbitrarily termed “low” in thisarticle. A large range of these “low” fre-quencies can cause coupling of the electric

86 MRS BULLETIN/FEBRUARY 2004

Colloids under External Control

Figure 2. SEM image of a two-layer square structure made by “controlled drying” on atemplate with a pitch comparable to the particle diameter.The left inset is an enlargementof the structure; the right inset shows ordering of vacancies in a monolayer of spheresdeposited at a lower particle concentration.

field to all kinds of different dynamicalprocesses that involve the colloids or theirinteractions. Static and constant fields canmove charged particles (electrophoresis),can polarize both the double layer and theparticle, and can lead to electrode reactionsif the electrodes are in direct contact withthe liquid. Inhomogeneous fields can movepolarized particles (dielectrophoresis). Allof these effects have already been used tomake new materials. Electrophoresis hasbeen used to accelerate sedimentation.18

Two-dimensional crystals have been cre-ated by a combination of interactionscaused by the polarization of double layersand dielectrophoresis19 and by attractionsresulting from electrohydrodynamic flowsinduced by the presence of the particlesand current flows.20 Two-dimensional bi-nary crystals of nearly equal-sized poly-styrene and silica spheres were made usingthe different frequency-dependent polariz-abilities of the two particles.21

Three-dimensional crystallization hasbeen initiated by dielectrophoresis in ahard-sphere system without significanteffects arising from induced dipolar inter-actions between the spheres.22 On the otherhand, dipolar interactions by polarizationof the “hard-sphere-like” particles (with-out dielectrophoresis) have been used togrow body-centered-tetragonal (bct) col-loidal crystals.23 In addition, the electricfield could in this instance be used to switchbetween bct and fcc crystals by a marten-sitic transition. The induced dipolar inter-actions were also used to grow large fcc orbct single crystals, as well as crystal struc-tures with part-fcc and part-bct layerstackings.24 In other work, it was shownthat induced dipolar interactions can alsobe combined with long-range repulsivepotentials if the frequency of the ac field ishigh enough. A very rich phase diagramwith several new colloidal phases is theresult of this combination of long-rangepotentials.25 Moreover, the dipolar interac-tions can be switched on and off veryrapidly, creating interesting possibilitiesnot only for model studies but also for ap-plications. For instance, a lattice constantin a colloidal crystal can be switched be-tween different values, and thus the angleof a light beam that is Bragg-scattered bythis lattice can be switched.

Most work on magnetic particles (ormagnetizable particles that do not have apermanent magnetic moment) has untilnow been done on 2D systems in whichthe dipolar interactions are repulsive only,and the fact that most magnetic particlesabsorb light is not a problem. Beautifulwork identified one of the clearest examplesof a 2D hexatic phase,26 having the elasticproperties of 2D crystals and characterized

by long-range bond order as measured bycorrelation functions that describe the rangeof the symmetry between near neighbors,but short-range positional order as meas-ured by the radial distribution functionthat describes correlation in the positionbetween particles.27

High-Frequency ElectromagneticFields: Light

The distinction between high and lowfrequency is based on the fact that if thefrequency of the electromagnetic radiationis chosen so high that the wavelengthenters the colloidal domain, forces can begenerated and limited to the single-particlelevel. In this regime, light needs to be highlyfocused, and the refractive index of theparticles needs to be larger than that of thesuspending medium—although with“beam-shaping” (e.g., donut-shapedbeams), even this requirement can be re-laxed. If these conditions are met, it be-comes possible to locate or trap colloids inthe region of high intensity close to thefocus. Many ways already exist to generatelarge arrays of optical tweezers that can beused to simultaneously manipulate manyparticles (see References 28–29 and citedwork therein). Optical tweezers in combi-nation with high-accuracy position detec-tion can be used to measure interactionenergies between colloids with sub-kT reso-lution. Anisotropies in the particle shapeor optical properties, moreover, can beused to orient or rotate particles, making itpossible to exert torques as well.28

In short, optical tweezers are veryversatile and have already been used inseveral different ways. By sticking colloidsto oppositely charged surfaces, 2D arrange-ments of particles can be made that cansubsequently be used to direct 3D crystal-lization.30 Such a procedure can also beused to build up structures in 3D;31 how-ever, this procedure falls more into thecategory of “do-it-yourself” organizationinstead of manipulated self-organization.Two-dimensional traps have also beenused in combination with interferencepatterns to arrange multiple colloids onone trapping site, creating 2D “molecular”colloidal crystals.32 Holding multiple par-ticles trapped in three dimensions has alsobeen demonstrated.33 In Figure 3 and Ref-erence 29, we demonstrate that these tech-niques can also be applied in concentrateddispersions by using tracer particles with ahigh-index core in a dispersion of matchedparticles with a fluorescent core. It is pos-sible to image in 3D the effect that the 3Dtrapped structures have on the rest of thedispersion because multiple trappingplanes can be generated through a differ-ent lens than that used for the 3D confocal

imaging.29 The fact that the tracer particleshave the same outer shell does not onlyensure that interactions with the matchedparticles are identical, but also that opti-cally induced interactions between thecores can be neglected as a result of the in-creased distance between the cores. In Fig-ure 3a, a square arrangement of trappedparticles is shown in a hexagonal (111)plane inside a 3D colloidal crystal. In Fig-ure 3b, the same arrangement is shown



Figure 3. Confocal micrographs of thereflection signal of tracer particles (red)in a dispersion of index-matched particleswith fluorescent cores (green). In theimaging plane, 3 � 3 optical traps werecreated.Traps were created inside(a) an fcc (111) crystal plane and (b) aconcentrated colloidal liquid with avolume fraction close to freezing.Theimages shown are averaged over 10frames, 1 s apart. Note that thefluorescent spheres are not influencedby the ninth empty trap position.Thebulk silica particles are 1050 nm indiameter with 400-nm-diameterfluorescent cores (FITC, fluoresceinisothiocyanate); the tracer spheres havepolystyrene cores (diameter, 772 nm )with 100-nm-diameter silica shells; thetrapping wavelength is 1064 nm.

inside a colloidal liquid close to crystalliz-ing. The particles close to the trappedspheres have already started to order. Theeffects were made visible by averagingseveral frames, causing the particles withno long-range order in the disordered liq-uid to blur. Also, note that at the ninth po-sition where a trap is present but no traceris trapped, no effects are visible on thematched fluorescent particles.

In Reference 29, it is also shown that laserbeams that are not focused to a diffraction-limited spot can be used to concentrateparticles by dielectrophoresis in wayssimilar to those mentioned in the sectionon low-frequency electric and magneticfields.22 The radiation pressure can also beused to press particles against a wall andessentially confine them to a 2D plane. Byscanning another more focused laser beamin a square array, a programmable “fence”around the 2D system was realized.34

GravityPhotonic crystals built up from colloids

can be made through crystallization of theparticles in a heterogeneous process thatstarts at the container bottom with thecrystals growing in the [111] directionparallel to gravity. The larger colloidalparticles (around 1 �m) used in photoniccrystals aimed at bandgaps in the near-infrared have gravitational lengths closeto the particle size. In this limit, a mean-field description is likely to break down.Experiments aimed at investigating earliertheoretical predictions have only beenperformed recently.35, 36 An interestingfinding, both in theory and simulationsand in experiments, is that the first twolayers start crystallizing in unison, whilethe other layers follow sequentially.35 An-other experimental finding is that thestacking errors can be significantly reducedif the crystal growth rate is reduced, butthat the same effect, at least close to thebottom wall, can also be induced by havinga template there with the symmetry of a(111) plane.36

Usually, a gravitational field is consid-ered a nuisance for binary crystal forma-tion, because the larger particles generallysediment faster. However, in Figure 4, weshow that it is also possible to use gravityto grow binary crystals that would not evenhave formed otherwise. Here, two sizes ofpoly(methyl methacrylate) spheres withdifferent surface charge densities have beenused. The large spheres sedimented (up-ward in this case, because the density ofthe spheres is less than that of the solvent),first forming a random stacking of close-packed planes. The small and almost hardspheres sedimented later and could moveinto the octahedral holes, because they did

likely to change soon. Several groups arepursuing real-space rheological experi-ments.39–41 Our approach makes use of aconfocal microscope and allows quantita-tive analysis of the particles in a thin layer,even during shear. The reason that theparticles appear to be stationary in oneimaging plane that can be selected by theconfocal microscope is because they arestationary with respect to the outside lab-oratory frame. By moving both the lowerplate and an upper cone of the shear cell inopposite directions, it is possible to set upa flow with constant shear (at least in thecolloidal liquid) for which there is a planeof zero velocity with respect to the outsideworld. By changing the relative speeds ofthe cone and plate, this plane can be movedwith respect to the bottom plate throughwhich the imaging is done. Figure 5 showsa metastable liquid at a volume fraction of0.35 (freezing volume fraction, 0.3) ofslightly charged colloids before (Figure 5a)



Figure 4. Binary dispersion of green(diameter, 740 nm) and red (diameter,2.16 �m) fluorescent poly(methylmethacrylate) spheres, showing animage plane between two layers of redspheres.The red spheres interactedwith a soft repulsive interparticle potentialand crystallized at a volume fraction ofaround 0.25. For this dispersion, theindex was matched and the density wasalmost matched, creating milligravityconditions and resulting in slowsedimentation of the green, almost hard-sphere-like particles in the interstitials ofthe randomly stacked red spheres.

Figure 5. Confocal micrographs of theplane of zero velocity, located 20 �mfrom the lower plate at a shear rate of0.5 s�1: (a) at time t � 0 s; (b) at time t � 256 s. Particle diameter, 2.25 �m.

not experience a repulsion from thecharged larger particles.

ShearDespite the fact that shear-induced

crystallization and, at higher shear rates,shear-induced melting have been studiedfrom the mid-1980s, there are only a fewpapers in the literature in which flow isused to manipulate or improve colloidalcrystallization from a materials point ofview. Both particles with a hard-sphere-like interparticle potential37 and chargedspheres38 have been crystallized quite suc-cessfully under the influence of shear toobtain larger colloidal crystals. It is inter-esting that in both cases, the crystals thatwere pure fcc during shear turned intotwinned crystals soon after cessation ofthe shear. The mechanism responsible forthis is still unclear.

Most research until now used scatteringmethods to infer structural information. Inparticular, if no clear idea for the structureis known in advance, or if defects or im-perfections are an issue, the interpretationof k-space (momentum space) informationcan be quite difficult and indirect. Untilnow, direct microscopy in combinationwith shear has been rare; this situation is

and after (Figure 5b) 256 s of shear. Fig-ure 5b is a confocal image taken while theshear was still being applied. These arepreliminary measurements,39 but it is clearthat by this method a lot of the theories onshear-induced crystallization and meltingcan be tested.

CombinationsQuite a few of the examples given here

are more or less already combinations ofmore than one external field. For instance,the hard-sphere crystals grown on atemplate by colloidal epitaxy were con-centrated on the template by gravity.8However, this example was mentioned inthe section on wall effects because themetastable hcp crystals would have prob-ably also formed without this externalfield, such as in the case of long-range re-pulsive systems. In several other cases,however, the combination of two externalfields is already opening up new possibil-ities. Combinations with electric fields areespecially popular topics of research.

For instance, in the work of Refer-ence 42, the gravitational field plays an es-sential role in making a martensitic fcc–bcttransition go in a layer-by-layer fashion asa function of the electric field used to in-duce this transition. Here, the electric fieldwas directed perpendicular to the gravita-tional field. Electrophoresis has been usedto move particles to a place where opticaltweezers can stick them to a wall.43 In an-other combination of electrophoresis andlight, the position of 2D colloidal crystalgrowth on an electrode was induced bythe currents at the electrode surface, asmentioned earlier,20,21 but in this case, thecurrents were influenced by illumination.44

On tin-doped indium oxide electrodes,the current density can be increased withlight, resulting in the ability to spatiallyarrange the crystallization process. Thecombination of magnetically induced par-ticle repulsions in 2D systems and opticaltweezers or tweezer arrays has led to in-sights into the effects of pinning arrays45

and the measurement of the elastic con-stants of a 2D crystal.46 In both cases, theexternal magnetic field controlled thestrength of the repulsions and thus the ef-fective temperature of the experiments,giving a kind of control that is difficult toachieve without a field. A combination ofmagnetic and electric fields has also beenused to control the properties of a 2D sys-tem of liquid-crystal droplets.4.7

Also, flow and the manipulation of col-loids with optical tweezers have beencombined. Insights gained from the studyof liquids flowing past trapping sitescreated by optical tweezers may lead tonew separation methods.48 Controlling the

arrangement of colloids inside microfluidiccells can switch flows or even apply apumping action, causing flow.49 Electro-rheological fluids, in which an externalelectric field is used to change the viscosityof a concentrated dispersion in millisecondsby inducing strong dipolar attractions be-tween the colloids, are another example ofone field regulating the response to an-other field.

Outlook Before spending some words on possible

future directions, it is important to repeatthat the overview given here is far fromcomplete. For instance, external (thermo-dynamic) fields set up by gradients intemperature,22 pressure, or solvent compo-sition have not been treated, even thoughall of these are promising methods for ex-erting external control over, for instance,the colloidal particle concentration, theinterparticle potential, or both. This illus-trates how, in the last few years, researchon external control of colloids and theirself-organization has taken off. It is nothard to predict that this trend, includingan increase in combinations of fields, willcontinue.

It is also likely that there will be a strongincrease in the use of colloids as modelsystems for investigating fundamentalquestions related to issues important tomaterials science. Examples are the effectof boundary conditions (e.g., stick–slipboundary conditions in the case of liquidcrystals, or issues related to flow pastwalls), the structure and dynamics ofdefects, and fundamental issues in tri-bology. In addition, there is a drive in thephotonic-crystal community to investi-gate the role of polydispersity on long-range order and the effects and possibleprevention of defects (point defects, inter-stitials, stacking errors, grain boundaries).Clearly, the effects of polydispersity areparticular to colloids, but the other issuesassociated with defects are of generalinterest.

From the examples given, it already fol-lows that the degree of control that externalfields allow will make it possible to pre-pare, in a controlled way, colloidal modelsystems that are (far) out of equilibrium.This will enable a more systematic studyof states (far) out of equilibrium, hopefullyclarifying on a fundamental level manyprocesses in both nature and industry.

Finally, electrorheological fluids areconsidered a “smart” material because theirviscoelastic properties can be altered by anexternal field. This allows for the materialsproperties to be dynamically adjusted.The increased knowledge that is beinggained right now on manipulating self-

organization will no doubt also result inan enhanced ability to control the proper-ties of other materials based on colloids.

AcknowledgmentsI would like to thank all of my collabo-

rators on the work presented and reviewedin this article: from Utrecht University,Christina Christova, Didi Derks, RoelDullens, Damir Fific, Christina Graf, JacobHoogenboom, Astrid van der Horst,Arnout Imhof, Karin Overgaag, KrassimirVelikov, Peter Vergeer, Dirk Vossen, AllanWouterse, and Anand Yethiraj; from theFOM Institute for Atomic and MolecularPhysics (AMOLF), Marileen Dogterom;from Brandeis University, UjithaDassanyake and Seth Fraden; and fromDIMES (the Delft Institute of Microelec-tronics and Submicrontechnology), Anjavan Langen-Suurling and Jan Romijn.This work is part of the research programof the Stichting voor Fundamenteel Onder-zoek der Materie (FOM), which is financiallysupported by the Nederlandse Organisatievoor Wetenschappelijk Onderzoek (NWO).

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