Physics Today - ETH Z...and other small solutes, colloids are referred to as a general class of complex fluids. Their complexity is ame-liorated somewhat by treating all the colloidal

Physics Today Simple Ordering in Complex FluidsAlice P. Gast and William B. Russel Citation: Physics Today 51(12), 24 (1998); doi: 10.1063/1.882495 View online: http://dx.doi.org/10.1063/1.882495 View Table of Contents: http://scitation.aip.org/content/aip/magazine/physicstoday/51/12?ver=pdfcov Published by the AIP Publishing

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SIMPLE ORDERING INCOMPLEX FLUIDS

Colloidal particles suspended in solution provide intriguingmodels for studying phase transitions.

Alice P. Gast and William B. Russel

Ordering and the formation of crystals have long fas-cinated mankind. The reverence bestowed on gem-

stones and the fantastic properties attributed to crystallinematter arise from the unique optical, geometric and physi-cal properties of the ordered state. Although scientificinquiry has focused mostly on molecular and atomic crys-tals, much also can be learned from the study of super-molecular and colloidal arrays.

Colloidal suspensions, commonly referred to simplyas colloids, are composed of small particles that are 10-100nm in diameter—too small to see with the unaided eye—and dispersed in a solvent. Everyday examples abound,from milk to inks and paints to fog and smoke. Thebest-known example of an ordered colloid—a colloidalcrystal—is the opal, formed from a uniform array of silicaspheres compressed and fused over geological timescales.In the laboratory, the achievable size and uniformity ofcolloidal particles make them useful as ceramic precursors,optical filters, porous sieves, encapsulants and carriers ofactive compounds, as well as in the liposome technologyused by the cosmetics industry. In addition, colloidsformed from polystyrene beads with specific functionalitiesattached, such as antigens or reagents, are finding use inbiodiagnostics and combinatorial chemistry.

One important feature of colloids is that the submi-crometer particles are subject to constant Brownian mo-tion from the thermal fluctuations in the surroundingsolvent. Thus, to some degree, the particles can be con-sidered as effective molecules and treated according to thetheories of statistical mechanics. Because the solventsoften contain—in addition to the colloidal particles—dis-solved ions, polymer molecules, surface-active moleculesand other small solutes, colloids are referred to as ageneral class of complex fluids. Their complexity is ame-liorated somewhat by treating all the colloidal particlesor aggregates as an effective single-component system,with the interactions among particles being mediated bythe small-molecule solutes and the solvent. In addition,since the volume of a suspension is typically 50c/r or moresolvent, the interactions can be readily tuned throughsubtle changes in the solution chemistry rather than bydifficult pressure and temperature excursions. Studies ofcolloids at high concentration have revealed a myriad ofinteresting phenomena, including crystallization into a va-riety of structures, crystal twinning, the glass transition,

ALICE P. GAST is a professor in the department of chemicalengineering at Stanford University in Stanford, California.WILLIAM B. RUSSEL is a professor in the department ofchemical engineering at Princeton University in Princeton, NewJersey.

binary alloy formation and dendritic growth instabilities(figure 1).

Hard spheres: Entropy creates orderThe ability to tailor interactions between colloidal particleshas provided fertile ground for scientists interested in thefundamental aspects of phase behavior.1 Perhaps one ofthe most important answers to physicists' dreams has beenthe development of colloidal particles that interact bymeans of hard-sphere repulsions. Hard spheres interactwith each other only when they touch, and then with adivergent repulsion representing their impenetrable physi-cal volume. Thus, with hard particles, packing alonecauses ordering and no heat or energy is liberated uponcrystallization. This is a rather intuitive concept foranyone who has tried to pack a jar of marbles or rack aset of billiard balls; however, its thermodynamic conse-quences are more subtle.

Entropy is usually thought to bring about disorder.In a system of hard spheres, however, as in a set ofschoolchildren spacing themselves apart before beginningtheir exercises, particles gain entropy by arranging them-selves equidistantly from one another to maximize thespace in their vicinity, and thus they are compelled toorder. That entropy drives hard particles into crystallinearrays was first discovered through computer simulationsover 40 years ago (see box 1 on page 26). This seeminglysimple phase transition went without physical verificationuntil the development of hard polymer and silica spheres.The key to full characterization of the transition was theuse of a nonpolar suspending fluid that nearly matchedthe refractive index of the particles: Not only were thesuspensions rendered optically transparent, but the ubi-quitous van der Waals attraction between the spheres wassuppressed sufficiently to be balanced by the particle-sol-vent interaction. These hard particles provided the op-portunity to study crystallization, the glass transition,growth instabilities and nucleation in a system extensivelyinvestigated by means of computer simulation and statisticalmechanics.

As noted in box 1, hard spheres first order when theyoccupy approximately 50% of the system volume. Theonset of freezing immediately produces a solid at themelting volume fraction of 4> = 0.545, and the crystal canbe further compressed up to the closest packing density of0.74. Thus the phase diagram, while simple, has a remark-ably large region of fluid-solid coexistence and a solid phasethat persists over a fairly wide concentration range.

Hard spheres order into dense structures formed bystacking hexagonally ordered planes of spheres (figure 2).Until the past few years, computer simulations detectedno energy difference between face-centered cubic (FCC)

24 DECEMBER 1998 PHYSICS TODAY © 1998 AmSI'fen Institute i 'hysics, S:00.11-9::S-


arrays, created by repeated stacking in the three availableinterstitial sites, and hexagonal close-packed (HCP) crys-tals, formed by repeated stacking in only two of theinterstitial sites. The lowest-energy configuration hasremained an open question in experiments on colloids,although the small energy differences between stackingarrangements detected in recent computer simulationsand analysis indicate a preference for the FCC structure.Both ground-based experiments and those done undermicrogravity conditions in the space shuttle by PaulChaikin and his coworkers at Princeton University andNASA indicate a prevalence of randomly stacked HCPstructures, though an FCC component emerges if enoughtime is allowed.

Gravity clearly influences two features of the order-ing transition. First, instabilities during crystal growthanalogous to those observed in snowflakes produce milli-meter-sized dendrites in microgravity (figure 3) and yetare suppressed by viscous stresses and sedimentation innormal gravity. Second, there is a glass transition forhard-sphere colloids in the vicinity of 4> = 0.58, identifiedby Peter Pusey and Bill van Megen in 1986.2 Often, acrystalline phase develops near the top of a colloidal glassover time, showing the glass to be a metastable phasecaused by the arrested mobility of the particles that slightdilution due to sedimentation could relieve. Chaikin andhis coworkers found that a sample at </> = 0.59, whichformed a persistent colloidal glass on the ground, crystal-lized in microgravity, albeit heterogeneously.3

The nucleation and growth of hard-sphere colloidal

FIGURE 1. COLLOIDAL CRYSTALLITES ofcharged polystyrene spheres 67 nm in diameterat a volume traction of </> = 0.017 in a solutionwith a molar ionic strength of 10 s.a: Crystallites growing into disordered regionsundergo an instability that produces thesebroad fingers, 100-200 /xm across, b: Randomswitching between two FCC twin structurescauses the striped appearance when viewedthrough crossed polarizers. (Photos by S.Nilsen and Y. Monovoukas.)

crystals are readily studied by light scatter-ing and microscopy. According to classicnucleation theory, the competition betweenthe free energy driving the ordering transi-tion and the energy required to create thenew solid-liquid interface produces an en-ergy barrier for growth and establishes aminimum size—the critical nucleus size—that crystallites must achieve before grow-ing spontaneously.4 In 1995 Bruce Ackersonof Oklahoma State University and the lateKlaus Schatzel detected the decrease in thecritical nucleus size with supersaturation,observing a small value of around 10 par-ticle radii in the middle of the coexistenceregion.5 Crystal growth is often limited bythe diffusion of particles to the growingcrystal front, resulting in the formation ofdendrites mentioned above and shown infigure 3. Evidence for a region of lowerconcentration in the fluid around a growingcrystallite, confirming the diffusion limita-tion, comes from the shape of the scatteringstructure factor at low angles, which exhib-its a ring of high intensity. Low-angle andBragg scattering studies are now assem-bling the experimental picture, supporting

aspects of the Ackerson-Schatzel model and detectingeffects of interactions between crystals that are also seenin molecular systems.

Soft spheres: tunable repulsionsThe addition of a "soft," or long-range, repulsion to colloi-dal particles can keep them sufficiently separated thatthe van der Waals attraction is negligible, rendering thesuspension stable against aggregation under a variety ofconditions.4-6 Most commonly, aqueous suspensions arestabilized by the screened electrostatic repulsion betweencharges imparted to the particle surfaces; the range of theinteraction is characterized by the Debye length K"1, whichscales inversely with the square root of the ionic strength ofthe suspension.

Another way to prevent aggregation is to attach sol-uble polymer chains by one end to the particle surface,thus creating a dense "brush" with flexible bristles stretch-ing toward the free solvent. An encounter between twoparticles compresses the brushes, generating a repulsion.In both charged and polymer brush suspensions, the softrepulsion extends over a range that can be comparable toor greater than the particle size.

Particles interacting by means of such soft repulsionexhibit a Kirkwood-AJder transition but at quite lowparticle volume fractions. These tenuous "liquid crys-tals"—with particles spatially ordered but surrounded byfluid and separated in space by distances comparable totheir size—are easily melted by flow. The soft-sphere dis-order-order transition can be provoked by two means:

DECEMBER 1998 PHYSICS TODAY 25


Box 1. Kirkwood-Alder Transition

In 1939, John G. Kirkwood speculated that repulsive particleswould order at a density below the close-packed limit. Some

years later, Kirkwood and his student Bernie J. Alder surmisedthat this transition should happen for hard spheres at a volumefraction of </> = 0.50. The first-order solidification transitionin hard spheres was first observed in 1957 through moleculardynamics calculations by Alder and Tom E. Wainwright atLawrence Livennore National Laboratory in California, andin Monte Carlo simulations by William Wood and J. D.Jacobson at Los Alamos National Laboratory. In moleculardynamics, the equations of motion for all the particles in thesimulation are solved for each time step. Periorming thecalculations was a major accomplishment in those days, giventhat computers were in their infancy (and required the labori-ous use of punched cards, paper tape and line printers): Hun-dreds of hours on an IBM-704 were needed to search for thetransition at the highest densities in the molecular dynamicssimulations (at the now paltry rate of 2000 collisions per hourfor simulations with 108 particles). Therefore it is not surpris-ing that 11 years passed before, in 1968, the efforts of WilliamHoover and Francis Ree and of Alder, Hoover, and WilliamYoung resulted in the accurate determination of the densities4> = 0.494 and 0.545 for the fluid and solid when they coexist.Now referred to AS the Kirkwood-Alder transition, this phasetransition has become the cornerstone of our understanding ofcolloidal ordering.

The figure shows the equation of state that Alder, Hooverand Young found for hard spheres, presented as pressure(normalized by the thermal energy &7*and the FCC close-pack-

ing density rc0) versus volume fraction (f> (solid line). Thefirst-order ordering transition begins at cf> = 0.494 and the solidfirst melts at <\> = 0.545, but both phases have metastablebranches (dashed lines). The data (red dots) are from x-raydensitometry performed on an equilibrium sediment of poly-styrene spheres 720 ntn in diameter in a 3 millimolar saltsolution by Maarten Rutgers and his colleagues at PrincetonUniversity and the Exxon Corporate Laboratory.

0.45 0.5 0.55 0.6VOLUME FRACTION i>

increasing the particle volume fraction or increasing therange of the repulsion. Increasing the range is easily ac-complished in charged suspensions by removing screeningions from the fluid, thereby increasing the Debye length.As with hard spheres, the ordered soft particles assume cubicarrangements. The FCC phase prevails at higher concen-trations or with shorter range repulsions. As the range ofthe repulsion is increased, a lower-density, body-centeredcubic (BCC) phase forms, as shown in figure 4.

The scattering and microscopy techniques employedfor studying hard spheres are also used to examine the

FCC BCC

crystallization behavior of charged colloids and other softspheres, often producing vivid colors (as seen on the coverand in figure 1) because of the strong diffraction.' Again,the growth can be unstable,8 producing dendrites like thelarge fingers shown in figure la. The very slight energydifference between the two possibilities for stacking thehexagonally packed planes of FCC crystals produces stack-ing faults and twins, as evident in the striations shownon the cover and in figure lb. These stacking faults havebeen directly visualized by Henk Lekkerkerker and hiscolleagues at Utrecht University through confocal scan-ning microscopy of fluorescently labeled silica particles.Diffusion is not always the limiting element in crystalgrowth: Thomas Palberg and his coworkers at the Uni-versity of Mainz have detected BCC crystals that grow byreaction-limited kinetics.

The colloidal nature of soap molecules has been knownto scientists for many years. In addition to their abilityto support foam, clean surfaces and lower interfacialtension, soap molecules associate in water, with their oilytails aggregating into small structures known as micelles.The scattering of light from micelles is familiar to anyonewho has noted the turbidity of leftover dish or bathwater.

FIGURE 2. THE STRUCTURES formed in cubic packing ofrepulsive particles. Hard spheres order themselves in stackedhexagonal arrays (top). Orderings cycling through all threepossible layer positions (red, blue, green, red and so on) formface-centered cubic (FCC) crystals; alternation between onlytwo positions (for example, red, blue, red and so on) produceshexagonal close-packed (HCP) structures. The FCC and HCPstructures are the most dense, both having a maximumpacking fraction of 4> = 0.74. The body-centered cubic (BCC)structure has a maximum packing of <j> = 0.68 and is stabilizedby repulsions having a longer range.

26 DECEMBER 1998 PHYSICS TODAY


FIGURE 3. DENDRITIC GROWTH of crystallites of hard-spherepoly(methylmethacrylate) colloidal particles 508 nm indiameter at a volume fraction of r/> = 0.504 in a mixture ofdecahn and tetrahn. Grown in microgravity on the spaceshuttle, the dendritic crystallites are 2-3 mm in diameter andpersist for months. (Reprinted by permission from Nature,vol. 387, p. 883, copyright 1997, Macmillan Magazine Ltd.)

Such association colloids, as they are called, can also beformed on a larger scale by polymeric surfactants or byblock copolymers consisting of two polymer chains cova-lently attached to one another. When mixed with a solventthat dissolves one of the chains but not the other, thesecopolymers produce spherical micelles with compact, in-soluble cores surrounded by a polymer brush.

Polymeric micelles are critical to several applications,including separations, such as the scavenging of traceorganics or metals for environmental processes; encapsu-lation, as in cosmetics and drug delivery; and use asrheological modifiers—for instance, as additives in lubri-cating oils to change the temperature behavior of theviscosity.

In addition, micelles provide a nice model system forstudying the effect of curvature on polymer brushes. Poly-mers tethered to large particles or to the cores of largemicelles have concentration profiles that are parabolic inform. The structure of chains attached to highly curvedsurfaces is better represented as a starlike configurationwith a rapid power-law decay of the concentration profile.These two situations, illustrated in figure 5, produce subtlydifferent interactions and qualitatively different phasebehavior. The more brushlike systems with shorter-ranged and steeper repulsions order into FCC arraysobserved for hard spheres, whereas the starlike micellesform BCC arrays.

At higher concentration, the polymeric nature of theinteraction produces a curious melting of the micellarcrystals; this is one example of a reentrant liquid-solid-liquid phase transition.9 The effect arises from increasedscreening in the semidilute polymer brushes, which causesthem to relax from their highly stretched configuration atdilute concentrations and therefore interact less stronglywith their neighbors.

BCC-FCC transitionThe formation of BCC and FCC crystals in complex fluidsis analogous to the ordering in metals, so the determina-tion of the FCC-BCC phase boundary is of fundamentalinterest.10 Although many complex fluids exhibit a struc-tural transition from the higher-density FCC phase to thelower-density BCC phase as the range of the repulsionincreases, no general model for this crossover exists. Per-haps the earliest studies of this behavior were the simu-lations with inverse power-law potentials U(r) « r~" con-ducted by Jean-Pierre Hansen of the University of Parisand William Hoover and his coworkers at Lawrence Liver-

0.002 0.004 0.006V O L U M E F R A C T I O N <j>

0.008 D.C1

FIGURE 4. GENERALIZED PHASE DIAGRAM for soft sphericalparticles interacting through screened Coulomb repulsion(Yukawa potential). The vertical axis is the volume that isinaccessible to one particle due to the presence of another; itscales as the cube of the Debye screening length, which sets thecharacteristic range of the interaction. As the range or thevolume fraction cj> is increased, these particles order into eitherbody-centered cubic (BCC) or face-centered cubic (FCC) arrays.

more National Laboratory in the early 1970s. They foundthat, for interaction potentials with n < 7, colloids frozeinto a stable BCC phase; subsequent concentration of thisphase produced a BCC-FCC transition. More recentsimulations and density functional calculations have foundthe triple point for BCC, FCC and liquid coexistence tobe near n = 6. The basic principle is that, for moderatelysoft potentials, the FCC structure has the lower energyand the BCC has higher entropy. Thus, for a sufficientlyhigh melting temperature, an FCC-BCC transition canprecede the transition to the fluid. Indeed, in chargedcolloidal systems in the liquid phase, a transient BCC-likestructure was observed in time-resolved scattering experi-ments by Ackerson and Noel Clark years ago at theUniversity of Colorado.

BCC-FCC transitions are found experimentally inseveral complex fluids. In charged colloids, the BCC-FCC-liquid triple point occurs when the interparticle spacingis 4.9 times the Debye length. Polymeric micelles crossthe polymorphic threshold when the hydrodynamic radiusof the micelle is three times that of the core, and a similartransition is found in nanoparticles carrying fatty mono-layers on their surfaces. The coexistence between BCCand FCC phases detected in charged colloids by Chaikinand his colleagues has verified the first-order nature ofthis phase transition.

Attractions: the "glue" that creates liquidsThe disorder—order transition for particles having purelyrepulsive interactions persists when attractive interac-tions are added. In addition, attractions of sufficientlylong range introduce a gas-liquid phase transition. Thereare several ways to control the attractive interactions.Sometimes the gas-liquid transition can be provoked bycareful manipulation of hard-sphere systems, since thevan der Waals attraction depends weakly on the tempera-ture. In aqueous systems, adding electrolytes to screenthe electrostatic repulsion between charged particles caninduce aggregation by means of van der Waals attraction.The onset of aggregation, however, is generally abrupt,and produces persistent nonequilibrium aggregates thatobscure the equilibrium gas-liquid phase transition.

A more popular approach is to add a nonadsorbingsoluble polymer (or surfactant micelles or smaller colloidal

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R • 0: star

r-/?

• oo; brush

r-R

FIGURE 5. THE CONFIGURATION OF TETHERED POLYMERS,as well as their concentration profile as a function of distancer, depends on the radius R of the colloidal particles or micellarcores to which they are attached, a: On small particles ormicelles, the polymers form a starhke configuration, b:Polymers form a planar brush on the surface of a largecolloidal particle or micelle.

particles) to an otherwise stable suspension to produce aweak, long-range attraction between colloidal particles.The soluble additives are excluded from a region compa-rable to their size near the particle surface, producingwhat is called a depletion layer, as sketched in figure 6.When two particles approach closely enough for theirdepletion layers to overlap, the osmotic pressure exertedon each particle by the dissolved polymer outside theregion of overlap causes a weak attraction. The magni-tude is proportional to the polymer concentration, and therange scales with the depletion layer thickness (or polymersize), thereby allowing one to tune the interaction toproduce the desired phase behavior. Aggregation causedby the depletion force was exploited in the 1930s toconcentrate rubber latex particles, but scientific studybegan in earnest only 20 years ago in the groups of AgienusVrij at Utrecht University and Brian Vincent at the Uni-versity of Bristol.

Box 2. Colloidal Alloys in Binary Mixtures

Renewed interest in binary dispersions for depletion sepa-ration prompts a look back at the beautiful and complex

structures created by Sei Hachisu (University of Tsukuba)and his coworkers in the 1980s.'7 Motivated by the obser-vation made by John Sanders (Commonwealth Scientific andIndustrial Research Organisation) in the 1950s and CherryMurray (Bell Laboratories) in 1978 that opals contain twonarrow size ranges of silica spheres, Hachisu proceeded tocreate a myriad of unique structures from binary mixturesof uniformly sized colloidal particles. The structure andstability of the crystals that were formed depended criticallyon the particle sizes. Using a metallurgic microscope,Hachisu observed many lattices, including the simple NaCl,MgCu: (diamond lattice) and even a strange NaZn,, array.These experiments further demonstrate that colloidal parti-cles are useful model systems for the study of phase behavior.

Solid

10

2.50.2 0.4 0.6

VOLUME FRACTION d>0.8

FIGURE 6. SCHEMATIC PHASE DIAGRAM for particlesinteracting by means of the attractive depletion force. Thisforce arises from the osmotic pressure exerted on the particlesfrom small nonadsorbing polymers that are excluded from aregion called the depletion layer that surrounds each panicle.The behavior of the colloid-polymer system depends on the ratioof the particle radius a to the polymer's radius of gyration rg, aswell as on the temperature T, the polymer osmotic pressure P,and the colloidal particle volume fraction 4>. For small ratiosa/r„ the system has a stable liquid phase between the triple point(A) and the critical point (C). As the ratio increases, the criticalpoint and triple point approach each other, until the liquidphase disappears for ratios greater than 3.

It was with the depletion interaction that Peter Sperryof the Rohm and Haas Co (experimentally) and we alongwith Carol Hall (theoretically) discovered 15 years agothat the presence of a gas-liquid transition depends keenlyon the range of the attraction. As illustrated in figure 6,changing the particle-polymer size ratio produces a seriesof phase envelopes. The critical point disappears into anunstable regime when the polymer (and hence the attrac-tive well) is about one-third the size of the particle. Asimilar absence of the gas-liquid transition is found forproteins and large molecules such as the fullerene Cm.Simple models by Marc Baus and his colleagues at theFree University of Brussels and George Benedek's groupat MIT link the disappearance of the gas-liquid phasetransition to the range of the attractive potential and thenumber of neighbors in the solid phase. Lekkerkerkerand his coworkers have extended our earlier model toaccount for partitioning of the polymer between the twophases. Complementary experiments by Pusey and hiscolleagues have delineated the phase diagram of binarypolymer-colloid systems, again noting the disappearanceof the gas-liquid critical point.11 The depletion mecha-nism has found important application in protein separa-tions, as explored by Hall and her coworkers at NorthCarolina State University, and as a means to fractionateemulsion droplets with surfactant micelles, a techniquepioneered by Jerome Bibette of the University of Bor-deaux. Arjun Yodh and his colleagues at the Universityof Pennsylvania have exploited the depletion interactionto produce phase separation in binary dispersions (seebox 2 on this page).

28 DECEMBER 1998 PHYSICS TODAY


In the limit of very short range attractions betweenparticles, the simplest model for the interparticle interac-tion is the adhesive hard-sphere potential of Rodney J.Baxter at the Australian National University. Extensivesimulations and density functional calculations have iden-tified the phase boundary (binodal) and limit of thermo-dynamic stability (spinodal) associated with the gas-liquidtransition, a percolation transition and the liquid-solid tran-sition. The general phase diagram resembles that of thedepletion interaction shown in figure 6 for small depletionlayer thickness, where the gas-liquid transition is unstableand subsumed into the gas-solid transition. Elegant ex-periments at Utrecht University by Kees de Kruif, JanDhont and their coworkers confirmed the spinodal andproduced a poorly equilibrated fluid-solid transition.

The utility of the adhesive sphere model for complexfluids and protein solutions was illustrated by Chip Zuk-oski and his colleagues at the University of Illinois in1996.12 They measured the second virial coefficient tocharacterize protein-protein and other colloidal interac-

FlCURE 7. TwO-DIMtNS)ONAL CRYSTALS of the proteinstreptavidin bonded to a biotinylated lipid monoLiyer. Thesymmetry ol the crystals (the individual light green objects)depends on the pH of the aqueous buffer solution on whichthey float: pH = 8, 4, 5.2 (from top to bottom). Each field ofview is 350 /_tm x 550 /j.m.

tions using the adhesive-sphere potential. Then, by lo-cating the systems on the adhesive-sphere phase diagram,they confirmed an idea advanced by Abraham George andW. William Wilson at Mississippi State University thatonly a narrow range of virial coefficients produce goodprotein crystals. Stronger attractions reduce mobility andincrease the rate of crystallization, preventing the rear-rangements necessary for defect-free crystals; weaker at-tractions require higher concentrations that promote theformation of glassy, rather than crystalline, phases.

Two-dimensional crystallizationThe intriguing features of crystals and their beautifulsymmetries persist when the system is confined to twodimensions. Many examples of two-dimensional orderedarrays are found throughout the world: rows of corn, thebreeding grounds of the king penguin, the scales on asalmon and the paving stones on the rue Moufftard. Ona slightly smaller yet not colloidal scale are the ingeniousmesoscopic polymer objects created by George Whitesidesand his coworkers at Harvard University.1'' These shapeshave both hydrophilic and hydrophobic edges and, whenfloated on a water surface, will assemble into orderedarrays in which the hydrophobic edges are connected. Amyriad of structures can be envisioned and phase segre-gation can be realized by altering the object thickness.

When a system is strictly confined to two dimensions,the nature of the melting transition may change. Thisidea was first suggested over 25 years ago, and thetransition from a two-dimensional solid to a two-dimen-sional liquid is termed the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) transition after its discoverers.The KTHNY theory predicts that two-dimensional solidsmelt by means of sequential and continuous phase tran-sitions rather than a single, first-order, discontinuoustransition. Two-dimensional crystals exhibit both quasi-long-range positional order and long-range bond orienta-tion order. The proposed transition proceeds from thissolid to a liquid through an intermediate phase, termedthe hexatic, having quasi-long-range bond orientationalorder but short-range positional order. This theory hasbeen much debated, with many computer simulationsattempting to resolve the issue and, recently, colloidsproving to be very useful models.

Confining charged colloidal particles between two flatplates, Cherry Murray and her coworkers at Bell Laborato-ries were able to observe the KTHNY transition through ahexatic phase with an optical microscope. Recently, AndyMarcus and Stuart Rice14 at the University of Chicagoconfined uncharged particles stabilized by short-range repul-sions produced by bound polymers. Their experiments dididentify an equilibrium hexatic phase, but unlike thepredictions of KTHNY, this phase was separated from thesolid and from the liquid by first-order phase transitions.As with the three-dimensional BCC-FCC and gas-liquidtransitions, the range of the interparticle interactions maybe a key to the phase behavior in two dimensions.

The complex structure of proteins can often be deci-phered using the power of crystallography—but only if theproteins can be crystallized. Some proteins form two-di-mensional arrays when attached to a lipid monolayerfloating on top of an aqueous solution. The monolayer of

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proteins can then be transferred to an electron microscopegrid for imaging and study by electron diffraction. Thisapproach to protein crystallization was pioneered by RogerKornberg and his colleagues at Stanford University in theearly 1980s to characterize protein structure. The concen-tration and orientation of proteins into a monolayer reducestheir degrees of freedom and can provoke ordering in systemseluding crystallization in solution. The groups of Kornbergand of Helmut Ringsdorf at the University of Mainz haveused these techniques to characterize new structures andto assemble multilayers of two-dimensional arrays.15

These lipid-bound arrays provide another avenue to-ward a physical understanding of two-dimensional crys-tallization. For example, a two-dimensional growth insta-bility analogous to that observed in colloidal suspensionsoccurs when impurities dilute the growing crystallites.Also, altering the acidity of the aqueous phase changesthe protein—protein interactions and results in new crys-talline lattice structures and morphologies for the den-drites produced by the instability. Figure 7 displays crys-tals of several shapes formed with the tetrameric proteinstreptavidin bound to a partially biotinylated lipid mono-layer.16 Interestingly, binding streptavidin to biotin at twoof four sites breaks the symmetry in the molecule andproduces anisotropic and sometimes chiral morphologies.Thus the appearance of chiral structures—an area offundamental interest—can be probed with these systems.Of greater importance is that with proteins comes theability to perform point mutations—altering interactionsin a specific way to study their impact on crystallization.Thus, although proteins remain complex in their detailedstructure and interactions, they provide ample opportunityto study the general phenomenon of crystallization at bothcolloidal and molecular scales.Alice Gast's and Bill Russel's research on ordering is supported bythe National Science Foundation and NASA's Microgravity Sci-ences Program.

References1. C. A. Murray. D. G. Gner, Am. Scientist 83, 238 (1995).2. P. N. Pusey, in Liquids, Freezing, and Glass Transition, J. P.

Hansen, D. Levesque, J. Zinn-Justin, eds., Elsevier, Amster-dam (1991), p. 763.

3. J. Zhu, M. Li, R. Rogers, W. Meyer, R. H. Ottewill, E. Phan.STS-73 Space Shuttle Crew, W. B. Russel, P. M. Chaikin.Nature 387, 883(1997).

4. A. W. Adamson, A. P. Gast, Physical Chemistry of Surfaces, 6thed., Wiley, New York (1997).

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30 DECEMBER 1998 PHTSTCTTODTTY"


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Physics Today - ETH Z...and other small solutes, colloids are referred to as a general class of complex fluids. Their complexity is ame-liorated somewhat by treating all the colloidal