CU-Boulder PHYS 7450 - Spontaneous patterning of quantum dots at the air-water interface

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Spontaneous patterning of quantum dots at the air-water interfaceRichard P. Sear, Sung-Wook Chung, Gil Markovich, William M. Gelbart,*and James R. Heath†Department of Chemistry and Biochemistry, University of California at Los Angeles,405 Hilgard Avenue, Los Angeles, California 90095-1569~Received 25 June 1998; revised manuscript received 8 March 1999!Nanoparticles deposited at the air-water interface are observed to form circular domains at low density andstripes at higher density. We interpret these patterns as equilibrium phenomena produced by a competitionbetween an attraction and a longer-ranged repulsion. Computer simulations of a generic pair potential withattractive and repulsive parts of this kind, reproduce both the circular and stripe patterns. Such patterns have apotential use in nanoelectronic applications. @S1063-651X~99!50306-1#PACS number~s!: 68.10.2mSpontaneous formations of spatial patterns arise spectacu-larly and yet commonly in a wide variety of nonlinear kinetic@1# and biological @2# processes. Still, more interestingly,they are observed in a surprisingly diverse set of equilibriumsituations involving fluids and solids in two and three dimen-sions. For example, in two dimensions ~2D!, systems as ap-parently disparate as magnetic garnets, Langmuir monolay-ers, and thin films of adsorbates all form periodic structuresconsisting of uniformly spaced domains with circular orstriped shapes @3#. In the garnets, the magnetization normalto the plane is high inside these domains and low in betweenthem whereas, in the Langmuir films, it is the number den-sity of molecules that is different inside and outside thecircles and stripes. The order parameter in these two cases isclearly different, but the spatial modulation — the pattern —is the same. The size of the patterns, i.e., the period of theirspatial modulation, varies from nm’s ~adsorbates on metals@4#! to micrometers ~Langmuir films @5#! to cm’s ~ferrofluids@6#!. In all of these cases, the onset of modulation, and itscharacteristic length scale, is caused by the competition be-tween an attractive interaction and a longer-ranged repul-sion; the former favors a bulk phase separation, while thelatter transmutes this into a microphase transition, involvingan equilibrated distribution of domains ~e.g., circles, andstripes in 2D, and spheres, cylinders and lamellae in 3D@3,7#!, all of which are of finite size in at least one direction.In Langmuir monolayers, for example, the attractions areassociated with van der Waals interactions between the alkylchains ~hydrophobic ‘‘tails’’! of the amphiphilic moleculesat the surface of water. The longer-ranged repulsions arisefrom the oriented dipoles that comprise the hydrophilic‘‘heads’’ of these species. This two-dimensional system hasbeen modeled as a dipolar lattice gas by Hurley and Singer@8#, and treated in the continuum limit by McConnell @9#.Inmany other instances of domain formation and microphaseseparation, the physical origin of the competing interactionsis more subtle. In the case of diblock copolymers, for ex-ample, the effective repulsions are due to the fact that thetwo blocks are connected to each other, and it is this con-straint that limits the size of the ~spherical, cylindrical, andlamellar! domains @10#. In aqueous solutions of surfactant,the spontaneous appearance of micelles can be understoodsimilarly in terms of the demixing between heads and tailsbeing frustrated by their connectivity @11,12#. More explic-itly, several groups @13,14# have shown how the basic phys-ics of structural organization and phase behavior in am-phiphilic systems can be recast into lattice models involvingferromagnetic ~attractive! nearest-neighbor interactions andantiferromagnetic ~repulsive! next-nearest-neighbor interac-tions.In this Rapid Communication we demonstrate that quan-tum dots — nanoparticles — at the air-water interface alsoorganize spontaneously to form spatially modulated phases.We observe in particular that nanoparticles at submonolayercoverage form both circular and stripe domain patterns, de-pending on the extent of coverage. These structures are ar-gued to be equilibrium states of the system, driven by thecompetition between attractions and longer-ranged repul-sions between the nanoparticles. Computer simulation resultsconfirm that a simple interaction potential consisting of thesecompeting parts does indeed lead to the experimentally ob-served structures. While our results are related in fundamen-tal ways to the spatial patterns reported for the many othersystems mentioned above, we shall feature the concentrationdependence of the observed spatial patterns. In particular, thereversible conversion from circles to stripes in 2D, upon in-crease in nanoparticle coverage, is argued to be analogous tomore general phenomena observed, for example, in surfac-tant solutions where micellar aggregates evolve from globu-lar to cylindrical to bilayer forms as the volume fraction israised @7#. In all of these cases, the interactions between theclusters are the ones that lead to their reorganization intolower-curvature shapes that can pack more efficiently.In recent years, chemically synthesized quantum dotshave begun to appear as the active elements in various pro-totype photonic @15,16# and electronic @17,18# devices. Si-multaneous with these developments, techniques for the pat-terned assembly of nanoparticles via templating approacheshave been reported @19–21#. Nontemplated,thermodynamically-controlled patterning can potentially pro-duce organization at nanometer length scales that cover largeareas. Such approaches may prove useful for certain defect-tolerant device-related applications @22#. From a more fun-damental point of view, the spherical symmetry of these par-*Electronic address: [email protected]†Electronic address: [email protected] COMMUNICATIONSPHYSICAL REVIEW E JUNE 1999VOLUME 59, NUMBER 6PRE 591063-651X/99/59~6!/6255~4!/$15.00 R6255 ©1999 The American Physical Societyticles makes modeling of their interactions and phasebehavior easier than with complex molecular structures.Circles and stripes of silver quantum dots were preparedusing two different approaches. All experiments utilized hex-ane or heptane solutions of 4–6-nm-diameter Ag particlesthat were surface passivated with octanethiol. The structuresof the ~sub!monolayer films were sampled by transferring theLangmuir films to a transmission electron


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