Self-Assembly of Mesoscale Objects intoOrdered Two-Dimensional ArraysNed Bowden, Andreas Terfort, Jeff Carbeck,George M. Whitesides*Regular arrays of topologically complex, millimeter-scale objects were prepared byself-assembly, with the shapes of the assembling objects and the wettability of theirsurfaces determining the structure of the arrays. The system was composed of solidobjects floating at the interface between perfluorodecalin and water and interacting bylateral capillary forces; patterning of the wettability of the surfaces of the objects directsthese forces. Self-assembly results from minimization of the interfacial free energy of theliquid-liquid interface. Calculations suggest that this strategy for self-assembly can beapplied to objects on a micrometer scale.This report describes the directed self-as-sembly of small objects (between 1 and 10mm in length) into regular, two-dimension-al arrays. It extends ideas emerging frommolecular self-assembly to much larger ob-jects and describes an approach for the fab-rication of complex systems that has poten-tial for application in microelectronics, op-tics, microelectromechanical systems, anddisplays (1). These self-assembled systemshave analogies to bubble rafts (2, 3) andrelated aggregates formed by spheres on sur-faces (4, 5); they differ in that the use ofnonspherical objects with designed shapesand wettabilities makes it possible to gen-erate aggregates with complex structures.The individual objects were made ofpolydimethylsiloxane (PDMS), a hydro-phobic polymer with a surface free energy(gSV) equal to 22 to 24 erg cm22(6–8).First, the PDMS was cured in a mold of thedesired shape. Designated surfaces werethen made hydrophilic by oxidation withan O2plasma (6, 9); surfaces that were tobe hydrophobic were either covered withtape before the oxidation or generated bycutting of the PDMS after oxidation toexpose a fresh hydrophobic surface. Foreach of the objects in Fig. 1, the lower face[the face in contact with the perfluorodeca-lin (C10F18)] was hydrophobic, and thesides were either hydrophobic or hydrophil-ic according to the design summarized inthe insets. The upper face was usually madehydrophilic to prevent any C10F18from set-tling on top of the objects and causing themto sink into the C10F18-H2O interface. TheC10F18wetted the hydrophobic sides andformed menisci; the hydrophilic sides barelyperturbed the C10F18-H2O interface (10,11). The system was placed on a rotaryshaker that oscillated gently in the plane ofthe interface. The frequency of rotation wasadjusted for each system to allow the in-plane movement of the liquid to bring theobjects close to one another and to break upmisformed aggregates; a typical frequencywas 1 to 2 Hz. When two hydrophobic sidesof PDMS came within a critical distance ofone another (;5 mm), they moved intocontact. This movement was driven by theminimization of the interfacial free energyof the system, caused by eliminating thecurved menisci at the hydrophobic surfaces.A thin layer of C10F18remained betweenthe objects, even at their closest contact(12). Self-assembly was completed after ;5to 30 min.A variety of self-assembled arrays can bemade by controlling the hydrophobicity ofthe sides of the objects (Fig. 1A). Thecontrast between Fig. 1B and Fig. 1C dem-onstrates the level of control that we canachieve: In Fig. 1B, alternate sides of thehexagons are hydrophobic and the objectsform an open network; in Fig. 1C, all of thesides of the hexagons are hydrophobic andthe objects form a close-packed array.A shape-selective lock-and-key geome-try allows the formation of aggregates frommore than one component (Fig. 2, Athrough C). The objects in Fig. 2A havethree favorable choices for contact (Fig.2C). The amplitude of oscillation of thesystem during equilibration was set to belarge enough to break apart pairs interact-ing head-to-head and tail-to-tail but toleave together those interacting morestrongly head-to-tail. Head-to-tail contactis favored energetically by two complemen-tary factors: it maximizes the area of hydro-phobic surface in close proximity; and it iskinetically stable to dissociation caused bystirring, because the oscillating motion atthe interface—a motion that seems to in-Department of Chemistry and Chemical Biology, HarvardUniversity, 12 Oxford Street, Cambridge, MA 02138,USA.*To whom correspondence should be addressed.Fig. 1. Crystalline aggregates generated by the self-assembly of (A) crosses,(B) hexagons in an open network, and (C) hexagons close-packed. Panel (A)shows an extended two-dimensional square array formed from crosseshaving hydrophobic ends; the two crosses with arrows pointed toward themwere completely oxidized; these pieces were rejected by the array. Theyclearly show the shape of the individual pieces. Hatched faces in the insetsindicate hydrophobic surfaces and white faces indicate hydrophilic surfaces.The top faces are clear and hydrophilic.REPORTShttp://www.sciencemag.orgzSCIENCEzVOL. 276z11 APRIL 1997 233fluence the objects primarily by shear—hasminimal influence on pairs of objects onceassembled into a head-to-tail configuration.A third method for self-assembly usesthe area of hydrophobic side surfaces, andthus the strength of the attractive capillaryforce, to direct the self-assembly of differentobjects (Fig. 3, A through D). A mixture oftwo types of PDMS objects with the samesquare bases, but heights that differed by afactor of 5, were agitated at the interfacebetween C10F18and water. The order of theattractive forces in the system was tall-tall . tall-short . short-short. The degreeof agitation was set to allow the tall ob-jects to form an array; when agitation wasstopped, the short objects coagulatedaround this array in a disordered state.The above experiments were carried outwith objects having dimensions of 1 to 10mm. We investigated the lower limits to thesize of the objects that could be assembledby lateral capillary forces at the C10F18-H2Ointerface by calculating the change in in-terfacial free energy as two perpendicularsurfaces moved from infinite separation tosome finite separation, d. We calculated theheight h (in meters) of the C10F18-H2Ointerface between the two objects using thelinearized Laplace equation (13) (Fig. 4A)]2h]x251g~Drgh 2DP0! (1)where g (in joules per square meter) is theinterfacial free energy, Dr (in kilograms percubic meter) is the difference in densitybetween the two fluids, the zero for h is setat the C10F18-H2O