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Building Polyhedra by Self-Assembly

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Building Polyhedra by Self-Assembly Building polyhedra by self-assembly Govind Menon Experiments Computations Shivendra Pandey Ryan Kaplan, Daniel Johnson David Gracias (lab) Brown University Johns Hopkins University NSF support: DMS 07-7482 (Career), EFRI-10-22638 and 10-22730(BECS). Main reference: Artificial Life, Vol. 20 (Fall 2014) Part 1. Biology, technology, and a little math... This talk is a description of a common mathematical framework to describe self-assembly of polyhedra. I will contrast two problems: The self-assembly of the bacteriophage MS2 (Reidun Twarock's team) Surface tension driven self-folding polyhedra (our work). Examples of icosahedral symmetry in nature C 60 molecule, 0.7 nm Adenovirus, 90 nm Radioalarian 10 µm Widely different self-assembly mechanisms at different scales. It is a very interesting to understand the types of symmetry, the “coding of symmetry” in the genome, and the interplay between symmetry and the pathways of self-assembly. Google Ngram Viewer Ngram Viewer Graph these case-sensitive comma-separated phrases: self assembly between 1900 and 2008 from the corpus English with smoothing of 5 . Search lots of books 0 Tweet 0 Search in Google Books: 1900 - 1974 1975 - 2001 2002 - 2003 2004 - 2005 2006 - 2008 self assembly (English) Run your own experiment! Raw data is available for download here. © 2010 Google - About Google - About Google Books - About Google Books NGram Viewer 1 of 1 One of the first uses of the phrase “self assembly” is by Caspar and Klug in their work on the structure of viruses. They distinguish grades of organization in a cell as sub-assembly and self-assembly and write: Self-assembly (of a virus) is a process akin to crystallization and is governed by the laws of statistical mechanics. The protein subunits and the nucleic acid chain spontaneously come together to form a simple virus particle because this is their lowest free energy state .” Caspar and Klug; Cold Spring Harbor Symposium, (1962) Our work is on synthetic self-assembly. We want biology to inspire the design of devices and materials. In turn, we hope that synthetic models will shed light on biological self-assembly. Typical themes: stripped down interactions (e.g. one dominant energy scale) , simple shapes built out of a few simpler motifs, some randomness. R EPORTS R EPORTS mm), we limited the heighttwo of setsthe solder of dots film differentiated by symmetry: This self-assembled, 3D parallel network The shape and the distribution of solder dots on the wires to ϳ15% that{1} of andthe dots. {2, 5, When 8, and 11}. During self-assem- mimicked bus lines in circuits in which a on the assembling faces raises interesting Forming Electrical Networks in the faces self-assembled, thebly, larger dots fromdots fused one set on a TO connect to dots number of electrical components are powered questions regarding the design of patterns into connections, but thefrom smaller the same wires set did on another TO. These dots by the same common wires. that best enable the “recognition” of one pat- Three Dimensions by not touch and fuse (Fig.are 2C). used It was,for parallel as a or bus-line connections. For the realization of a 3D network with tern by another. Other concepts adapted from result, unnecessary to insulateThe other the wiresdots, {3, to 6, 9, and 12} and {4, 7, serial connectivity (Fig. 4), we used the sets 2D self-assembly, such as hierarchical self- Self-Assembly prevent shorting, even when10, theyand 13}, crossed form on two distinct sets related by of solder dots {3, 6, 9, and 12} and {4, 7, 10, assembly (16) and shape-selective self-as- juxtaposed faces of two TOs.reflection symmetry. Upon assembly, dots and 13} (Fig. 2D) that were off the axes of sembly [that is, use of lock-and-key struc- David H. Gracias, Joe Tien, Tricia L. Breen, Carey Hsu, We wished to demonstrate,from one by set self-as- on a TO (e.g., outputs from one symmetry of the square face (14). The im- tures (17, 18)], offer more sophisticated strat- George M. Whitesides* sembly in 3D, networksprocessor) that are connect widely to those from the other set portant feature of the assembled 3D network egies for the fabrication of asymmetrical net- used in current 2D IC technology.on another In TO these (e.g., inputs to a second pro- was that the cathode of one LED always works incorporating more than one repeating Self-assembly of millimeter-scale polyhedra, with surfaces patterned with sol- systems, pins on processorscessor). belong These to dotsone are used for serial, input/ connected to the anode of another LED unit. der dots, wires, and light-emitting diodes, generated electrically functional, of three groups: bus linesoutput (driving connections. voltage, across the assembling faces. The serial net- We have demonstrated parallel and serial three-dimensional networks. The patterns of dots and wires controlled the clock), inputs, and outputs.Figure Bus lines 3 shows con- the realization of a 3D works were traced by illuminating sets of connectivity separately; it is possible to ex- nect processors in parallel; outputs of one structure of the networks formed; both parallel and serial connections were network with parallel connectivity, using LEDs (e.g., Fig. 4D) (15). tend these ideas to more complex networks generated. processor connect serially to inputs of ad- self-assembly. The pattern of solder dots con- The 3D assemblies can be designed to be involving different combinations of parallel jacent processors. sisted of dots {2, 5, 8, and 11} and {1} (Fig. porous: this porosity may allow for cooling and serial connections. The LEDs in our dem- Most fabrication of microelectronic devices mechanical structures: examples include In the pattern of solder dots (Fig. 2D), the A self-assembling circuit is carried out by photolithography and is “flip-chip” technology (9) and the rotation of five dots that lie on reflection2D), axeswhich comprise were on the axes of symmetry of fluid to be pumped through the assemblies. onstrations are simple bipolar electronic de- intrinsically two-dimensional (2D) (1). The parts of microstructures into nonplanar orien- the square face (13). In the assembled aggre- gate, LEDs on one TO connected to those on 3D interconnections required in current de- tations (10, 11). During assembly, recogni- Fig. 3 (left). Aself-as- vices are fabricated by the superposition of tion of the pattern of dots on one face by that the adjacent TO in parallel, along three or- sembled 2 ϫ 2 ϫ 3 stacked, parallel planes and by their connec- on another orients and registers the patterns, thogonal directions. The fidelity of the inter- aggregate containing tion using perpendicular vias (2–4). We dem- and generates dot-on-dot electrical connec- connections was visualized by lighting up the 12 TOs and demon- onstrate self-assembly as a strategy to form tions among polyhedra. Self-assembly of LEDs connected in parallel in the assembly. strating parallel con- interconnections between electronic devices polyhedra can generate networks in which the nectivity. (A)Thepat- tern of copper dots, and prefabricated circuits, and to form 3D LEDs are connected either in parallel or in on March 23, 2011 wires, and contact pads electrical circuits. series. Figure 1 outlines both the fabrication used. (B)Apatterned on March 23, 2011 Previous uses of self-assembly to fabri- of the patterned polyhedra and their self- TO with three LEDs, cate electronic devices include shape-directed assembly into 3D structures that include elec- prior to assembly. (C)A fluidic self-assembly of light-emitting diodes trical networks (12). photograph of the self- (LEDs) on silicon substrates (5) and coplanar We used a scheme in which LEDs were assembled aggregate integration of segmented integrated circuit mounted on the hexagonal faces of the TO, and a penny (to indi- (IC) devices (6) into 2D “superchips” using and the solder dots were placed on the square cate size). Two electri- cally isolated pairs of capillary forces at the surface of a flotation faces. To maximize the rate of self-assembly, wires connected to a liquid (7). We demonstrate the formation of all of the square faces of the TO had the same www.sciencemag.org battery illuminate six two classes of 3D electrical networks—par- fourfold symmetric pattern of solder dots. LEDs in an electrically www.sciencemag.org allel and serial—by self-assembly, as an ear- With this pattern, correct registration of pat- continuous loop involv- ly step toward a strategy for fabricating 3D terns on juxtaposed faces occurred in one of ing three TOs. (D)Cir- microelectronic devices. The basic unit in four indistinguishable ways; dots on the pat- cuit diagram showing these assemblies is a polyhedron [a truncated terns that transformed into each other under the parallel network octahedron (TO)], on whose faces electrical fourfold rotational symmetry were equivalent formed. The gray cir- cles represent individu- circuits are printed. In the present demonstra- and served the same function. On the 3 mm al TOs. The blue half- tions, these circuits include LEDs to demon- by 3 mm square face, the width of all of the Downloaded from circles represent solder strate electrical connectivity and trace the solder dots was ϳ1 mm (Fig. 2). A common dots that connect on Downloaded from networks; in the future, they will include size was required: the solder wetted the cop- juxtaposed faces of devices with more complex functionality per with a well-defined contact angle, and two TOs. The LEDs are (e.g., processors). The LEDs are wired to each drop of the same size therefore had the shown in black. The patterns of solder dots on adjacent faces of same height. Empirical testing suggested that network contains 16 the polyhedron.
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