Featured Research

from universities, journals, and other organizations

Best routes found to self-assembling 3-D shapes

Date:
December 7, 2011
Source:
Brown University
Summary:
Researchers have found optimal configurations for creating 3-D geometric shapes — like tiny, highly simplified geodesic domes that assemble by themselves. The team developed the algorithmic tools and tested selected configurations. The research may lead to advances from drug-delivery containers to 3-D sensors and electronic circuits.

2-D nets for 3-D shapes A few of the 2.3 million possible 2-D designs — planar nets — for a truncated octahedron (right column). The question is: Which net is best to make a self-assembling shape at the nanoscale?
Credit: Shivendra Pandey/Gracias Lab, Johns Hopkins University

Researchers at Brown and Johns Hopkins universities have found optimal configurations for creating 3-D geometric shapes -- like tiny, highly simplified geodesic domes that assemble by themselves. The Brown team developed the algorithmic tools, and the Johns Hopkins team tested selected configurations. The research may lead to advances from drug-delivery containers to 3-D sensors and electronic circuits.

Results published in Proceedings of the National Academy of Sciences.

Material chemists and engineers would love to figure out how to create self-assembling shells, containers or structures that could be used as tiny drug-carrying containers or to build 3-D sensors and electronic devices.

There have been some successes with simple 3-D shapes such as cubes, but the list of possible starting points that could yield the ideal self-assembly for more complex geometric configurations gets long fast. For example, while there are 11 2-D arrangements for a cube, there are 43,380 for a dodecahedron (12 equal pentagonal faces). Creating a truncated octahedron (14 total faces -- six squares and eight hexagons) has 2.3 million possibilities.

"The issue is that one runs into a combinatorial explosion," said Govind Menon, associate professor of applied mathematics at Brown University. "How do we search efficiently for the best solution within such a large dataset? This is where math can contribute to the problem."

In a paper published in the Proceedings of National Academy of Sciences, researchers from Brown and Johns Hopkins University determined the best 2-D arrangements, called planar nets, to create self-folding polyhedra with dimensions of a few hundred microns, the size of a small dust particle. The strength of the analysis lies in the combination of theory and experiment. The team at Brown devised algorithms to cut through the myriad possibilities and identify the best planar nets to yield the self-folding 3-D structures. Researchers at Johns Hopkins then confirmed the nets' design principles with experiments.

"Using a combination of theory and experiments, we uncovered design principles for optimum nets which self-assemble with high yields," said David Gracias, associate professor in of chemical and biomolecular engineering at Johns Hopkins and a co-corresponding author on the paper. "In doing so, we uncovered striking geometric analogies between natural assembly of proteins and viruses and these polyhedra, which could provide insight into naturally occurring self-assembling processes and is a step toward the development of self-assembly as a viable manufacturing paradigm."

"This is about creating basic tools in nanotechnology," said Menon, co-corresponding author on the paper. "It's important to explore what shapes you can build. The bigger your toolbox, the better off you are."

While the approach has been used elsewhere to create smaller particles at the nanoscale, the researchers at Brown and Johns Hopkins used larger sizes to better understand the principles that govern self-folding polyhedra.

The researchers sought to figure out how to self-assemble structures that resemble the protein shells viruses use to protect their genetic material. As it turns out, the shells used by many viruses are shaped like dodecahedra (a simplified version of a geodesic dome like the Epcot Center at Disney World). But even a dodecahedron can be cut into 43,380 planar nets. The trick is to find the nets that yield the best self-assembly. Menon, with the help of Brown undergraduate students Margaret Ewing and Andrew "Drew" Kunas, sought to winnow the possibilities. The group built models and developed a computer code to seek out the optimal nets, finding just six that seemed to fit the algorithmic bill.

The students got acquainted with their assignment by playing with a set of children's toys in various geometric shapes. They progressed quickly into more serious analysis. "We started randomly generating nets, trying to get all of them. It was like going fishing in a lake and trying to count all the species of fish," said Kunas, whose concentration is in applied mathematics. After tabulating the nets and establishing metrics for the most successful folding maneuvers, "we got lists of nets with the best radius of gyration and vertex connections, discovering which nets would be the best for production for the icosahedron, dodecahedron, and truncated octahedron for the first time."

Gracias and colleagues at Johns Hopkins, who have been working with self-assembling structures for years, tested the configurations from the Brown researchers. The nets are nickel plates with hinges that have been soldered together in various 2-D arrangements. Using the options presented by the Brown researchers, the Johns Hopkins's group heated the nets to around 360 degrees Fahrenheit, the point at which surface tension between the solder and the nickel plate causes the hinges to fold upward, rotate and eventually form a polyhedron. "Quite remarkably, just on heating, these planar nets fold up and seal themselves into these complex 3-D geometries with specific fold angles," Gracias said.

"What's amazing is we have no control over the sequence of folds, but it still works," Menon added.

Contributing authors include Shivendra Pandey from Johns Hopkins and Nghi Nguyen from the University of Massachusetts-Amherst. The National Science Foundation funded the research.


Story Source:

The above story is based on materials provided by Brown University. Note: Materials may be edited for content and length.


Journal Reference:

  1. S. Pandey, M. Ewing, A. Kunas, N. Nguyen, D. H. Gracias, G. Menon. Algorithmic design of self-folding polyhedra. Proceedings of the National Academy of Sciences, 2011; DOI: 10.1073/pnas.1110857108

Cite This Page:

Brown University. "Best routes found to self-assembling 3-D shapes." ScienceDaily. ScienceDaily, 7 December 2011. <www.sciencedaily.com/releases/2011/12/111207113004.htm>.
Brown University. (2011, December 7). Best routes found to self-assembling 3-D shapes. ScienceDaily. Retrieved July 24, 2014 from www.sciencedaily.com/releases/2011/12/111207113004.htm
Brown University. "Best routes found to self-assembling 3-D shapes." ScienceDaily. www.sciencedaily.com/releases/2011/12/111207113004.htm (accessed July 24, 2014).

Share This




More Matter & Energy News

Thursday, July 24, 2014

Featured Research

from universities, journals, and other organizations


Featured Videos

from AP, Reuters, AFP, and other news services

Creative Makeovers for Ugly Cellphone Towers

Creative Makeovers for Ugly Cellphone Towers

AP (July 24, 2014) Mobile phone companies and communities across the country are going to new lengths to disguise those unsightly cellphone towers. From a church bell tower to a flagpole, even a pencil, some towers are trying to make a point. (July 24) Video provided by AP
Powered by NewsLook.com
Algonquin Power Goes Activist on Its Target Gas Natural

Algonquin Power Goes Activist on Its Target Gas Natural

TheStreet (July 23, 2014) When The Deal's Amanda Levin exclusively reported that Gas Natural had been talking to potential suitors, the Ohio company responded with a flat denial, claiming its board had not talked to anyone about a possible sale. Lo and behold, Canadian utility Algonquin Power and Utilities not only had approached the company, but it did it three times. Its last offer was for $13 per share as Gas Natural's was trading at a 60-day moving average of about $12.50 per share. Now Algonquin, which has a 4.9% stake in Gas Natural, has taken its case to shareholders, calling on them to back its proposals or, possibly, a change in the target's board. Video provided by TheStreet
Powered by NewsLook.com
Robot Parking Valet Creates Stress-Free Travel

Robot Parking Valet Creates Stress-Free Travel

AP (July 23, 2014) 'Ray' the robotic parking valet at Dusseldorf Airport in Germany lets travelers to avoid the hassle of finding a parking spot before heading to the check-in desk. (July 23) Video provided by AP
Powered by NewsLook.com
Boeing Ups Outlook on 52% Profit Jump

Boeing Ups Outlook on 52% Profit Jump

Reuters - Business Video Online (July 23, 2014) Commercial aircraft deliveries rose seven percent at Boeing, prompting the aerospace company to boost full-year profit guidance- though quarterly revenues missed analyst estimates. Bobbi Rebell reports. Video provided by Reuters
Powered by NewsLook.com

Search ScienceDaily

Number of stories in archives: 140,361

Find with keyword(s):
Enter a keyword or phrase to search ScienceDaily for related topics and research stories.

Save/Print:
Share:

Breaking News:
from the past week

In Other News

... from NewsDaily.com

Science News

Health News

Environment News

Technology News



Save/Print:
Share:

Free Subscriptions


Get the latest science news with ScienceDaily's free email newsletters, updated daily and weekly. Or view hourly updated newsfeeds in your RSS reader:

Get Social & Mobile


Keep up to date with the latest news from ScienceDaily via social networks and mobile apps:

Have Feedback?


Tell us what you think of ScienceDaily -- we welcome both positive and negative comments. Have any problems using the site? Questions?
Mobile: iPhone Android Web
Follow: Facebook Twitter Google+
Subscribe: RSS Feeds Email Newsletters
Latest Headlines Health & Medicine Mind & Brain Space & Time Matter & Energy Computers & Math Plants & Animals Earth & Climate Fossils & Ruins