Smart shirts capable of tracking heart rate, skin-like sensors to measure recovery after a stroke, and tattoo-like devices to monitor glucose levels in people with diabetes — these are some of the flexible electronics that engineers hope one day to design. To facilitate this need for flexibility, Stanford researchers are reinventing wires, circuits and transistors that can stretch and bend the way our bodies do.
Some of the strategies for designing such body-hugging circuitry are based in part on the use of carbon nanotubes and silver nanowires that have been engineered for flexibility. But there’s a catch: Experiments have shown that when flexible nanowires are stretched, these materials lose some of their conductance, which impedes their ability to transmit electricity and robs systems of the predictable performance that is the prerequisite for designing reliable products. More puzzling yet, when the stretch is released, conductance remains in a lowered state. This unpredictability has made flexible nanowires difficult to work with because engineers want to know in advance precisely how components will behave when they are used.
“This phenomenon had been reported before, but nobody had found an explanation for it,” said Wei Cai, associate professor of mechanical engineering, senior author in a Stanford team that has not only discovered why conductivity changes but has developed a way to predict the performance of bendable nanowires.
“Now, instead of a big question mark or a lot of trial and error, we provide a model on which people can base their designs,” said Cai, who along with six co-authors published these findings in Proceedings of the National Academy of Sciences. By creating this predictive framework, they have laid the groundwork for engineers to not merely imagine but design, prototype and, one day, produce electronics that stretch and bend in useful ways.
Our current conception of a wire is akin to a rope, which can only be tugged so far. Recognizing the need for a new paradigm to define what constitutes a wire, flexible circuit designers have turned to carbon nanotubes, conductive materials that might be imagined as infinitesimal bits of hair scattered on a barbershop floor. In a delicate process, engineers spray a network of these overlapping electron highways onto rectangles of a rubbery substance to form a stretchy sheet of circuit film. Electrons zip from one end of the carbon film to the other, moving along the tubes and, when necessary, jumping from tube to tube.
How fast electrons move through the film depends on the inherent conductivity of the carbon nanotube, the length of the individual tubes, the length of the rectangle and the ease with which electrons can transfer from one tube to another.
When experimentalists have stretched these rubber rectangles up to twice their original dimensions, the conductivity of the nanotube networks goes down and the resistance goes up. That makes basic electronic sense. The longer the rectangle, the further the electrons must travel.
But when the rubber circuits were allowed to snap back to their original size, resistance remained high and conductivity low. Researchers didn’t understand why until the Stanford team figured it out.
Imagine a tangled web of rubber jump ropes loosely attached to an elastic tarp. When you stretch the tarp, the ropes will slide against each other and get longer. But when you release the tarp, the ropes don’t snap back to their preliminary positions. They buckle and curl into each other, and that’s what happens with the carbon nanotubes. They end up with a wavier shape, said Lihua Jin, a former postdoctoral candidate at Stanford, now an assistant professor in mechanical and aerospace engineering at UCLA, and the first author on the paper.
The team saw this pattern emerge in their simulations and then reproduced those results in experiments. Using this data, they figured out how to account mathematically for this wavy transformation. “Each tube is still conducting, but when you stretch it and then it comes back to the original shape, the tubes have a different arrangement,” said Cai. “That gives you a different conductivity.”
Essentially, the Stanford formula is based on the interim length between the end points of each tube. After a tube is stretched and released, it curls into itself, resembling the letter “S.” The Stanford engineers take the “S” shape and draw a straight line between the two end points. That line becomes the hypotenuse of a right triangle. The remaining two sides of the triangle give researchers two distances: one that follows the stretching direction and one that is perpendicular to the stretching direction.
“If you have a tube that lies mostly along the stretching direction, then it does not contribute to conductance in the perpendicular direction,” said Jin. Basically, the researchers need to know the average conductivity in the stretching direction as well as the perpendicular direction.
Researchers average together all the stretching distances and then all the perpendicular distances. The next step is to create a ratio between those mean lengths and the length of the rubber circuit. When that ratio changes, so do the electronic characteristics of the rubber circuit. If you stretch a film 60 percent, for example, the resistance always doubles. That’s true no matter the starting size.
“We have stumbled upon a general behavior,” said Cai. “It’s not like you need carbon nanotubes from a particular vendor and with this diameter and length; as long as you have a lot of thin wires on a film, you see this principle.”
Their work provides circuit designers with certainty, guidelines and predictions for making these flexible material systems. The process is no longer a shot in the dark. After the first stretch, the conductivity remains constant. So, manufacturers will one day be able to pre-stretch one of these flexible nanowire constructs and, as long as they don’t overstretch it past the pre-engineered point, be confident in its conductive stability and ultimate usefulness as a product.
This knowledge could also be useful for making sensors. For example, a patient recovering from a hand injury is working on making a fist. With a sensor placed on the knuckle, each time the conductivity changes, the doctor would know that the patient has stretched a little bit more.
The next step for Cai and his team at Stanford is to tackle the same question for using nanotubes as semiconductors, which involves discovering how the electrical properties of stretchable transistors change with the deformation that occurs when they are bent.
“These flexible systems are becoming closer and closer to reality,” Cai said.