Mathematics illuminates wee sensor assembly
Posted June 18, 2007
For Darryl Holm, it’s about the geometry.
Holm, an applied mathematics professor at London’s Imperial College, studies how shape affects complex systems. The mathematics of how things fit together has governed his work, from climate modeling to imaging science.
Now he’s focused on nanosensors – molecules formed into tiny shapes thousands of times thinner than a hair, but potentially capable of detecting substances in minuscule amounts.
Holm’s work breaks new ground in understanding how these nanosensors self-assemble. It’s part of a continuing collaboration with researchers in the United States. In fact, he’s still a fellow at Los Alamos National Laboratory, a U.S. Department of Energy facility where he worked for more than 30 years.
Nanoscale science holds the promise of tiny, fast computers and other devices. That potential – and the obstacles to it – depends on how molecules behave at such small scales.
Holm and his colleagues wanted to model the basic principles that underlie both how individual molecules come together to form a simple nanosensor and how the molecules’ geometry affects that process.
Holm and Vakhtang Putkaradze at Colorado State University modeled construction of a nanosensor just 1 centimeter long, but containing roughly 10 trillion molecules. The string of molecules can conduct electricity. If a molecule of the substance being detected binds to the sensor, the circuit breaks, indicating the presence of the target substance.
To build such sensors, nanoscientists, such as those at the Center for High Technology Materials at the University of New Mexico, first apply the sensor molecules to a template – a groove etched into a surface.
But the molecules “won’t stay in the grooves because they’re quantum things. They hop around and they have something like Brownian motion (the random motion of small particles suspended in a gas or liquid) going for them if they have any temperature,” Holm says. To get them to stay in place, “you paint something that is going to shrink across them, and you want that shrinkage to force them into the little grooves and line them up.”
Holm wants to know how this “shrink wrapping” works on the molecular scale. The small motions of the molecules compete with the larger scale external force that forms the line, pushing the molecules closer to each other.
As the molecules converge, their shape will affect if and how they will clump. If they clump together, or aggregate, in a straight line, the mathematical model will produce a singularity representing the desired concentration of molecules along a line.
