Century-Old Equation Tested

Researchers at the Rice University have recently conducted a series of tests on an elegant set of equations that was developed around 1908 by German physicist Gustav Mie. What the formulas do is basically predict the interaction of electromagnetic waves with a spherical metal particle. The predictions are so precise that, even today, the calculations are used as a base for nanotechnology, as well as a host of other fields of research. The Rice team decided to investigate whether the data would hold more thorough scrutiny or not.

“The Mie theory is used extensively whenever you deal with nanoparticles and their optical properties. That's the foundation of every calculation,” Rice graduate student Alexei Tcherniak says. He is the primary author of a new scientific study detailing the investigation, which appears in the online March issue of the respected ACS scientific publication Nano Letters. The expert adds that most research groups in the world use the Mie equations to predict how nanoscale plasmonic particles scatter radiation, and then base their following step on top of that. Needless to say, if the calculations were to be wrong, then many innovations at the nanoscale would be left without any solid background.

“Since technology is moving toward single-particle detection, we wanted to see whether Mie's predictions would hold,” Tcherniak says of the goal of this research. He explains that these mathematical models are currently being used in a wide variety of fields, and that they could lead to the development of advanced microscopic optical sensors, sub-wavelength “super lenses,” catalysis and photo-thermal cancer therapies that could benefit millions. Rice Assistant Professor of Chemistry and Electrical and Computer Engineering Stephan Link also contributed to the investigation.

“Average properties fall exactly on the predictions of Mie theory. But we show that individual particles deviate quite a bit,” the former graduate student says. In order to view each individual particle, the experts turned to using scanning electron microscope (SEM) imaging, a technique that relies on the principle of quantum tunneling to view very small particles. After they were photographed, the nanoparticles were analyzed with single-particle photo-thermal imaging and laser dark-field scattering, so that researchers could discover their individual absorption and scattering properties.

“Mie theory was around long before anyone knew about nanoparticles, so it's a neat thing to be able to test it. This is important because they really put together the building blocks that will enable scientists to look at more complex structures. This was not an easy job,” Link concludes. The investigation was supported with grant money secured from the US National Science Foundation (NSF), the Robert A. Welch Foundation, and 3M.