每日科技报告 第42期Calculations Put to Test on Single Nanoparticles

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Calculations Made by Physicist Gustav Mie in 1908 Put to Test on Single Nanoparticles

Calculations are fine, but seeing is believing. That's the thought behind a new pa-per by Rice University students who decided to put to the test calculations made more than a century ago.

In 1908, the German physicist Gustav Mie came up with an elegant set of equations to describe the interaction of electromagnetic waves with a spherical metal particle. The theory has been a touchstone ever since for researchers seeking to quantify how nanoscale plasmonic particles scatter radiation.

In 1908, the German physicist Gustav Mie came up with an elegant set of equations to describe the interaction of electromagnetic waves with a spherical metal particle. The theory has been a touchstone ever since for researchers seeking to quantify how nanoscale plasmonic particles scatter radiation.
"The Mie theory is used extensively whenever you deal with nanoparticles and their optical properties," said Alexei Tcherniak, a Rice graduate student and primary author of the new pa-per in the online edition of Nano Letters this month. "That's the foundation of every calculation."
Tcherniak and Stephan Link, a Rice assistant professor of chemistry and electrical and computer engineering, co-authored the pa-per with former graduate student Ji Won Ha and current Rice graduate students Liane Slaughter and Sergio Dominguez-Medina.
Better characterization of single nanoparticles is important to researchers pursuing microscopic optical sensors, subwavelength "super lenses," catalysis and photothermal cancer therapies that use nanoparticles.
"Since technology is moving toward single-particle detection, we wanted to see whether Mie's predictions would hold," Tcherniak said. "Average properties fall exactly on the predictions of Mie theory. But we show that individual particles deviate quite a bit." Particles that differ in size can return similar signals because they vary in shape and orientation on the substrate, with which they also interact. Mie's theory, developed for spherical particles in solution long before single-particle spectroscopy, did not consider these factors.
The project began as a sideline in the students' attempt to track single nanoparticles in solution. It became their primary focus when they realized the scope of the task, which involved analyzing five sets of gold particles ranging from 51 to 237 nanometers wide -- the "biologically relevant" sizes, Tcherniak explained.
Each set of particles was photographed with a scanning electron microscope and then analyzed for its absorption and scattering properties via single-particle photothermal imaging and laser dark-field scattering.
It was tedious, they admitted.
"When you need to find a particle 50 nanometers across on a sample that is 5-by-5 millimeters, you're looking for a needle in a haystack," Tcherniak said. Slaughter and Dominguez-Medina nodded in agreement and recalled a summer of long days required to categorize several hundred particles -- enough "to get all those points on the graph."
They used a couple of strategies to locate particles. One was to put micron-scale grid coordinates on the glass slide containing nanoparticle samples. "That let us know roughly where they were," Tcherniak said.
Another involved applying a bit of astronomy to their microscopy. They found themselves looking for "constellations" in the patterns of specks. "We started saying, 'Oh, that looks like a nose. Do we have a nose anywhere else?'" Slaughter said. "We were so tired; the names might not have been very good."
But their results are.
"Mie theory was around long before anyone knew about nanoparticles, so it's a neat thing to be able to test it," said Link of his students' work. "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."

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Mie was born in Rostock. From 1886 he studied mathematics and physics at the University of Rostock. In addition to his major subjects, he also attended lectures in chemistry, zoology, geology, mineralogy, astronomy as well as logic and metaphysics. In 1889 he continued his studies at the University of Heidelberg and received a doctorate degree in mathematics at the age of 22.

In 1897 he got his Habilitation at the University of Göttingen in theoretical physics and in 1902 became extraordinary professor for theoretical physics at the University of Greifswald. In 1917 he became full professor for experimental physics at Martin Luther University of Halle-Wittenberg. In 1924 he became Professor at the University of Freiburg, where he worked up to his retirement in 1935.

In Freiburg, during the Nazi dictatorship, Mie was member of the university opposition of the so-called "Freiburger Kreis" (Freiburg circle) and one was participant of the original "Freiburger Konzils" (Freiburg council).

He died at Freiburg im Breisgau in 1957.

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During his Greifswald years he worked on the computation of scattering of an electromagnetic wave by a homogeneous dielectric sphere, which was published in 1908 under the title of “Contributions to the optics of turbid media, particularly of colloidal metal solutions” in Annalen der Physik. The term Mie scattering is still related to his name. Using Maxwell's electromagnetic theory applied to spherical Gold particles Gustav Mie provided a theoretical treatment of plasmon resonance absorption of Gold colloids. The sharp absorption bands depend on the particle size and explain the change in colour that occurs as the size of the colloid nanoparticles is increased from 20 to 1600 nm. He wrote further important contributions to electromagnetism and also to relativity theory. In addition he was employed on measurements units and finally developed his Mie system of units in 1910 with the basic units Volt, Ampere, Coulomb and Second (VACS-system).