Nanotechnology Now







Heifer International

Wikipedia Affiliate Button


DHgate

Home > Press > Combining Centuries-Old Mathematical Theorems Provides an Efficient Approach for Characterizing the Shape of Nanoparticles

Abstract:
Gregg Gallatin, a researcher at the NIST Center for Nanoscale Science and Technology, has shown that combining a nineteenth century flux theorem with an eighteenth century mathematical operation provides a convenient technique for using scattered light to count nanoparticles and to characterize their shapes.*

Combining Centuries-Old Mathematical Theorems Provides an Efficient Approach for Characterizing the Shape of Nanoparticles

Gaithersburg, MD | Posted on March 20th, 2012

This technique is useful both for determining how a given distribution of nanoparticle shapes affects the properties of nanoparticle functionalized materials as well as for categorizing how biological systems incorporate nanoparticles of different shapes. The mathematical approach, which combines Gauss's Law with Fourier transforms, can also be used as a starting point to solve a wide variety of standard problems in mathematics and physics beyond nanotechnology. Because of the ubiquity of digital data derived from Fourier transforms, the approach is likely to find broad application to a range of physical science and engineering measurements. Using the technique, Gallatin demonstrates how Porod's law, which describes how x-rays scatter from small spherically-shaped particles, can be re-derived and extended to the broader case of particles that are nonspherical, thereby providing a powerful and useful approach for determining the shape of nanoparticles using x-ray scattering. He then demonstrates that this approach can be further extended to visible light scattering, which depends on the moments of the nanoparticle shape and therefore provides a more general method for measuring nanoparticle shape from scattering data. The technique of combining Gauss's Law with Fourier transforms can also be applied to the classical physics problem of Fraunhofer diffraction, providing an explicit formula for the diffraction pattern of arbitrary polygonal-shaped openings in an opaque screen in terms of the vertices of the polygon. It is also applicable to a variety of mathematics problems, including the Hopf Umlaufsatz, which states that the angle of the tangent along a simple smooth closed curve turns by 360 degrees when making a complete circuit around the curve; Stokes' Law, which relates integrals over an area in two dimensions to the one dimensional curve bounding the area; and the isoperimetric inequality, which states that a circle is the shape that encloses the largest area for a given circumference. Given the simplicity and generality of this mathematical technique, Gallatin believes that it can be applied to many other problems as well.


*Fourier, Gauss, Fraunhofer, Porod and the shape from moments problem, G. M. Gallatin, Journal of Mathematical Physics 53, 013509-013509-13 (2012).

####

About National Institute of Standards and Technology (NIST)
The National Institute of Standards and Technology (NIST) is an agency of the U.S. Department of Commerce.

For more information, please click here

Contacts:
Gregg Gallatin
301-975-2140

Copyright © National Institute of Standards and Technology (NIST)

If you have a comment, please Contact us.

Issuers of news releases, not 7th Wave, Inc. or Nanotechnology Now, are solely responsible for the accuracy of the content.

Bookmark:
Delicious Digg Newsvine Google Yahoo Reddit Magnoliacom Furl Facebook

Related News Press

News and information

Advantest to Exhibit at SEMICON Korea in Seoul, South Korea February 4-6 Showcasing Broad Portfolio of Semiconductor Products, Technologies and Solutions January 29th, 2015

Park Systems Announces Innovations in Bio Cell Analysis with the Launch of Park NX-Bio, the only 3-in-1 Imaging Nanoscale Tool Available for Life Science Researchers January 29th, 2015

2015 Nanonics Image Contest January 29th, 2015

Iranian Scientists Use MOFs to Eliminate Dye Pollutants January 29th, 2015

Laboratories

Nanoscale Mirrored Cavities Amplify, Connect Quantum Memories: Advance could lead to quantum computing and the secure transfer of information over long-distance fiber optic networks January 28th, 2015

New pathway to valleytronics January 27th, 2015

Nanoshuttle wear and tear: It's the mileage, not the age January 26th, 2015

Physics

New pathway to valleytronics January 27th, 2015

Visualizing interacting electrons in a molecule: Scientists at Aalto University and the University of Zurich have succeeded in directly imaging how electrons interact within a single molecule January 26th, 2015

Nano-beaker offers insight into the condensation of atoms January 21st, 2015

Govt.-Legislation/Regulation/Funding/Policy

Nanoscale Mirrored Cavities Amplify, Connect Quantum Memories: Advance could lead to quantum computing and the secure transfer of information over long-distance fiber optic networks January 28th, 2015

Detecting chemical weapons with a color-changing film January 28th, 2015

'Bulletproof' battery: Kevlar membrane for safer, thinner lithium rechargeables January 28th, 2015

Researchers Make Magnetic Graphene: UC Riverside research could lead to new multi-functional electronic devices January 27th, 2015

Announcements

Advantest to Exhibit at SEMICON Korea in Seoul, South Korea February 4-6 Showcasing Broad Portfolio of Semiconductor Products, Technologies and Solutions January 29th, 2015

Park Systems Announces Innovations in Bio Cell Analysis with the Launch of Park NX-Bio, the only 3-in-1 Imaging Nanoscale Tool Available for Life Science Researchers January 29th, 2015

2015 Nanonics Image Contest January 29th, 2015

Iranian Scientists Use MOFs to Eliminate Dye Pollutants January 29th, 2015

NanoNews-Digest
The latest news from around the world, FREE



  Premium Products
NanoNews-Custom
Only the news you want to read!
 Learn More
NanoTech-Transfer
University Technology Transfer & Patents
 Learn More
NanoStrategies
Full-service, expert consulting
 Learn More










ASP
Nanotechnology Now Featured Books




NNN

The Hunger Project







© Copyright 1999-2015 7th Wave, Inc. All Rights Reserved PRIVACY POLICY :: CONTACT US :: STATS :: SITE MAP :: ADVERTISE