Nanotechnology Now

Our NanoNews Digest Sponsors





Heifer International

Wikipedia Affiliate Button


android tablet pc

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

First Observation of Electronic Structure in Ag-Rh Alloy Nanoparticles Having Hydrogen Absorbing: Storage Property –Attempting to solve the mystery of why Ag-Rh alloy nanoparticles have a similar property to Pd– October 30th, 2014

Iranians Present Model to Predict Photocatalytic Process in Removal of Pollutants October 30th, 2014

Production of Biocompatible Polymers in Iran October 30th, 2014

Amorphous Coordination Polymer Particles as alternative to classical nanoplatforms for nanomedicine October 30th, 2014

Lomiko Signs Licensing Agreement to Produce and Supply Power Converter Systems to E-Commerce Customers October 29th, 2014

Laboratories

Tiny carbon nanotube pores make big impact October 29th, 2014

New evidence for an exotic, predicted superconducting state October 27th, 2014

National Synchrotron Light Source II Achieves 'First Light' October 23rd, 2014

Physics

Sussex physicists find simple solution for quantum technology challenge October 28th, 2014

New evidence for an exotic, predicted superconducting state October 27th, 2014

Govt.-Legislation/Regulation/Funding/Policy

'Electronic skin' could improve early breast cancer detection October 29th, 2014

New solar power material converts 90 percent of captured light into heat: SunShot Project aims to make solar cost competitive October 29th, 2014

Tiny carbon nanotube pores make big impact October 29th, 2014

Microrockets fueled by water neutralize chemical and biological warfare agents October 29th, 2014

Announcements

First Observation of Electronic Structure in Ag-Rh Alloy Nanoparticles Having Hydrogen Absorbing: Storage Property –Attempting to solve the mystery of why Ag-Rh alloy nanoparticles have a similar property to Pd– October 30th, 2014

Iranians Present Model to Predict Photocatalytic Process in Removal of Pollutants October 30th, 2014

Production of Biocompatible Polymers in Iran October 30th, 2014

Amorphous Coordination Polymer Particles as alternative to classical nanoplatforms for nanomedicine October 30th, 2014

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 1999-2014 7th Wave, Inc. All Rights Reserved PRIVACY POLICY :: CONTACT US :: STATS :: SITE MAP :: ADVERTISE