Nanotechnology Now

Our NanoNews Digest Sponsors

Heifer International

Wikipedia Affiliate Button

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

Physics

A step closer to understanding quantum mechanics: Swansea Universityís physicists develop a new quantum simulation protocol October 22nd, 2017

The secret to improving liquid crystal's mechanical performance: Better lubricating properties of lamellar liquid crystals could stem from changing the mobility of their structural dislocations by adding nanoparticles October 13th, 2017

News and information

A step closer to understanding quantum mechanics: Swansea Universityís physicists develop a new quantum simulation protocol October 22nd, 2017

Creation of coherent states in molecules by incoherent electrons October 21st, 2017

Strange but true: turning a material upside down can sometimes make it softer October 20th, 2017

Leti Coordinating Project to Develop Innovative Drivetrains for 3rd-generation Electric Vehicles: CEA Techís Contribution Includes Litenís Knowhow in Magnetic Materials and Simulation And Letiís Expertise in Wide-bandgap Semiconductors October 20th, 2017

Laboratories

Spin current detection in quantum materials unlocks potential for alternative electronics October 15th, 2017

Injecting electrons jolts 2-D structure into new atomic pattern: Berkeley Lab study is first to show potential of energy-efficient next-gen electronic memory October 13th, 2017

Rice U. lab surprised by ultraflat magnets: Researchers create atom-thick alloys with unanticipated magnetic properties October 13th, 2017

Govt.-Legislation/Regulation/Funding/Policy

Leti Coordinating Project to Develop Innovative Drivetrains for 3rd-generation Electric Vehicles: CEA Techís Contribution Includes Litenís Knowhow in Magnetic Materials and Simulation And Letiís Expertise in Wide-bandgap Semiconductors October 20th, 2017

Bringing the atomic world into full color: Researchers turn atomic force microscope measurements into color images October 19th, 2017

Long nanotubes make strong fibers: Rice University researchers advance characterization, purification of nanotube wires and films October 17th, 2017

Spinning strands hint at folding dynamics: Rice University lab uses magnetic beads to model microscopic proteins, polymers October 17th, 2017

Announcements

A step closer to understanding quantum mechanics: Swansea Universityís physicists develop a new quantum simulation protocol October 22nd, 2017

Creation of coherent states in molecules by incoherent electrons October 21st, 2017

Strange but true: turning a material upside down can sometimes make it softer October 20th, 2017

Leti Coordinating Project to Develop Innovative Drivetrains for 3rd-generation Electric Vehicles: CEA Techís Contribution Includes Litenís Knowhow in Magnetic Materials and Simulation And Letiís Expertise in Wide-bandgap Semiconductors October 20th, 2017

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