Gans theory
Encyclopedia
Gans theory or Mie-Gans theory is the extension of Mie theory
for the case of spheroidal particles. It gives the scattering characteristics of both oblate and prolate spheroidal particles much smaller than the excitation wavelength.
Since it is a solution of the Maxwell equations it should technically not be called a theory.
The theory is named after Richard Gans
who first published the solution for gold particles in 1912 in an article entitled "Über die Form ultramikroskopischer Goldteilchen". A subsequent article in 1915 discussed the case of silver particles.
In Gans theory, the absorption
is only dependent on the aspect ratio of the particles and not on the absolute dimensions. This dependence is introduced through so called polarization- or shape factors related to the three dimensions of the particle. For the case of spheroids, this reduces to only two different factors since the particle is rotational symmetric
around one axis.
It is currently being applied in the field of nanotechnology
to characterize silver and gold nanorod
s. A popular alternative for this is the Discrete dipole approximation
(DDA) method. Gans theory gives the exact solution for spheroidal particles; real nanorods, however, have a more cylindrical shape. Using DDA, it is possible to better model the exact shape of the particles. As the name suggests, this will only give an approximation.
Mie theory
The Mie solution to Maxwell's equations describes the scattering of electromagnetic radiation by a sphere...
for the case of spheroidal particles. It gives the scattering characteristics of both oblate and prolate spheroidal particles much smaller than the excitation wavelength.
Since it is a solution of the Maxwell equations it should technically not be called a theory.
The theory is named after Richard Gans
Richard Gans
Richard Martin Gans , German of Jewish origin, born in Hamburg, was the physicist who founded the Physics Institute of the National University of La Plata, Argentina...
who first published the solution for gold particles in 1912 in an article entitled "Über die Form ultramikroskopischer Goldteilchen". A subsequent article in 1915 discussed the case of silver particles.
In Gans theory, the absorption
Absorption (electromagnetic radiation)
In physics, absorption of electromagnetic radiation is the way by which the energy of a photon is taken up by matter, typically the electrons of an atom. Thus, the electromagnetic energy is transformed to other forms of energy for example, to heat. The absorption of light during wave propagation is...
is only dependent on the aspect ratio of the particles and not on the absolute dimensions. This dependence is introduced through so called polarization- or shape factors related to the three dimensions of the particle. For the case of spheroids, this reduces to only two different factors since the particle is rotational symmetric
Rotational symmetry
Generally speaking, an object with rotational symmetry is an object that looks the same after a certain amount of rotation. An object may have more than one rotational symmetry; for instance, if reflections or turning it over are not counted, the triskelion appearing on the Isle of Man's flag has...
around one axis.
It is currently being applied in the field of nanotechnology
Nanotechnology
Nanotechnology is the study of manipulating matter on an atomic and molecular scale. Generally, nanotechnology deals with developing materials, devices, or other structures possessing at least one dimension sized from 1 to 100 nanometres...
to characterize silver and gold nanorod
Nanorod
In nanotechnology, nanorods are one morphology of nanoscale objects. Each of their dimensions range from 1–100 nm. They may be synthesized from metals or semiconducting materials. Standard aspect ratios are 3-5. Nanorods are produced by direct chemical synthesis...
s. A popular alternative for this is the Discrete dipole approximation
Discrete dipole approximation
The discrete dipole approximation is a method for computing scattering of radiation by particles of arbitrary shape and by periodic structures. Given a target of arbitrary geometry, one seeks to calculate its scattering and absorption properties...
(DDA) method. Gans theory gives the exact solution for spheroidal particles; real nanorods, however, have a more cylindrical shape. Using DDA, it is possible to better model the exact shape of the particles. As the name suggests, this will only give an approximation.