# Why do shape and size have the greatest effect on the optical properties of nanoparticles?

The LSPR properties of nanoparticles depend on a number of factors, including shape, size, material, crystal structure, dielectric environment, etc. However, it has been consistently shown that shape and size have the greatest effect on the optical properties of nanoparticles. Exactly WHY, however, is this true? Does anyone have an explanation at the molecular level?

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As Surface Plasmon Resonance phenomenon is mainly seen in metal nanoparticles, I don't know whether this answer will help you? The size dependent optical phenomenon of semiconductor nanoparticles (e.g., $\ce{CdS}$) can be explained using the effective mass approximation model.

where r is radius of the particle (the rest details of the above equation can be find in the link).

so the energy gap is inversely proportional to the radius of the particle.

When the radius of the particle decreases, the band gap increases so it will emit high energy wavelength (i.e., wavelength in blue region) and when the particle size is large the energy gap will be less so it will emit light in red region (lesser energy).

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Thanks for your answer! However, isn't the effective mass approximation model only applicable to spherical nanoparticles (i.e. quantum dots)? I'm writing a paper on the synthesis of silver nanoplates and nanodisks, and I was wondering in general why shape and size have the greatest control over LSPR modes. Are you familiar with the Discrete Dipole Approximation method? I believe that it is an alternative (for arbitrary geometries) to Mie Theory, which only applies to spherical shapes. If so, could you explain the reasoning behind how, given any shape/size, DDA can derive the LSPR modes? –  jojoma42 Dec 21 '12 at 4:41
@jojoma42 yes the above equation is for spherical nanoparticles and i am sorry i dont know about discrete dipole approximation method –  Eka Dec 22 '12 at 13:47
@jojoma42 i have found these links for DDA 1) ftp://ftp.astro.princeton.edu/draine/papers/pdf/… and physics.ohio-state.edu/~stroud/optics1.ppt DDA is an approximation technique which is used to find approximate value of scattering and absorbtion of irregularly shaped nanoparticles by breaking up nanoparticles into smaller volumes with dipole movement. The relathionship of size and absorbance can be find in this link pubs.acs.org/doi/full/10.1021/jp984796o . Hope this is useful to you –  Eka Dec 22 '12 at 14:49

Optical properties of nanoparticles come from electronic spectra of one excited electron trapped within. The energy levels in the spectra are derived from lengths of waves, that resonates with energy well within particle. Of course, this lengths depends on size and form of the resonator. Note: this IS oversimplification, but it allows to grab the concept.

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