I would like to get explanation for the following points
1. Light absorption of the plasmonic metal nanoparticle is more significant than scattering when the particle size is small (less than 50 nm for Ag).
2. For large-sized metal nanoparticles (greater than 50 nm for Ag), scattering is more dominant effect than light absorption of the nanoparticles.
As per my understanding, the absorption and scattering of metal NPs are related to the localized surface plasmon resonance (LSPR) effect.
I am looking forward to the theoretical understanding of the above-mentioned points.
Hi Shamjid I think your question is a little confused - or maybe you are between the 2 parts of the refractive index: the real part and the imaginary (absorptive) part. When the particle size gets smaller the scattering becomes weak - proportional to Volume2 in the Rayleigh region (< 60 nm typically). However, light lost in the system is a number concentration effect (Beer-Lambert). So in terms of scattering as the size gets smaller the absorptive part of the RI plays a more important role. This is explained by Mie theory and the trapped electrical and magnetic modes in the particles as the size is around or below the wavelength of light. See for example:
February 25th, 2014
The life of Gustav Mie and the development of the Lorenz-Mie solution to Maxwell’s equations http://tinyurl.com/mt97tp3
A little more to add. Taken from a 2006 webinar of mine (open in IE only):
Optical Properties: the Gladstone-Dale approach
http://www.brainshark.com/brainshark/vu/view.asp?pi=141109&text=M021507):
For small particles Intensity is proportional to a V2λ-4 (Rayleigh), but absorption is proportional to Vλ-1 (Beer-Lambert). Thus as particles become smaller absorption becomes more important than scattering and the RI becomes less important than the absorption coefficient.
scattering cross section depend on the a^6 and absorption cross section depend on the a^3 where a is the radius of metal nano particle. Thats why for smaller particle absorption dominate and for larger particle scattering dominates.
@ Shinki Midha
scattering cross section depend on the a^6 and absorption cross section depend on the a^3 where a is the radius of metal nano particle. Thats why for smaller particle absorption dominate and for larger particle scattering dominates.
Say, a=30 nm and 100 nm. How we compare those?
a^6=(30*10^-9)^6 = 7.29*10^-46
a^3=(30*10^-9)^3 = 2.7*10^-23
and
a^6=(100*10^-9)^6 = 1*10^-42
a^3=(100*10^-9)^3 = 1*10^-21
In both the cases, a^6 is smaller than a^3. Therefore, scattering is less than absorption. However, by theory scattering is higher for large particles.
Can you explain why it so?
You state: 'However, by theory scattering is higher for large particles'.
This is not always the case (although it's a good generalization) - in the region where the size of particle is approximately the wavelength of impinging light then there are situations where the scattering actually decreases with size giving rise to the well-known Mie minima. Mie theory models this behavior exactly.
I would like to the get answer for the dependence of scattering and absorption on nanoparticle size regarding a^3 and a^6.
yes,the above approximation is valid when size of particle is much much less than the wavelength of particle. for more details go to mie theory
or chapter 5 of book plasmonics fundamentals and application by stefan maier
@ Shinki Midha
Using the approximation method, we can not compare scattering and absorption of the 30 nm and 100 nm sized nanoparticles?
@Shamjid You are correct - you cannot compare the scattering with an approximation here. You need Mie theory as it’s not always the case that increasing the size will increase the scattering intensity. This is especially true in the submicron region.
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