why the dielectric of nanoparticles is high at low frequencies and reduce rapidly with the utilized frequency at all temperatures.
Dear Zaid Hamid
Please consult the following articles for the details answer of your question:
https://www.hindawi.com/journals/isrn/2012/706398/
http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1516-14392016000200478
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4409379/
Dear Zaid,
I do not really know whether I understands your question, but I assume that you mean "dielectric constant" ?
In any dispersive material system, the dielectric response function is time/frequency dependent. This means that it is not a constant, although in some frequency ranges it can become frequency independent. For linear and causal systems, there is a general relation - Kramers-Kronig relationship - that relates the real part of the dielectric response function(non-dissipative) to its imaginary(dissipative) part.
Now, starting from frequency w->infinity, the real part is constant and equal one - dielectric constant of vacuum. As you pass through various "absorption bands (X-rays, UV, VIS, IR, FIR and various dielectric relaxational absorption process), the dissipation is finite there and because the real part is kind of integral of the imaginary part, It must increase as the frequency decreases. Finally for w->0, you obtain the dc limit - the dc dielectric constant of the material.
There exist various semi-empirical relations that relate this real part of the dielectric response function to the electron band structure of the material (be that glasses, solids, liquids, etc...) and the band gap of the material in question, but to my knowledge, there is not a general expression resulting from "first principle calculations". I might be wrong here though. The other effect that has been pointed out by Behman above , are size quantum effects.
So, I am not really surprised that in also in your system the real part of the dielectric response function increases with decreasing frequency of measurement.
With best regards
Petr
P.S.: You might like to consult the following :
1. J.D.Jackson :Classical Electrodynamics (Wiley, 1999)
2. J.C.Phillips and G.Lucovsky: Bonds and Bands in Semiconductors (Momentum Press 1973).
3. F.Han: Modern Course in the Quantum Theory of Solids (World Scientific 2013)
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