Is there anyway to determine the electron density of a nanomaterial from a measurable phenomenon like absorbance spectrum?
I would say that from the absorption spectrum one can retrieve the plasmon frequency of the system via the absorption cross-section (if you have nanoparticles, for instance). Then the plasmon frequency is proportional to the square root of the electron density.
Sure. The absorption cross section is defined here:
http://en.wikipedia.org/wiki/Plasmonic_nanoparticles
The plasma frequency can be found here>
http://en.wikipedia.org/wiki/Plasma_oscillation
Please look at the references therein for deeper explanations.
The absorption spectrum is dependent on the morphology of nanomaterial as well. It means that you have to know it up front (or measure it). Otherwise I can not understand how from different absorption spectrum of gold NPs with different shapes and sizes one can still deduce the same electron density.
From the position, you can have an idea whether it is due to dipolar or multipolar excitation. There are many review articles particularly by Prof. El Sayed. Then, from the right approximation, you can make a rough estimate.
More eligible than wikipedia..
Article Size dependence of Au NP-enhanced surface plasmon resonance ...
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