From the literature absorption of single mono layer of graphene is about 2%, when using the calculation based on model of Beer-Lambert for gold or silver the obtained result is also about 2%. From this we can see that model Beer-Lambert does not described well mono layers. How can it be that a monolayer of graphene absorbs so much light and can Beer-Lambert be used for calculation of absorption in the case of the monolayer sheet?
Thank you in advance!
The Beer-Lambert law applies to an ensemble of non interacting chromophores, and describes the absorbance in terms of the concentration and thickness, usually of a solution. In such a solution, if the chromophores start to interact, and for example aggregate, the absorption per species decreases (usually) and the Beer-Lambert law breaks down. Going from Graphite to a single exfoliated Grahene layer, is essentially analogous to "disaggregating" the absorbing species, and the absorption of the isolated sheet is much higher that of the equivalent layer in the graphene aggregate.
Hi Vladimir,
please see the link, especially its section on 'Optics'; it is in the middle part.
There is a description on how a monolayer of graphene will produce the high absorption.
Please see the .docx file; it is a screen shot of the beginning of the Optics section.
I must admit that I do not understand this. But I think this behavior is a special behavior of the graphene monolayer, because in the first chapter of the link it is stated that graphene is 'nearly transparent'.
Except from this example the Lambert-Beer law should be valid down to monolayer thickness. I havn't seen any contradiction to this law up to now.
https://en.wikipedia.org/wiki/Graphene
The Beer-Lambert law applies to an ensemble of non interacting chromophores, and describes the absorbance in terms of the concentration and thickness, usually of a solution. In such a solution, if the chromophores start to interact, and for example aggregate, the absorption per species decreases (usually) and the Beer-Lambert law breaks down. Going from Graphite to a single exfoliated Grahene layer, is essentially analogous to "disaggregating" the absorbing species, and the absorption of the isolated sheet is much higher that of the equivalent layer in the graphene aggregate.
Dear Vladimir Farber,
in my opinion, the Beer-Lambert law describes the phenomenology related to light attenuation by samples.
As you noted, for dilute solutions, in the range where the solvent is transparent, light scattering can be taken into account by measuring the solution against the solvent as a standard. Thus, it is possible to define the absorbance A(λ) = - log10 (I/I0) = μ(λ) c b, where I0 is the incident light intensity, μ is a coefficient independent on concentration, which is called mass absorption coefficient, c the concentration, and b the light path through the sample. I is the measured intensity. Here, dilute solution means A(λ)≤1. The coefficient μ should be a well behaved function of λ.
As a phenomenological law, the Beer-Lambert law can also be applied to graphene monolayers (fixed b, c). However, whereas it seems obvious that diluted solutions have an isotropic behavior (for example), the assumption that graphene monolayers have an isotropic behavior has to be verified beforehand.
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