I am to model/analyze the linear scattering of visible light beam through a medium containing dispersed graphene layers which are not necessarily planar sheets but naturally have ripples. There are many papers on Rayleigh and Mie scattering available in the literature having described the scattering for spherical/cylindrical particles. However, I am not able to find a source containing an expressive model with inclusion of dispersed thin films and particularly the grahene flakes (Can the mechanisms mentioned above be assumed as an estimation for the case of dispersed films?) On the other hand, considering a transition from thin films to graphene layers, does the scattering mechanism remain unchanged if assuming the special characteristic s of graphene?
Appreciate in advance for any contribution.
Scattering from flakes or thin materials is a common situation. As well as graphene you mention, there are clays, mica, and graphite with similar thin dimensions. The keys here are:
- The flakes flow align in a moving stream and show their projected area to the laser beam. See attached.
- Thus, with Mie theory, it's the projected area contour that is evaluated rather than a true volume diameter extracted. This is exactly analogous to microscopy where the particles are situated with the x and y axes in line with the light and examination of the z.axis thickness needs specialized sample preparation (e.g. embedding in epoxy and microtoming before examination under TEM)
- The refractive index that is important in the analysis is the one in the z-axis
- With an assumption of the RI, then the 'missing mass' (from a comparison of the calculated - Bouguer's law - and actual volume concentrations) a calculation can be made of the aspect ratio of the particles
This webinar may also be of interest (open in IE only; not enabled for mobile viewing):
Complementary information from analytical imaging and light scattering techniques
http://www.brainshark.com/brainshark/vu/view.asp?pi=133863612&text=M021507
Dear Dr. Alan F Rawle
Many thanks for the reply containing valuable points, useful for my research.
@ Morteza A Sharif (by PM)
Dear Dr. Alan F Rawle
Saying thanks, I have almost studied the suggested articles. But what about the scattering for different frequencies? My real problem is to discern if the light will scatter through dispersed graphene layers equally for all frequencies as in the case of Mie scattering or will scatter more for higher frequencies as in the case of Rayleigh scattering. If one of the two cases is valid, how I can approve it?
Appreciate promptly, Morteza
I have copied and pasted your message above so all can benefit from the replies by experts.
You have one major incorrect statement above. Mie theory deals with all wavelengths (we talk about wavelengths, not frequencies, in light scattering). In both the Rayleigh approximation (yes, it's an approximation, not an exact theory) and Mie theory, the wavelength is taken care of with a size parameter - circumference/wavelength. In both cases as the wavelength of impinging light decreases then the amount of scattering increases. Rayleigh approximation will give results similar to the exact solution provided by Mie when the size of the particle is typically d < λ/10 where λ is the wavelength of the impinging radiation. For a He-Ne laser at 632.8 nm this 'dividing line' is around 60 nm.
You have not discussed the possibility of multiple scattering that will complicate the situation whatever theory or approximation you use. This may be helpful:
The life of Gustav Mie and the development of the Lorenz-Mie solution to Maxwell’s equations http://tinyurl.com/mt97tp3
Dear Dr. Alan F Rawle
All right and I would have noticed earlier my carelessness about the fundamental difference between the frequency and wavelength when the light propagates inside a medium.
However, as we know, graphene flakes are nanodimensional sheets in thickness with lateral sizes of tens of micrometers. So, there will be a duality if we try to use the model of Rayleigh scattering. Furthermore, as you described, a multiple scattering process will interfer within a medium containing dispersed graphene layers which will make it hard to model the general scattering mechanism. On the other hand, through my last experimental observation, I found that the shorter wavelengths are scattered more. This maybe in consistency with Rayleigh scattering but I doubt if I could mention it inside my report since of the lack of accuracy.
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