Not sure which papers you're reading at the moment, but you're OP mentions that you're going to look at MWCNTs in acetone. This is a very different situation compared to studies of SWCNTs and their optical properties as discussed in the article posted by VEskizeybek and the large pool of research work in this area.

Generally speaking, in my experience, absorption (an optical process... UV, Vis, IR are electromagnetic energy regions not names of processes like absorption, transmission, reflection, etc.) spectra taken of MWCNTs in nearly any solvent and/or solution environment will nominally only show changes for the pi-plasmon peak in the UV spectral region (roughly around 220 - 270 nm).

I vaguely recall work from 10+ yrs ago that tries to relate the pi-plasmon peak shift to MWCNT diameters... I don't recall much confidence in the work as I've never seen it used in analytical QA reports for MWCNTs, even when I worked as a research scientist for a CNT manufacturer.

Hello,

This article may be useful for you;

http://www.nature.com/ncomms/2013/130927/ncomms3542/full/ncomms3542.html

Yes: The smaller the diameter the greater the strain in the nanotube. This should shift the spectra to somewhat higher frequency (shorter wavelength) unless the strain becomes too large and the lattice is damaged.In effect you are increasing the depth of the effective potentials of which there are a great many so this can be tricky. The most general answer is that there should be a shift and you need to get some idea of relative diameters from TEM. When you introduce acetone you can expand the lattice which may give you a red shift.

Not sure which papers you're reading at the moment, but you're OP mentions that you're going to look at MWCNTs in acetone. This is a very different situation compared to studies of SWCNTs and their optical properties as discussed in the article posted by VEskizeybek and the large pool of research work in this area.

Generally speaking, in my experience, absorption (an optical process... UV, Vis, IR are electromagnetic energy regions not names of processes like absorption, transmission, reflection, etc.) spectra taken of MWCNTs in nearly any solvent and/or solution environment will nominally only show changes for the pi-plasmon peak in the UV spectral region (roughly around 220 - 270 nm).

I vaguely recall work from 10+ yrs ago that tries to relate the pi-plasmon peak shift to MWCNT diameters... I don't recall much confidence in the work as I've never seen it used in analytical QA reports for MWCNTs, even when I worked as a research scientist for a CNT manufacturer.

If you are comparing same types of CNT samples, shifts in the intensity of the absorbance peaks can be used to estimate the concentration of your dispersion based on the Beer-Lambert Law. This principle has been utilized widely to determine dispersion stability of CNTs.

If you are comparing different types of CNT samples, then several other factors come in that affect changes in absorption peaks. For example, it has been shown that peak intensity is affected by MWCNT oxidation, while peak wavelength is affected by MWCNT length.

Refer to this paper for details: http://www.hindawi.com/journals/jnm/2011/938491/

Furthermore, absorption spectra of SWCNTs, DWCNTs, and MWCNTs all have differences in whether they display semiconducting or metallic bands.

This paper has an example comparing SWCNTs and DWCNTs: http://scitation.aip.org/content/aip/journal/apl/103/13/10.1063/1.4823541

Hope this helps a little, and best of luck in your work.

I agree completely with Volkan

Single wall carbon nanotubes with particular chirality and diameter (chiral indices) have different electron density of states dependence on energy. This density of states is characterized by van Hove singularities that shut up at a particular energy. Optical transition will happen between the singularities in valence and conduction bands of states. Therefore absorption of the photons of particular wavelength would depend on the diameter and chirality of the tube.

Hello.

The relationship of SWCNT resonance energies on diameter are fairly well known and come form a so-called tight-binding model. These resonances have been measured in a variety of environments, mostly via SWCNT fluorescence.

The observed spectral shifts generally depend on how much the environment can reduce electron-hole interaction, or exciton binding energy with respect to vacuum. This generally depends on the polarizability of the medium. However, for nanotubes this polarizability of their environment is not something that can be easily defined and measured, except in a few select cases when the environment is uniform, i.e. there are no surfactants or other nanotubes in close proximity.

One relevant paper you may take a look at:

http://pubs.rsc.org/en/content/articlelanding/2010/cp/b927053a#!divAbstract

Regarding MWCNTs,

I doubt you will see any pronounced peaks in UV-VIS absorption spectra of "dispersed" MWCTNs, with dispersed being also highly questionable. I would expect too much spectral overlap + broadening. Be aware that if the dispersion process is mechanical, i.e. sonication, you may see some SWCNT might be coming out of MWNCT. If needed, could give you a reference where it was shown for double-walled NTs.

I agree with Dr. Rocha..

there are far too many variables in MWCNTs like number of walls, d-spacing, crystallinity, length, catalyst impurities etc..

it is very difficult to get only Metallic or only semiconducting SWCNTs. the commertial grade SWCNTs have the mixture of these semi conducting and metallic forms. we have reported Stress induced metallization of SWCNTs embidded in glass matrix. In our study, the recored absorption spectrum of SWCNTs film on quatrz substate and SWCNTs embidded in transparent glass matrix shows different properties. Film exhibits the charecteristic absorption bands of semi-conducting and metallic  SWCNTs. where as in case of SWCNTs embidded in glass matrix, the recorded absorption spectrum show different charecteristics due to the stress induced by the glass. The semiconducting SWCNTs absorption band intensities are greatly reduced and shifted to lower/higher wavelength region. mejority of semiconducting SWCNTs are transformed to small band gap metallic SWCNTs when embidded in galss matrix. electrical conductivity propertie on this composite have also been evaluated and discussed in details. You can have  a look on our publication.

This seems to be a good question. I would rather put it little differently. Can we not calculate optical absorption by invoking electron band structure resulting in imaginary part of the dielectric constant and then extract a standard graphite like infinite diameter band structure based results to realize finite diameter dependence on the imaginary part and thus diameter dependence of absorption spectra. Some body willing to go ahead? We can join in.