what optical property can I use to demonstrate that nanomaterials have better properties with respect to materials of the same composition but that they are not nanomaterials?
A good reference text is: M Quinten “Optical Properties Of Nanoparticle Systems - Mie and beyond” Wiley-VCH (2011)
You need to define what you mean by 'better properties'. For example, supported metal catalysts have much better reactivity as the surface area is increased, quantum dots only show their colors in a very narrow size range....
Optical properties with that of other physical and thermodynamical properties depend on the size of the material in the nanoscale range. fo example the energy gap in semiconductors increases with the decrease of solids nanosize. For more details on properties and the structure of nanoscale range solids I suggest you to se the following presentation
"Solid Surface and Nanoscale materials Structure" M. S. Omar Presentation · July 2016 with 156 Reads DOI: 10.13140/RG.2.2.31947.59684 Charmo, University of Charmo, University of Salahaddin, DOI:10.13140/RG.2.2.31947.59684