The use of dilute acid to functionalize graphene to Raman to determine whether there is damage to the structure.How to know Raman graphene structure is destroyed?
First you need to do some plot treatments to compare them. Try following.
Do baseline corrections to both of the plots
Normalize both of your data
Plot them together in same graph
The peak around 1581 is G-band (normally its around 1582 cm-1) (this comes from Sp2 hybridization from stretching of the C−C bond)
The other peak around 1327 is called D-band (this is the crystallographic defect related peaks which tells you crystal damage information as you referred to, low peak intensity (compare to G-band): low crystal defect and high peak intensity: high crystal defect)
Now compare the D-band from both of the samples to compare their defects.
Also compare ID/IG from both of ur samples to compare defects.
Have an observation: You have very low intensity of your G' band (around 2700 cm-1) compare to G-band. That's mean you have many graphene layers. So may be your sample is either graphite or many layers of graphene.
Also you have some shifts in both D and G bands.. this may come from: Either both of your Raman measurements were not calibrated appropriately or you have some charge transfer from your functionalization process.
Hope this will provide you a good starting. Read the following paper very carefully and you can understand most of the things.
Good luck,
CB...
Article Perspectives on Carbon Nanotubes and Graphene Raman Spectroscopy