How can I estimate/calculate the number of functional groups grafted to graphene with respect to number of carbon present in the system after modification with any group?
Some people use XPS but that requires that the functional groups have either heavy atoms which won't be common contaminants or a large sample number to ensure statistical significance. If your group if electroactive electrochemistry is a pretty simple way.
You can do a H1-NMR. Look for papers by Green et al on Bingle functionalization of carbon nanotubes. TGA can also be used for quantitative calculations. It has been used for nanotubes and you would have to tweak the analysis process for graphene (http://cnx.org/content/m22972/latest/). High-Res XPS might be of help. We have performed quantitative elemental analysis using a high-res XPS. I think it would still give you some semi-quantitative data on the oxidation state of carbon.
Thanks Jason and Gaurav for your reply. But in few paper published by James Tour published in JACS are specifying for example in this way "1 functional group per 7 carbon atom". How is this specification is possible.Rather how is total number of carbon they are calculating.
That's hard to say, I think some of those claims are less than accurate, and I think you can only approximate. I am curious about the NMR experiment. Do you mean a solid state experiment? The signal to noise would be extremely low for that and SLG is not soluble or dispersible without destroying the conjugation. Are you working with GO or CVD graphene?
I don't know which paper by James Tour are you referring to. A statement like that may have been as a result of TGA analysis. Check out the link I posted in my previous comment. As far as NMR is concerned, look at this: http://pubs.acs.org/doi/abs/10.1021/ja0355675. They perform NMR and XPS in this study.
I don't know about the SNR, but if its graphene and its functionalized, I am assuming that it would be stable in water after sonication and centrifugation for NMR analysis.
The best way is XPS. Then if you want to quantify the acid groups you can do acid-base titration to calculate the number of acid sites. CHNS elemental analysis may also help.
If you have a look at the paper; High-res XPS, Raman and FTIR have been used for qualitative analysis of functionalization. As I previously mentioned, TGA is used in this study to compute the extent of functionalization based on %weight losses. Read the last paragraph before conclusion. If you go through the TGA link I posted in my first comment, you would understand how it's done. Again, XPS is a point surface technique to analyze the oxidation states of elements. It can quantitative, but for you application, TGA would serve the best.