Sorry. I have not had a look at the paper, so I will only write general ideas.

First, grafting percentage can mean two different values: either mass fraction of the grafting polymer with respect to the total sample mass, or the fraction of grafted sites with respect to the total number of sites that can be theoretically grafted polymer.

Calculation of that values from the elemental analysis result generally presumes the following:

Case A (mass fraction of grafting polymer). If the grafted material does not contain an element containing in the grafting polymer, than it is easy to calculate the mass of polymer knowing its repeating units gross formula. For example, if a material contains X wt% of oxygen, and if you know that this is a carbon grafted with poly(ethylene oxide), then 1 g of material contains 0.0X g of oxygen, or 0.0X/16*44 of poly(ethylene oxide), and X/16*44 is the "grafting percentage". Similarly, the mass fraction of the grafting polymer can be calculated if the pristine material contains some element absent in the grafting polymer. In principle, having known the gross formulae of both grafted and grafting material, it is possible to calculate the "grafting percentage" even if all the elements are contained in both pieces of material - you will have to write a system of linear equations.

Case B. Fraction of reactive sites grafted with polymer. This is a bit tricky, and it may not be calculated in general. However, in some special cases this is also possible. Assume reaction of particles modified with COCl groups with some amine-bearing species. In this case, decrease of Cl content makes possible to calculate the number of grafted and non-grafted COCl sites. Also, the decrease of Cl content due to grafting should be accounted for the weight fraction of grafting polymer as well! However, normally I would go for IR or NMR or titration to determine the fraction of grafted reactive sites, thus, I assume that case A is more popular in literature (not sure about your particular reference!).

Hope this helps...

Ups, sorry, just have sent and noticed that I have describe a reverse task - calculating of grafting percentage from the elemental analysis. However, the math and ideas are essentially the same.

Hi Dr Karpushkin

Thank you for your great explanation and helping. I learn something new and i hope can utilize in my research. However the situation for my previous question is like this:

1) result from the elemental test machine ( elemental percentage)

2) result from calculation of the elemental percentage based on mass of grafted polymer (the mass get after grafting process)

Then we compare both result to know it agreement

Can i ask you something from your explanation in case A?

From you equation 0.0X/16*44, is it 44 is the molar mass Ethylene oxide? if yes, can we use it since the material is polymer and not monomer

Sorry for the inconvenience cause from my question

Really appreciate for you helping

thanks

Yes, karpushkin explained well

Yes, 44 is the molar mass of ethylene oxide, and, at the same time, that of poly(ethylene oxide) repeating units - as in case of ring-open polymerization the elemental compositions of the monomer and of the respective polymer repeating units are equal.

If you have experimentally determined the increase of the sample weight after grafting - then, of course, you can calculate the theoretical elemental composition of the whole sample as if it were a mixture of the nascent sample and the grafting polymer. However, you have to make sure that: a) the unbound polymer has been thoroughly washed out before weighing, and b) that no side reactions other than grafting polymerization are expected.

Hi Prof Evgeny Karpushkin

I have experimentally determined the increased of the sample weight after grafting and I have remove any homopolymer by soxhlet extraction and i assume there is no side reactions other than grafting

However I am still not clear how to use the weight we gain to calculate the elemental composition. Can you give me an example?

Let say I grafted PolyDiallyldimethylammonium chloride ( Monomer is DADMAC, molar mass= 161.5) into cassava starch (AGU unit =162 dalton), how can i get the elemental composition? I want to calculate N% which this N come from PolyDADMAC and there is no N in the starch.