I have two polymers made into nanoparticles. Please tell me a simple method to calculate the degree of grafting or degree of cross linking between them?
It is important to define at which graphitization your polymere is.
In a Broad sense, graphitization phenomenon, despite wide range of application (metallurgy, geology, …) at polymer seems be case sensitive.
But a set of factors macroscopic and microscopic factors can be taken in account to reach some practical objective.
As a whole, the graphitizing is not a science, yet. Thus, depending on the case-to-case or in the maximum, sometimes particular set of rules can attend a small set of materials. The process consist in a sequence well knew.
From a long molecule of a polymer is necessary to reach an amount of carbon amorphous in the presence of oxygen. Some carbon loss can be expected since in this first step is sine qua non condiction the formation of Gas CO and CO2 and H2O. From this step, a complex sequence strongly dependent of temperature, always involving gradual increasing of temperature with paralell increase of crystallinity degree, take way, with absence of oxygen. In the practice, the complete sequence of steps should be carried from a natural or an engenierred polymer up to graphite.
Then, as macroscopic factors, it is possible to notice the time, temperature and atmosphere, at step of cycle carried out in the oxygen presence, called of first stage of the graphitizing cycle that finishes with preparation of amorphous-carbon. From amorphous-carbon sup to graphite, the macroscopic parameters are time, temperature, atmosphere of vacuo or inert being temperature the major factor, but seems to exist a kinect factor, which necessitate some engineering of the process. The question of pressure can be approached as follow: in the first step of cycle, the effect of the partial gases pressure in not clear, but seems that high pressure can help in the second stage of graphitization process being that an compensation mechanism can be operational, as an example more high pressure gives necessary minor level of temperature.
As microscopic factors, intrinsic features of molecules of polymer can be provide some insight to reach more rapidly the graphite material. Here, taking into consideration, the second stage of preparation, size of polymer molecule, ramification degree, presence, type and number of heteroatom, and at the end: presence, number and intrinsic distribution of cross-linked bonds. From this point, the importance of Tg of polymer is relevant. Therefore, different class of polymers cannot be compared in a simple way with relation the feasibility of graphitization, in this sense two polymers with very distinct Tg should be only compared in a careful way.
As commented above, the question is complex, but whether a qualitative analaysis is fundamental as a simple procedure, in a comparative way, you can use Mid-infrared spectroscopy and use the integrated area of some selected vibrational bands.
In an alternative way, the thecnique of X-Ray diffraction can be used, again the integrated area at a particular region of intensity of diffractogram ( in cps unity (counts per second)) taked at region of "halo" ( 2-theta at around 10 - 20o depending on the material to material) formation at region that exhibits an increasing of the crystallinity (see crystalline material exhibits lines of diffraction with high intensity of cps, then if cps increases the crystallinity increases, despite of a priori the material be amorphous (absence of systematic of diffraction lines)).
See, it is necessary have in mind that the procedure discrebed above gives only qualitaive date being careful and systematic approaching.
Personally I think it easier to run GPC with multiple detectors as long as one of the polymers being grafted had a uv absorbance and the other did not. I have used this technique with polymers with carbonyl and phenyl groups with good success. You will need a GPC equipped with Viscosity, LS, RI, and uv detectors.
if the two polymers have different thermal stabilities, there should be different thermal decomposition steps for them in the TGA curve for the grafted product
The degree of grafting can be fairly easily calculated by NMR. Just quantitate the differences between the orginial and the graft. As far as crosslinking goes thats even easier. If you know of a good solvent just try and dissolve the cross linked polymer. Whatevers cross linked wont dissolve.