There are many ways you can achieve this, but the simplest way is to first solvent extract (for example with Soxhlet extraction) the additives and chromatographipally separate those components into rather pure components. Do not attempt structural determination unless you achieve high purity as the interpretation of the results will be a nightmare. If you can obtain large amount of additives, then you can separate those first by solubility difference to different solvents. If you cannot collect high enough amount to do solvent separation, you can then use column chromatographic separation. You can also use SEC or HPLC chromatographs to separate based on either the molecular weight or chemical structure. The amount of the additively you can collect by these methods is very small (micrograms at best), but using 1H NMR spectroscopy and/or FT-IR spectroscopy, you can still obtain signals to analyze the molecular structure. For these techniques, the extensive data base for such additives are published, if you have access to such computer data base. If you have mass spectrometer, you can use even less amount of samples.
As Hatsuo Ishida said, the best way is the percolation process. You can use Acetone or Alcohols as your solvents. These solvents are non-solvents for NR.
There is one another way to separate your additives. Use Hydrocarbons or Chlorinate Hydrocarbons, as well as Ethers to solve your NR. After then, add non-solvent I mentioned above into your system. Now start adding emulsifier. Keep on adding emulsifier till you can see sediments. By phase separation, divide your system into two, one containing sediments of the polymer and another containing of your additives. by evaporating the solvent and non-solvent, you can use FTIR or HNMR to identify the additives. be careful that your solvent and non-solvent should be dissolved and your solvent should have lower boiling point than non-solvent.