How strong is the peak in relation to the strongest peak in the IR spectrum ?

Did You observe this peak in the IR spectrum of the pure dextran sample ? This compound is known to show a signal at above 2000 cm-1, confirmed by the SDBS ( http://sdbs.db.aist.go.jp/sdbs/cgi-bin/cre_index.cgi?lang=eng ), which shows a spectrum of dextran (KBr pellet)  containing a dublet centred at approx. 2100 cm-1.

Your signal might also arise from aromatic systems, which can show (weak) overtones around 2000 cm-1.

Thank you Jarosz

In Dextran FTIR spectrum there is a small and broad peak in 2160 nm-1 (intensity is about 5%). But in synthesized polymer with different degree of grafting fatty acid there is a peak around 2120 nm-1 with intensity of  10 to 60%

The shift in the peak position (assuming the 2160 cm-1 signal is not present in the modified polymer) could be accounted for by the fatty acid substituent affecting the oscillator strength of the bond.

In dextran, there are several IR signals originating from water molecules bound within the structure of the polymer (due to the numerous hydroxyl groups), which could be what we are looking at here - if the reaction was carried out in water (or produced water as a side-product), some of it could have been trapped in the polymer, explaining the rise in the IR signal.

This could be verified by freeze-drying the sample and seeing whether an IR signal corresponding to ice will appear at approx. 800cm-1, similar to what has been done for pure dextran by A.N.J.Heyn ( http://onlinelibrary.wiley.com/doi/10.1002/bip.1974.360130304/abstract ).