How can we establish a correlation between FTIR intensity and the C1s peak observed in XPS analysis?
That's not straightforward and will have to be done individually for every system.
The simplest case is the one in which there are IR peaks which are characteristic of functional group, primarily carbonyls, and there are equally characteristic XPS components with a corresponding shift. However, the experimental reality tends not to give us this favor in most other cases.
The case of mediocre complexity is when there is a fingerprint peak group in IR, e.g. for C-C or C-O, which also have their characteristically shifted correspondences in XPS.
The worst case is that you have functionalities which don't really give that much of a characteristic signal, then correlating the two methods will not be possible in a handwaving manner and without quantum chemistry you're lost, although QC is already pretty helpful in the "easier" cases.
Jürgen Weippert The deconvolution of the C 1s spectrum reveals two distinct narrow peaks. The higher peak at 285.7 eV is attributed to CH2 groups, while the second peak, centered at 287.9 eV, corresponds to H–C–F bonds. Is it possible to compare the intensity of the C 1s peaks with the corresponding FTIR intensity bands for these groups?
Do I guess correctly that you have a partially flourinated PE derivative and you want to check the fluorination degree as in this work?
Article Surface Modification of Polymers Treated by Various Fluorinating Media
That sounds like the middle complex case, in this paper there is also a correlation to XPS.
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