There is one recent study that seems on point [Zhao et al, J Mol Struct 1064(2014) 37-43]. These authors (see attached file) used benzoyl peroxide thermal decomposition (170C), where benzoyl radicals extract hydrogen atoms from paraffin, to make paraffin chain radicals ("chain" initiation) and benzoic acid later extracted. In the presence of acrylic acid monomers (AA), such radicals initiate grafting of AA onto paraffin chains that then: (1) are terminated by another paraffin chain radical (single AA cross-link of paraffin chains); (2) undergo chain transfer creating another paraffin chain radical and resulting in a single AA graft to the first chain; (3) two such chain-AA radicals terminate to result in di-AA cross-links between chains; (4) such chain-AA radicals initiate polymerization of AA, resulting in oligomeric AA chains grafted onto paraffin chains. I also would imagine grafting of  polyAA onto paraffin chains could similarly be obtained as demonstrated by Kang et al [Macromolecules 29 (1996) 6872-6879] for grafting polyAA onto polytetraflouroethylene (PTFE), using an Ar plasma to create chain radicals (on paraffin chain films) and then using UV to drive AA homopolymerization in an aqueous aolution contacting the radical-containg films, to obtain polyAA grafted onto, in addition to solution polymer (polyAA).

I guess that Philippe wand to have double bonds. The above procedures (1-4) lead to reacted AA. Some midchain radicals (publication) may be long-living but be not useful within a UV curable resin. Nevertheless the carbonic acid can be linked with an acrylic ester containing a primary OH group using basic chemical reactions.

Article Introduction to analyzing the solidification of multifunctio...

Thank you all for your very interesting answers.