A functionalized fatty substance chosen from among the compounds of formulas (IIa), (IIb) or (IIc): in which: • G, the same or different, represents -NR 1 H; -C OH; • n is 1 or 2; • R 1 is a hydrogen atom; a C 1 -C 10 radical alkyl, linear or branched, non-substituted or substituted by at least one group chosen from among -OH, -C OH, -NH 2,-C H, • L 1 is a -CH 2 group; a direct bond; • L 2 is: - a C 1 -C 20 alkyl, linear or branched, optionally comprising one or more heteroatoms chosen from among an oxygen atom, nitrogen atom, sulfur atom, non-substituted or substituted by at least one group chosen among -OH, -C OH, -C H, -NHR 2 where R 2 represents a hydrogen atom; a C 1 -C 10 alkyl radical, linear or branched, non-substituted or substituted by at least one group chosen from among -OH, -C OH, -NH 2, - C H, - a C 3 to C 8 carbo- or heterocycle, in particular a cycloaliphatic group, an aryl group, a heteroaryl group. • R 3 is: - a hydroxyl group, - an alkoxy group of -OX type, with X chosen from among a C 1 -C 20 alkyl, linear or branched, optionally substituted by at least one group chosen from among -OH, -C OH, - NH 2, -C H, - a -NY'Y" amine group where Y' and Y", the same or different represent a hydrogen atom, a C 1 -C 20 alkyl, linear or branched, optionally substituted by at least one group chosen from among -OH, -C OH, -NH 2, -C H, - a thio group of SZ type, with Z chosen from among a C 1 -C 20 alkyl, linear or branched, optionally substituted by at least one group chosen from among -OH, -C OH, -NH 2, -C H, • R 4 is: - an oxygen atom; - a nitrogen atom; • R 5 is: - a C 1 -C 20 alkyl group, linear or branched, optionally substituted by at least one group chosen from among -OH, -C OH, -NH 2, -C H, • l is an integer between 1 and 10; • m is an integer between 1 and 3; • p is an integer between 0 and 10. • G, the same or different, represents -NR 1 H; -C OH; • n is 1 or 2; • R 1 is a hydrogen atom; a C 1 -C 10 radical alkyl, linear or branched, non-substituted or substituted by at least one group chosen from among -OH, -C OH, -NH 2,-C H, • L 1 is a -CH 2 group; a direct bond; • L 2 is: - a C 1 -C 20 alkyl, linear or branched, optionally comprising one or more heteroatoms chosen from among an oxygen atom, nitrogen atom, sulfur atom, non-substituted or substituted by at least one group chosen among -OH, -C OH, -C H, -NHR 2 where R 2 represents a hydrogen atom; a C 1 -C 10 alkyl radical, linear or branched, non-substituted or substituted by at least one group chosen from among -OH, -C OH, -NH 2, - C H, - a C 3 to C 8 carbo- or heterocycle, in particular a cycloaliphatic group, an aryl group, a heteroaryl group. - a C 1 -C 20 alkyl, linear or branched, optionally comprising one or more heteroatoms chosen from among an oxygen atom, nitrogen atom, sulfur atom, non-substituted or substituted by at least one group chosen among -OH, -C OH, -C H, -NHR 2 where R 2 represents a hydrogen atom; a C 1 -C 10 alkyl radical, linear or branched, non-substituted or substituted by at least one group chosen from among -OH, -C OH, -NH 2, - C H, - a C 3 to C 8 carbo- or heterocycle, in particular a cycloaliphatic group, an aryl group, a heteroaryl group. • R 3 is: - a hydroxyl group, - an alkoxy group of -OX type, with X chosen from among a C 1 -C 20 alkyl, linear or branched, optionally substituted by at least one group chosen from among -OH, -C OH, - NH 2, -C H, - a -NY'Y" amine group where Y' and Y", the same or different represent a hydrogen atom, a C 1 -C 20 alkyl, linear or branched, optionally substituted by at least one group chosen from among -OH, -C OH, -NH 2, -C H, - a thio group of SZ type, with Z chosen from among a C 1 -C 20 alkyl, linear or branched, optionally substituted by at least one group chosen from among -OH, -C OH, -NH 2, -C H, - a hydroxyl group, - an alkoxy group of -OX type, with X chosen from among a C 1 -C 20 alkyl, linear or branched, optionally substituted by at least one group chosen from among -OH, -C OH, - NH 2, -C H, - a -NY'Y" amine group where Y' and Y", the same or different represent a hydrogen atom, a C 1 -C 20 alkyl, linear or branched, optionally substituted by at least one group chosen from among -OH, -C OH, -NH 2, -C H, - a thio group of SZ type, with Z chosen from among a C 1 -C 20 alkyl, linear or branched, optionally substituted by at least one group chosen from among -OH, -C OH, -NH 2, -C H, • R 4 is: - an oxygen atom; - a nitrogen atom; - an oxygen atom; - a nitrogen atom; • R 5 is: - a C 1 -C 20 alkyl group, linear or branched, optionally substituted by at least one group chosen from among -OH, -C OH, -NH 2, -C H, - a C 1 -C 20 alkyl group, linear or branched, optionally substituted by at least one group chosen from among -OH, -C OH, -NH 2, -C H, • l is an integer between 1 and 10; • m is an integer between 1 and 3; • p is an integer between 0 and 10.