Method of using certain cationic polymers as antioxidants or free-radical scavengers

A method for providing a free-radical scavenging and/or antioxidant effect comprising

• including in a cosmetic treatment composition at least one free-radical scavenger or at least one antioxidant chosen from at least one quaternary diammonium polycondensates comprising repeat units corresponding to the formula (I) below
• in which formula (I):
• R13, R14, R15 and R16, which are identical or different, represent cyclic or non-cyclic aliphatic, or arylaliphatic groups comprising 1 to 6 carbon atoms or hydroxyalkylaliphatic groups comprising 1 to 4 carbon atoms, or else R13, R14, R15 and R16, together or separately, constitute, with the nitrogen atoms to which they are attached, heterocycles optionally comprising a second heteroatom other than nitrogen or else R13, R14, R15 and R16 represent a linear or branched C1-C6 alkyl group substituted with a nitrile, ester, acyl, amide or —CO—O—R17-D or —CO—NH—R17-D group where R17 is an alkylene group and D a quaternary ammonium group;
• A1 and B1 represent polymethylene groups comprising 2 to 6 carbon atoms that may be linear or branched, saturated or unsaturated, and that may contain, linked to or inserted in the main chain, at least one aromatic rings, or at least one entity chosen from oxygen and sulphur atoms and sulphoxide, sulphone, disulphide, amino, alkylamino, hydroxyl, quaternary ammonium, ureido and ester groups;
• and
• X− is a mineral or organic acid anion.