Ethylene copolymer with peg, cationic and anionic units, cosmetic composition including same and treatment method

An ethylenic copolymer or its salts comprising, as % by weight with respect to the total weight of the polymer:

• a) from 25 to 95% by weight of monomer of formula (I), alone or as a mixture:
• in which:
• R1 is a hydrogen atom or a methyl radical,
• Z is a divalent group chosen from —COO—, —CONH—,
• R2 is a saturated or unsaturated, optionally aromatic, linear, branched or cyclic, divalent carbon-based radical which comprises from 1 to 18 carbon atoms and which can comprise from 1 to 4 heteroatoms chosen from O, N or S;
• m is 0 or 1,
• n is an integer between 65 and 700,
• R3 is a hydrogen atom or a saturated or unsaturated, optionally aromatic, linear, branched or cyclic, carbon-based radical which comprises from 1 to 30 carbon atoms and which can comprise from 1 to 4 heteroatoms chosen from O, N or S;
• b) from 4 to 50% by weight of cationic monomer or one of its salts, alone or as a mixture, of formula (II):
• in which:
• R1 is a hydrogen atom or a methyl radical,
• Z′ is a divalent group chosen from —COO—, —C(O)— and —CONH—,
• x′ is 0 or 1,
• R2′ is a saturated or unsaturated, optionally aromatic, linear, branched or cyclic, divalent carbon-based radical of from 1 to 18 carbon atoms which can comprise from 1 to 4 heteroatoms chosen from O, N or S,
• m′ is 0 or 1;
• X is chosen from:
• (a) a group of formula —N(R6)(R7) with R6 and R7 representing, independently of one another, either (i) a hydrogen atom, or (ii) a saturated or unsaturated, optionally aromatic, linear, branched or cyclic, alkyl group comprising from 1 to 12 carbon atoms, or (iii) R6 and R7 form, with the nitrogen atom, a saturated or unsaturated, optionally aromatic, ring comprising 5, 6 or 7 ring members chosen from CH, CH2, O, N, NH, S or C(O);
• or else
• (b) X represents an —R6′—N—R7′— group, in which R6′ and R7′ form, with the nitrogen atom, a saturated or unsaturated, optionally aromatic, ring comprising 5, 6 or 7 ring members chosen from CH, CH2, O, N, NH, S or C(O);
• c) from 1 to 35% by weight of anionic monomer and/or its salts, alone or as a mixture, chosen from maleic anhydride and those of formula (III):
• in which:
• R1, Z′, x′, R2′ and m′ have the meanings given above for the formula (II);
• and
• Y is a group chosen from —COOH, —SO3H, —OSO3H, —PO3H2 and —OPO3H2.