A process for treating keratin fibers using a basic pH composition, one or more acetoacetate compounds, and one or more specific polyamine compounds.

Abstract

The present invention relates to a process for treating keratin fibers using a basic pH composition, one or more compounds with acetoacetate functions and one or more specific polyamine compounds.

Description

Title of the invention: A process for treating keratin fibers using a basic pH composition, one or more acetoacetate compounds, and one or more specific polyamine compounds Technical field of the invention

[0001] The present invention relates to a process for treating keratin fibers using a basic pH composition, one or more compounds with acetoacetate functions and one or more specific polyamine compounds. Context of the invention

[0002] Many people are not satisfied with the appearance of their hair, especially people with curly hair who most often seek to obtain straight hair and, conversely, those with straight hair wish to have curly hair.

[0003] In order to change the shape of hair permanently, three main types of techniques can be used.

[0004] A first technique consists, initially, of opening the disulfide bonds (-SS-) of keratin (keratocystin) using a composition containing a suitable reducing agent (reduction step). Then, after rinsing the treated hair, generally with water, the disulfide bonds are reconstituted in a second step by applying an oxidizing composition to the hair, which has been previously held under tension, for example, with curlers (oxidation step, also called fixing step), in order to ultimately give the hair the desired shape. This technique thus makes it possible to create waves (perming process) and / or straighten (or relax) hair.

[0005] The new shape imposed on the hair by such a chemical treatment is eminently durable over time and resists in particular the action of washing with water or shampoos, in contrast to simple classic techniques of temporary deformation, such as setting.

[0006] The reducing compositions for carrying out the first step generally contain, as reducing agents, sulfites, bisulfites, alkylphosphines or preferably thiols. Among the latter, particular examples include cysteine ​​and its various derivatives, cysteamine and its derivatives, thiolactic acid or thioglycolic acid, their salts as well as their esters, in particular glycerol thioglycolate.

[0007] The oxidizing compositions required for the implementation of the fixation step are most often hydrogen peroxide-based compositions.

[0008] However, such a technique is not yet entirely satisfactory. Indeed, although it proves very effective in modifying the shape of hair, it remains damaging to hair fibers, mainly due to the high levels of reducing agents used in the reducing compositions as well as the varying application times that can occur during such a process.

[0009] This technique can thus, in the long term, lead to an alteration in hair quality resulting in a decrease in its cosmetic properties, such as its vitality and shine, and a degradation of its mechanical properties, particularly its mechanical resistance, due to swelling of the hair during rinsing between the reduction and oxidation stages, which can also result in an increase in its porosity, particularly when the treated hair is already weakened, such as colored or bleached hair.

[0010] Furthermore, the use of reducing agents can lead to unsatisfactory durability for hair straightening, particularly for relaxing or backcombing hair. Finally, odor problems are very common, both with the reducing compositions used, especially those containing thiols, and with the reduced hair itself.

[0011] The second technique commonly used to achieve hair straightening or smoothing involves performing a so-called lanthionization operation, using a composition containing a base belonging to the hydroxide family. This results in the replacement of disulfide bonds (-CH2-SS-CH2-) by lanthione bonds (-CH2-S-CH2-).

[0012] Compared to the first technique described above using a reducing agent, this lanthionization technique does not require a fixation step, since the formation of lanthione bridges is irreversible.

[0013] It is therefore carried out in a single step and allows for the creation of either waves, styling, backcombing, or straightening of the hair. This technique is primarily used for styling naturally curly hair.

[0014] However, the hydroxides used in this process have the major drawback of being caustic. This causticity can, in some cases, affect the scalp, sometimes causing irritation, and also affect the condition of the hair, making it rough to the touch and much more brittle. The use of hydroxides can also, in some cases, cause discoloration of the natural hair color.

[0015] Finally, the third technique commonly used involves combining heat with an alpha-keto acid, such as glyoxylic acid. Such a process is described, for example, in application WO2011 / 104282. However, alpha-keto acids, particularly at high concentrations, may not be well tolerated, especially when the scalp is sensitive and / or irritated. Their volatility, amplified by the use of heat, for example via a curling or straightening iron, can also be problematic. Furthermore, cosmetic formulations with an acidic pH can damage the hair and / or alter its color.

[0016] All these reasons, and in particular the impact of these types of treatment on the quality of the hair, represent a deterrent for users, especially for those who might be tempted to repeat such treatments at more regular intervals in order to explore the level of hair styling that suits them best.

[0017] There is therefore a real need to develop a process for the permanent deformation of keratin fibers that provides good shaping performance, including a substantial reduction in hair volume and, when the hair is curly, improved curl relaxation and / or definition. The effect obtained must be long-lasting after one or more shampoos and allow the user greater control over the desired level of styling, making it possible to repeat the process while preserving the quality and integrity of the treated keratin fibers. Ideally, such a process should eliminate the need for a flat iron. Furthermore, such a process should also use less malodorous compositions, particularly without reducing agents such as thiols.Finally, the formulation of environmentally friendly cosmetic products—that is, products whose design and development take environmental issues into account—is becoming a major concern in order to help address global challenges. It is therefore essential to offer more sustainable cosmetic processing methods that can thus respond to these environmental challenges.

[0018] The applicant has surprisingly discovered that all or part of these objectives can be achieved by the process according to the present invention. Summary of the invention

[0019] According to a first aspect, the present invention relates to a process for treating keratin fibers comprising the following step(s): i) application on keratin fibers: a) of one or more compounds A chosen from among the compounds of formula (I), their optical isomers, their geometric isomers, their salts, their solvates such as hydrates, and their mixtures: Formula (I) in which: - R1 represents a versatile hydrocarbon radical in C2 to CM, linear or branched, saturated or unsaturated, conjugated or not, acyclic or cyclic, aromatic or not, R1 being further: a) possibly substituted by one or more hydroxy groups OH, dialkylamino-N(R)2 with R representing a (Ci-C4)alkyl group, carboxy-C(O)-OH, a vinyl group, and / or b) possibly interrupted by one or more heteroatoms or groups selected from O, S, carbonyl -C(O)-, amine -N(R'), or their combinations, in which R' represents a hydrogen atom, a linear or branched alkyl group having from 1 to 4 carbon atoms possibly substituted by at least one hydroxy group (OH) or possibly substituted by -XC(O)-C(Ra)(Rb)-C(O)-R2; - R2 represents a monovalent hydrocarbon radical in C1 to C6, linear or branched, saturated or unsaturated; - Ra, and Rb, identical or different, represent a hydrogen atom or a (CrC4)alkyl group; - X is a heteroatom or group chosen from O, S, N(R') or , -S-CH2-C(O)-O-, -OC(O)-CH2-S-, -OC(O)-N(R')-, -N(R')-C(O)-O-, -N(R')-C(O)-N(R')-, R' being as defined previously; - n denotes an integer ranging from 2 to 10, particularly from 3 to 9; and b) of one or more polyamine compounds B selected from compounds of formula (II), their optical isomers, their geometric isomers, their salts, their solvates such as hydrates, and their mixtures: H2N—T—NH2 (II) Formula (II) in which T represents a divalent hydrocarbon group, linear or branched, saturated or unsaturated, preferably saturated, comprising from 4 to 22 carbon atoms, optionally substituted by an -NH2 group, the T group being substituted by one or more hydroxyl (-OH) groups and / or interrupted by one or more groups chosen from -C(0)-, -NRa- or their combinations such as -NRa-C(O)- or -C(O)-NRa-, with Ra representing a hydrogen atom or a (Ci-C4)alkyl group; and i') application to the keratin fibers of a pretreatment composition (P) having a pH between 8 and 12.5, preferably between 8.5 and 12.5, step i') being carried out before step i); it being understood that: ■ Compound(s) A are included in a composition (A) and polyamine compound(s) B are included in a composition (B) separate from composition (A), composition (A) being applied to the keratin fibers before or after composition (B), preferably before composition (B), or compound(s) A and polyamine compound(s) B are included in the same composition (C); and ■ where step i') is absent, one of the two compositions (A) and (B) or each of the two compositions (A) and (B) or composition (C) has a pH between 8 and 12.5, preferably between 8.5 and 12.5.

[0020] According to a second aspect, the present invention relates to the composition (C) as defined above.

[0021] According to a third aspect, the present invention relates to a two- or three-compartment device comprising: - a first compartment containing a composition (A) as defined above; - a second compartment distinct from the first compartment containing a composition (B) as defined above; - possibly a third compartment distinct from the first and second compartments containing a pretreatment composition (P) as defined previously.

[0022] According to a fourth aspect, the present invention relates to the use of a composition (A) as defined above associated with a composition (B) as defined above and possibly associated with a pretreatment composition (P) as defined above or of a composition (C) as defined above, possibly associated with a pretreatment composition (P) as defined above, for the relaxation of loops and / or the smoothing of keratin fibers. Detailed description of the invention

[0023] For the purposes of the present invention, and unless otherwise indicated:

[0024] ■ By "keratin fibers" we mean fibers of human or animal origin such as that hair, body hair, eyelashes, eyebrows, wool, angora, cashmere or the fur. According to the present invention, the keratin fibers are preferably human keratin fibers, more preferably hair;

[0025] ■ an "aryl" radical represents a mono- or polycyclic hydrocarbon group, condensed or not, comprising from 6 to 14 carbon atoms, and of which at least one ring is aromatic; preferably the aryl radical is a phenyl, biphenyl, naphthyl, indenyl, anthracenyl, or tetrahydronaphthyl;

[0026] ■ a "heteroaryl" radical represents a mono- or polycyclic group, condensed or not, comprising 5 to 14 links, 1 to 6 heteroatoms chosen from nitrogen, oxygen, sulfur and selenium atoms, and of which at least one ring is aromatic; preferably a heteroaryl radical is chosen from acridinyl, benzimidazolyl, benzobistriazolyl, benzopyrazolyl, benzopyridazinyl, benzoquinolyl, benzothiazolyl, benzotriazolyl, benzoxazolyl, pyridinyl, tetrazolyl, dihydrothiazolyl, imidazopyridinyl, imidazolyl, indolyl, isoquinolyl, naphthoimidazolyl, naphthooxazolyl, naphthopyrazolyl, oxadiazolyl, oxazolyl, oxazolopyridyl, phenazinyl, phenooxazolyl, pyrazinyl, pyrazolyl, pyrilyl, pyrazoyltriazyl, pyridyl, pyridinoimidazolyl, pyrrolyl, quinolyl, tetrazolyl, thiadiazolyl, thiazolyl, thiazolopyridinyl, thiazoylimidazolyl, thiopyrylyl, triazolyl, xanthylyl; ■ by "(hetero)aryl" we mean the aryl or heteroaryl groups;

[0027] ■ by "(hetero)cycloalkyl" means cycloalkyl or heterocycloalkyl groups;

[0028] ■ the "aryl" or "heteroaryl" radicals or the aryl or heteroaryl part of a radical can be substituted by at least one substituent attached to a carbon atom, chosen from: - an alkyl radical in Ci-C6, preferably in Ci-C4; - a halogen atom such as chlorine, fluorine or bromine; - a hydroxy group; - a C1-C2 alkoxy radical; a C2-C4 (poly)-hydroxyalkoxy radical; - an amino radical; - an amino radical substituted by one or two alkyl radicals, identical or different, in Ci-C6, Ci-C6, preferably in CrC4; - an acylamino radical (-N(R)-C(O)-R') in which the radical R is a hydrogen atom; - an alkyl radical in CrC4 and the radical R' is an alkyl radical in CrC4; a carbamoyl radical (R2N-C(O)-) in which the radicals R, identical or not, represent a hydrogen atom, an alkyl radical in CrC4; - an alkylsulfonylamino radical (R'S(O)2-N(R)-) in which the radical R represents a hydrogen atom, a Ci-C4 alkyl radical and the radical R' represents a C1-C4 alkyl radical, a phenyl radical; - an aminosulfonyl radical (R2N-S(O)2-) in which the R radicals, identical or not, represent a hydrogen atom, an alkyl radical in CrC4; - a carboxylic radical in acidic or salified form (preferably with an alkali metal or an ammonium, substituted or unsubstituted); - a cyano group (CN); - a polyhalogeno(Ci-C4)alkyl group, preferably trifluoromethyl (CF3); ■ The cyclic or heterocyclic part of a non-aromatic radical can be substituted by at least one substituent attached to a carbon atom chosen from the following groups: - hydroxy; - CrC4 alkoxy, (poly)hydroxyalkoxy C2-C4; - alkylearbonylamino (RC(O)-NR'-) in which the radical R' is a hydrogen atom, an alkyl radical in Ci-C4 and the radical R is an alkyl radical in CrC4, amino substituted by one or two identical or different alkyl groups in CrC4; - alkylearbonyloxy (RC(O)-O-) in which the radical R is an alkyl radical in CrC4, amino substituted by one or two identical or different alkyl groups in CrC4; - alkoxycarbonyl (RO-C(O)-) in which the radical R is an alkyl radical in CrC4;

[0029] ■ a cyclic radical, heterocyclic radical, or a non-aromatic part of an aryl radical or heteroaryl, can also be substituted by one or more oxo groups;

[0030] ■ A hydrocarbon chain is unsaturated when it comprises one or more double bonds and / or one or more triple bonds; preferably one or more double bonds;

[0031] ■ A "cyclic" or "cycloalkyl" radical is a non-cyclic hydrocarbon radical aromatic, mono or polycyclic, condensed or not, containing from 5 to 14 carbon atoms, which may have from 1 to several unsaturations, preferably the cycloalkyl is a cyclohexyl group;

[0032] ■ A "heterocyclic" or "heterocycloalkyl" radical is a non-cyclic radical aromatic mono or polycyclic, condensed or non-condensed, containing 3 to 9 links, comprising 1 to 4 heteroatoms chosen from nitrogen, oxygen, sulfur and selenium atoms, preferably the heterocycloalkyl is chosen from epoxide, piperazinyl, piperidinyl, morpholinyl, or dithiolane;

[0033] ■ an "alkyl" radical is a saturated hydrocarbon radical, linear or branched, in particularly in Ci-C6, preferably in CrC4;

[0034] ■ an "(Cx-Cy) alkyl group" is an alkyl radical comprising x to y atoms of carbon;

[0035] ■ an "alkylene group" is a divalent hydrocarbon radical, linear or branched, saturated;

[0036] ■ a "(Cx-Cy)alkylene group" means an alkylene group comprising from x' to y' carbon atoms;

[0037] ■ an "alkoxy" radical is an alkyl-oxy radical for which the alkyl radical is a hydrocarbon radical, linear or branched, in Ci-C6 preferably in Ci-C4;

[0038] ■ a "(poly)(hydroxy)alkyl" radical designates a Ci-C6 alkyl radical, of preferably in Ci-C4 possibly substituted by one or more hydroxy radicals, preferably substituted by 1 to 4 hydroxy groups, more particularly between 1 and 3;

[0039] ■ a "sugar" radical is a monosaccharide or disaccharide radical; Examples include as sugar radical: sucrose (or saccharose), glucose, galactose, ribose, fucose, maltose, fructose, mannose, arabinose, xylose, or lactose;

[0040] ■ By "monosaccharide", we mean a monosaccharide sugar comprising at 5 carbon atoms, preferably of formula CX(H2O)X, with x an integer greater than or equal to 5, preferably x is greater than or equal to 6, in particular x is inclusively between 5 and 7, preferably x = 6, they may be of D or L configuration, and of alpha or beta anomer, as well as their salts and solvates such as hydrates;

[0041] ■ By "disaccharide", we mean a disaccharide sugar which is a compound made up of two sugars linked together by O-glycosidic bonds said compounds being made up of two monosaccharides (also called mono-glycosidics) as defined above said mono-glycosidic units comprising at least 5 carbon atoms, preferably 6, particularly the mono-glycosidic units being linked together in 1,4 or 1,6 in anomer a (alpha) or |3# (beta), each glycosidic unit being able to be of L or D configuration, as well as its salts and solvates such as the hydrates of said monosaccharides; more specifically, it concerns compounds formed of two sugars (or monosaccharides) having the general formula: -[Cx(H2O)y)]2- or -[(CH2O)X ]2-, with x an integer greater than or equal to 5, preferably x is greater than or equal to 6, in particular x is inclusively between 5 and 7, preferably x = 6, and y an integer which represents x - 1;

[0042] ■ By "polysaccharide", we mean a polysaccharide sugar which is a polymer consisting of at least 3 monosaccharides linked together by O-glycosidic bonds, said polymers being composed of monosaccharide units (also called mono-glycosidic units) as defined above, said monosaccharide units comprising at least 5 carbon atoms, preferably 6, particularly the units monosaccharides are linked together in 1,4 or 1,6 in anomer a (alpha) or |3# (beta), each glycosidic unit being able to be of L or D configuration, as well as its salts and solvates such as the hydrates of said monosaccharides; more particularly refers to polymers formed from a number of sugars (or monosaccharides) having the general formula: -[Cx(H2O)y)]w- or -[(CH2O)X]W-, with x an integer greater than or equal to 5, preferably x is greater than or equal to 6, in particular x is inclusively between 5 and 7, preferably x = 6, and y an integer which represents x - 1, and w is an integer greater than or equal to 2, particularly inclusively between 3 and 3000, more particularly between 5 and 2500, preferably between 10 and 2300, particularly inclusively between 15 and 1000, more particularly between 20 and 500, preferably between 25 and 200;

[0043] ■ By "salt", we mean an addition salt with an organic acid or base or mineral. The addition salts with an organic or mineral acid are in particular chosen from the salts derived i) from hydrochloric acid HCl, ii) from hydrobromic acid HBr, iii) from sulfuric acid H2SO4, iv) from alkylsulfonic acids: Alk-S(O)2OH such as methylsulfonic acid and ethylsulfonic acid; v) from arylsulfonic acids: Ar-S(O)2OH such as benzenesulfonic acid and toluenesulfonic acid; vi) from alkoxysulfinic acids: Alk-OS(O)OH such as methoxysulfinic acid and ethoxysulfinic acid; vii) from aryloxysulfinic acids such as tolueneoxysulfinic acid and phenoxysulfinic acid; viii) from phosphoric acid H3PO4; ix) of triflic acid CF3SO3H and x) of tetrafluoroboric acid HBF4;xi) of carboxylic organic acids R°-C(O)-OH (l'z) formula (Fz) in which R° represents a (hetero)aryl group such as phenyl, (hetero)aryl(Ci-C4)alkyl such as benzyl, or (Ci-Cio)alkyl said alkyl group being optionally substituted preferably by one or more hydroxy groups, amino radicals, or carboxy groups, R° preferably designating a (Ci-C6)alkyl group optionally substituted by 1, 2 or 3 hydroxy groups, or more preferably the monocarboxylic acids of formula (l'z) are chosen from acetic acid, glycolic acid, lactic acid, and mixtures thereof, and more particularly from acetic acid and lactic acid; and the polycarboxylic acids are chosen from tartaric acid, succinic acid, fumaric acid, citric acid and mixtures thereof;and xii) amino acids having more carboxylic acid radicals than amino groups such as gamma-carboxyglutamic acid, aspartic acid, glutamic acid, in particular gamma-carboxyglutamic acid. Addition salts with an organic or mineral base are in particular chosen addition salts with an organic or mineral base such as alkali metal hydroxides, alkaline earth metal hydroxides, alkali or alkaline- metal carbonates; earthy, alkali or alkaline-earth metal bicarbonates, addition salts with so-called basic amino acids such as arginine, lysine, addition salts with possibly hydroxylated amines;

[0044] ■ the "solvates" represent the hydrates as well as the association with alcohols linear or branched C1-C4 linear or branched such as ethanol, isopropanol, n-propanol; ■ by "reducing agent" we mean an agent capable of reducing the disulfide bonds of hair, such as compounds chosen from among thiols, alkali sulfites, hydrides and phosphines;

[0045] The expressions "at least one" and "one or more" are synonymous and can be used interchangeably.

[0046] The expressions "between ... and ...", "includes from ... to ...", "made up of ... to ...", and "ranging from ... to ..." should be understood inclusive of bounds, unless otherwise specified. Keratin fiber processing method

[0047] According to a first aspect, the present invention relates to a process for treating keratin fibers as defined above.

[0048] The process according to the present invention is preferably a process for relaxing loops and / or smoothing keratin fibers.

[0049] The applicant found, surprisingly, that the process according to the invention made it possible to obtain a smoothing of the keratin fibers of good quality and lasting for at least one shampoo, while preserving the quality and integrity of the keratin fibers, in particular of weakened hair.

[0050] It has also been observed that the process according to the invention makes it possible to transform the shape of the hair by making successive applications without causing significant damage to the hair fiber. The process can be repeated to increase the effects, until the desired level of straightening is achieved. However, and this constitutes an advantage of the present invention, from the very first application of the process according to the invention, even without putting tension on the hair, a substantial reduction in hair volume is observed. When the hair is curly, a loosening of the curls and / or a better definition of them are also observed. The process according to the invention also makes it possible to avoid using a flat iron.

[0051] Finally, unpleasant odors such as the odor of thiols which are released during conventional straightening processes, or which remain on hair straightened according to prior art processes are much less marked or even absent when implementing the process according to the invention. Compounds A

[0052] The compound(s) A used in the process according to the present invention are chosen from compounds of formula (I), their optical isomers, their geometric isomers, their salts, their solvates such as hydrates, and their mixtures:

[0053] Formula (I) in which: - R1 represents a versatile hydrocarbon radical in C2 to CM, linear or branched, saturated or unsaturated, conjugated or not, acyclic or cyclic, aromatic or not, R1 being further: a) possibly substituted by one or more hydroxy groups OH, dialkylamino-N(R)2 with R representing a (Ci-C4)alkyl group, carboxy-C(O)-OH, a vinyl group, and / or b) possibly interrupted by one or more heteroatoms or groups selected from O, S, carbonyl -C(O)-, amine -N(R'), or their combinations, in which R' represents a hydrogen atom, a linear or branched alkyl group having from 1 to 4 carbon atoms possibly substituted by at least one hydroxy group (OH) or possibly substituted by -XC(O)-C(Ra)(Rb)-C(O)-R2; - R2 represents a monovalent hydrocarbon radical in C1 to C6, linear or branched, saturated or unsaturated; - Ra, and Rb, identical or different, represent a hydrogen atom or a (CrC4)alkyl group; - X is a heteroatom or group chosen from O, S, N(R') or , -S-CH2-C(O)-O-, -OC(O)-CH2-S-, -OC(O)-N(R')-, -N(R')-C(O)-O-, -N(R')-C(O)-N(R')-, R' being as defined previously; - n denotes an integer ranging from 2 to 10, particularly from 3 to 9. Preferably, compound(s) A are chosen from compounds of formula (la), their optical isomers, their geometric isomers, their salts, their solvates such as hydrates, and their mixtures: (there) Formula (the) in which: - R1 is as defined above, particularly represents a versatile hydrocarbon radical in C2 to CM, preferably in C3-Ci2, preferably in C4-Ci0, linear or branched, saturated or unsaturated, conjugated or not, acyclic or cyclic, aromatic or not, R1 being further: a) possibly substituted by one or more hydroxy groups OH, and / or b) possibly interrupted by one or more heteroatoms or groups chosen from O, S, -N(R'), preferably interrupted by one or more oxygen atoms in which R' is as defined above; - R2 is as defined previously, preferably R2 represents a (Ci-C6)alkyl group, linear or branched, preferably a (Ci-C4)alkyl group, more preferably methyl or tert-butyl such as methyl; and - n is as defined previously, preferably n denotes an integer from 2 to 9.

[0054] According to one embodiment, the compounds of formula (I) or (la) are such that R1 represents a C6 to C8 C6-C ...

[0055] According to another embodiment, the compounds of formula (I) or (la) are such that R1 represents a C5 to C2 saturated monocyclic or bicyclic hydrocarbon polyvalent radical, optionally interrupted by one or more heteroatoms or groups selected from O, S, -N(R'), in which R' represents a hydrogen atom, an alkyl group having from 1 to 4 carbon atoms, preferably interrupted by one or more oxygen atoms. Preferably, according to this other embodiment, R1 represents a monosaccharide or polysaccharide motif, in particular a disaccharide, on which n hydroxyl groups have been substituted by n -OC(O)-CH2-C(O)-R2 groups with R2 and n as defined above.

[0056] Suitable monosaccharides according to the invention include, but are not limited to, ribose, glucose, mannose, galactose, fructose, sorbose and inositol.

[0057] According to one embodiment, the disaccharides are selected from cellobiose, maltose, lactose, raffinose, sucrose, trehalose, melibiulose, melibiose, mannobiose, kojibiose, nigerose, isomaltose, rutinose, rutinulose, xylobiose, preferably sucrose.

[0058] According to another preferred embodiment of the invention, the compounds of formula (I) or (la) are such that R1 represents a C2-Ci2, preferably C3-Ci0, linear or branched, saturated or unsaturated, preferably saturated, acyclic hydrocarbon polyvalent radical.

[0059] Preferably, the compounds of formula (I) or (la) are such that R1 represents a versatile acyclic hydrocarbon radical, selected from the radicals mannitol, xylitol, sorbitol, trimethylolpropane, di(trimethylolpropane), 2-methyl-1,3-propanediol, 2-hydroxymethyl-1,3-propanediol, 2,2-dimethyl-1,3-propanediol, erythritol, pentaerythritol or dipentaerythritol, more preferably mannitol, xylitol, sorbitol, trimethylolpropane, di(trimethylolpropane), 2-methyl-1,3-propanediol, 2-hydroxymethyl-1,3-propanediol, erythritol, pentaerythritol or dipentaerythritol.

[0060] According to a particular embodiment of the invention, the compounds of formula (I) or (la) are such that n denotes an integer from 2 to 9, more particularly n denotes an integer from 3 to 9, even more particularly n denotes an integer from 4 to 9 such as 6 or 8.

[0061] According to one embodiment, the compounds of formula (I) or (la) are such that n equals 2. According to another embodiment, the compounds of formula (I) or (la) are such that n equals 3. According to another embodiment, the compounds of formula (I) or (la) are such that n equals 4. According to another embodiment, the compounds of formula (I) or (la) are such that n equals 5. According to another embodiment, the compounds of formula (I) or (la) are such that n equals 6. According to another embodiment, the compounds of formula (I) or (la) are such that n equals 7. According to another embodiment, the compounds of formula (I) or (la) are such that n equals 8. According to another embodiment, the compounds of formula (I) or (la) are such that n equals 9.

[0062] Preferably, the compound(s) A are chosen from the following compounds, their optical isomers, their salts, their solvates such as hydrates, and their mixtures: (Composed) ■HW' . Structure;^ (1) 700865-73-2 3-oXo-1,1^1,7-heptanectiyQ butanoic acid ester 57 & V "W 'X-.-"'' '-y' 'X'Y' 'V1 (2) 632336,1-20-0 1.8-octaned^yl) butaroic acid ester X-' ■,« jv --y X-' \ex> (3) 501426-98-8 3-oxo-1,T-(1,1Q-decan^yl) butanoic acid ester x-' X' ''' '.'' 'x<''' (4) 174498-06-7 3-oxo-tT-(13-propanediyî) to add butanoïqœ y ? vy x.-- ■ ' Vs--- X (5J 160187-52-0 3-0xa-1 .2-dimefty^- 1,2-ethanediyl butanoic acid ester 0 0 s oy*Xx y^X (S) 145020-19-5 3-oxo-2-biftyk2-êthyk 1,3-propanedjyi butanoic acid ester -7 v 7-' (7} 87530-36-7 3-oxo-l, 1,2,2-tetramethylM ,2-ethanediyl butanoic acid ester tî \ / * vox X" X' ''X / \ ;j :t . (Gum-like) CAS Name ohihi^ Chemical Structure R 58213-75-5 3-oxo* 1,1X1 -methy k 153-prDpanediyl) butanoic acid ester !.< <■' (S) 58213-74-4 3-OX0-1.1-122-dimethylM-(1-methylethyl)-1,3-propanediyl] butanoic acid ester u û X'Y"' (W) 39564-28-8 3-oxo-1fT-(1t5-pentanediyl) butanoic acid ester ..Y ' (11) 14276-67-6 3-oxo- 1,f -(2,2-dimethylMG-propanediyl) butanoic acid ester O £5 •? a (12) 13018-41-2 3-oxo-154-butanediy( butanoic acid ester -'•''•K (13) 6079-90-9 3-oxo-l -methylM .2-ethanediyi butanoic acid ester r' v (14) 5459-04-1 3-üxo-1.2-êtharædiyi butanosic acid ester GG ■< .xx. (Compound) Chemical Name Chemical Structure (15) 2388-18-3 3-oxo-1,T'-(1,6-hexanediyl) butanoic acid ester 3-oxo-1,6-hexanediyl ester d: botanoic acid (9Ci) (16) 32818-60-3 bis(3-oxobutanoate) of 1,r-[252-Bis[(1,3-dOXobutoxy)methylQ-1,3-propanediyl] A AA .$• <.--x .•X (17) 51980-20-2 bis(3-oxobotanoate) of 1,T-[22-Bis(hydroxymethyl> 1,3-propanediyl)] -> G y A / A. A'x. z\ x ô 0 (18) O ck Az\ / V x, ,,0,, ...-■s, / 'sj" ' bo (18) 13097356-6 3-0X0-135-benzenetriyl butanoic acid ester GO AA 0 a § § As AAAA Ax x \ / Xÿÿ (Compound) WCAS Chemical Name Chemical Strœteæ (20) 139264-86-1 3-oxo-1,2,4-benzenetriyl butanoic acid ester L, CO XrX 'XOQ 1 I 1 1 1 1 X / X$ / (21) 22208-25-9 Trimethyloipropane triacetoacetate K-FLEX7301 \ / ~\ F t 0--X \ (22) 2360524-48-5 C >7 x -. .A. .A. .A. Àx -^x ---''x ■ <<"• A" X.-'" xf XV'- x<' V (23) 66229-33-2 3-oxo-2-butyl-2-I(1,3-dioxobutoxy)methylO-1,3-propanediyt butanoic acid ester •jX 11-(2,2-^5(((4,4-dimethyi-1.3- dioxopeoty|i)oxylmeth y^-13-prapanediy^ pentanoic acid ester. A—X / :> (Compounded) N'GAS Chemical name Structural (25) 6079-98-7 tris(3-oxobutanoate ) of 147^-(1,2,3-propanetriyO 0 ¢3 < © © \“ (26) tetra-acetoace7-Xertate de 1 meso*ent wwp"^ “XT (27) 169533-29-3 qD- Glucopy ranunuse t 1 ;2.3î4;6-peritakis(3- oxobutanoate) a 0 xv V $ <> (28) 2254710-55- 7 S-amno-2.3-4-[2 )-D -xyopyranoxyjoxy]-benzoic acid 'xx ( Corn posed i NXAS Nçm chîmsqu© Strufîtw chmwÉ|ue (29) 1236300-10- 9 2,3.4,6-18031^3(3-QXDbutanoateJ de aD-Glucppyranoside, 1,3.4,6-te 1,3-d»xcbutyl)-pD- fructofumTOsyl, . 1,4:3,6-diahydra-, 2,5-bts(3-pxobutanoate) JX __________< j (32) 2254710-49- 9 J '' XS: v •^''X î <>. (Çompçsê) R* CAS Chinese name Structured chemical (33} sorbitd hexa-acetoacetate f'" v- OG 9 o o'"' "oo" ■■■ ç Y 1 vyb (34} 216756-89-7 D-Gîucitoi, 4-OpD-galadopyranos^-, poiyacetoacetate / 0 G—R1 „ / \ n V. v / \ . / \ / ' "' / \ Sî □ 81 with R1 chosen from -C(O)-CH2-C(OJ-CHî. H with at least two radicals RI represent -G(O)-CH>0 (0)-C Hs (35} 101655-52-1 Sucrese, poiy'acetoacetate 1 X-. RI__ Y, with R1 chosen from -C(O)-GH2-G(O)-CH3S H with at least two radicals RI represent -C(Q)-CHs-C(G)-CHa (Compound) itcas Chemical Name Chemical Structure (36) Ghoese polyacetoacetate "Il or - o J i V (37) Mannose polyacetoacetate «1 y RÏ \ / (38) Xylfel polyacetoacetate RI. ■'--rV-' Q 0 &r (39) SorbM polyacetoacetate ^,0 o of preference radicals RI represent -C(O)-CHz-G(O)-CHs (CGmppsé) hF CAS' Chemical name (40) RI Ri (jf ? Rt yû RV xR:i three RI radicals represent ^(9>CH2-C(O)-CH3, and three RI radicals represent a hydrogen atom (41) 147^_g4_9 i 3 0 l 1 _ Ü _ . 'x / 'Y yy Q 0 (42) 2552-36-5 iî h H ,X ,,X ..X 'y* y (43) 139814-56-5 9 9 / \X hh (44) 96189-30-1 ' ^■;x .-' "x ■ x ° X x_ x, '•■ " y •■'■' (45) 75639-01-9 :.5 t? (Compound) CAS No. Homch^ Chemical Stnictoœ (46) Dipentaerythrifo] poîyacetoacetate K > z $ o / / Sx preferably 5 or 6 RI radicals, plus, preferably S RI radicals represent -G(O>CH2-C(O>GH3)

[0063] wherein identical or different RIs represent a hydrogen atom or a -C(O)-CH2-C(O)-CH3 group, it being understood that at least two RI radicals represent -C(O)-CH2-C(O)-CH3, preferably at least three RI radicals represent -C(O)-CH2-C(O)-CH3.

[0064] More preferably, the compound(s) A are chosen from compounds (16), (18), (21), (35), (36), (37), (38), (39), (40) and (46), their optical isomers, their salts, their solvates such as hydrates, and their mixtures.

[0065] Even more preferably, the compound(s) A are chosen from compounds (16), (21), (35), (38), (39) and (46), their optical isomers, their salts, their solvates such as hydrates, and their mixtures.

[0066] Most preferably, the compound(s) A are chosen from compounds (16), (35) and (46), their optical isomers, their salts, their solvates such as hydrates, and their mixtures.

[0067] The compounds of formula (I) can be obtained by (poly)condensation(s) of n equivalents of dicarbonyl reagent with a nucleophilic reagent R'(XH)n comprising n equivalents of -XH nucleophilic functions according to the following scheme: | Q ro $ i Scheme n| [ R ' R R3 >■ - n FÔCH 1 X XX 'X 4'R? L r3 VX in which: - R1, R2, Ra, Rb and n are such as defined for the compound of formula (I); - R3 represents a hydrogen atom, an (Ci-C4)alkyl group such as methyl, ethyl, isobutyl, t-butyl, or an electrofuge group such as CHal3, or Hal3C-SO2- as triflate, with Hal, identical or different, representing a halogen atom; and - X' represents an oxygen atom, or sulfur, preferably O.

[0068] These (poly)condensation methods are known to those skilled in the art; examples include “From rigid and flexible foams to elastomers via Michael addition chemistry”, Polymer, 106, 128-139, (2016), “Dynamic Curing Agents for Amine-Hardened Epoxy Vitrimers with Short (Re)processing Times”, Macromolecules, 53(7), 2485-2495 (2020), “Super photo-base initiated organic-inorganic hybrid coatings by plural-cure mechanisms”, Progress in Organic Coatings, 127, 222-230 (2019) or patent application PL159100: Method for manufacturing acetylacetate esters.

[0069] According to a particular embodiment of the invention, R'(XH)n is selected from the acyclic polyols R'(OH)n, in particular selected from glycerol, trimethylolpropane, ethylene glycol, diethylene glycol, triethylene glycol, tetraethylene glycol, propylene glycol, dipropylene glycol, butylene glycol, trimethylolethane, pentamethylene glycol, trimethylpentanediol, pentyl glycol, isosorbide, pentaerythritol, dipentaerythritol, hexamethylene glycol, hexylene glycol, hexandediol, neopentyl glycol, 1,2-propanediol; 1,3-propanediol; 1,2-butanediol, 1,3-butanediol, 2,3-butanediol, 1,4-butanediol; 2,4-butanediol, 3,4-butanediol; 1,4-Pentanediol; 1,5-pentanediol, 2,2,4-Trimethyl-l,3-pentanediol, 1,6-hexanediol, 1,2 octanediol, 1,8 octane diol, 1,10-decanediol, 2-methyl-l,3-propane diol, hexylene glycol, isoprene glycol.

[0070] According to one variant, R'(XH)n is chosen from among the cyclic polyols R'(OH)n in particular chosen from among the monosaccharides and disaccharides, as defined above, alone or in mixture.

[0071] Preferably, R'(XH)n is chosen from the polyols R'(OH)n alone or in mixtures in particular from mannitol, xylitol, sorbitol, glycerol, glucose, trimethylolethane, trimethylolpropane, di(trimethylolpropane), 2-methyl-1,3-propanediol, 2-hydroxymethyl-1,3-propanediol, 2,2-dimethyl-1,3-propanediol, 1' erythritol, pentaerythritol, dipentaerythritol, and mixtures thereof, more particularly from trimethylolethane, trimethylolpropane, erythritol, pentaerythritol, glycerol, glucose, sucrose and sorbitol, and mixtures thereof.

[0072] According to another embodiment, R'(XH)n is chosen from among the diamines R'(NH2)2 in particular the hydroxyalkylated aliphatic diamines such as ro,o'-bis(diethanolaminomethyl)-p-nonylphenol, the N,N,N,N'-tetra(2-hydroxypropyl)ethylenediamine (Quadrol L, available from BASF) and N,N,N, N-tetra(2-hydroxyethyl)ethylenediamine, and their mixture.

[0073] According to another advantageous embodiment, the compound(s) of formula (I) or (la) are obtained by (poly)condensation(s) of n equivalents of propylenedioxy carbonyl reagent with a polyamine nucleophilic reagent R'(NH2)n comprising n equivalents of -NH2 nucleophilic functions according to the following scheme: Diagram in which: - R1, R2, Ra, and n are such as defined for the compound of formula (I); - R'-NH2 is notably chosen from among ethylenediamine, 1,3-diaminopropane, cadaverine, hexamethylenediamine, 1,2-diaminopropane, 1,2-diaminocyclohexane, phenylenediamine; and - Rb, and Rc', identical or different, represent a hydrogen atom, a (Ci-C4)alkyl group.

[0074] This type of synthesis process is known to those skilled in the art; for example, "Acetoacetylation with 2,2,6-trimethyl-4H-l,3-dioxin-4-one: a convenient alternative to diketene", Journal of Organic Chemistry, 50(14), 2431-5, (1985) or "Synthesis of new Biginelli polycondensates: renewable materials with tunable high glass transition temperatures", Polymer International, 70(5), 506-513 (2021).

[0075] According to another advantageous embodiment, the compounds of formula (I) or (la) are obtained by (poly)condensation(s) of n equivalents of diketene reagent with a nucleophilic reagent R*(X)n comprising n equivalents of -XH nucleophilic functions according to the following scheme: Diagram in which: - R1, and n are such that defined for the compound of formula (I); and

[0076] - X' represents an oxygen atom, or sulfur atom, or N(R') with R'=H.

[0077] This type of process is known to those skilled in the art. For example, one can cite "Acetoacetamides, 2-hydroximinoacetoacetamides, and 2,3-bis(hydroximino)-bu tyramides", Journal für Praktische Chemie (Leipzig), 323(2), 337-44, (1981) or Angewandte Makromolekulare Chemie, 9, 96-105, (1969). Polyamine compounds B

[0078] The polyamine compound(s) B used in the process according to the present invention are chosen from the compounds of formula (II), their optical isomers, their geometric isomers, their salts, their solvates such as hydrates, and their mixtures: H2N—T—NH2 (II) Formula (II) in which T represents a divalent hydrocarbon group, linear or branched, saturated or unsaturated, preferably saturated, comprising from 4 to 22 carbon atoms, optionally substituted by an -NH2 group, the group T being substituted by one or more hydroxyl (-OH) groups and / or interrupted by one or more groups selected from -C(O)-, -NRa- or their combinations such as -NRa-C(O)- or -C(O)-NRa-, with Ra representing a hydrogen atom or a (Ci-C4)alkyl group.

[0079] According to a first variant, T represents a divalent, linear or branched, saturated hydrocarbon group comprising from 4 to 22 carbon atoms, preferably from 10 to 22 carbon atoms, more preferably from 15 to 20 carbon atoms, optionally substituted by an -NH2 group, the group T being interrupted by one or more groups selected from -C(O)-, -NRa- or their combinations such as -NRa-(CO)- or -(CO)-NRa-, Ra being as defined above, preferably interrupted by one or more groups selected from -NRa-C(O)- or -C(O)-NRa-, Ra being as defined above and the group T being optionally substituted by one or more hydroxyl groups (-OH).

[0080] Preferably, according to this first variant, T represents a divalent, linear or branched, saturated hydrocarbon group comprising 10 to 22 carbon atoms, preferably 15 to 20 carbon atoms, optionally substituted by an -NH2 group, the T group being interrupted by 2 or 3 groups chosen from -NH-(CO)- or -(CO)-NH- and the T group being optionally substituted by one or more hydroxyl groups (-OH), in particular a hydroxyl group (-OH).

[0081] According to this first variant, the polyamine compound(s) B are preferably chosen from the following compounds (1) and (2), their optical isomers, their salts, their solvates such as hydrates, and their mixtures:

[0082] According to a second variant, T represents a divalent, linear or branched, saturated hydrocarbon group comprising from 4 to 22 carbon atoms, preferably from 4 to 15 carbon atoms, more preferably from 4 to 10 carbon atoms, substituted by one or more hydroxyl groups (-OH).

[0083] According to this second variant, T is preferably uninterrupted by one or more groups chosen from -C(O)-, -NRa- or their combinations such as -NRa -C(O)- or -C(O)-NRa-, Ra being as defined previously.

[0084] Preferably, according to this second variant, T represents a branched, saturated divalent hydrocarbon group comprising 4 to 15 carbon atoms, preferably 4 to 10 carbon atoms, substituted by one or more hydroxyl groups (-OH), preferably by a hydroxyl group (-OH).

[0085] According to this second variant, the polyamine compound(s) B are preferably chosen from the following compound (3), its optical isomers, its salts, its solvates such as hydrates, and mixtures thereof: (3).

[0086] The compound of formula (3) is marketed by BLD Pharmatech Ltd. (CAS: 25441-01-4).

[0087] Preferably, the polyamine compound(s) B are chosen from the following compounds (1), (2) and (3), their optical isomers, their salts, their solvates such as hydrates, and their mixtures: Additional characteristics of the process

[0088] The process according to the invention can be implemented on natural keratin fibers, in particular natural hair.

[0089] The process according to the invention can also be implemented on damaged and / or sensitized keratin fibers, in particular damaged and / or sensitized hair.

[0090] By "damaged keratin fibers" we mean dry, rough, brittle, split and / or soft keratin fibers.

[0091] By "sensitized keratin fibers" is meant bleached, artificially colored, straightened and / or permed keratin fibers.

[0092] The process according to the invention can advantageously be implemented on curly, frizzy or kinky keratin fibers, in particular curly, frizzy or kinky hair.

[0093] Compositions (P), (A), (B) and / or (C) can be applied to dry or wet keratin fibers, preferably wet, preferably with a bath ratio of 0.1 to 10. By bath ratio, we mean the ratio between the total weight of the applied composition and the total weight of keratin fibers to be treated.

[0094] Preferably, the application of compositions (P), (A), (B) and / or (C) to keratin fibers is carried out at room temperature, i.e. at a temperature between 25 °C and 30 °C. First method of implementation

[0095] According to a first embodiment, the process according to the invention comprises steps i) and i') as described above.

[0096] Preferably, according to this first embodiment, the pretreatment composition (P) implemented in step i') comprises neither compound(s) A as defined above nor polyamine compound(s) B as defined above. Second embodiment

[0097] According to a second embodiment, the process according to the invention includes step i) as described above and does not include step i') as described above.

[0098] According to the first embodiment, the keratin fibers are preferably not rinsed and not dried after application of the pretreatment composition (P).

[0099] According to a preferred embodiment of the method according to the invention, the compound(s) A are included in a composition (A) and the polyamine compound(s) B are included in a composition (B) separate from composition (A), composition (A) being applied to the keratin fibers before composition (B), then composition (A) is left on the keratin fibers for a period of at least 10 seconds, preferably from 1 minute to 5 hours, more preferably from 5 minutes to 1 hour, even more preferably from 5 minutes to 40 minutes, then composition (B) is applied to the keratin fibers without intermediate rinsing, then composition (B) is left on the keratin fibers for a period of at least 10 seconds, preferably from 1 minute to 5 hours, more preferably from 5 minutes to 1 hour,even more preferably, ranging from 5 minutes to 40 minutes, and finally the keratin fibers are air-dried or dried with a heating device, washed with shampoo and then air-dried or dried with a heating device.

[0100] According to a variant of the process according to the invention, the compound(s) A and the polyamine compound(s) B are contained in a single composition (C), the composition (C) is left to rest on the keratin fibers for a period of at least 10 seconds, preferably from 1 minute to 5 hours, more preferably from 5 minutes to 1 hour, even more preferably from 5 minutes to 40 minutes, then the keratin fibers are dried in ambient air or with the aid of a heating device, washed with shampoo and then dried in ambient air or with the aid of a heating device

[0101] The temperature of the heating device can range from 45°C to 230°C, preferably from 45°C to 100°C, more preferably from 50°C to 80°C. A hair dryer, a heated helmet, an iron, or a heated brush can be used as a heating device, for example.

[0102] The drying step can also be a combination of air drying or drying with a heating device at a temperature ranging from 50°C to 80°C such as a hair dryer or a heated helmet, possibly followed by a step of passing through the iron, preferably a straightening iron.

[0103] Characteristics of compositions (P), (A), (B) and (C)

[0104] The pH of compositions (P), (A), (B) and / or (C) can be adjusted to the desired value by means of alkalizing agents or acidifying agents commonly used or by means of conventional buffer systems.

[0105] Acidifying agents can be chosen from mineral or organic acids such as hydrochloric acid, orthophosphoric acid, sulfuric acid, carboxylic acids such as acetic acid, tartaric acid, citric acid, lactic acid, sulfonic acids.

[0106] The alkalizing agents may be chosen from organic or mineral bases, preferably chosen from: a) ammonia or one of its salts such as ammonium chloride; b) alkanolamines in particular mono-, di- or tri-(Ci-C6)alkanolamines such as mono-, di- and triethanolamines, isopropanolamine, 2-amino-2-methyl-l-propanol (AMP), 2-amino-2-methyl-l,3-propanediol (AMPD) and 2-amino-l,3-propanediol and their derivatives; c) oxyethylenated and / or oxypropylenated (Ci-C6)alkylenediamines; d) mineral or organic hydroxides; e) basic amino acids such as arginine, lysine, omithine, citrulline and histidine; (f) silicates or metasilicates of alkali or alkaline earth metals such as sodium metasilicates; (g) carbonates and bicarbonates, particularly of primary, secondary or tertiary amine, alkali metal or alkaline earth, or ammonium; and

[0107] h) compounds other than polyamine compounds as defined above selected from the compounds of the following formula (III): Formula (HD in which:) - W represents a (Ci-C6)alkylene group possibly substituted by at least one hydroxyl group or a (Ci-C6)alkyl group and / or possibly interrupted by at least one heteroatom such as O or NRU; - Rx, Ry, Rz, Rt and Ru, identical or different, represent a hydrogen atom, or a group chosen from: (Ci-C6)alkyl, hydroxyalkyl in Ci-C6, or aminoalkyl in Cr C6.

[0108] Examples of such compounds of formula (III) include 1,3-diaminopropane, 1,3-diamino-2-propanol, spermine, spermidine.

[0109] Mineral or organic hydroxides are preferably chosen from among the hydroxides of an alkali metal, the hydroxides of an alkaline earth metal, such as sodium or potassium hydroxides, the hydroxides of a transition metal, such as the hydroxides of metals in groups III, IV, V and VI of the periodic table of elements, the hydroxides of lanthanides or actinides, the hydroxides of quaternary ammoniums, and guanidinium hydroxide.

[0110] The hydroxide can be formed in situ such as guanidine hydroxide, formed by reaction of calcium hydroxide and guanidine carbonate.

[0111] Preferably, the organic or mineral bases are chosen from ammonia or one of its salts such as ammonium chloride, carbonates or bicarbonates such as ammonium or sodium carbonate, ammonium or sodium bicarbonate, basic amino acids such as arginine, alkanolamines such as monoethanolamine (MEA), 2-amino-2-methyl-l-propanol (AMP), 2-amino-2-methyl-l,3-propanediol (AMPD) and 2-amino-l,3-propanediol.

[0112] Preferably, the pH of compositions (P), (A), (B) and / or (C), preferably the pH of compositions (P), (A), (B) and (C) is adjusted using an alkaline buffer system.

[0113] An alkaline buffer system is typically obtained by mixing a weak base and one of its salts.

[0114] The formulation of alkaline buffer systems is well known to those skilled in the art.

[0115] More preferably, the pH of compositions (P), (A), (B) and / or (C), of Preferably the pH of compositions (P), (A), (B) and (C) is adjusted using an alkaline buffer system NH4OH / NH4C1.

[0116] According to a variant of the invention, step i') of the process according to the invention is present and the pretreatment composition (P) has a pH between 8 and 12.5, preferably between 8.5 and 12.5.

[0117] According to this variant, the pH of the composition (P) is preferably adjusted using an alkaline buffer system, more preferably using an NH4OH / NH4C1 alkaline buffer system.

[0118] According to a preferred embodiment of the invention, the compound(s) A are included in a composition (A) and the polyamine compound(s) B are included in a composition (B) separate from composition (A), composition (A) being applied to the keratin fibers before or after composition (B), preferably before composition (B).

[0119] According to this preferred variant, when step i') is absent, one of the two compositions (A) and (B) or each of the two compositions (A) and (B), preferably each of the two compositions (A) and (B) has a pH between 8 and 12.5, preferably between 8.5 and 12.5.

[0120] According to this preferred variant, when step i') is present, one of the two compositions (A) and (B) or each of the two compositions (A) and (B), preferably each of the two compositions (A) and (B) has a pH preferably between 8 and 12.5, more preferably between 8.5 and 12.5.

[0121] According to this preferred embodiment, the pH of compositions (A) and / or (B), preferably the pH of compositions (A) and (B), is preferably adjusted using an alkaline buffer system, more preferably using an NH4OH / NH4C1 alkaline buffer system.

[0122] According to another variant of the invention, the compound(s) A and the polyamine compound(s) B are included in the same composition (C).

[0123] According to this other variant, when step i') is absent, the composition (C) has a pH between 8 and 12.5, preferably between 8.5 and 12.5.

[0124] According to this other variant, when step i') is present, the composition (C) has a pH preferably between 8 and 12.5, more preferably between 8.5 and 12.5.

[0125] According to this other variant, the pH of the composition (C) is preferably adjusted using an alkaline buffer system, more preferably using an NH4OH / NH4C1 alkaline buffer system.

[0126] Composition (C) can be obtained by extemporaneous mixing of a first composition comprising compound(s) A with a second composition comprising polyamine compound(s) B.

[0127] Preferably, the compound(s) A are present in the composition (A) or (C) in a total content ranging from 0.2% to 80% by weight, preferably ranging from 0.5% to 50% by weight, more preferably ranging from 2% to 35% by weight, relative to the total weight of the composition comprising the compound(s).

[0128] Preferably, the polyamine compound(s) B are present in composition (B) or (C) in a total content ranging from 0.2% to 60% by weight, of preference ranging from 0.5% to 40% by weight, more preferably ranging from 3% to 40% by weight, relative to the total weight of the composition comprising it or them.

[0129] Compositions (P), (A), (B) and (C) are cosmetic compositions, i.e. which comprise a cosmetically acceptable medium, i.e. a medium compatible with human keratin fibers.

[0130] According to a preferred embodiment, the compositions (P), (A), (B) and / or (C) comprise water and optionally one or more polar and / or protic solvents, preferably chosen from monoalcohols having 2 to 6 carbon atoms, more preferably chosen from ethanol, propanol, n-butanol, isopropanol, isobutanol, tert-butanol, pentanol, hexanol, and mixtures thereof, even more preferably chosen from n-butanol, ethanol, and mixtures thereof, most preferably ethanol.

[0131] According to a more preferred embodiment, the compositions (P), (A), (B) and / or (C) comprise water and one or more polar and / or protic solvents, preferably chosen from monoalcohols having 2 to 6 carbon atoms, more preferably chosen from ethanol, propanol, n-butanol, isopropanol, isobutanol, tert-butanol, pentanol, hexanol, and mixtures thereof, even more preferably chosen from n-butanol, ethanol, and mixtures thereof, most preferably from ethanol.

[0132] Preferably, compositions (P), (A), (B) and / or (C) comprise water in a total weight content of 5% to 99% by weight, preferably of 40% to 95% by weight, relative to the total weight of the composition comprising it.

[0133] When present, the polar and / or protic solvent(s) are present in compositions (A), (B) and / or (C) in a total weight content ranging from 0.01% to 99% by weight, preferably ranging from 0.01% to 80% by weight, relative to the total weight of the composition comprising them.

[0134] Compositions (P), (A), (B) and (C) can be presented in all galenic forms classically used for hair application. Composition (C)

[0135] According to a second aspect, the present invention relates to a composition (C) as defined above, the composition (C) preferably having a pH between 8 and 12.5, more preferably between 8.5 and 12.5, the pH of the composition (C) being preferably adjusted using an alkaline buffer system, more preferably using an NH4OH / NH4C1 alkaline buffer system. Kit

[0136] According to a third aspect, the present invention relates to a two- or three-compartment device comprising: - a first compartment containing a composition (A) as defined previously; - a second compartment distinct from the first compartment containing a composition (B) as defined above; - possibly a third compartment distinct from the first and second compartments containing a pretreatment composition (P) as defined previously. Use

[0137] According to a fourth aspect, the present invention relates to the use of a composition (A) as defined above associated with a composition (B) as defined above and possibly associated with a pretreatment composition (P) as defined above or of a composition (C) as defined above, possibly associated with a pretreatment composition (P) as defined above, for the relaxation of loops and / or the smoothing of keratin fibers. Examples

[0138] The following examples serve to illustrate the invention without, however, being limiting in nature.

[0139] In the following examples, unless otherwise indicated, when compositions are implemented, the contents are indicated as a mass percentage in relation to the total weight of the composition considered.

[0140] The compounds A that can be used in the examples are as follows:

[0141] * Compound No. 1: K-FLEX 7301 marketed by KING Industrie oooo

[0142] • Compound No. 2: Glucose with acetoacetate function (5eq)

[0143] Compound 2 was synthesized according to the following scheme:

[0144] Scheme in which identical or different RI represents a hydrogen atom or a -methylcarbonylmethylcarbonyl group -C(O)-CH2-C(O)-CH3, it being understood that at least two RI radicals represent -C(O)-CH2-C(O)-CH3, in particular 5 RI radicals represent -C(O)-CH2-C(O)-CH3.

[0145] In a one-liter three-necked flask equipped with a mechanical stirrer and a distillation column, 100 g of D-glucose and 482.90 g of tert-butyl acetoacetate are introduced. The reaction mixture is heated in an oil bath (oil bath temperature 150°C–160°C) for 5 hours. After 5 hours, NMR confirms the grafting of the acetoacetate group. The reaction mixture is then concentrated using a rotary evaporator at 150°C under continuous vacuum. A highly viscous, dark brown liquid is obtained, which, upon analysis, corresponds to the expected product.

[0146] • Compound No. 3 Mannose with acetoacetate function (5eq)

[0147] Compound 3 was synthesized according to the following scheme:

[0148] Scheme in which identical or different RI represents a hydrogen atom or a -C(O)-CH2-C(O)-CH3 group, it being understood that at least two RI radicals represent -C(O)-CH2-C(O)-CH3, in particular 5 RI radicals represent -C(O)-CH2 -C(O)-CH3.

[0149] In a one-liter three-necked flask equipped with a mechanical stirrer and a distillation column, 100 g of D-mannose and 482.90 g of tert-butyl acetoacetate are introduced. The reaction mixture is heated in an oil bath (oil bath temperature 140°C–150°C) for 5 h. After 5 h, NMR confirms the grafting of the acetoacetate group. The reaction mixture is then concentrated using a rotary evaporator at 150°C under continuous vacuum. A viscous yellow liquid is obtained, which, upon analysis, corresponds to the expected product.

[0150] • Compound No. 4 Xylitol with acetoacetate function (5eq)

[0151] Compound 4 was synthesized according to the following scheme:

[0152] Scheme in which identical or different RI represents a hydrogen atom or a -C(O)-CH2-C(O)-CH3 group, it being understood that at least two RI radicals represent -C(O)-CH2-C(O)-CH3, in particular 5 RI radicals represent -C(O)-CH2 -C(O)-CH3.

[0153] In a 500 mL three-necked flask equipped with a mechanical stirrer and a distillation column, 25 g of xylitol and 142.69 g of tert-butyl acetoacetate are introduced. The reaction mixture is heated in an oil bath (oil bath temperature 140°C–150°C) for 5 h. After 5 h, NMR confirms the grafting of the acetoacetate group. The reaction mixture is then concentrated using a rotary evaporator at 150°C under continuous vacuum. A highly viscous brown liquid is obtained, which, upon analysis, corresponds to the expected product.

[0154] * Compound No. 5 Sorbitol with acetoacetate function (6eq)

[0155] Compound 5 was synthesized according to the following scheme:

[0156] Scheme in which identical or different RI represents a hydrogen atom or a -C(O)-CH2-C(O)-CH3 group, it being understood that at least two RI radicals represent -C(O)-CH2-C(O)-CH3, in particular 6 RI radicals represent -C(O)-CH2 -C(O)-CH3.

[0157] In a one-liter three-necked flask equipped with a mechanical stirrer and a distillation column, 100 g of sorbitol and 573.20 g of tert-butyl acetoacetate are introduced. The reaction mixture is heated in an oil bath (oil bath temperature 140°C–150°C) for 5 h. After 5 h, NMR confirms the incorporation of the acetoacetate group. The reaction mixture is then concentrated using a rotary evaporator at 150°C under continuous vacuum. A viscous, orange-yellow liquid is obtained, which, upon analysis, corresponds to the expected product.

[0158] • Compound No. 6 Sorbitol with acetoacetate function (3eq)

[0159] Compound 6 was synthesized according to the following scheme:

[0160] Scheme in which identical or different RI represents a hydrogen atom or a -C(O)-CH2-C(O)-CH3 group, it being understood that at least two RI radicals represent -C(O)-CH2-C(O)-CH3, in particular 3 RI radicals represent -C(O)-CH2-C(O)-CH3

[0161] In a one-liter three-necked flask equipped with a mechanical stirrer and a distillation column, 100 g of sorbitol and 260.54 g of tert-butyl acetoacetate are introduced. The reaction mixture is heated in an oil bath (oil bath temperature 140°C–150°C) for 5 h. After 5 h, NMR confirms the grafting of the acetoacetate group. The reaction mixture is then concentrated using a rotary evaporator at 150°C under continuous vacuum. A viscous yellow liquid is obtained, which, upon analysis, corresponds to the expected product.

[0162] * Compound No. 7 Dipentaerythritol with acetoacetate function (6eq)

[0163] Compound 7 was synthesized according to the following scheme:

[0164] Scheme in which identical or different RI represents a hydrogen atom or a -C(O)-CH2-C(O)-CH3 group, it being understood that at least two RI radicals represent -C(O)-CH2-C(O)-CH3, in particular 6 RI radicals represent -C(O)-CH2 -C(O)-CH3.

[0165] In a one-liter three-necked flask equipped with a mechanical stirrer and a distillation column, 50 g of dipentaerythritol and 195.33 g of tert-butyl acetoacetate are introduced. The reaction mixture is heated in an oil bath (oil bath temperature 140°C–150°C) for 4 hours. After 4 hours, NMR confirms the incorporation of the acetoacetate group. The reaction mixture is then concentrated using a rotary evaporator at 150°C under continuous vacuum. A viscous, orange-brown liquid is obtained, which, upon analysis, corresponds to the expected product.

[0166] 9 Compound No. 8 Pentaerythritol tetraacetoacetate

[0167] Compound 8 was synthesized according to the following scheme:

[0168] In a one-liter three-necked flask equipped with a mechanical stirrer and a distillation column, 100 g of Pentaerythritol and 510.89 g of Tert-butyl acetoacetate are introduced. The reaction mixture is heated using an oil bath (oil bath temperature 140°C-150°C) for 4 hours.

[0169] After 4 hours, NMR confirms the grafting of the acetoacetate group. The reaction mixture is then concentrated using a rotary evaporator at 150 °C under continuous vacuum. A translucent yellow viscous liquid is obtained, which, after analysis, corresponds to the expected product.

[0170] • Compound No. 9 Sucrose with acetoacetate function (8eq)

[0171] Compound 9 was synthesized according to the following scheme: RI

[0172] Scheme in which identical or different RI represents a hydrogen atom or a -C(O)-CH2-C(O)-CH3 group, it being understood that at least two RI radicals represent -C(O)-CH2-C(O)-CH3, in particular 8 RI radicals represent -C(O)-CH2 -C(O)-CH3.

[0173] In a one-liter three-necked flask equipped with a mechanical stirrer and a distillation column, 100 g of sucrose and 406.55 g of tert-butyl acetoacetate are introduced. The reaction mixture is heated in an oil bath (oil bath temperature 140°C–150°C) for 4 hours. After 4 hours, NMR confirms the grafting of the acetoacetate group. The reaction mixture is then concentrated using a rotary evaporator at 150°C under continuous vacuum. A viscous, orange-yellow liquid is obtained, which, upon analysis, corresponds to the expected product. Synthesis of the polyamine compound (1)

[0174] Compound (1) was synthesized according to the following scheme: OQOP .........................” SOCUN” “Si’’ --------------* “K’ H’ HHH AB compound

[0175] A solution of azelaic acid dichloride (11.9 mL, 59.2 mmol, 1 equiv.) in anhydrous CH2Cl2 (148 mL) is added dropwise to a solution of N-(tert-Butoxycarbonyl)-1,5-diaminopentane (Compound A) (24.7 g, 118 mmol, 2 equiv.) and N,N-Diisopropylethylamine (DIPEA) (21.9 mL, 124 mmol, 2.10 equiv.) in CH2Cl2 (148 mL) at 0°C. The ice bath is removed and the mixture is stirred at room temperature for 2 h. Water (200 mL) is added to the mixture and the volatiles are removed under reduced pressure. The resulting white solid is filtered and washed successively with water, a 10% aqueous solution of KHSO4, water, an aqueous solution of saturated NaHCO3, and finally water. The resulting white solid is dried in a desiccator under reduced pressure with P2O5 for approximately 24 hours to yield the crude product as a white solid.

[0176] The solid is triturated in diethyl ether, filtered, and washed twice with diethyl ether before being dried under reduced pressure to give compound B as a white solid (35.4 g). The solid is engaged in the next step without further purification.

[0177] HCl (4N in 1,4-dioxane, 296 mL, 1.18 mol, 20 equiv.) is added dropwise to a suspension of compound B (35.4 g, 59.2 mmol, 1 equiv.) in dioxane (592 mL), and the mixture is stirred at room temperature for 22 h. The solid is filtered and washed with diethyl ether (2 x 70 mL). This solid is resuspended in water (200 mL), and Amberlite IR78 (OH form) resin is added until pH 10-11 is reached. The resin is removed by filtration, and the filtrate is concentrated under reduced pressure to give a white solid. The solid is resuspended in ethanol, and the suspension is stirred for 1 h at 50°C before being filtered. The filtrate is concentrated to give a white solid.

[0178] The resulting white solid is dissolved in water (approx. 100 mL) and passed through an Amberlite IR78 (OH form) resin column. The product-containing fractions are collected and concentrated under reduced pressure, then co-evaporated twice with ethanol to give a white solid. Compound (1) is obtained in 90% yield in two steps. Synthesis of the polyamine compound (2)

[0179] Compound (2) was synthesized according to the following scheme:

[0180] N,N-Diisopropylethylamine (DIPEA) (544 mL, 3.12 mol, 6.00 eq.) is added to a citric acid solution (100.00 g, 0.51 mol, 1.00 eq.) in tetrahydrofuran (1041 mL) in a 4 L double-jacketed glass reactor with mechanical stirring. Acetonitrile (1050 mL) is then added to the gelatinous mixture. To the resulting homogeneous solution, 1,(3-Dimethylaminopropyl)-3-Ethylcarbodiimide hydrochloride (EDCI) (399.1 g, 2.08 mol, 4.00 eq.) and then 2-Hydroxypyridine 1-oxide (HOPO) (231.3 g, 2.08 mol, 4.00 eq.) are added. The mixture The reaction mixture is stirred at room temperature for 10 minutes, then a solution of N-(tert-Butoxycarbonyl)-1,5-diaminopentane (368.5 g, 1.82 mol, 3.50 eq.) in acetonitrile (200 mL) is added. The reaction mixture is heated at 50°C for 3 h. The reaction mixture is concentrated under vacuum. The resulting oil is reconstituted in ethyl acetate (1400 mL) and water (800 mL). The phases are separated, and the organic phase is washed with water (800 mL), HCl (2 x 800 mL), saturated NaHCO3 (2 x 800 mL), and brine (1 x 1600 mL). The organic phase is then dried over Na2SO4, filtered and concentrated under vacuum to obtain compound C (390 g, 96%) in the form of a brown oil.

[0181] Hydrogen chloride (4M in dioxane) (1.70 L, 6.96 mol, 14.0 eq.) is added to a solution in 1,4-dioxane (1.30 L, 0.36 M) of compound C (390.0 g, 0.497 mol, 1.00 eq.) previously obtained in a 4 L double-jacketed glass reactor with mechanical stirring. The reaction mixture is stirred at 25 °C overnight. The supernatant is then removed by aspiration, and the remaining solid is dissolved in a methanol / water mixture (1.40 L, 9:1). The solution is filtered through Amberlite IRN-78 (-2 kg), and the resin is washed before use with 2 L of 2M NaOH, 3 L of water, and 3 L of methanol. The resulting filtrate is concentrated under vacuum and then resuspended in water (1.0 L). The solution is treated with activated carbon (100 g, until no further discoloration is observed) and then filtered through Celite buffer. The resulting filtrate is concentrated under vacuum to reduce the volume to approximately µL, and the solution is lyophilized for 3 days.The gum obtained is then dried under high vacuum at 50°C for 2 days to obtain compound (2) with a yield of 86% in the form of a yellow gum.

[0182] The following compositions Al to A5 and B1 to B5 were prepared and then tested according to operating procedures 1 or 2 described below. Compositions A1 to A5

[0183] [Tables2] Ingredients Al A2 A3 A4 A5 Compound #8 - - - - 10 Compound #9 10 10 10 - - Compound #7 - - - 10 - pH 10 Buffer NH4OH / NH4C 1 to 10% in Water / Ethanol (50 / 50) Qsp 100 Qsp 100 Qsp 100 Water / Ethanol (50 / 50) solvent at pH 10 (pH adjusted by adding NH4O2) q.s. 100 Water / Ethanol (50 / 50) solvent at natural pH of 7.5 - - q.s. 100 - - Compositions B1 to B5

[0184] [Tables3] Ingredients B1 B2 B3 B4 B5 Polyamine compound (D 10 10 10 - - Polyamine compound (3) - - - - 10 Polyamine compound (2) - - - 10 - Buffer pH 10 NH4OH / NH4C 1 to 10% in Water / Ethanol (50 / 50) Qsp 100 Qsp 100 Qsp 100 Solvent Water / Ethanol (50 / 50) at pH 10 (pH adjusted by adding NH4OH) Qsp 100 Solvent Water / Ethanol (50 / 50) at - - Qsp 100 - - Spontaneous pH of 7.5 Reference compositions REF1, REF2 and REF3

[0185] [Tables4] Ingredients REF1 REF2 REF3 Buffer pH 10 NH4OH / NH4Cl at 10% in Water / Ethanol (50 / 50) Qsp 100 - - Solvent Water / Ethanol (50 / 50) at pH 10 (pH adjusted by adding NH4OH) Qsp 100 Solvent Water / Ethanol (50 / 50) at spontaneous pH of 7.5 - - Qsp 100 Hair strands tested

[0186] Strands of 2.7 g of natural hair, 27 cm in length and exhibiting a type IV curl pattern, were used in the examples. The strands were washed with two successive DOP shampoos (0.4 g / g of hair) before application of the compositions to be tested according to procedure 1 or 2 described below. Operating procedure 1 (Without pretreatment step)

[0187] 405 mg of the composition Ax to be tested are applied to a wet wick, The hair is first wrung out and patted dry with absorbent paper. This application is done with the fingers while massaging the hair fiber. After a processing time ranging from 5 minutes to 5 hours, the strand of hair is then combed and hung to dry at room temperature.

[0188] After drying, 405 mg of the By composition to be tested are applied to the strand, without intermediate rinsing. This application is done with the fingers while massaging the hair fiber. After a processing time ranging from 5 minutes to 5 hours, the hair strand was then combed and hung to dry at room temperature. Procedure 2 (With pretreatment step)

[0189] A lock of hair is placed in a glass chute, then 5.4 g of a REFz composition are applied to the damp lock. After a processing time of 30 minutes, the wick is wrung out and dabbed on absorbent paper then the wick is treated according to procedure 1.

[0190] Operating procedure 3 - Reference (Without pretreatment step)

[0191] 405 mg of the REFz formula to be tested are applied to a previously moistened wick The hair is wrung out and patted dry with absorbent paper. This application is done with the fingers while massaging the hair fiber. After a processing time ranging from 5 minutes to 5 hours, the strand of hair is then combed and hung to dry at room temperature.

[0192] For each of the strands treated according to one of the operating methods 1 to 3, measurements of the width at half height and of the length of the strand were taken after shampooing, drying at room temperature and combing and compared with the value obtained for a control hair strand which had only been washed with two successive DOP shampoos (0.4 g / g of hair).

[0193] The processing conditions implemented in the different examples are summarized in the table below:

[0194] [Tables5] Example Operating Procedure Composition Ax applied / Application time composition Ax Composition B y applied / Application time composition By Composition RE Fz applied / Application time composition REFz Example 1 (Invention) 1 Al / 15 min B1 / 30 min - Example 2 (Invention) 1 Al / 15 min B1 / 300 min - Example 3 (Invention) 1 Al / 15 min B1 / 15 min - Example 4 (Invention) 1 Al / 5 min B1 / 5 min - Example 5 (Invention) 1 A2 / 15 min B2 / 30 min - Example 6 (Invention) 1 A3 / 15 min B3 / 30 min - Example 7 (Invention) 1 A3 / 15 min B3 / 300 min - Example 8 1 Al / 15 min B4 / 15 min - (Invention) Example 9 (Invention) 1 A1 / 15 min B4 / 30 min - Example 10 (Invention) 1 A5 / 15 min B5 / 30 min - Example 11 (Invention) 1 A1 / 15 min B5 / 30 min - Example 12 (Invention) 1 A4 / 15 min B5 / 30 min - Example 13 (Invention) 1 A1 / 15 min B3 / 30 min - Example 14 (Invention) 1 A3 / 15 min B1 / 30 min - Example 15 (Invention) 1 A2 / 15 min B3 / 30 min - Example 16 (Invention) 1 A3 / 15 min B2 / 30 min - Example 17 (Invention) 2 A3 / 15 min B3 / 30 min REF1 / 30 min Example 18 (Invention) 2 A3 / 15 min B3 / 30 min REF2 / 30 min Example 19 (Comparative) 3 - - REF1 / 30 min Example 20 (Comparative) 3 - - REF2 / 30 min Example 21 (Comparative) 3 - - REF3 / 30 min Results#:

[0195] [Tableauxô] Treatment type Width at half-height of strand (cm) Strand length (cm) Control (Untreated hair) 10 23 Example 1 (Invention) 4 27 Example 2 (Invention) 5 28 Example 3 (Invention) 7 25 Example 4 (Invention) 6 25 Example 5 (Invention) 7 26 Example 6 (Invention) 8 25 Example 7 (Invention) 9 25 Example 8 (Invention) 7 25 Example 9 (Invention) 4 27 Example 10 (Invention) 6.5 25 Example 11 (Invention) 7 25 Example 12 (Invention) 6 26 Example 13 (Invention) 3.5 27 Example 14 (Invention) 4 27 Example 15 (Invention) 7.5 25.5 Example 16 (Invention) 7.5 26.5 Example 17 2.8 27.5 (Invention) Example 18 (Invention) 5 26.5 Example 19 (Comparative) 9.5 24 Example 20 (Comparative) 10.5 24 Example 21 (Comparative) 10 24

[0196] The widths at half maximum (WMM) of the strands treated according to Examples 1 to 18 of the invention are less than those measured on the strands treated according to Comparative Examples 19 to 21 or on the control strand, and the lengths of the strands treated according to Examples 1 to 18 of the invention are greater than those measured on the strands treated according to Comparative Examples 19 to 21 or on the control strand. The process according to the present invention therefore makes it possible to obtain good quality straightening, notably reducing the volume of the hair thus treated, without the use of a flat iron.

Claims

1. Demands A process for treating keratin fibers comprising step i) and optionally the following step(s) i'): i) application on keratin fibers: a) of one or more compounds A chosen from among the compounds of formula (I), their optical isomers, their geometric isomers, their salts, their solvates such as hydrates, and their mixtures: Formula (I) in which: - R1 represents a versatile hydrocarbon radical in C2 to CM, linear or branched, saturated or unsaturated, conjugated or not, acyclic or cyclic, aromatic or not, R1 being further: a) possibly substituted by one or more hydroxy groups OH, dialkylamino-N(R)2 with R representing a (Ci-C4)alkyl group, carboxy-C(O)-OH, a vinyl group, and / or b) possibly interrupted by one or more heteroatoms or groups selected from O, S, carbonyl -C(O)-, amine -N(R'), or their combinations, in which R' represents a hydrogen atom, a linear or branched alkyl group having from 1 to 4 carbon atoms possibly substituted by at least one hydroxy group (OH) or possibly substituted by -XC(O)-C(Ra)(Rb)-C(O)-R2; - R2 represents a monovalent hydrocarbon radical in C1 to C6, linear or branched, saturated or unsaturated; - Ra, and Rb, identical or different, represent a hydrogen atom or a (Ci-C4)alkyl group; - X is a heteroatom or group chosen from O, S, N(R') or , -S-CH2-C(O)-O-, -OC(O)-CH2-S-, -OC(O)-N(R')-, -N(R')-C(O)-O-, -N(R')-C(O)-N(R')-, R' being as defined previously; - n denotes an integer ranging from 2 to 10, particularly from 3 to 9; and

2. b) of one or more polyamine compounds B selected from compounds of formula (II), their optical isomers, their geometric isomers, their salts, their solvates such as hydrates, and their mixtures: H2N—T—NH2 (II) Formula (II) wherein T represents a divalent hydrocarbon group, linear or branched, saturated or unsaturated, preferably saturated, comprising from 4 to 22 carbon atoms, optionally substituted by an -NH2 group, the T group being substituted by one or more hydroxyl (-OH) groups and / or interrupted by one or more groups selected from -C(O)-, -NRa- or their combinations such as -NRa-C(O)- or -C(O)-NRa-, with Ra representing a hydrogen atom or a (Ci-C4)alkyl group; and (i') application to the keratin fibers of a pretreatment composition (P) having a pH between 8 and 12.5, preferably between 8.5 and 12.5, step (i') being carried out before step (i); it being understood that: ■ Compound(s) A are included in a composition (A) and polyamine compound(s) B are included in a composition (B) separate from composition (A), composition (A) being applied to the keratin fibers before or after composition (B), preferably before composition (B), or compound(s) A and polyamine compound(s) B are included in the same composition (C); and ■ when step i') is omitted, one of the two compositions (A) and (B) or each of the two compositions (A) and (B) or composition (C) has a pH between 8 and 12.5, preferably between 8.5 and 12.

5. A method according to the preceding claim, wherein the compound(s) A are selected from the compounds of formula (la), their optical isomers, their geometric isomers, their salts, their solvates such as hydrates, and mixtures thereof: Formula (the) in which: - R1 is as defined in the preceding claim, particularly represents a C2 to Cm hydrocarbon polyvalent radical, preferably C3-C12, preferably C4-C10, linear or branched, saturated or unsaturated, conjugated or not, acyclic or cyclic, aromatic or not, R1 further being: a) optionally substituted by one or more hydroxyl groups OH, and / or b) optionally interrupted by one or more heteroatoms or groups selected from O, S, -N(R'), preferably interrupted by one or more oxygen atoms in which R' is as defined in the preceding claim; - R2 is as defined in the preceding claim, preferably R2 represents a (Ci-C6)alkyl group, linear or branched, preferably a (Ci-C4)alkyl group, more preferably methyl or tert-butyl such as methyl; and - n is as defined in the preceding claim, preferably n denotes an integer from 2 to 9.

3. A method according to any one of the preceding claims, wherein the compounds of formula (I) or (la) are such that: R1 represents a C6-C8 hydrocarbon polyvalent radical, linear or branched, unsaturated monocyclic or bicyclic, preferably monocyclic, optionally aromatic such as phenyl; or R1 represents a C5-C12 hydrocarbon polyvalent radical, saturated monocyclic or bicyclic, optionally interrupted by one or more heteroatoms or groups selected from O, S, -N(R'), wherein R' represents a hydrogen atom, an alkyl group having from 1 to 4 carbon atoms, preferably interrupted by one or more oxygen atoms; preferably R1 represents a monosaccharide or polysaccharide motif, in particular a disaccharide, on which n hydroxyl groups have been substituted by n -OC(O)-CH2-C(O)-R2 groups with R2 and n as defined in any one of the preceding claims;or R1 represents a versatile acyclic hydrocarbon radical in C2 to C12, preferably in C3-C10, linear or branched, saturated or unsaturated, preferably saturated.;

4. A method according to any one of the preceding claims, wherein the compounds of formula (I) or (la) are such that n denotes

5. an integer from 2 to 9, more specifically n denotes an integer from 3 to 9, more specifically from 4 to 9. A process according to claim 1, wherein the compound(s) A are selected from the following compounds, their optical isomers, their salts, their solvates such as hydrates, and their mixtures: {SompsseJ NohVçhtrrsque :• Structure W 700865-73-2 3-oxo-1,t'-(1,7-heptanecftyl) butanoic acid ester 'S' (21 632336-20-0 3-©xo-1,7-(1,8- 'odanediyl) butanoic acid ester ;7 -y CT 501426-98-8 3-oxo-1,T-(1,10- decanedsyl) butanoic acid ester W 174498-06-7 3-oxo-t ,7-(1,3-propanedtyl) butanoic acid ester CT 160187-52-0 3-oxo-l ,2-dimethyl- 72-ethanediyl butanoic acid ester CT 145020-19-5 3-oxo-2-buty-2-ethyl-1,3-propane-2-butanoic acid ester (7) 87530-38-7 3-oxo-1,1,2,2-tetramethyl-2-ethyl-1,3-propane-2-butanoic acid ester ..•■A. / \ (Compound) Chemical name Stroctorc- chemical (8| 58213-75-5 3-Dxa-lJ'-(1-r^ 1,3-propan-ectiyl) butanoic acid ester Ç{ 0 < -yt G (S| 53213-74-4 3-oxo-l f 1'-|2r2-chmethyi-1-(1 -metbyliéthy 1)-1,3-propanediyO butanic acid ester \ (10) 39564-28-8 3-oxo-l ,1-(1,5-peotariedjyt) butanoic acid ester GG <> (11) 14276-67-6 3-oxo-l ,1-(2,2- dtmeth^-1 .3-propanediyl) ester of butanoic acid 0 G 0 ''■-S. \ (12) 13Û18-41-2 3-oxo-l,4-butanediyl butanoic acid ester S (14) 5459-64-1 3-oxo-l,2-êthaœdiyi butanoic acid ester §. s (Compound) NW sheets Structure .disc (16) 2388-18-3 a; r5 u- J qj & .a- c «3 4« â ® ; t- s (JJ fu ■ v -t? su i- .3? ? X □ » .. Æ —- te cr 4" S « *TX) 3 S | ■§ ® « w S % 8 $ % % 0J -' Tj pj Qj XJ c J ……… Ç...... ….". (16) 32818-80-3 bis{3-oxobutanoate) of 1,T42,2-His[(1,3-dsoxobi.!-toxy)methyi]-1,3-propanediyl] 3 .-— 1 1 / ..... / .....' ■Ö S'-X"x <0* X0 ■ ■ / rt ....." * % (17) 51980-20-2 bs(3-oxophetanoate) de 1,1-(2,2- Bis(hydfoxyfnéthyî)“ 1,3-propanediy5 J / ...... g < y < i / * X (15) ......0 130973-05-6 3-oxo-1.3,5-benzenefcyi butapoic acid ester AÂ, 0 £> jf A - A....... (Compound-111110:11 Ndmçhimlue: Chemical Structure ¢20) 139264--86-1 3-OXO-1,2 ;4-benzene butanoic acid ester Tr' ” ” ¢21} 22208-25-3 Trimethylisothiazolinone Triacetoacetate propagates K-FLEX 7301 - V JV” STT '........ ¢22) 2360524-48-5 V? 'V ¢23) 66229-33-2 3-oxo-2-butyi-2-[( 1,3-dsoxobutoxymethyl]-' ,3-propanediyl butanoic acid ester ¢24) 1579231-50-Y 4,4-dimethyl!-3-oxo-, 1,r-[2,2-bjs[[(4,4-dimethyi-1t3-dioxopentyÇoxÿlmeth yi}-1,3-propanediylI pectoic acid ester, \ ,À> S'""\ $ 1 <• \....... (Cwripose) Name Status: cbsmiqüe {25} 6079-98-7 {ns(3-oxQbutafioaieJ of 1, r,r-( 1,2,3-propanetriy!) oh {28} CT acetone of acetoa-5 , _p> Ÿ ¢27) 169533-29-3 sOG^copyranose, 1 ;2,3,4,6-penîakis(3-oxobulanoate) / ,.....{ l..... / \ ' / \_r'" / \....... J ■ - 5-5-27} 20 artxno-2:^ [2.3,4-tns-O-{ 1,3-dioxobuty{)-0 -xyiopyranosyî Joxy]-d'ackte benzoic- (Compounded) N' CAS bfcæ chemique (29) 1236300-10- 2,3.4t6-tetrakis(3-oxobutacoste) de «-D- G1 ucopy rauoside, 1,3-4.6-teirakis-di-ox-pGbuD1,3 fructofuranosy}, .•À ! I l ' ' . . x*"' y. (30) 86481-26-4 D-Gktopyranose. peatakis(3-oxobutanoate) ç >% ' vX <x-' x- (31) 944473-12-5 D-^udtôl, 1,4:3.6- dianhydî’o-, 2.5-bis(3- oxobutanoate) <s.....i>(32} 2254710-49- X ^..X. . .J . V-''% (Compound) Chemical structure (33) sofbitol hexa-acetaacetate V' .■X. goo:' 'o î? tr" ''V"" v %> S 0 -... J ';Ç Ô {34) 21'6756-89-7 D-Gkidtd, 4-OgD-gai aetopyEanosy I-, poiyacetoacetate Ri / \ Z™" Z \ \ / \ / \ s si \ ch—»' / 7 \ ss sm with RI chosen from -C(O)-CHi-C(O)-CH3. H with at least two, radicals RI represent -Ç(O)-CHî-C(O)-CHî (35) 101655-52-1 Sucrose. polyacetoacetate 'HC « / %1 / 'V-« $ i R ■ - „ X ' 0 with Ri chosen from -C(O)-CH2-C(Ct)-CH3, H with at least two radicals R1 represent -C(O)-CH2-C(O)-CHs Eremic name Chemical structure (36) Glucose poSyacetoaceîate RI / s\„ \ ■ / S; p / ~ ' U'-Î {37} Mannose patyacetoacetaie PI y R\ “s 'v7 / \ (38) Xy^stot pciyaceloacelate ^'x RI xx X ^X R1 JY (39} Sorbitoi pdyacetoacetate XX 1 Â '°" ï ï ::--pi preferably 6 radicals RI represent -qO^Hi-C / OÏ-CHs Chemical name / R1 0' - IX c" ri «X ' Xi So radicals RI represent -C(C'>CH2-C(O)-CHî? and three RI rafts represent a hydrogen atom {41} 1471-84-9 JL 1 JL - V - Y 1 0 OX" {42} 2552-36-5 K 1 8 X (43} 139614-56-5 X < ? OO Ç f X,.-' MH {44} 9616S-3Û-1 X <■ {45} 7563S-D1-S > ' 'Y y xv '" ï (Compound) ||)|^SâS|| Chemical structure: {46} Dipentaeryihrito! poiyacêtoacetate ' ' 'v XJ $ / .xss-.^xs-X'X''*'*,*'fc' / < <> / x preferably 5 or 6 R I radicals. more preferably 6 R I radicals represent -O(O)-CH2-C(O)-CHî in which identical or different RIs represent a hydrogen atom or a -C(O)-CH2-C(O)-CH3 group, it being understood that at least two RI radicals represent -C(O)-CH2-C(O)-CH3, preferably at least three RI radicals represent -C(O)-CH2-C(O)-CH3; preferably from compounds (16), (18), (21), (35), (36), (37), (38), (39), (40) and (46), their optical isomers, their salts, their solvates such as hydrates, and mixtures thereof; more preferably from compounds (16), (21), (35), (38), (39) and (46), their optical isomers, their salts, their solvates such as hydrates, and mixtures thereof; even more preferentially among compounds (16), (35) and (46), their optical isomers, their salts, their solvates such as hydrates, and their mixtures.

6. A method according to any one of the preceding claims, wherein T represents a divalent, linear or branched, saturated hydrocarbon group comprising from 4 to 22 carbon atoms, preferably from 10 to 22 carbon atoms, more preferably from 15 to 20 carbon atoms, optionally substituted by an -NH2 group, the group T being interrupted by one or more groups selected from -C(O)-, -NRa- or their combinations such as -NRa-C(O)- or -C(O)-NRa-, Ra being as defined in the preceding claim, preferably interrupted by one or more groups selected from -NRa-C(O)- or -C(O)-NRa-, Ra being as defined in the preceding claim and the group T being optionally substituted by one or more hydroxyl (-OH) groups;preferably T represents a divalent, linear or branched, saturated hydrocarbon group comprising 10 to 22 carbon atoms, preferably 15 to 20 carbon atoms, optionally substituted by an -NH2 group, the T group being interrupted by 2 or 3 groups selected from -NH-(CO)- or -(CO)-NH- and the T group being optionally substituted by one or more hydroxyl groups (-OH), in particular a hydroxyl group (-OH);

7. A method according to any one of claims 1 to 5, wherein T represents a divalent, linear or branched, saturated hydrocarbon group comprising from 4 to 22 carbon atoms, preferably from 4 to 15 carbon atoms, more preferably from 4 to 10 carbon atoms, substituted by one or more hydroxyl groups (-OH).

8. A method according to any one of claims 1 to 5, wherein the polyamine compound(s) B are selected from the following compounds (1), (2) and (3), their optical isomers, their salts, their solvates such as hydrates, and their mixtures: X / X Â U) 0 o (2) JJ" NH, <3> -

9. A method according to any one of the preceding claims, wherein the compound(s) A are included in a composition (A) and the polyamine compound(s) B are included in a composition (B) separate from composition (A), composition (A) being applied to the keratin fibers before or after composition (B), preferably before composition (B).

10. A method according to the preceding claim, wherein step i') is omitted and one of the two compositions (A) and (B) or each of the two compositions (A) and (B), preferably each of the two compositions (A) and (B) has a pH between 8 and 12.5, preferably between 8.5 and 12.

5.

11. A method according to claim 9, wherein step i') is present and one of the two compositions (A) and (B) or each of the two compositions (A) and (B), preferably each of the two compositions (A) and (B) has a pH between 8 and 12.5, preferably between 8.5 and 12.

5.

12. A method according to any one of claims 9 to 11, wherein the pH of compositions (A) and / or (B), preferably the pH of compositions (A) and (B), is adjusted using an alkaline buffer system, preferably using an NH4OH / NH4Cl alkaline buffer system

13. A process according to any one of claims 1 to 9, 11 or 12, wherein step i') is present and the pH of the pretreatment composition (P) is adjusted using an alkaline buffer system, preferably using an NH4OH / NH4Cl alkaline buffer system.

14. A method according to any one of the preceding claims, wherein: ■ the compound(s) A are present in composition (A) or (C) in a total content of 0.2% to 80% by weight, preferably of 0.5% to 50% by weight, more preferably of 2% to 35% by weight, relative to the total weight of the composition comprising them; and / or ■ the polyamine compound(s) B are present in composition (B) or (C) in a total content of 0.2% to 60% by weight, preferably of 0.5% to 40% by weight, more preferably of 5% to 40% by weight, relative to the total weight of the composition comprising them.

15. A method according to any one of the preceding claims, wherein the keratin fibers are curly, crimped, or frizzy keratin fibers.

16. A method according to any one of the preceding claims, wherein the method is a method for relaxing loops and / or smoothing keratin fibers.

17. Composition (C) as defined in any one of claims 1 to 8 or 14, composition (C) preferably having a pH between 8 and 12.5, more preferably between 8.5 and 12.5, the pH of composition (C) preferably being adjusted using an alkaline buffer system, more preferably using an NH4OH / NH4C1 alkaline buffer system.

18. A device with two or three compartments comprising: - a first compartment containing a composition (A) as defined in any one of claims 1 to 12 or 14; - a second compartment separate from the first compartment containing a composition (B) as defined in any one of claims 1 to 12 or 14; - optionally a third compartment separate from the first and second compartments containing a pretreatment composition (P) as defined in claim 1 or 13.

19. Use of a composition (A) as defined in any one of claims 1 to 12 or 14 associated with a composition (B) as defined in any one of claims 1 to 12 or 14 and optionally associated with a pretreatment composition (P) as defined in claim 1 or 13 or of a composition (C) as defined in any one of claims 1 to 8, 14 or 17, optionally associated with a pretreatment composition (P) as defined in claim 1 or 13, for the relaxation of loops and / or the smoothing of keratin fibers.