Classifications

• • C—CHEMISTRY; METALLURGY
  • C09—DYES; PAINTS; POLISHES; NATURAL RESINS; ADHESIVES; COMPOSITIONS NOT OTHERWISE PROVIDED FOR; APPLICATIONS OF MATERIALS NOT OTHERWISE PROVIDED FOR
  • C09D—COATING COMPOSITIONS, e.g. PAINTS, VARNISHES OR LACQUERS; FILLING PASTES; CHEMICAL PAINT OR INK REMOVERS; INKS; CORRECTING FLUIDS; WOODSTAINS; PASTES OR SOLIDS FOR COLOURING OR PRINTING; USE OF MATERIALS THEREFOR
  • C09D4/00—Coating compositions, e.g. paints, varnishes or lacquers, based on organic non-macromolecular compounds having at least one polymerisable carbon-to-carbon unsaturated bond ; Coating compositions, based on monomers of macromolecular compounds of groups C09D183/00 - C09D183/16
• • C—CHEMISTRY; METALLURGY
  • C07—ORGANIC CHEMISTRY
  • C07F—ACYCLIC, CARBOCYCLIC OR HETEROCYCLIC COMPOUNDS CONTAINING ELEMENTS OTHER THAN CARBON, HYDROGEN, HALOGEN, OXYGEN, NITROGEN, SULFUR, SELENIUM OR TELLURIUM
  • C07F7/00—Compounds containing elements of Groups 4 or 14 of the Periodic Table
  • C07F7/02—Silicon compounds
  • C07F7/08—Compounds having one or more C—Si linkages
  • C07F7/18—Compounds having one or more C—Si linkages as well as one or more C—O—Si linkages
  • C07F7/1804—Compounds having Si-O-C linkages

Definitions

• Fluorochemical compounds are well known and commercially used to coat or render various substrates oil- and water-repellent and to provide other desirable properties thereto such as soil repellency and soil release.
• Fluorochemical alkanesulfonamido silanes having at least 4 carbon atoms in the fluoroalkyl group are known for treating substrates.
• fluorochemical oligomeric silanes having at least 4 carbon atoms in the fluoroalkyl group are known for treating hard surfaces, (e.g., glass or crystalline ceramics).
• the present invention provides a fluorochemical composition comprising at least one silane of the formula (I):
• R is a Ci to Ce alkyl group or an aryl group; m and n are each independently integers from 1 to 20; Z is selected from the group consisting of hydrogen and a group of the formula -(CtH 2t )-X-Q-Si(Y') w (Y)3 -w , in which t is an integer from 0 to 4; -X- is selected from the group consisting of -O-, -S- and -NH-; -Q- is selected from the group consisting of -C(O)NH-(CH 2 ) V - and -(CH 2 ) V -; v is an integer from 1 to 20; Y is a hydrolyzable group; Y' is a non-hydrolyzable group; and w is an integer from 0 to 2; and
• R' is selected from the group consisting of a Ci to Ce alkyl group, an aryl group, and a group of the formula -(CH 2 ) v -Si(Y') w (Y)3 -w , with the proviso that when Z is hydrogen, R' is a group of the formula -(CH 2 )v-Si(Y') w (Y)3 -w .
• the present invention includes a fluorochemical composition as above described with an organic solvent in an amount sufficient to dissolve and/or disperse the silane(s).
• the present invention provides the above described fluorochemical composition further comprising at least one compound of the formula (II): M(Y') s (Y) r . s
• M is selected from the group consisting of Si, Ti, Zi, Al, V, Sn, and Zn;
• Y' is a non-hydrolyzable group; Y is a hydrolyzable group; s is 0, 1 or 2; and r is 4, 3 or 2.
• the present invention provides the combination of at least one silane of formula I and at least one compound of formula II with an organic solvent in an amount sufficient to dissolve and/or disperse both components.
• the present invention also includes methods of treating siliceous substrates by applying to at least a portion of the surface of the substrate a fluorochemical composition comprising at least one silane of formula I and, optionally, at least one compound of formula II in an organic solvent.
• the present invention provides methods for making a silane of the formula I.
• the present invention provides a method of preparing a silane of the formula Rf 3 SO 2 -N(R)CH 2 CHZ 1 CH 2 N(R)SO 2 Ra, the method comprising: reacting (a) a compound of the formula (III):
• Ra is C q F 2q+ i, wherein q is an integer from 1 to 5, with the proviso that at least one of p or q is 1; each R is independently a Ci to Ce alkyl group or an aryl group; W is selected from the group consisting of I-, Br-, Cl-, and OCN-; and
• Z' is a group of the formula -O-Q-Si(Y') w (Y)3_ w , wherein -Q- is selected from the group consisting of -C(O)NH-(CH 2 ) V - and -(CH 2 ) V -; v is an integer from 1 to 20; Y is a hydrolyzable group; Y' is a non-hydrolyzable group; and w is an integer from 0 to 2.
• Compositions according to the present invention are typically efficient and effective oil and water repellents for siliceous surfaces, (e.g., sanitary ceramics, ceramic tiles, and glass).
• compositions according to the present invention which contain two fluorochemical groups, are more effective in creating high oil- and water-repellent surfaces than compositions containing a single fluorochemical group of the same molecular size.
• compositions according to the invention provide comparable performance to perfluorooctanesulfonamido silanes.
• compositions according to the present invention can be used to modify the wettability of sandstone bearing at least one of oil or gas.
• the sandstone is a subterranean gas reservoir that is blocked by liquid hydrocarbons (gas condensate) near the well bore.
• the wettability modification increases fluid mobility through the sandstone. When used in oil and/or gas bearing formations, such an increase in fluid mobility may correspond to higher hydrocarbon production for a well located on the formation.
• the fluorochemical composition comprises at least one silane of the formula (I): R fa SO 2 -N(R)(C n H 2n )CHZ(C m H 2m )N(R)SO 2 R ft
• R fa is C p F 2p+ i, wherein p is an integer from 1 to 5; Ra is C q F 2q+1 , wherein q is an integer from 1 to 5, with the proviso that at least one of p or q is 1;
• R is a Ci to Ce alkyl group or an aryl group; m and n are each independently integers from 1 to 20; Z is selected from the group consisting of hydrogen and a group of the formula -(C t H 2t )-X-Q-Si(Y')w(Y)3- w , in which t is an integer from 0 to 4; -X- is selected from the group consisting of -O-, -S- and -NH-; -Q- is selected from the group consisting of -C(O)NH-(CH 2 ) V - and -(CH 2 ) V -; v is an integer from 1 to 20; Y is a hydrolyzable group; Y' is a non-hydrolyzable group; and w is an integer from 0 to 2; and R is selected from the group consisting of a Ci to Ce alkyl group, an aryl group, and a group of the formula -(CH 2 ) v -
• M is selected from the group consisting of Si, Ti, Zi, Al, V, Sn, and Zn; Y' is a non-hydrolyzable group;
• Y is a hydrolyzable group; s is 0, 1 or 2; and r is 4, 3 or 2.
• the perfluoroalkanesulfonamide groups may each contain 1 to 5 carbon atoms and may be linear, branched or cyclic.
• the perfluoroalkyl groups, R& and R& are both trifluoromethyl, (i.e., p and q are each 1).
• R& is trifluoromethyl, and R& contains 2 to 5 carbon atoms, (i.e., p is 1 and q is an integer from 2 to 5).
• R& contains 4 carbon atoms (i.e., p is 1 and q is 4).
• R& is trifluoromethyl, and R& contains 2 to 5 carbon atoms, (i.e., q is 1 and p is an integer from 2 to 5). In some of these embodiments, R& contains 4 carbon atoms (i.e., q is 1 and p is 4).
• m is an integer from 1 to 6 and n is an integer from 1 to 6.
• p and q are both 1, and m and n are each independently integers from 1 to 6.
• p is 4; q is 1 ; and m and n are each independently integers from 1 to 6.
• the sum of n and m is 2; X is O; and Q is -C(O)NH(CH 2 )3-.
• alkyl refers to straight chain, branched, and cyclic alkyl.
• Ci to Ce alkyl includes methyl, ethyl, propyl, isopropyl, butyl, cyclobutyl, isobutyl, and tertiary butyl.
• R and R' are each independently -CH 3 or -CH 2 CH 3 .
• R and R' are each -CH 3 .
• R is -CH 3 or -CH 2 CH 3 .
• aryl as used herein includes aromatic rings or multi-ring systems optionally containing at least one ring heteroatom (e.g., O, S, N).
• aryl groups include phenyl, naphthyl, biphenyl, and pyridinyl.
• Aryl groups may be unsubstituted or may be substituted by up to five substituents (e.g., alkyl, as above defined, alkoxy of 1 to 4 carbon atoms, halo (i.e., fluoro, chloro, bromo, iodo), hydroxyl, amino, and nitro).
• substituents when substituents are present, the substituents are halo and alkyl substituents.
• v is an integer from 1 to 10, and in one embodiment, v is 3.
• Q is -(CH 2 ) V -, wherein v is an integer from 1 to
• Q is -C(O)NH(CH 2 ) V - wherein v is an integer from 1 to 10.
• Z is -0-Q-Si(Y) 3 , in which each Y is independently -Cl or a C 1 -C 4 alkoxy group.
• Z is hydrogen and R' is -(CH 2 ) v -Si(Y) 3 , in which each Y is independently -Cl or a Ci to C 4 alkoxy group.
• hydrolyzable group in connection with the present invention refers to a group which either is directly capable of undergoing condensation reactions under appropriate conditions or which is capable of hydrolyzing under appropriate conditions, thereby yielding a compound, which is capable of undergoing condensation reactions.
• Appropriate conditions include acidic or basic aqueous conditions, optionally in the presence of another condensation catalyst, (e.g., Sn-compounds).
• the hydrolyzable groups Y may be the same or different and are generally capable of hydrolyzing under appropriate conditions, for example, under acidic or basic aqueous conditions, such that the fluorochemical oligomer can participate in condensation reactions.
• the hydrolyzable groups upon hydrolysis yield groups capable of undergoing condensation reactions, (e.g, silanol groups).
• hydrolyzable groups include halogens (i.e., chlorine, bromine, iodine or fluorine), alkoxy groups -OR" (wherein R" represents a lower alkyl group, preferably containing 1 to 6, more preferably 1 to 4 carbon atoms and which may optionally be substituted by one or more halogen atoms), acyloxy groups -0(CO)-R", aryloxy groups -OR” (wherein R" represents an aryl moiety, preferably containing 6 to 12, more preferably containing 6 to 10 carbon atoms, which may be optionally substituted by one or more substituents independently selected from halogens, and Ci to C 4 alkyl groups which may optionally be substituted by one or more halogen atoms).
• halogens i.e., chlorine, bromine, iodine or fluorine
• R" and R" may include linear, branched and/or cyclic structures.
• hydrolyzable groups include methoxy, ethoxy, and propoxy groups and chlorine.
• each hydrolyzable group, Y is independently -Cl or a Ci to C 4 alkoxy group.
• each Y is independently -Cl, -OCH 3 or -OCH 2 CH 3 .
• the non-hydrolyzable groups Y' may be the same or different and are generally not capable of hydrolyzing under conditions for condensation reactions, (e.g., acidic or basic aqueous conditions where hydrolyzable groups are hydrolyzed).
• the non-hydrolyzable groups Y' may be independently a hydrocarbon group, for example, an alkyl group, in some embodiments containing 1 to 4 carbon atoms.
• each non- hydrolyzable group, Y' is independently a Ci to Ce alkyl group or an aryl group.
• Y' is -CH 3 or -CH 2 CH 3 .
• M is Si; Y' is -CH 3 or -CH 2 CH 3 ; and each Y is independently -Cl, -OCH 3 or -OCH 2 CH 3 .
• Representative fluorochemical compounds of the invention include
• a fluorochemical composition of the invention comprises at least one of [CF 3 SO 2 N(CH 3 )CH 2 ] 2 CHOC(O)NH(CH 2 ) 3 Si(OCH 3 ) 3 or
• a fluorochemical composition of the invention comprises at least one of [CF 3 SO 2 N(CH 3 )CH 2 ] 2 CHOC(O)NH(CH 2 ) 3 Si(OCH 2 CH 3 ) 3 or
• the fluorochemical compounds of the invention may be prepared by conventional methods.
• [CF 3 SO 2 N(CH 3 )CH 2 ] 2 CHOH may be made by reacting two moles Of CF 3 SO 2 NH(CH 3 ) with either l,3-dichloro-2-propanol or epichlorohydrin in the presence of base.
• [CF 3 SO 2 N(CH 3 )CH 2 ] 2 CHOCH 2 CH 2 CH 2 Si(OCH 3 ) 3 can be made from [CF 3 SO 2 N(CH 3 )CH 2 ] 2 CHOH by alkylation with ClCH 2 CH 2 CH 2 Si(OCH 3 ) 3 or by alkylation with allyl chloride, followed by hydrosilation with HSiCl 3 and methanolysis. Reaction of [CF 3 SO 2 N(CH 3 )CH 2 ] 2 CHOH with OCNCH 2 CH 2 CH 2 Si(OCH 3 ) 3 yields [CF 3 SO 2 N(CH 3 )CH 2 ] 2 CHOCONHCH 2 CH 2 CH 2 Si(OCH 3 ) 3 .
• a useful intermediate for the preparation of a silane of formula I is a compound of the formula (III):
• R& is C p F 2p+1 , wherein p is an integer from 1 to 5, and R is a Ci to Ce alkyl group or an aryl group.
• Intermediates of formula III can be made, for example, by the reaction of a compound of formula R f3 SO 2 NH(R) with an excess of epichlorohydrin.
• a particularly useful intermediate of the formula III is N-methyl-N-(oxiran-2- ylmethyl)perfluorobutane- 1 -sulfonamide.
• Another particularly useful intermediate of the formula (III) is N-methyl-N-(oxiran-2-ylmethyl)trifluoromethanesulfonamide.
• the present invention provides a method of preparing a silane of the formula R fa SO 2 - ⁇ (R)CH 2 CHZ'CH 2 ⁇ (R)SO 2 R fc , the method comprising: reacting (a) a compound of the formula (III):
• W is selected from the group consisting of I-, Br-, Cl-, and OCN-;
• Z' is a group of the formula -O-Q-Si(Y') w (Y)3_ w , wherein -Q- is selected from the group consisting of -C(O)NH-(CH 2 ) V - and -(CH 2 ) V -;
• v is an integer from 1 to 20;
• Y is a hydrolyzable group;
• Y' is a non-hydrolyzable group; and
• w is an integer from O to 2.
• R& is C p F 2p+ i, wherein p is an integer from 1 to 5; Ra is C q F 2q+ i, wherein q is an integer from 1 to 5, with the proviso that at least one of p or q is 1; and R is a Ci to Ce alkyl group or an aryl group.
• p is an integer from 2 to 5.
• p is 4.
• p is 1.
• R is a Ci to C 4 alkyl group; in some of these embodiments, R is -CH 3 .
• a compound of formula R fa SO 2 -N(R)CH 2 CH(OH)CH 2 N(R)SO 2 R fc is reacted with a compound of formula
• Hal-(CH 2 )v-Si(Y') w (Y)3-w wherein Hal is selected from the group consisting of I, Br, and Cl.
• a compound of formula R fa SO 2 -N(R)CH 2 CH(OH)CH 2 N(R)SO 2 R fc is reacted with a compound of formula
• Reacting the compounds of formulae III and R ⁇ -SO 2 -NHR and a base may be carried out in a suitable solvent (e.g., tetrahydrofuran).
• a suitable solvent e.g., tetrahydrofuran
• the compounds and the base may be combined in any order.
• the compound of formula III may be added to a solution of a compound of formula R ft ,-SO 2 -NHR, or a compound of formula Ra-SO 2 -NHR, optionally in a solvent, may be added to a solution of a compound of formula III.
• Many suitable bases are known to one of skill in the art.
• the base may be sodium hydroxide, sodium methoxide, or a combination thereof, and may be present as an aqueous solution.
• the reaction can be carried out by agitating and optionally heating the compounds of formulae III and Ra-SO 2 -NHR and a base. Heating may be carried out at a temperature of at least 50 0 C, or, in some embodiments, at least 60 0 C. The temperature may be as high as the reflux temperature of the solvent.
• Reacting a compound of formula R fa SO 2 -N(R)CH 2 CH(OH)CH 2 N(R)SO 2 R ft with a compound of formula Hal-(CH 2 ) v -Si(Y') w (Y)3_ w can be carried out in the presence of base in a suitable solvent (e.g., tetrahydrofuran, methanol, or diglyme).
• a suitable solvent e.g., tetrahydrofuran, methanol, or diglyme.
• the reaction can be carried out at an elevated temperature (e.g., the reflux temperature of the solvent).
• the bases described above for the reaction of compounds of formulae III and Ra-SO 2 -NHR can be used.
• Reacting a compound of formula R fa SO 2 -N(R)CH 2 CH(OH)CH 2 N(R)SO 2 R ft with a compound of formula OCN-(CH 2 ) v -Si(Y') w (Y)3_ w may be carried out at room temperature in a suitable solvent (e.g., tetrahydrofuran) in the presence of a catalyst (e.g., dibutyltin dilaurate).
• a suitable solvent e.g., tetrahydrofuran
• a catalyst e.g., dibutyltin dilaurate
• Compositions of the present invention may include at least one organic solvent.
• the organic solvent or blend of organic solvents used must be capable of dissolving at least one silane of formula I and, optionally, a mixture of at least one silane with at least one compound of formula II.
• Suitable organic solvents include aliphatic alcohols, (e.g., methanol, ethanol, isopropanol); ketones (e.g., acetone or methyl ethyl ketone); esters (e.g., ethyl acetate, methylformate); ethers (e.g., diethyl ether or dipropyleneglycol monomethylether (DPM)); and mixtures thereof.
• aliphatic alcohols e.g., methanol, ethanol, isopropanol
• ketones e.g., acetone or methyl ethyl ketone
• esters e.g., ethyl acetate, methylformate
• ethers e.g., diethyl ether or dipropyleneglycol monomethylether (DPM)
• DPM dipropyleneglycol monomethylether
• the combination may be a mixture or a condensation product obtainable after a substantially complete condensation reaction of the at least one fluorochemical silane and the at least one non-fluorinated compound of formula II.
• substantially complete condensation reaction is meant that the reaction is either complete or at least 80% of the hydrolyzable groups in the mixture have disappeared, in some embodiments at least 90%.
• the present invention provides a composition comprising a condensation product obtainable after a partial condensation reaction of the at least one fluorochemical silane and the at least one non-fluorinated compound.
• a condensation product obtainable after a partial condensation reaction of the at least one fluorochemical silane and the at least one non-fluorinated compound.
• a partial condensate means that at least 20%, in some embodiments, at least
• At least 50% of the hydrolyzable groups are still available for further condensation reaction.
• Representative examples of compounds of formula II include tetramethoxysilane, tetraethoxysilane (TEOS), methyltriethoxysilane (MTEOS), dimethyldiethoxysilane
• the combination or condensation product of silanes of formula I and compounds of formula II may also contain organic solvents as defined above in an amount sufficient to dissolve the compounds.
• the weight ratio of compounds of formulae I and II is in a range from about 100:0 to about 1 :99, in some embodiments, in a range from about 50:50 to about 10:90.
• the combination of at least one silane of formula I and at least one compound of formula II is a condensation reaction product
• the reaction product is obtainable by reacting the components and, optionally, an additional crosslinking agent.
• the reaction product is a partial condensate or alternatively a substantial complete condensation product is formed.
• the polycondensation reaction is conveniently carried out by mixing the starting components in an organic solvent preferably at room temperature, in the presence of sufficient water to effect hydrolysis of the hydrolyzable groups.
• the amount of water can be in a range from 0.1% to 20 % by weight of the total composition, or even in a range from 1% to 10% by weight.
• an organic or inorganic acid or base catalyst should preferably be used.
• Organic acid catalysts include acetic acid, citric acid, formic acid, triflic acid, and perfluorobutyric acid.
• inorganic acids include sulfuric acid and hydrochloric acid.
• useful base catalysts include sodium hydroxide, potassium hydroxide, sodium fluoride, potassium fluoride and triethylamine.
• the acid or base catalyst will generally be used in amounts in a range from about 0.01% to 10%, in some embodiments in a range from 0.05% to 5% by weight of the total composition.
• composition of the present invention comprising the components of formulae I and II and optional additional crosslinking agent, and/or the partial or complete polycondensation products thereof, is generally applied to the substrate in amounts sufficient to produce a coating that is water and oil repellent.
• This coating can be extremely thin, (e.g., 1 to 50 molecular layers, though in practice a useful coating may be thicker).
• Suitable substrates that can be treated in a particularly effective way with the fluorochemical composition, comprising the fluorochemical condensate mixture, of this invention include substrates having a hard surface that preferably has groups capable of reacting with the fluorinated condensate.
• Particularly preferred substrates include ceramics and glass.
• Various articles can be effectively treated with the fluorochemical composition of the present invention to provide a water and oil repellent coating thereon. Examples include ceramic tiles, bathtubs or toilets, glass shower panels, construction glass, various parts of a vehicle (e.g., mirror or windscreen), and ceramics, (e.g., glass, crystalline ceramic, and enamel pottery materials).
• Treatment of the substrates results in rendering the treated surfaces less retentive of soil and more readily cleanable due to the oil and water repellent nature of the treated surfaces. These desirable properties are maintained despite extended exposure or use and repeated cleanings because of the high degree of durability of the treated surface as can be obtained through the compositions of this invention. Additionally, the treated surfaces have a good durability against exposure to UV light, (i.e., the repellency properties do not substantially degrade upon exposure to UV light).
• the fluorochemical composition preferably in the form of a solvent composition as disclosed above, is applied to the substrate.
• the amount of fluorochemical composition to be coated on the substrate will generally be that amount sufficient to produce a coating which is water and oil repellent, such a coating having at 20 0 C a contact angle with distilled water of at least 80°, and a contact angle with n-hexadecane of at least 40°, measured after drying and curing of the coating.
• such a coating has at 20 0 C a contact angle with distilled water of at least 85°, and a contact angle with n-hexadecane of at least 45°, measured after drying and curing of the coating.
• the substrate should be clean prior to applying the compositions of the invention so as to obtain optimum characteristics, particularly durability. That is, the surface of the substrate to be coated should be substantially free of organic contamination prior to coating. Cleaning techniques depend on the type of substrate and include, for example, a solvent washing step with an organic solvent, such as acetone or ethanol.
• compositions for application to a substrate are prepared by diluting a concentrate comprising a solution of at least 25% by weight of solids in an organic solvent, by adding to the concentrate an organic solvent or mixture of solvents.
• a coating method for application of the fluorochemical composition includes spray application.
• a substrate to be coated can typically be contacted with the treating composition at room temperature (typically, about 20 0 C to about 25°C).
• the mixture can be applied to substrates that are preheated at a temperature of, for example, in a range from 60 0 C to 150 0 C.
• a temperature of, for example, in a range from 60 0 C to 150 0 C.
• the treated substrate can be dried and cured at ambient or elevated temperature, (e.g., at 40 0 C to 300 0 C) and for a time sufficient to dry and cure.
• the coating composition may be cured by irradiation (e.g., by means of UV- irradiators, a laser, etc.) in a manner known to one of skill in the art in the presence of an initiator.
• the process may also require a polishing step to remove excess material.
• a portion (20 g) was purified by vacuum distillation [boiling point (bp) 192 "C/0.5 mmHg (67 Pa)] to provide 16.7 g of [CF 3 SO 2 N(CH 3 )CH 2 ] 2 CHOH.
• Part B In a 125-mL bottle, a solution of [CF 3 SO 2 N(CH 3 )CH 2 ] 2 CHOH from Part A (7.6 g,
• the solution from Part B (1.0 g) was diluted with ethanol (18 g), concentrated hydrochloric acid (1.0 g of 37%), and isopropanol (5 g) to give a 1% solution.
• the test solution was coated on a glass slide about one week after it was prepared according to the procedure described above.
• the advancing and receding contact angles were measured as described above.
• the advancing and receding contact angles versus water were 84° and 40°, respectively.
• the advancing and receding contact angles versus n-hexadecane were 44° and 9°, respectively.
• the residue was purified by one-plate distillation [bp 90 "C/0.06 mmHg (8 Pa)] to provide 155.2 g of N-methyl-N-(oxiran-2- ylmethyl)perfluorobutane-l -sulfonamide, which was 98% pure by GLC.
• the solution from Part C (2.0 g) was diluted with ethanol (38 g), concentrated hydrochloric acid (1.0 g of 37%), and isopropanol (1.8 g) to give a 1% solution.
• the test solution was coated on a glass slide within two days after it was prepared according to the procedure described above.
• the advancing and receding contact angles were measured as described above.
• the advancing and receding contact angles versus water were 97° and 40°, respectively.
• the advancing and receding contact angles versus n-hexadecane were 60° and 37°, respectively.

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