Binder, method of preparing the binder, and anode and lithium battery including the binder

1. A binder comprising:

a third polymer comprising a cross-linked product of a first polymer and a second polymer,

wherein the first polymer comprises a first functional group and is at least one selected from a polyamic acid and a polyimide,

wherein the second polymer comprises a second functional group and is water-soluble, and

wherein the first polymer and the second polymer are cross-linked by an ester bond formed by a reaction of the first functional group and the second functional group,

wherein the polyamic acid is represented by Formula 1 or Formula 2:

wherein, in Formulae 1 and 2,

M is an alkali metal;

Ar 1 and Ar 3 are each independently an aromatic group selected from a substituted or unsubstituted tetravalent C6-C24 arylene group and a substituted or unsubstituted tetravalent C4-C24 heteroarylene group, wherein the aromatic group is one aromatic ring, a ring comprising at least two aromatic rings fused to each other, or a ring comprising at least two aromatic rings linked by a single bond, —O—, —S—, —C(═O)—, —S(═O) 2 —, —Si(Ra)(Rb)-, a C1-C10 alkylene group substituted or unsubstituted with a halogen, or —C(═O)—NH—, wherein Ra and Rb are each independently a substituted or unsubstituted C1-C10 alkyl group;

Ar 2 and Ar 4 are each independently an aromatic group selected from a substituted or unsubstituted divalent C6-C24 arylene group and a substituted or unsubstituted divalent C4-C24 heteroarylene group, wherein the aromatic group is one aromatic ring, a ring having at least two aromatic rings fused to each other, or a ring comprising at least two aromatic rings linked by a single bond, —O—, —S—, —C(═O)—, —S(═O) 2 —, —Si(Ra)(Rb)-, a C1-C10 alkylene group substituted or unsubstituted with a halogen, or —C(═O)—NH—, wherein Ra and Rb are each independently a substituted or unsubstituted C1-C10 alkyl group;

X 1 is —C(═O)OH, —OH, —C(═O)—NH 2 , or —C(═O)H; and

n and m are each a molar ratio of a repeating unit, where 0<n<1, 0<m<1, and n+m=1.

2. The binder of claim 1 , wherein the first functional group and the second functional group are each independently at least one selected from a carboxyl group, a hydroxyl group, an amide group, and an aldehyde group.

3. The binder of claim 1 , wherein the first polymer further comprises an alkali metal.

4. The binder of claim 3 , wherein an amount of the alkali metal in the first polymer is in a range of about 0.2 equivalents to about 1.0 equivalents at an equivalent ratio with respect to a carboxyl group or an amide group.

5. The binder of claim 1 , wherein the polyamic acid is represented by Formula 3 or Formula 4:

wherein, in Formulae 3 and 4,

M is lithium or sodium;

R 1 , R 2 , R 3 , R 4 , R 5 , R 6 , R 7 , R 8 , R 9 , R 10 , R 11 , R 12 , R 13 , R 14 , R 15 , and R 16 are each independently a hydrogen, a halogen, —C(═O)OH, —OH, —C(═O)—NH 2 , —C(═O)H, a C1-C10 alkyl group substituted or unsubstituted with a halogen, a C6-C20 aryl group substituted or unsubstituted with a halogen, or a C2-C20 heteroaryl group substituted or unsubstituted with a halogen;

Y 1 is a single bond, —O—, —S—, —C(═O)—, —S(═O) 2 —, —Si(Ra)(Rb)-, a C1-C10 alkylene group substituted or unsubstituted with a halogen, or —C(═O)—NH—, wherein where Ra and Rb are each independently a substituted or unsubstituted C1-C10 alkyl group, and R is a C1-C10 alkyl group;

at least one selected from R 3 , R 4 , R 5 , and R 6 is —C(═O)OH, —OH, —C(═O)—NH 2 , or —C(═O)H; and

n and m are each a molar ratio of a repeating unit, where 0<n<1, 0<m<1, and n+m=1.

6. The binder of claim 1 , wherein the polyimide is represented by Formula 5 or Formula 6:

wherein, in Formulae 5 and 6,

M is an alkali metal;

Ar 1 and Ar 2 are each independently an aromatic group selected from a substituted or unsubstituted tetravalent C6-C24 arylene group and a substituted or unsubstituted tetravalent C4-C24 heteroarylene group, wherein the aromatic group is one aromatic ring, a group comprising at least two aromatic rings fused to each other, or a ring comprising at least two aromatic rings linked by a single bond, —O—, —S—, —C(═O)—, —S(═O) 2 —, —Si(Ra)(Rb)-, a C1-C10 alkylene group substituted or unsubstituted with a halogen, or —C(═O)—NH—, where Ra and Rb are each independently a substituted or unsubstituted C1-C10 alkyl group;

Ar 2 and Ar 4 are each independently an aromatic group selected from a substituted or unsubstituted divalent C6-C24 arylene group and a substituted or unsubstituted divalent C4-C24 heteroarylene group, wherein the aromatic group is one aromatic ring, a ring comprising at least two aromatic rings fused to each other, or a ring comprising at least two aromatic rings linked by a single bond, —O—, —S—, —C(═O)—, —S(═O) 2 —, —Si(Ra)(Rb)-, a C1-C10 alkylene group substituted or unsubstituted with a halogen, or —C(═O)—NH—, where Ra and Rb are each independently a substituted or unsubstituted C1-C10 alkyl group;

X 1 is —C(═O)OH, —OH, —C(═O)—NH 2 , or —C(═O)H; and

n and m are each a molar ratio of a repeating unit, where 0<n<1, 0<m<1, and n+m=1.

7. The binder of claim 1 , wherein the polyimide is represented by Formula 7 or Formula 8:

wherein, in Formulae 7 and 8,

M is lithium or sodium;

R 1 , R 2 , R 3 , R 4 , R 5 , R 6 , R 7 , R 8 , R 9 , R 10 , R 11 , R 12 , R 13 , R 14 , R 15 , and R 16 are each independently a hydrogen, a halogen, —C(═O)OH, —OH, —C(═O)—NH 2 , —C(═O)H, a C1-C10 alkyl group substituted or unsubstituted with a halogen, a C6-C20 aryl group substituted or unsubstituted with a halogen, or a C2-C20 heteroaryl group substituted or unsubstituted with a halogen;

Y 1 is a single bond, —O—, —S—, —C(═O)—, —S(═O) 2 —, —Si(Ra)(Rb)-, a C1-C10 alkylene group substituted or unsubstituted with a halogen, or —C(═O)—NH—, where Ra and Rb are each independently a substituted or unsubstituted C1-C10 alkyl group;

at least one selected from R 3 , R 4 , R 5 , and R 6 is —C(═O)OH, —OH, —C(═O)—NH 2 , or —C(═O)H; and

n and m are each a molar ratio of a repeating unit, where 0<n<1, 0<m<1, and n+m=1.

8. The binder of claim 1 , wherein the polyamic acid is represented by Formula 9 or Formula 10, and the polyimide is represented by Formula 11 or Formula 12:

wherein, in Formulae 9 to 12,

n and m are each a molar ratio of a repeating unit, where 0<n<1, 0<m<1, and n+m=1.

9. The binder of claim 8 , wherein 0<n<0.5, 0.5<m<1, and n+m=1.

10. The binder of claim 1 , wherein the second polymer is a polymerization reaction product or its hydrolysate of at least one monomer selected from a vinyl monomer, an acetate monomer, an alcohol monomer, a (meth)acryl monomer, an acrylamide monomer, and a methacrylamide monomer.

11. The binder of claim 1 , wherein the second polymer is a polymerization reaction product or its hydrolysate of at least one monomer selected from vinyl acetate, vinyl alcohol, butyl (meth)acrylate, 2-hydroxyethyl (meth)acrylate, 2-hydroxypropyl (meth)acrylate, 4-hydroxybutyl (meth)acrylate, 6-hydroxyhexyl (meth)acrylate, 8-hydroxyoctyl (meth)acrylate, 2-hydroxyethyleneglycol (meth)acrylate, 2-hydroxypropyleneglycol (meth)acrylate, acrylic acid, methacrylic acid, 2-(meth)acryloyloxy acetic acid, 3-(meth)acryloyloxy propyl acid, 4-(meth)acryloyloxy butyric acid, itaconic acid, maleic acid, 2-isocyanatoethyl (meth)acrylate, 3-isocyanatopropyl (meth)acrylate, 4-isocyanatobutyl (meth)acrylate, (meth)acrylamide, ethylene di(meth)acrylate, diethyleneglycol (meth)acrylate, triethyleneglycol di(meth)acrylate, trimethylenepropane tri(meth)acrylate, trimethylenepropane triacrylate, 1,3-butanediol (meth)acrylate, 1,6-hexanediol di(meth)acrylate, allyl acrylate, and N-vinyl caprolactam.

12. The binder of claim 1 , wherein the second polymer is a polyvinyl alcohol.

13. The binder of claim 12 , wherein a saponification degree of the polyvinyl alcohol is in a range of about 60% to about 99%.

14. The binder of claim 12 , wherein a weight average molecular weight of the polyvinyl alcohol is in a range of about 10,000 Daltons to about 500,000 Daltons.

15. The binder of claim 1 , wherein a weight ratio of the first polymer and the second polymer is in a range of about 1:99 to about 50:50.

16. The binder of claim 1 , wherein the cross-linking is at a temperature of about 160° C. or greater.

17. The binder of claim 1 , wherein an indentation modulus of the third polymer is greater than each of a modulus of the first polymer and a modulus of the second polymer.

18. The binder of claim 1 , wherein an indentation hardness of the third polymer is greater than each of an indentation hardness of the first polymer and an indentation hardness of the second polymer.

19. The binder of claim 1 , wherein the third polymer has a network structure comprising the cross-linked product of the first polymer and the second polymer.

20. The binder of claim 1 , wherein a weight average molecular weight of the third polymer is in a range of about 10,000 Daltons to about 1,000,000 Daltons.

21. The binder of claim 1 , wherein the third polymer is represented by one of Formulae 13 to 16:

wherein, in Formulae 13 to 16,

n and m are each a molar ratio of a repeating unit, where 0<n<1, 0<m<1, and n+m=1; and

p is a polymerization degree which is in a range of about 250 to about 12,500.

22. The binder of claim 1 , further comprising a fourth polymer selected from hydroxyethyl cellulose ether, dextran, carboxymethylcellulose, alginate, cellulose nanofiber, xanthan gum, and guar gum.

23. A method of preparing a binder according to claim 1 , the method comprising

preparing a third composition by mixing together a first composition comprising a non-aqueous solvent and a first polymer and a second composition comprising a second polymer and water,

wherein the first polymer comprises a first functional group and is selected from at least one of a polyamic acid and a polyimide, and

the second polymer comprises a second functional group and is water-soluble; and

heating the third composition at a temperature of about 160° C. or greater to prepare a third polymer.

24. The method of claim 23 , wherein the first polymer further comprises an alkali metal.

25. A binder comprising a cross-linked product of a first polymer and second polymer, wherein the first polymer is at least one of a polyamic acid or a polyimide, each of which comprises an alkali metal and a first functional group, and the second polymer comprises a second functional group and is water-soluble,

wherein the first polymer and the second polymer are cross-linked by an ester bond formed by a reaction of the first functional group and the second functional group, and

the cross-linked product comprises a weight ratio of the first polymer to the second polymer in a range of about 1:99 to about 50:50.

26. The binder of claim 25 , wherein the second polymer is a polymerization reaction product or its hydrolysate of at least one monomer selected from vinyl acetate, vinyl alcohol, butyl (meth)acrylate, 2-hydroxyethyl (meth)acrylate, 2-hydroxypropyl (meth)acrylate, 4-hydroxybutyl (meth)acrylate, 6-hydroxyhexyl (meth)acrylate, 8-hydroxyoctyl (meth)acrylate, 2-hydroxyethyleneglycol (meth)acrylate, 2-hydroxypropyleneglycol (meth)acrylate, acrylic acid, methacrylic acid, 2-(meth)acryloyloxy acetic acid, 3-(meth)acryloyloxy propyl acid, 4-(meth)acryloyloxy butyric acid, itaconic acid, maleic acid, 2-isocyanatoethyl (meth)acrylate, 3-isocyanatopropyl (meth)acrylate, 4-isocyanatobutyl (meth)acrylate, (meth)acrylamide, ethylene di(meth)acrylate, diethyleneglycol (meth)acrylate, triethyleneglycol di(meth)acrylate, trimethylenepropane tri(meth)acrylate, trimethylenepropane triacrylate, 1,3-butanediol (meth)acrylate, 1,6-hexanediol di(meth)acrylate, allyl acrylate, or N-vinyl caprolactam.

27. The binder of claim 25 , wherein the polyamic acid is represented by Formula 2

wherein, in Formula 2,

M is an alkali metal;

Ar 1 and Ar 3 are independently an aromatic group selected from a substituted or unsubstituted tetravalent C6-C24 arylene group and a substituted or unsubstituted tetravalent C4-C24 heteroarylene group, wherein the aromatic group is one aromatic ring, a ring comprising at least two aromatic rings fused to each other, or a ring comprising at least two aromatic rings linked by a single bond, —O—, —S—, —C(═O)—, —S(═O) 2 —, —Si(Ra)(Rb)-, a C1-C10 alkylene group substituted or unsubstituted with a halogen, or —C(═O)—NH—, wherein Ra and Rb are each independently a substituted or unsubstituted C1-C10 alkyl group;

Ar 2 and Ar 4 are independently an aromatic group selected from a substituted or unsubstituted divalent C6-C24 arylene group and a substituted or unsubstituted divalent C4-C24 heteroarylene group, wherein the aromatic group is one aromatic ring, a ring having at least two aromatic rings fused to each other, or a ring comprising at least two aromatic rings linked by a single bond, —O—, —S—, —C(═O)—, —S(═O) 2 —, —Si(Ra)(Rb)-, a C1-C10 alkylene group substituted or unsubstituted with a halogen, or —C(═O)—NH—, wherein Ra and Rb are each independently a substituted or unsubstituted C1-C10 alkyl group;

X 1 is —C(═O)OH, —OH, —C(═O)—NH 2 , or —C(═O)H; and

n and m are each a molar ratio of a repeating unit, where 0<n<1, 0<m<1, and n+m=1; and

the polyimide is represented by Formula 6:

wherein, in Formula 6,

M is an alkali metal;

Ar 1 and Ar 3 are each independently an aromatic group selected from a substituted or unsubstituted tetravalent C6-C24 arylene group and a substituted or unsubstituted tetravalent C4-C24 heteroarylene group, wherein the aromatic group is one aromatic ring, a group comprising at least two aromatic rings fused to each other, or a ring comprising at least two aromatic rings linked by a single bond, —O—, —S—, —C(═O)—, —S(═O) 2 —, —Si(Ra)(Rb)-, a C1-C10 alkylene group substituted or unsubstituted with a halogen, or —C(═O)—NH—, where Ra and Rb are each independently a substituted or unsubstituted C1-C10 alkyl group;

Ar 2 and Ar 4 are each independently an aromatic group selected from a substituted or unsubstituted divalent C6-C24 arylene group and a substituted or unsubstituted divalent C4-C24 heteroarylene group, wherein the aromatic group is one aromatic ring, a ring comprising at least two aromatic rings fused to each other, or a ring comprising at least two aromatic rings linked by a single bond, —O—, —S—, —C(═O)—, —S(═O) 2 —, —Si(Ra)(Rb)-, a C1-C10 alkylene group substituted or unsubstituted with a halogen, or —C(═O)—NH—, where Ra and Rb are each independently a substituted or unsubstituted C1-C10 alkyl group;

X 1 is —C(═O)OH, —OH, —C(═O)—NH 2 , or —C(═O)H; and

n and m are each a molar ratio of a repeating unit, where 0<n<1, 0<m<1, and n+m=1.