Polymer, composite positive active material including the same, and lithium secondary battery including electrode including the positive active material

A polymer comprising:

• a repeating unit represented by at least one of Formula 1a or Formula 1b
• wherein, in Formulae 1a and 1b,
• CY1 is a group represented by at least one of Formula 1-2 or Formula 1-4,
• CY2 is a group represented by Formula 1-3,
• L1 and L2 are each independently a single bond, a substituted or unsubstituted C1-C20 alkylene group, a substituted or unsubstituted C2-C20 alkenylene group, or a substituted or unsubstituted C2-C20 alkynylene group, and
• a1 and a2 are each independently an integer from 1 to 5, and two or more L1 are the same or different from one another when a1 is 2 or greater, and two or more L2 are the same or different from each other when a2 is 2 or greater,
• wherein, in Formulae 1-2 and 1-3,
• X and Y are each independently O or S,
• R1, R2, and R11 to R14 are each independently hydrogen, deuterium, —F, —Cl, —Br, —I, a hydroxyl group, a cyano group, a nitro group, an amino group, an amidino group, a hydrazine group, a hydrazone group, a carboxylic acid group or a salt thereof, a sulfonic acid group or a salt thereof, a phosphoric acid group or a salt thereof, a substituted or unsubstituted C1-C60 alkyl group, a substituted or unsubstituted C2-C60 alkenyl group, a substituted or unsubstituted C2-C60 alkynyl group, a substituted or unsubstituted C1-C60 alkoxy group, a substituted or unsubstituted C3-C10 cycloalkyl group, a substituted or unsubstituted C1-C10 heterocycloalkyl group, a substituted or unsubstituted C3-C10 cycloalkenyl group, a substituted or unsubstituted C1-C10 heterocycloalkenyl group, a substituted or unsubstituted C6-C60 aryl group, a substituted or unsubstituted C6-C60 aryloxy group, a substituted or unsubstituted C6-C60 arylthio group, a substituted or unsubstituted C1-C60 heteroaryl group, a substituted or unsubstituted monovalent non-aromatic condensed polycyclic group, or a substituted or unsubstituted monovalent non-aromatic condensed heteropolycyclic group,
• b1 and b2 are each independently an integer from 1 to 3, and two or more R1 are the same or different from one another when b1 is 2 or greater, and two or more R2 are the same or different from one another when b2 is 2 or greater, and
• in Formula 1-4,
• R21 and R22 are each independently hydrogen, deuterium, —F, —Cl, —Br, —I, a hydroxyl group, a cyano group, a nitro group, an amino group, an amidino group, a hydrazine group, a hydrazone group, a carboxylic acid group or a salt thereof, a sulfonic acid group or a salt thereof, a phosphoric acid group or a salt thereof, a substituted or unsubstituted C1-C60 alkyl group, a substituted or unsubstituted C2-C60 alkenyl group, a substituted or unsubstituted C2-C60 alkynyl group, a substituted or unsubstituted C1-C60 alkoxy group, a substituted or unsubstituted C3-C10 cycloalkyl group, a substituted or unsubstituted C1-C10 heterocycloalkyl group, a substituted or unsubstituted C3-C10 cycloalkenyl group, a substituted or unsubstituted C1-C10 heterocycloalkenyl group, a substituted or unsubstituted C6-C60 aryl group, a substituted or unsubstituted C6-C60 aryloxy group, a substituted or unsubstituted C6-C60 arylthio group, a substituted or unsubstituted C1-C60 heteroaryl group, a substituted or unsubstituted monovalent non-aromatic condensed polycyclic group, or a substituted or unsubstituted monovalent non-aromatic condensed heteropolycyclic group,
• b21 and b22 are each independently an integer from 0 to 3, and two or more R21 are the same or different from one another when b21 is 2 or greater, and two or more R22 are the same or different from one another when b22 is 2 or greater,
• Z1 and Z2 are each independently an electron withdrawing group,
• C1 and c2 are each independently an integer of 1 to 4,
• the sum of b21and c1 is 4,
• the sum of b22 and c2 is 4,
• is a binding site to L1 in Formulae 1a and 1b, and
• is a binding site to L2 in Formula 1b.