Composite membrane for lithium battery, cathode for lithium battery, and lithium battery comprising the composite membrane

A composite membrane for a lithium battery, the composite membrane comprising:

• a random copolymer of a first repeating unit represented by Formula 1 and a second repeating unit represented by Formula 2
• Formula 1
• wherein, in Formula 1, Ar1 is a substituted or unsubstituted C6-C30 arylene group or a substituted or unsubstituted C6-C30 heteroarylene group,
• R1, R2, and R3 are each independently hydrogen, an unsubstituted or substituted C1-C20 alkyl group, an unsubstituted or substituted C6-C20 aryl group, or an unsubstituted or substituted C3-C30 heteroaryl group,
• A is a chemical bond, an unsubstituted or substituted C1-C30 alkylene group, an unsubstituted or substituted C6-C30 arylene group, an unsubstituted or substituted C3-C30 heteroarylene group, an unsubstituted or substituted C4-C30 cycloalkylene group, or an unsubstituted or substituted C3-C30 heterocycloalkylene group,
• is a 3-membered to 31-membered ring system comprising 2 to 30 carbon atoms,
• X is S, N, N(R), or P(R′), wherein R and R′ are each independently hydrogen, an unsubstituted or substituted C1-C30 alkyl group, an unsubstituted or substituted C1-C30 heteroalkyl group, an unsubstituted or substituted C1-C30 alkoxy group, an unsubstituted or substituted C6-C30 aryl group, an unsubstituted or substituted C7-C30 arylalkyl group, an unsubstituted or substituted C6-C30 aryloxy group, an unsubstituted or substituted C3-C30 heteroaryl group, an unsubstituted or substituted C4-C30 heteroarylalkyl group, an unsubstituted or substituted C3-C30 cycloalkyl group, an unsubstituted or substituted C2-C30 alkenyl group, an unsubstituted or substituted C3-C30 heteroaryloxy group, an unsubstituted or substituted C3-C30 heterocycloalkyl group, or an unsubstituted or substituted C3-C30 alkynyl group, and
• Y− is an anion,
• wherein, in Formula 2, R4, R5, and R6 are each independently hydrogen, an unsubstituted or substituted C1-C20 alkyl group, an unsubstituted or substituted C6-C20 aryl group, or an unsubstituted or substituted C3-C30 heteroaryl group,
• each R7 is independently hydrogen, an unsubstituted or substituted C1-C20 alkyl group, or unsubstituted or substituted C6-C20 aryl group, and
• a is an integer of 1 to 10, and
• in Formulae 1 and 2, m and n are mole fractions of the first repeating unit represented by Formula 1 and the second repeating unit represented by Formula 2, respectively, wherein the sum of m and n is 1, and m and n are each independently greater than 0 and less than 1.