Rubber composition, crosslinked rubber composition, pneumatic tire, and method for producing isobutylene polymer

A method for producing an isobutylene polymer having a structural unit represented by the following formula (1) and a structural unit represented by the following formula (2), comprising a step of copolymerizing isobutylene and a vinyl ether compound represented by the following formula (7):

• CH2═CH—O—(X)n—Y (7)
• wherein X represents a divalent group, Y represents a substituted or unsubstituted alicyclic group having an unsaturated bond, and n represents 0 or 1,
• in a reaction liquid to which a Lewis acid catalyst, a protic complexing agent and an aprotic complexing agent are added,
• wherein in the step, when a total molar number of the Lewis acid catalyst, a total molar number of the protic complexing agent and a total molar number of the aprotic complexing agent, added to the reaction liquid, are defined as A, B1 and B2, respectively, and a total molar number of the vinyl ether compound subjected to the copolymerization is defined as D, A/(B1+B2+D) is 1 to 10, A/B1 is 5 to 400 and B2/B1 is 0 to 50:
• wherein, X represents a divalent group, Y represents a substituted or unsubstituted alicyclic group having an unsaturated bond, and n represents 0 or 1.