Thermoplastic elastomer composition, use thereof, method for producing same, ethylene/α-olefin/unconjugated polyene copolymer and use thereof

A thermoplastic elastomer composition obtained by dynamically cross-linking a mixture containing

• a crystalline olefin polymer (A),
• an ethylene.α-olefin (C4-C20).non-conjugated polyene copolymer (1B) satisfying the following requirements (1), (2), and (4), and
• a phenol resin-based cross-linking agent (C);
• wherein the crystalline olefin polymer (A) is a crystalline propylene polymer, and
• wherein the α-olefin of the ethylene.α-olefin.non-conjugated polyene copolymer (1B) is 1-butene, and the non-conjugated polyene of the ethylene.α-olefin.non-conjugated polyene copolymer (1B) is at least one selected from the group consisting of 5-ethylidene-2-norbornene and 5-vinyl-2-norbornene;
• (1) a B value represented by the following equation (i) is 1.20 to 1.80:
• B value=([EX]+2[Y])/[2×[E]×([X]+[Y])] (i),
• wherein [E], [X], and [Y] represent a mole fraction of structural units derived from the ethylene, a mole fraction of structural units derived from the C4-C20 α-olefin, and a mole fraction of structural units derived from the non-conjugated polyene respectively, and [EX] represents a diad chain fraction of the structural units derived from the ethylene—the structural units derived from the C4-C20 α-olefin;
• and
• (2) in the copolymer (1B), a molar ratio of the structural units derived from the ethylene to the structural units derived from the α-olefin (C4-C20) is 40/60 to 70/30;
• and
• (4) a content of the structural units derived from the non-conjugated polyene is 0.5 to 3.0 mol %, relative to a total of the structural units derived from the ethylene, the structural units derived from the α-olefin (C4-C20), and the structural units derived from the non-conjugated polyene as 100 mol %.