α-Olefin polymer and process for production thereof

An α-olefin polymer of one or more kinds of α-olefins each having 20 to 40 carbon atoms, wherein the polymer meets the following requirements (1) to (4):

• (1) the a-olefin polymer has a molecular weight distribution (Mw/Mn) determined from its weight average molecular weight (Mw) and number average molecular weight (Mn) in terms of polystyrene measured by gel permeation chromatography (GPC) of 2 or less, and has a weight average molecular weight (Mw) of 5,000 or less;
• (2) measurement of a melting point (Tm) of the α-olefin polymer with a differential scanning calorimeter (DSC) shows one melting peak, a melting heat absorption (ΔH) calculated from an area of the melting peak is 20 J/g or more, and the melting peak has a half value width of 10° C. or less;
• (3) when the weight average molecular weight (Mw) falls within a range of 1,000 to 5,000 and an average number of carbon atoms (Cn) of the α-olefins falls within a range of 20 to 40, the weight average molecular weight (Mw), the average number of carbon atoms (Cn), and the melting point (Tm) measured with the differential scanning calorimeter (DSC) satisfy the following relationship (a):
• 0.0025×Mw+(Cn×3.3812−29.5)≦Tm≦0.0025×Mw+((Cn+1)×3.3812−29.5) (a);
• and
• (4) a stereoregularity index [M2] derived from a chain of the α-olefins each having 20 to 40 carbon atoms is 20% by mol or more.