NOVELTY - A polymer electrolyte (4) is used in a lithium ion secondary battery (1) having an anode (2) containing an easily graphitized carbon material having a face distance (d002) of (002) plane of 3.4-3.7 Angstrom as measured by X-ray wide-angle diffraction method, and a size of 10-500 Angstrom with respect to microcrystal in c-axial direction. The polymer electrolyte comprises (in %mass) a polymer (5-60) of polymerizable boron compound, a high-molecular compound (39-94), and trimethyl borate (1-40).    USE - Polymer electrolyte is used in manufacture of secondary batteries (both claimed) e.g. lithium ion secondary batteries. Uses include but are not limited to mobile telephones, notebook personal computers, electric vehicles, electric tools, digital cameras, video cameras, portable audio players, portable liquid-crystal televisions, electronic organizers with communication function, handheld game machine devices, hybrid motor vehicles, and electric power storage systems.    ADVANTAGE - The polymer electrolyte improves the discharge capacity and cycle characteristics of secondary batteries.    DETAILED DESCRIPTION - A polymer electrolyte is used in a lithium ion secondary battery having an anode containing an easily graphitized carbon material having a face distance (d002) of (002) plane of 3.4-3.7 Angstrom as measured by X-ray wide-angle diffraction method, and a size of 10-500 Angstrom with respect to microcrystal in c-axial direction. The polymer electrolyte comprises (in %mass) a polymer (5-60) of polymerizable boron compound, a high-molecular compound (39-94), and trimethyl borate (1-40). The polymerizable boron compound is of formula: Z1-(-OA1-)h-O-B(-O-(-A1O-)i-Z2)(-O-(-A1O-)j-Z3), and the high-molecular compound is of formula: R1O-(A2O)k-R2.    Z1-Z3=(meth)acryloyl;    A1O=2-6C oxyalkylene;    h,i,j=1-10;    R1,R2=1-10C hydrocarbyl;    A2O=2-6C oxyalkylene;and    k=4-20.    INDEPENDENT CLAIMS are included for the following:    (1) secondary battery provided with the polymer electrolyte arranged between a cathode (3) and an anode; and    (2) manufacture of secondary battery, which involves curing a composition containing the polymerizable boron compound, high-molecular compound, and trimethyl borate to form a polymer electrolyte, and clamping the polymer electrolyte between the anode and cathode.    DESCRIPTION OF DRAWING(S) - The drawing shows a schematic cross-sectional view of the secondary battery.    Secondary battery (1)    Anode (2)    Cathode (3)    Polymer electrolyte (4)    Anode collector (5)