NOVELTY - Polymers comprise a single bond that can freely rotate in the molecule so that salt exhibits cationic conductivity by the action of exchanging cations coordinated on the anionic residue.    USE - The polymers are used for or as solid ionic conductive polymer electrolytes for or in batteries, preferably lithium batteries (claimed). They can be used as an electronic conductive material for connecting unit cells of a fuel cell system, or capacitors.    ADVANTAGE - The solid electrolyte that exhibits an ionic conductivity mechanism based on single bond rotation shows higher ionic conductivity.    DETAILED DESCRIPTION - Polymers of formula (1) comprise a single bond that can freely rotate in the molecule so that salt exhibits cationic conductivity by the action of exchanging cations coordinated on the anionic residue.    Rp = residue of a polymer of a compound having a polymerizable unsaturated bond    Q = organic residue of a valence of n+1 and connected directly or through another group to Rp by a single bond    Mk+ = cation of valence k    Z = organic functional group capable of forming an ionic bond with the cation Mk+ or an organic functional group having a coordination capability with Mk+    m, n and k = 1 or more    INDEPENDENT CLAIMS are also included for:    (1) intermediates of the polymers of formula (1a);    (2) a method for preparing the polymers comprising polymerization of an intermediate, preferably in an organic solvent; and    (3) a method for preparing a polymer sheet electrode in intimate contact with the anode and/or cathode of or for a lithium battery comprising polymerizing a monomer in solution in an organic solvent comprising a lithium salt dissolved on the anode and/or cathode; casting a solution in which the polymer and the lithium salt are dissolved in an organic solvent on the anode and/or cathode; and removing the organic solvent.    R = residue of a compound having a polymerizable unsaturated bond    Q, Z, Mk+, m, n, and k = as above    DESCRIPTION OF DRAWING(S) - The figure is a graph that shows the relationship between the ionic conductivity of the polymer electrolyte and the temperature.