NOVELTY - Producing an alkaline single ion conductor with high conductivity comprises (a) providing a hydrocarbon oligomer or polymer having immobilized acidic substituent groups including a sulfonic acid group, sulfamide group, a phosphonic acid group or a carboxy group, in its alkaline ion form where at least a part of the acidic protons of the substituent groups have been exchanged against alkali cations, and (b) solvating the hydrocarbon oligomer or polymer of step (a) in an aprotic polar solvent for a sufficient time to effect an solvent uptake of at least 5 wt.% and to obtain a solvated product.    USE - The method is useful for producing an alkaline single ion conductor, which is: a sodium or lithium single ion conductor; and used in an electric or electrochemical storage device including a lithium or sodium battery, a fuel cell or a supercapacitor (all claimed).    ADVANTAGE - The method provides the alkaline single ion conductor with high conductivity.    DETAILED DESCRIPTION - Producing an alkaline single ion conductor with high conductivity comprises (a) providing a hydrocarbon oligomer or polymer having immobilized acidic substituent groups including a sulfonic acid group, sulfamide group, a phosphonic acid group or a carboxy group, in its alkaline ion form where at least a part of the acidic protons of the substituent groups have been exchanged against alkali cations, and (b) solvating the hydrocarbon oligomer or polymer of step (a) in an aprotic polar solvent for a sufficient time to effect an solvent uptake of at least 5 wt.% and to obtain a solvated product, where the molar ratio of solvent/alkaline cation is 1:1-10:1, preferably 3:1-200:1, and the solvated product has a conductivity of at least 10-5 S/cm at 24 degrees C. INDEPENDENT CLAIMS are also included for:    (1) an alkaline single ion conductor obtainable by the method, comprising a hydrocarbon oligomer or polymer having immobilized acidic substituent groups, in its alkaline ion form, where the hydrocarbon oligomer or polymer is solvated in an aprotic polar solvent and has a molar ratio of solvent/alkali cation of 1:1-10:1, preferably 3:1-20:1, and a conductivity of at least 10-5 S/cm at 24 degrees C in the aprotic solvent; and    (2) use of a polyarylene compound comprising at least one structural elements of formula (-(-X1-Ar1(W1A1)n-Y1-)m-) (Ia), as an alkaline single ion conductor, preferably a lithium single ion conductor.    m = 1-1000000;    X1, Y1 = bridging group (optionally have electron-acceptor group or electron-donor group);    Ar1 = 5-18 aromatic or heteroaromatic ring system (optionally additionally substituted);    W1 = anion of acidic substituent group (optionally additionally substituted), where the anion of acidic substituent group includes sulfonic acid, sulfamide, phosphonic acid or carboxy;    A1 = alkali cation; and    n = 0.1-4.