The lowc onductivity of Na + electrolytes in solid polymer electrolytes (SPEs) curtails the development of Na polymer batteries.I nt his study,N aClO 4 (3-24 wt %, 90-9:1 O:Na) is dissolved in statistical copolymers of ethylene oxide (EO) and propylene oxide (PO) (0-20 mol %). Remarkably, the conductivity of these SPEs increases as the concentration of Na + decreases,t hus departing from the usual Nernstian behavior.U sing ac ombination of calorimetric measurements and molecular dynamic simulations,this unusual phenomenon is attributed to the presence of physical cross-links generated by Na + .Asaresult, polymers containing alow salt concentration (3 wt %) displayadrastically enhanced ionic conductivity (up to 0.2 10 À4 Scm À1 at 25 8 8C), thus paving the way for the design of all-solid-state PEO-based sodium batteries operational at room temperature.