“…1-5 When the redox-active sites are electrochemically reversible [6][7][8][9] and are bound to a polymer chain, an electron self-exchange reaction between the neighboring sites effects the redox mediation through the polymer layer, which requires that electroneutralization by electrolyte ions is accomplished throughout the layer to maintain the electroactivity. [10][11][12] Aliphatic, or non-conjugated polymers populated with organic robust radicals such as nitroxide, [13][14][15][16][17][18][19][20][21][22][23] nitronyl nitroxide, 24,25 spirobisnitroxide 26 and galvinoxyl 27,28 have been found to be the typical examples, and their ideal redox-mediating properties 29 are different from those of conventional redox polymers such as poly (vinylferrocene), [30][31][32][33] which has been dominated by the 'break-in effect' of the electroneutralizing ions to give rise to limited charge capacity and hysteresis during the charging/discharging process. The ideal, that is, diffusion-limited behavior by the so-called 'radical polymers' 34,35 has led to reversible and exhaustive charging with the simple redox diffusive process formulated by the finite diffusion equation 36 for the layer with a discrete thickness on a current collector, 37 and by the equation for semi-infinite diffusion 36 that applies to wholly gelated cells with the radical polymer.…”