  The steady state of ions diffusion in polymer electrolytes at arbitrary
applied voltage is analyzed in the framework of the Nernst-Planck-Poisson
equation (NPP). The exact solution of the set of equations is found without the
assumption of low ions concentration. The solution is independent of the
kinetic properties of the system. At constant voltage there is a master curve
for concentration in terms of the initial concentration. Enhancing the voltage
causes an increase of the ion concentration gradient and consequently the
applicability of the NPP is violated for high voltages. The analytical finding
is estimated by using experimental data from recent measurements (P. Kohn et al
Phys. Rev. Left. 99, 086104 (2007)). As the result we find an upper bound for
the validity of the NPP. Above this voltage higher order gradient terms become
relevant.
