  Steady-state solutions of the Poisson-Nernst-Planck model are studied in the
asymptotic limit of large, but finite domains. By using asymptotic matching for
integrals, we derive an approximate solution for the steady-state equation with
exponentially small error with respect to the domain size. The approximation is
used to quantify the extent of finite domain effects over the full parameter
space. Surprisingly, already for small applied voltages (several thermal
voltages), we found that finite domain effects are significant even for large
domains (on the scale of hundreds of Debye lengths). Namely, the solution near
the boundary, i.e., the boundary layer (electric double layer) structure, is
sensitive to the domain size even when the domain size is many times larger
than the characteristic width of the boundary layer. We focus on this
intermediate regime between confined domains and `essentially infinite'
domains, and study how the domain size effects the solution properties. We
conclude by providing an outlook to higher dimensions with applications to ion
channels and porous electrodes.
