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Plasma-boundaries floating in an ionized gas are usually negatively charged. They accumulate electrons more efficiently than ions leading to the formation of a quasi-stationary electron film at the boundaries. We propose to interpret the build-up of surface charges at inert plasma boundaries, where other surface modifications, for instance, implantation of particles and reconstruction or destruction of the surface due to impact of high energy particles can be neglected, as a physisorption process in front of the wall. The electron sticking coefficient se and the electron desorption time τe, which play an important role in determining the quasi-stationary surface charge, and about which little is empirically and theoretically known, can then be calculated from microscopic models for the electron-wall interaction. Irrespective of the sophistication of the models, the static part of the electron-wall interaction determines the binding energy of the electron, whereas inelastic processes at the wall determine se and τe. As an illustration, we calculate se and τe for a metal, using the simplest model in which the static part of the electron-metal interaction is approximated by the classical image potential. Assuming electrons from the plasma to loose (gain) energy at the surface by creating (annihilating) electron-hole pairs in the metal, which is treated as a jellium half-space with an infinitely high workfunction, we obtain se≈10-4 and τe≈10-2 s. The product seτe≈10-6 s has the order of magnitude expected from our earlier results for the charge of dust particles in a plasma but individually se is unexpectedly small and τe is somewhat large. The former is a consequence of the small matrix elements occurring in the simple model while the latter is due to the large binding energy of the electron. More sophisticated theoretical investigations, but also experimental support, are clearly needed because if se is indeed as small as our exploratory calculation suggests, it would have severe consequences for the understanding of the formation of surface charges at plasma boundaries. To identify what we believe are key issues of the electronic microphysics at inert plasma boundaries and to inspire other groups to join us on our journey is the purpose of this colloquial presentation. [ABSTRACT FROM AUTHOR]