Rational design of conductive carbon hosts for high energy density lithium sulfur batteries requires an understanding of the fundamental limitations to insulating active material loading. In this work, we investigate the electrochemistry of lithium sulfide films ranging in thickness from 30 to 3500 nm. We show that films thicker than approximately 40 nm cannot be charged at local charge densities above 1 mu A cm(-2), and by implication, the maximum useful pore diameter is near 60 nm in a practical cathode. "Activation" overpotentials for Li2S are identified in thicker films, resulting from polysulfide generation, but are shown not to improve the fundamental areal charge limitations. We develop a model for filling of conductive pores with active material to rationally design composites based on local charge density. For low-electrolyte applications, the importance of matching micropore volume to sulfide loading and cycling rate is emphasized.