The aggregate structure of sodium dodecyl sulfate (SDS) adsorbed at the graphite-water interface has been studied with the aid of molecular dynamics (MD) simulations. As expected, our results show that adsorbed SDS yields hemi-cylindrical micelles. The hemi-cylindrical aggregates in our simulations closely resemble all structural and morphological details provided by previous solution atomic force microscopy (AFM) experiments. More interestingly, our data indicate that SDS head groups do not provide a complete shield to the hydrophobic tails. Instead, we found regions in which the hydrophobic tails are exposed to the aqueous solution. By conducting a parametric study for SDS-like nonionic surfactants we show that electrostatic interactions between SDS head groups and counterions are responsible for the unexpected result. Our interpretation is corroborated by density profiles, analysis of the coordination states, and mean square displacement data for both the adsorbed SDS surfactants and the counterions in solution. Counterion condensation appears to be a physical phenomenon that could be exploited to direct the assembly of advanced nanostructured materials.