As was shown previously, the binding free energy of DS -adsorbing to the ACWI is roughly a factor of two more attractive than the free energy of DS -adsorbing to the AWI. In order to investigate this effect in more detail, we repeated our free energy calculations after removing the Na + counter ion, the results for which are shown in panels a and d of Fig. . Removal of the Na + ions simplifies the analysis avoiding having to deal with the ion diffusion, a slow degree of freedom which can potentially lead to statistical issues in resolving the average potential energies that are central to our analysis. Furthermore, for the low DS -to C 12 E 6 ratio considered here, the position of the Na + counter ion is entropy dominated and specific binding between the ion and DS -will have a minimal effect. Indeed, differences in the free energy profiles for the systems with and without Na + (shown in the SI) are very similar.