where X is the bulk mole fraction of monomer surfactant (assumed here to be the total concentration of surfactant without distinguishing between monomers, dimers, or micelles), Γ is the surface coverage, a is the hard-disk area, and ∆µ 0 ≡ µ σ,0 -µ b,0 is the free energy of adsorption at infinite dilution, i.e. with only one molecule. And B is the coefficient associated to attractive pairwise interactions between surfactant molecules, which won't be taken into account in our computational results. ∆µ 0 is calculated from the transfer free energy or difference in free energy between the bulk region and the adsorbed state. If the interface region is broad and not well defined, then the minimum of the PMF can be used directly for ∆µ 0 , considering that the surfactants are located at the Gibbs dividing surface, as proposed by Sresht et al. Here, however, we follow the approach used by Jaishankar et al., where the surfactants are not considered to be in a 2D plane above the hematite surface, but inside a 3D interface, where the different adsorbed states are taken into account. In this case, the expression for ∆µ 0 reads: