“…Despite the fact that clear nucleation events have not been observed in our simulations, the transition from an unordered to an ordered assembly on the surface can be described using the nucleation-elongation model for 2D self-assemblies at liquid/solid interface, developed by Matsuda et al − (Figure c). Our modified version of this model (eqs and ) assumes, that the assembly process can be described by two equilibrium constants: (a) a nucleation constant K n between an adsorbent molecule in solution or on the surface in an unordered state (denoted A 1 unord ) and a free surface adsorption site ( S ) on the one hand and an ordered state ( A 1 ord ) on the other hand (a molecule is in an ordered state when it has two close neighbors with the same orientation, by which we mean it can be parallel or antiparallel; see Supporting Information for details), which acts as a nucleus on the surface; and (b) an elongation constant K e between an adsorbent molecule in an unordered state and ordered clusters of any size ( A n ord ) adsorbed on the surface (note that, in the original model of Matsuda et al, this equilibrium is only between monomers in solvent and clusters on the surface): Using the steady-state approximation, an expression for the surface coverage of ordered molecules, θ, as a function of bulk concentration of adsorbent, c t , can be derived (a detailed derivation can be found in the Supporting Information): Here σ is the degree of cooperativity defined as the ratio between the two equilibrium constants for nucleation and elongation, σ = K n / K e , and α is the maximum concentration of ordered molecules on the graphite surface.…”