Percolation on patchwise heterogeneous surfaces under equilibrium conditions

Percolation of interacting particles on heterogeneous surfaces

“…The case of ω/k B T = 0 corresponds to non-interacting particles and θ c is independent of E/k B T . This particular case has been discussed in previous work [23]. Like in the ordered case, attractive values of ω/k B T produce minor values of θ c and vice versa.…”

“…Later, the influence of surface heterogeneities on the percolation features of non-interacting particles adsorbed at equilibrium on such surfaces was presented in Ref. [23]. The present contribution goes a step further, by investigating the mutual influence of surface heterogeneities and adsorbate-adsorbate interactions on the percolation properties of the adsorbed phase.…”

“…4 shows θ c as a function of E/k B T for four values of ω/k B T in the case of ordered sites. The case with ω/k B T = 0 corresponds to non-interacting particles and has been studied in previous work [23]. It is possible to observe that attractive interactions (ω/k B T = −1) between particles result in a curve below the non-interacting case (ω/k B T = 0).…”

“…The value of the exponent ν is calculated also by finite-size scaling for each case (see Refs. [15,16,23,30,31] for more details). The intersection of the lines with the y-axes represents the value of θ c for L = ∞.…”

“…This value can be understood in terms of effective neighbors (see Refs. [23,33]). A brief explanation would be that for θ = 0.5, a perfect chessboard structure is obtained.…”