Monte Carlo simulation of the electrical differential capacitance of a double electrical layer formed at the heterogeneous metal oxide/electrolyte interface

Monte Carlo modeling of ion adsorption at the energetically heterogeneous metal oxide/electrolyte interface: Micro- and macroscopic correlations between adsorption energies

“…The localized adsorption is usually described using the Ising-type model (called lattice gas); in our case this is a multistate Ising-type model (Potts model), whose Hamiltonian function is given by [24] …”

“…x j is the molar fraction of j -species and U i means the change in the system energy for H(k → l) [24]. In the calculation of U A , we have taken into account the fact that the internal energy (H) decreases by H(0 → H) and increases by…”

“…It is believed that the quasi-Gaussian distribution function described most of the adsorption systems [14,15]. In our instance, we can write the following expression for the quasi-Gaussian Γ distribution functions [20][21][22][23][24],…”

“…First of all, GCMC seems to be the most popular in the molecular modeling of the adsorption [19], and what is more, they have been successfully used to study e.d.l. formed at the energetically heterogeneous metal oxide/electrolyte interface [20][21][22][23][24]. We restrict our modeling to a 1-pK model in combination with the BSM model; however, the extension to the 2-pK or MUSIC model can be easily obtained.…”

Modeling the surface charge evolution of spherical nanoparticles by considering dielectric discontinuity effects at the solid/electrolyte solution interface

“…The acceptance criterion is sensitive to the value of the energy variation, E, during the protonation and deprotonation processes as defined in Table 1. Simulations are performed in the grand canonical ensemble, which has been successfully used to study energetically heterogeneous metal oxide/electrolyte interfaces [24,25].…”