Computer simulation and detailed mean-field approximation applied to adsorption on nanoparticles

Adsorption thermodynamics of interacting particles adsorbed on icosahedral and truncated octahedral nanoparticles was studied by a detailed mean-field approximation and Monte Carlo simulations. The nanoparticle is tackled as a multivariate surface, where different types of adsorption sites occur according to coordination with nearest neighbors. In addition, lateral couplings between the adsorbed particles are considered. The analysis covers a wide range of interactions, extending from physical to strong chemical bonds, and different sizes and shapes of nanoparticles.

Figure 1

Schematic representation of an icosahedral nanoparticle. (a) The adsorption sites at the facets, edges, and vertices are represented by black, red, and blue spheres, respectively. Energy assignation to each type of site according to the different approximations: (b) DMFA3, (c) DMFA4, and (d) DMFA6.

Figure 2

Adsorption isotherms for case I as described in the text, for $n=7$ and $w_{AB}/k_{B}T=0.0$, $-$1.0, $-$5.0, $-$10.0, and $-$20.0. Symbols, continuous lines, and dashed lines represent GCMC simulations, DMFA4, and DMFA3 data, respectively.

Figure 3

Adsorption isotherms for case II as described in the text, for $n=7$ and $w_{BB}/k_{B}T=0.0$, 1.50, 3.00, 4.50, and 5.25. Symbols, continuous lines, and dashed lines represent GCMC simulations, DMFA4, and DMFA3 data, respectively.

Figure 4

Adsorption isotherms for case III as described in the text, $n=7$ and $w_{AB}/k_{B}T=0.0$, $-$5.0, $-$10.0, and $-$15.0. Symbols, continuous lines, and dashed lines represent GCMC simulations, DMFA4, and DMFA3 data, respectively.

Figure 5

Adsorption isotherms for different sizes of the seed NP ($n$). The values of the interactions were set to reproduce the two plateaus ($w_{AB}/k_{B}T=-15.0$ and $w_{BB}/k_{B}T=-2.0$). Insets (a) and (b) show a zoom of the third and first plateau, respectively. Symbols, continuous lines, and dashed lines represent GCMC simulations, DMFA4, and DMFA6 data, respectively.

Figure 6

Integral error (in $k_{B}T$ units) as defined in Eq. (21) for cases II [(a)] and III [(b)]. Results in inset (c) correspond to $w_{AB}/k_{B}T=-15.0$, $w_{BB}/k_{B}T=-2.0$, and different sizes of the seed NP ($n$).

Figure 7

Adsorption isotherms for a TO nanoparticle with $n=4$. (a) Case I, $w_{AB}/k_{B}T=0.0$, $-$1.0, $-$2.0, $-$5.0, and $-$10.0. (b) Case II, $w_{BB}/k_{B}T=1.0$, 3.0, and 5.0. Symbols and continuous lines represent GCMC simulations and DMFA5 data, respectively.

Figure 8

Schematic representation of a truncated octahedron. (a) Types of adsorption sites. Blue and red spheres denote adsorption sites at (100) and (111) facets, respectively. Black and green spheres denote edge sites between (111)-(111) and (111)-(100) facets, respectively. (b) Energy assignation to each type of site according to the DMFA5 approximation described in the text.