Percolation of defective dimers irreversibly deposited on honeycomb and triangular lattices

Abstract

The percolation problem of irreversibly deposited dimers on honeycomb and triangular lattices is studied. A dimer is composed of two segments, and occupies two adjacent adsorption sites. Each segment can be either a conductive segment (segment type A) or a nonconductive segment (segment type B). Three types of dimers are considered: AA, BB, and AB. The connectivity analysis is carried out by accounting only for the conductive segments (segments type A), whereas the B segments occupy a site in the lattice but are not taken into account in the percolation study. Different cases were investigated, according to the types of dimers involved in the process. By means of numerical simulations and finite-size scaling techniques, the complete phase diagram separating the percolating from the nonpercolating regions was determined for each considered lattice. The present results are compared with the previous study of deposition of defective dimers on square lattices.

The Role of Dimer Formation in the Nucleation of Superlattice Transformations and Its Impact on Disorder

“…Ondry et al reported that NC dimer formation is tolerant to a degree of atomic lattice misalignment, resulting in dislocation defects in the bridge, , which corroborates our simulation results. As the superlattice transformation and attachment proceeds, the number of dimers and trimers in the superlattice increases, similar to observations in 2D polymerization and percolation studies. , …”

“…As the superlattice transformation and attachment proceeds, the number of dimers and trimers in the superlattice increases, similar to observations in 2D polymerization and percolation studies. 19,47 All NCs with identifiable in-plane orientation shown in Figure 6b are preferentially oriented along the same direction, indicating that dimer formation does not disrupt the overall atomic lattice alignment of NCs in the superlattice. This provides experimental evidence that NCs are, indeed, prealigned at the early stage of the superlattice transformation, in agreement with previously reported results.…”

SuSMoST: Surface Science Modeling and Simulation Toolkit

“…There are lattice models of various degrees of abstraction: Langmuir adsorption model, hard disks, [6,7] dimers, [8][9][10][11] k-mers, [12,13] binary gasses, [14][15][16][17][18] molecules of various symmetry, [19][20][21][22][23] tricarboxylic [24][25][26][27] acids, porphyrins, [28] monoatomic adsobates, [29,30] and so forth. [31,32] In spite of numerous successful applications of lattice models, this kind of simulation is still not a daily tool for surface science researchers.…”

“…Therefore, the lattice with the set of possible site states constitutes the model of the adsorption system. There are lattice models of various degrees of abstraction: Langmuir adsorption model, hard disks, [ 6,7 ] dimers, [ 8–11 ] k ‐mers, [ 12,13 ] binary gasses, [ 14–18 ] molecules of various symmetry, [ 19–23 ] tricarboxylic [ 24–27 ] acids, porphyrins, [ 28 ] monoatomic adsobates, [ 29,30 ] and so forth. [ 31,32 ]…”

SuSMoST: Surface Science Modeling and Simulation Toolkit

“…Therefore, the lattice with the set of possible site states constitute the model of the adsorption system. There are lattice models of various degrees of abstraction: Langmuir adsorption model, hard disks, 4,5 dimers, [6][7][8][9] k -mers, 10,11 binary gasses, [12][13][14][15][16] molecules of various symmetry, 17-20 tricarboxylic [21][22][23][24] acids, porphyrins, 25 etc. 26,27 In spite of numerous successful applications of lattice models, this kind of simulations is still not a daily tool for surface science researchers.…”