Generalized lattice-gas model for adsorption of functional organic molecules in terms of pair directional interactions

A generalized lattice-gas model that takes into account the directional character of pair interactions between the lattice sites is proposed. It is demonstrated that the proposed model can be successfully used to deeply understand the self-assembly process in adsorption monolayers of functional organic molecules driven by specified directional interactions between such molecules (e.g., hydrogen bonding). To illustrate the idea, representative cases of the general model with different numbers of identical functional groups in the chemical structure of the adsorbed molecule are investigated with Monte Carlo and the transfer-matrix methods. The model reveals that the phase behavior of the adsorption systems considered can be characterized as a hierarchical self-assembly process. It is predicted that in real adsorption systems of this type, the energy of hydrogen bonding sufficiently depends on the mutual orientation of the adsorbed molecules.

Figure 1

Lattice model of adsorption of the cross-shaped molecules with two identical functional groups in the trans position: (a) possible states of the lattice site and (b) possible interaction energies between the molecules adsorbed on nearest-neighbor sites.

Figure 2

Ordered structures found in the ground state of the adsorption layer of the cross-shaped molecules with two identical functional groups in the trans position on the square lattice.

Figure 3

Ground-state phase diagram of the adsorption layer of the cross-shaped molecules with two functional groups in the trans position on the square lattice in coordinates of $\mu /|w_1|$ and $w_2/\left|w_1\right|$.

Figure 4

Adsorption isotherms and entropy dependence on the surface coverage at $w_1/RT=7.5$ and $M=6$.

Figure 5

Patterns of the lattice (24×24) obtained at (a) $\mu /RT=-4$ and (b) $\mu /RT=2$.

Figure 6

Lattice model of adsorption of the cross-shaped molecules with two identical functional groups in the cis position: (a) possible states of the lattice site and (b) possible interactions between the molecules adsorbed on nearest-neighbor sites.

Figure 7

Ordered structures appearing in the ground state of the adsorption layer of the cross-shaped molecules with two functional groups in the cis position on the square lattice. All structures are thermodynamically stable only at $w_{1.1}<w_{1.2}$.

Figure 8

Ground-state phase diagram of the adsorption layer of the cross-shaped molecules with two functional groups in the cis position on the square lattice in coordinates of $\mu /|w_1|$ and $w_2/\left|w_1\right|$ at (a) $w_{1.1}<w_{1.2}$ and (b) $w_{1.1}>w_{1.2}$.

Figure 9

Ordered phases formed in the ground state of the model at $w_{1.1}>w_{1.2}$.

Figure 10

Adsorption isotherms and entropy dependence on the surface coverage computed with the transfer-matrix method at $w_{1.1}/RT=-7.5,w_{1.2}/w_{1.1}=0.5$, and different values of $w_2/\left|w_{1.1}\right|$.

Figure 11

Lattice patterns obtained with the Monte Carlo method at $w_{1.1}/RT=-7.5,w_{1.2}/w_{1.1}=0.5$, and $w_2/\left|w_{1.1}\right|=1$: (a) $\mu /RT=-3$, (b) $\mu /RT=4.2$, and (c) $\mu /RT=16$.

Figure 12

(a) Adsorption isotherms and (b) entropy dependence on the surface coverage calculated with the transfer-matrix method at $w_{1.2}/RT=-7.5,w_{1.1}/w_{1.2}=0.5$, and different values of the $w_2/\left|w_{1.2}\right|$ parameter.

Figure 13

Lattice patterns obtained in the Monte Carlo simulation at $w_{1.2}/RT=-7.5, w_{1.1}/w_{1.2}=0.5$, and $w_2/\left|w_{1.2}\right|=0.4$: (a) $\mu /RT=0$ and (b) $\mu /RT=6$.

Figure 14

Model of adsorption of triangular molecules with three identical functional groups on a triangular lattice: (a) possible states of the adsorbed molecule and (b) possible pair interactions between the molecules adsorbed on nearest-neighbor sites.

Figure 15

Ordered structures of the adsorption overlayer comprising the molecules with triangular shape and three FGs on a triangular lattice. Black triangles denote stable (fixed) molecules and gray triangles the molecule that rotates in the two-dimensional pore due to the energetic equivalence of all the positions. A rhombus highlights the cell units.