Extracting the equation of state of lattice gases from random sequential adsorption simulations by means of the Gibbs adsorption isotherm

An alternative approach for deriving the equation of state for a two-dimensional lattice gas is proposed, based on arguments similar to those used in the derivation of the Langmuir-Szyszkowski equation of state for localized adsorption. The relationship between surface coverage and excluded area is first extracted from random sequential adsorption simulations incorporating surface diffusion (RSAD). The adsorption isotherm is then obtained using kinetic arguments, and the Gibbs equation gives the relation between surface pressure and coverage. Provided surface diffusion is fast enough to ensure internal equilibrium within the monolayer during the RSAD simulations, the resulting equations of state are very close to the most accurate equivalents obtained by cumbersome thermodynamic methods. An internal test of the accuracy of the method is obtained by noting that adsorption RSAD simulations starting from an empty lattice and desorption simulations starting from a full lattice provide convergent upper and lower bounds on the surface pressure.

Figure 1

(a) Triangular lattice with nearest neighbor exclusion. (The center of the hexagonal molecule is represented by a circle, the nearest neighbors by a star.) (b) Equivalent model in a square geometry. Arrows indicate possible displacement of particles.

Figure 2

(a) Triangular lattice surface pressure by the adsorption method: effect of diffusion on the equation of state for lattice size of $d=99$. The parameter $D$ is the relative frequency of diffusion to insertion attempts. (b) The inset expands the phase transition region where sensitivity to diffusion appears.

Figure 3

Triangular lattice surface pressure by the adsorption method: (a) effect of lattice size on equation of state for surface diffusion of $D=1$, and (b) the inset expands the phase transition region where sensitivity to lattice size appears.

Figure 4

Triangular lattice surface pressure by the desorption method: (a) effect of diffusion on the equation of state for lattice size of $d=99$, and (b) the inset expands the phase transition region where sensitivity to diffusion appears.

Figure 5

Triangular lattice surface pressure by the desorption method: (a) effect of lattice size on the equation of state for surface diffusion of $D=1$, and (b) the inset expands the phase transition region where sensitivity to lattice size appears.

Figure 6

(a) Blocking function and (b) the inset shows a magnified view of the region bounded by dark blue dashed circle.

Figure 7

(a) Comparison between our EOS where $d=99$ and $D=4$ with those of Baxter [14] and Runnels and Combs [17]) for hard core molecules on a triangular lattice. (b)The inset shows a magnified view of the region bounded by dark blue dashed circle.

Figure 8

Analysis of the phase transition region where $d=99$ and $D=4$.