Thermodynamics of the one-dimensional parallel Kawasaki model: Exact solution and mean-field approximations

The adsorption isotherm for the recently proposed parallel Kawasaki (PK) lattice-gas model [Phys. Rev. E 88, 062144 (2013)] is calculated exactly in one dimension. To do so, a third-order difference equation for the grand-canonical partition function is derived and solved analytically. In the present version of the PK model, the attraction and repulsion effects between two neighboring particles and between a particle and a neighboring empty site are ruled, respectively, by the dimensionless parameters $\varphi$ and $\theta$. We discuss the inflections induced in the isotherms by situations of high repulsion, the role played by finite lattice sizes in the emergence of substeps, and the adequacy of the two most widely used mean-field approximations in lattice gases, namely, the Bragg-Williams and the Bethe-Peierls approximations.

Figure 1

Adsorption isotherms ($T=300$ K) for the one-dimensional PK lattice with null adsorption energy $\varepsilon$ when (a) $\theta =\varphi$, and when (b) the particle-particle attraction parameter $\varphi$ is varied with $\theta =1$.

Figure 2

Adsorption isotherms for the one-dimensional PK lattice with null adsorption energy $\varepsilon$ for several values of the parameters $\theta$ and $\varphi$. Temperature is fixed at 300 K.

Figure 3

Size effect on finite PK lattices with null adsorption energy $\varepsilon$. Temperature is fixed at 300 K.

Figure 4

Exact adsorption isotherms (solid lines) for the infinite PK model with $\theta =1$, $T=300$ K, and several values of $\varphi$, together with the curve resulting from both the Bragg-Williams (BW, dashed lines) and the Bethe-Peierls (BP, dotted lines) approximation.