^{1}, P. M. Pasinetti

^{1,a)}, F. Nieto

^{1}and A. J. Ramirez-Pastor

^{1}

### Abstract

In the present paper, the adsorption thermodynamics of a lattice-gas model which mimics a nanoporous environment is studied by considering nonadditive interactions between the adsorbed particles. It is assumed that the energy linking a certain atom with any of its nearest neighbors strongly depends on the state of occupancy in the first coordination sphere of such an adatom. By means of Monte Carlo(MC) simulations in the grand canonical ensemble,adsorption isotherms and differential heats of adsorption were calculated. Their striking behaviors were analyzed and discussed in terms of the low temperature phases formed in the system. Finally, the results obtained from MC simulations were compared with the corresponding ones from Bragg–Williams approximation.

This work was supported in part by CONICET (Argentina) under Project No. PIP 112-200801-01332, Universidad Nacional de San Luis (Argentina) under Project No. 322000, and the National Agency of Scientific and Technological Promotion (Argentina) under Project No. 33328 PICT 2005. All calculations were carried out using the BACO2 parallel cluster (composed by 60 PCs each with a 3.0 GHz Pentium-4 processor and 60 PCs each with a 2.4 GHz Core 2 Quad processor) located at Instituto de Física Aplicada (INFAP), CONICET, Universidad Nacional de San Luis, San Luis, Argentina.

I. INTRODUCTION

II. MODEL AND BASIC DEFINITIONS

III. BRAGG–WILLIAMS APROXIMATION

IV. RESULTS

V. CONCLUSIONS

### Key Topics

- Adsorption
- 41.0
- Monte Carlo methods
- 17.0
- Carbon nanotubes
- 9.0
- Adsorbates
- 7.0
- Phase transitions
- 7.0

## Figures

Schematic representation of the system. Black and white circles correspond to occupied and empty sites, respectively. Dashed (dotted) thick lines represent longitudinal (transverse) lateral interactions.

Schematic representation of the system. Black and white circles correspond to occupied and empty sites, respectively. Dashed (dotted) thick lines represent longitudinal (transverse) lateral interactions.

Adsorption isotherms for *P* _{ T } = 1.0 and *P* _{ L } = 0.7 and several values of temperature.

Adsorption isotherms for *P* _{ T } = 1.0 and *P* _{ L } = 0.7 and several values of temperature.

(a) Adsorption isotherms for *w*/*k* _{ B } *T* = 10.0, *P* _{ T } = 1.0, and several values of *P* _{ L } as indicated. (b) Energy per site, *u*, vs coverage for the same values of *P* _{ L } and *P* _{ T }. The solid lines are a guide to the eyes. The inset shows the corresponding curves of the differential heat of adsorption, *q* _{ d }.

(a) Adsorption isotherms for *w*/*k* _{ B } *T* = 10.0, *P* _{ T } = 1.0, and several values of *P* _{ L } as indicated. (b) Energy per site, *u*, vs coverage for the same values of *P* _{ L } and *P* _{ T }. The solid lines are a guide to the eyes. The inset shows the corresponding curves of the differential heat of adsorption, *q* _{ d }.

Schematic representations of the adlayer for *P* _{ T } = 1 and *P* _{ L } < 1. (a) At coverage *θ* = 1/3, the ordered phase is formed in each plane and successive planes are formed avoiding longitudinal interactions. (b) At coverage *θ* = 2/3, the * ordered phase is formed in each plane. The dotted segments indicate the “dimerlike” structure along the channels.

Schematic representations of the adlayer for *P* _{ T } = 1 and *P* _{ L } < 1. (a) At coverage *θ* = 1/3, the ordered phase is formed in each plane and successive planes are formed avoiding longitudinal interactions. (b) At coverage *θ* = 2/3, the * ordered phase is formed in each plane. The dotted segments indicate the “dimerlike” structure along the channels.

(a) Adsorption isotherms for *w*/*k* _{ B } *T* = 10.0, *P* _{ L } = 1.0, and several values of *P* _{ T } as indicated. Inset (i) shows the dependence of on *P* _{ T }. In inset (ii), the adsorption isotherm at the lowest temperature considered here, *w*/*k* _{ B } *T* = 20.0, is shown. It is possible to identify the different plateaus at *θ* = 1/3, 2/5, 2/3, 3/4, and 6/7. (b) Energy per site vs coverage. The curves correspond to the same cases showed in part (a) (the solid lines are a guide to the eyes). The inset shows the differential heat of adsorption, *q* _{ d }.

(a) Adsorption isotherms for *w*/*k* _{ B } *T* = 10.0, *P* _{ L } = 1.0, and several values of *P* _{ T } as indicated. Inset (i) shows the dependence of on *P* _{ T }. In inset (ii), the adsorption isotherm at the lowest temperature considered here, *w*/*k* _{ B } *T* = 20.0, is shown. It is possible to identify the different plateaus at *θ* = 1/3, 2/5, 2/3, 3/4, and 6/7. (b) Energy per site vs coverage. The curves correspond to the same cases showed in part (a) (the solid lines are a guide to the eyes). The inset shows the differential heat of adsorption, *q* _{ d }.

Typical snapshots of a transverse plane showing the various low temperature ordered structures for *P* _{ T } = 1 and *P* _{ L } = 0.2. (a) *θ* = 1/3, (b) *θ* = 2/5, (c) *θ* = 1/2, (d) *θ* = 2/3, (e) *θ* = 3/4, and (f) *θ* = 6/7. The longitudinal order (if any) is explained in the text.

Typical snapshots of a transverse plane showing the various low temperature ordered structures for *P* _{ T } = 1 and *P* _{ L } = 0.2. (a) *θ* = 1/3, (b) *θ* = 2/5, (c) *θ* = 1/2, (d) *θ* = 2/3, (e) *θ* = 3/4, and (f) *θ* = 6/7. The longitudinal order (if any) is explained in the text.

(a) Adsorption isotherms for *w*/*k* _{ B } *T* = 10.0, *P* _{ L } = 0.4, and several values of *P* _{ T } as indicated. In the inset, the case of *w*/*k* _{ B } *T* = 10.0, *P* _{ T } = 0.2, and different values of *P* _{ L } as indicated is shown. (b) Energy per site, *u*, vs coverage for the same values of nonadditivity as in part (a). The solid lines are a guide to the eyes. The inset shows the differential heat of adsorption, *q* _{ d }.

(a) Adsorption isotherms for *w*/*k* _{ B } *T* = 10.0, *P* _{ L } = 0.4, and several values of *P* _{ T } as indicated. In the inset, the case of *w*/*k* _{ B } *T* = 10.0, *P* _{ T } = 0.2, and different values of *P* _{ L } as indicated is shown. (b) Energy per site, *u*, vs coverage for the same values of nonadditivity as in part (a). The solid lines are a guide to the eyes. The inset shows the differential heat of adsorption, *q* _{ d }.

Comparison between the results from MC (symbols) and BWA (lines). Adsorption isotherms at *w*/*k* _{ B } *T* = 10.0 for (a) Case I and (b) Case II.

Comparison between the results from MC (symbols) and BWA (lines). Adsorption isotherms at *w*/*k* _{ B } *T* = 10.0 for (a) Case I and (b) Case II.

Absolute error (in *k* _{ B } *T* units), *E* _{ R }, vs surface coverage for the adsorption isotherms at *w*/*k* _{ B } *T* = 10.0 corresponding to (a) Case I and (b) Case II. The insets show the integral errors, *E* _{ I }, vs the corresponding nonadditive parameter.

Absolute error (in *k* _{ B } *T* units), *E* _{ R }, vs surface coverage for the adsorption isotherms at *w*/*k* _{ B } *T* = 10.0 corresponding to (a) Case I and (b) Case II. The insets show the integral errors, *E* _{ I }, vs the corresponding nonadditive parameter.

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