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Adsorption of binary mixtures on two-dimensional surfaces: theory and Monte Carlo simulations

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Abstract

The adsorption of binary mixtures on square lattices is studied by combining theoretical modeling and Monte Carlo (MC) simulations in grand canonical ensemble. The adsorption thermodynamics is analyzed through the total and partial isotherms. Two theoretical models have been used in the present study: (i) the first, which we called cluster approximation (CA), is based on exact calculations of configurations on finite cells. An efficient algorithm allows us to calculate the detailed structure of the configuration space for \(m = l \times l \) cells; and (ii) the second is a generalization of the classical quasi-chemical approximation (QCA) in which the adsorbate is a binary mixture of species \(a\) and \(b\). Adsorbate–adsorbate lateral interactions are incorporated in the context of the two mentioned approximations. Results from CA and QCA are compared with MC simulations. Close agreement between simulated and theoretical data supports the validity of the theoretical models to describe the adsorption of mixed gases on two-dimensional surfaces.

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References

  • Babarao, R., Hu, Z.Q., Jiang, J.W., Chempath, S., Sandler, S.I.: Storage and separation of CO2 and CH4 in silicalite, C168 schwarzite, and IRMOF-1: a comparative study from Monte Carlo simulation. Langmuir 23, 659 (2007)

    Article  CAS  Google Scholar 

  • Belardinelli, R., Manzi, S., Ramirez-Pastor, A.J., Pereyra, V.D.: Study of the adsorption of interacting dimers on square lattices by using a cluster-exact approximation. Surf. Sci. 540, 207 (2003)

    Article  CAS  Google Scholar 

  • Berker, A.N., Ostlund, S., Putnam, S.A.: Renormalization-group treatment of a Potts lattice gas for krypton adsorbed onto graphite. Phys. Rev. B 17, 3650 (1978)

    Article  CAS  Google Scholar 

  • Binder, K., Landau, D.P.: Phase diagrams and critical behavior in Ising square lattices with nearest- and next-nearest-neighbor interactions. Phys. Rev. B 21, 1941 (1980)

    Article  CAS  Google Scholar 

  • Binder, K., Heermann, D.W.: Monte Carlo Simulation in Statistical Physics. An Introduction. Springer, Berlin (1988)

    Book  Google Scholar 

  • Binder, K.: Applications of Monte Carlo methods to statistical physics. Rep. Prog. Phys. 60, 487 (1997)

    Article  CAS  Google Scholar 

  • Blume, M., Emery, V.J., Griffiths, R.B.: Ising Model for the \(\lambda \) transition and phase separation in He3-He4 mixtures. Phys. Rev. A 4, 1071 (1971)

    Article  Google Scholar 

  • Bulnes, F., Ramirez-Pastor, A.J., Zgrablich, G.: Surface diffusion of k-mers in one-dimensional systems. Surf. Sci. 601, 569 (2007)

    Article  CAS  Google Scholar 

  • Clark, A.: The Theory of Adsorption and Catalysis. Academic Press, New York (1970)

    Google Scholar 

  • Dávila, M., Riccardo, J.L., Ramirez-Pastor, A.J.: Fractional statistics description applied to adsorption of alkane binary mixtures in zeolites. J. Chem. Phys. 130, 174715 (2009)

    Article  Google Scholar 

  • Dunne, J.A., Rao, M., Sircar, S., Gorte, R.J., Myers, A.L.: Calorimetric heats of adsorption and adsorption isotherms. 2. O2, N2, Ar, CO2, CH4, C2H6, and SF6 on NaX, H-ZSM-5, and Na-ZSM-5 zeolites. Langmuir 12, 5896 (1996)

    Article  CAS  Google Scholar 

  • Dunne, L.J., Manos, G., Du, Z.: Exact statistical mechanical one-dimensional lattice model of alkane binary mixture adsorption in zeolites and comparision with Monte-Carlo simulations. Chem. Phys. Lett. 377, 551 (2003)

    Article  CAS  Google Scholar 

  • Ekiz, C., Keskin, M.: Multicritical phase diagrams of the Blume-Emery-Griffiths model with repulsive biquadratic coupling including metastable phases. Phys. Rev. B 66, 54105 (2002)

    Article  Google Scholar 

  • Freire, R.T.S., Mitchell, S.J., Plascak, J.A., Landau, D.P.: Monte Carlo study of the XY vector Blume-Emery-Griffiths model for 3He-4He mixtures in three dimensions. Phys. Rev. E 72, 056117 (2005)

    Article  CAS  Google Scholar 

  • García, G.D., Sánchez-Varretti, F.O., Romá, F., Ramirez-Pastor, A.J.: A simple statistical mechanical approach for studying multilayer adsorption of interacting rigid polyatomics. Surf. Sci. 603, 980 (2009)

    Article  Google Scholar 

  • García, G.D., Sánchez-Varretti, F.O., Bulnes, F., Ramirez-Pastor, A.J.: Monte Carlo study of binary mixtures adsorbed on square lattices. Surf. Sci. 606, 83 (2012)

    Article  Google Scholar 

  • Hill, T.L.: An Introduction to Statistical Thermodynamics. Addison-Wesley Publishing Company, Reading (1960)

    Google Scholar 

  • Hoston, W., Berker, A.N.: Multicritical phase diagrams of the Blume-Emery-Griffiths model with repulsive biquadratic coupling. Phys. Rev. Lett. 67, 1027 (1991)

    Article  Google Scholar 

  • Keskin, M., Erdin, A.: Multicritical phase diagrams of the BlumeEmeryGriffiths model with repulsive biquadratic coupling including metastable phases: the pair approximation and the path probability method with pair distribution. J. Magn. Magn. Mater. 283, 392 (2004)

    Article  CAS  Google Scholar 

  • Landau, D.P.: Critical and multicritical behavior in a triangular-lattice-gas Ising model: repulsive nearest-neighbor and attractive next-nearest-neighbor coupling. Phys. Rev. B 27, 5604 (1983)

    Article  Google Scholar 

  • Li, Y., Yi, H., Tang, X., Li, F., Yuan, Q.: Adsorption separation of CO2/CH4 gas mixture on the commercial zeolites at atmospheric pressure. Chem. Eng. J. 229, 50 (2013)

    Article  CAS  Google Scholar 

  • Liu, B., Smit, B.: Comparative molecular simulation study of CO 2/N 2 and CH 4/N 2 separation in zeolites and metal-organic frameworks. Langmuir 25, 5918 (2009)

    Article  CAS  Google Scholar 

  • Matsushima, T.: Interactions among adsorbates on metal surfaces. Surf. Sci. 558, 1 (2004)

    Article  CAS  Google Scholar 

  • Metropolis, N., Rosenbluth, A.W., Rosenbluth, N.M., Teller, A.H., Teller, E.: Equation of state calculations by fast computing machines. J. Chem. Phys. 21, 1087 (1953)

    Article  CAS  Google Scholar 

  • Myers, A.L., Prausnitz, J.: Thermodynamics of mixed-gas adsorption. AIChE J. 11, 121 (1965)

    Article  CAS  Google Scholar 

  • Patrykiejew, A., Sokolowski, S., Binder, K.: Phase transitions in adsorbed layers formed on crystals of square and rectangular surface lattice. Surf. Sci. Rep. 37, 207 (2000)

    Article  CAS  Google Scholar 

  • Phares, A.J., Wunderlich, F.J.: Structural ordering of interacting dimers on a square lattice. J. Math. Phys. 26, 2491 (1985)

    Article  Google Scholar 

  • Phares, A.J., Wunderlich, F.J.: Crystallization patterns of monomers with a nearest-neighbor interaction on a multilayered semi-infinite square lattice. Phys. Rev. E 52, 2236 (1995)

    Article  CAS  Google Scholar 

  • Phares, A.J., Wunderlich, F.J.: Monomer adsorption on a square lattice with first- and second-neighbor interactions. Phys. Rev. E 55, 2403 (1997)

    Article  CAS  Google Scholar 

  • Phares, A.J., Wunderlich, F.J.: Monomer adsorption on bcc (110) surfaces with first- and second-neighbor interactions. Surf. Sci. 425, 112 (1999)

    Article  CAS  Google Scholar 

  • Phares, A.J., Wunderlich, F.J.: Adsorption on bcc (110) surfaces with first-, second-, and third-neighbor interactions. Surf. Sci. 452, 108 (2000)

    Article  CAS  Google Scholar 

  • Phares, A.J., Wunderlich, F.J.: Adsorption patterns and adsorbateadsorbate interactions up to third neighbors on fcc(1 1 0) surfaces. Surf. Sci. 479, 43 (2001)

    Article  CAS  Google Scholar 

  • Phares, A.J., Wunderlich, F.J., Martin, J.P., Burns, P.M., Duda, G.K.: Coadsorption of two monomer species on a square lattice with first- and second-neighbor interactions. Phys. Rev. E 56, 2447 (1997)

    Article  CAS  Google Scholar 

  • Pinto, O.A., Nieto, F., Ramirez-Pastor, A.J.: Statistical thermodynamics of straight rigid rods with nonadditive lateral interactions: theory and Monte Carlo simulations. Phys. Rev. E 84, 061142 (2011)

    Article  CAS  Google Scholar 

  • Rżysko, W., Patrykiejew, A., Binder, K.: Phase transitions in a two-dimensional lattice gas model of orientable diatomic molecules. Phys. Rev. B 72, 165416 (2005)

    Article  Google Scholar 

  • Ramirez-Pastor, A.J., Aligia, A., Romá, F., Riccardo, J.L.: Multisite-occupancy adsorption and surface diffusion of linear adsorbates in low dimensions: rigorous results for a lattice gas model. Langmuir 16, 5100 (2000)

    Article  CAS  Google Scholar 

  • Romá, F., Ramirez-Pastor, A.J., Riccardo, J.L.: Critical behavior of repulsive linear k-mers on square lattices at half coverage: theory and Monte Carlo simulations. Phys. Rev. B 68, 205407 (2003)

    Article  Google Scholar 

  • Romá, F., Ramirez-Pastor, A.J.: Statistical thermodynamics of adsorbates with nonsymmetrical lateral interactions. Phys. Rev. E 69, 036124 (2004)

    Article  Google Scholar 

  • Rupprechter, G., Morkel, M., Freund, H.J., Hirschl, R.: Sum frequency generation and density functional studies of COH interaction and hydrogen bulk dissolution on Pd(111). Surf. Sci. 554, 43 (2004)

    Article  CAS  Google Scholar 

  • Smit, B., Maesen, T.L.M.: Molecular simulations of zeolites: adsorption, diffusion, and shape selectivity. Chem. Rev. 108, 4125 (2008)

    Article  CAS  Google Scholar 

  • Steele, W.A.: The Interaction of Gases with Solid Surfaces. Pergamon Press, New York (1974)

    Google Scholar 

  • Tovbin, Y.K.: Theory of physical chemistry processes at a gas-solid interface. Mir Publishers & CRC Press, Boca Raton (1991)

    Google Scholar 

  • Ungerer, P., Tavitian, B., Boutin, A.: Applications of Molecular Simulation in the Oil and Gas Industry: Monte Carlo Methods. Editions Technip, Paris (2005)

    Google Scholar 

  • Verma, P., Xu, X., Truhlar, D.G.: Adsorption on Fe-MOF-74 for C1–C3 hydrocarbon separation. J. Phys. Chem. C 117, 12648 (2013)

    Article  CAS  Google Scholar 

  • Wu, F.Y.: The Potts model. Rev. Mod. Phys. 54, 235 (1982)

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported in part by CONICET (Argentina) under project number PIP 112-201101-00615; Universidad Nacional de San Luis (Argentina) under project 322000; Universidad Tecnológica Nacional, Facultad Regional San Rafael, under project PID UTN 1835 Disp. 284/12; and the National Agency of Scientific and Technological Promotion (Argentina) under project PICT-2010-1466.

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Correspondence to P. M. Pasinetti.

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Sanchez-Varretti, F.O., Garcia, G.D., Pasinetti, P.M. et al. Adsorption of binary mixtures on two-dimensional surfaces: theory and Monte Carlo simulations. Adsorption 20, 855–862 (2014). https://doi.org/10.1007/s10450-014-9627-7

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  • DOI: https://doi.org/10.1007/s10450-014-9627-7

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