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Adsorption of interacting particles on bivariate diffusion-limited aggregates

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The adsorption of pairwise interacting particles on fractal surfaces has been studied by grand canonical Monte Carlo simulations. The substrate is built from a mixture of two types of objects: (i) objects with two bonds and (ii) objects with four bonds. These objects move on a square lattice, according to diffusion-limited aggregation (DLA) rules, and stick to each other only if they have a free bond pointing at each other and, of course, are first neighbors of each other. The resulting substrate, which is named as bivariate diffusion-limited aggregate (BDLA), is a fractal structure composed by two bonds units with fraction \(f_2\) and four bonds units with concentration \(f_4=1-f_2\). Different surface morphologies are obtained by varying \(f_2\) and \(f_4\). In the limit case of \(f_2=0\) and \(f_4=1\), the standard DLA model is recovered. In addition, repulsive lateral interactions between adsorbed particles are considered. Adsorption isotherms and differential heats of adsorption are calculated for different values of the parameters of the system. In the case of high repulsive couplings, a wide variety of structural orderings are observed in the adlayer. The main characteristics of these ordered phases are discussed in terms of the topological properties of the bivariate aggregates.

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  1. M. Jaroniec, R. Madey, Physical Adsorption on Heterogeneous Solids (Elsevier, Amsterdam, 1988)

    Google Scholar 

  2. W. Rudziński, D. Everett, Adsorption of Gases on Heterogeneous Surfaces (Academic Press, New York, 1991)

    Google Scholar 

  3. W. Rudziński, W.A. Steele, G. Zgrablich, Equilibria and Dynamics of Gas Adsorption on Heterogeneous Solid Surfaces (Elsevier Science, Amsterdam-New York, 1996)

    Google Scholar 

  4. K.V. Kumar, G. Srinivas, B. Wood, K.A. Ramisetty, A.A. Stewart, C.A. Howard, D. Brett, F. Rodriguez-Reinoso, J. Mater. Chem. A 7, 10104 (2019)

    Article  Google Scholar 

  5. P. Ripa, G. Zgrablich, J. Phys. Chem. 79, 2118 (1975)

    Article  Google Scholar 

  6. S. Ross, J.P. Olivier, On Physical Adsorption (Wiley, New York, 1964)

    Google Scholar 

  7. T.L. Hill, J. Chem. Phys. 17, 520 (1949)

    Article  ADS  Google Scholar 

  8. W.H. Zachariasen, J. Am. Chem. Soc. 54, 3841 (1932)

    Article  Google Scholar 

  9. E.I. Benegas, V.D. Pereyra, G. Zgrablich, Surf. Sci. Lett. 187, L647 (1987)

    ADS  Google Scholar 

  10. M. Quintana, M. Pasinetti, A.J. Ramirez-Pastor, G. Zgrablich, Surf. Sci. 600, 33 (2006)

    Article  ADS  Google Scholar 

  11. T.A. Witten Jr., L.M. Sander, Phys. Rev. Lett. 47, 1400 (1981)

    Article  ADS  Google Scholar 

  12. L. Niemeyer, L. Pietronero, H.J. Wiesmann, Phys. Rev. Lett. 52, 1033 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  13. P. Meakin, Phys. Rev. A 27, 2616 (1983)

    Article  ADS  Google Scholar 

  14. P. Meakin, T.A. Witten, Phys. Rev. A 28, 2985 (1983)

    Article  ADS  Google Scholar 

  15. P. Meakin, Phys. Rev. B 30, 4207 (1984)

    Article  ADS  Google Scholar 

  16. P. Meakin, Phys. Rev. B 29, 3722 (1984)

    Article  ADS  Google Scholar 

  17. M. Nazzarro, F. Nieto, A.J. Ramirez-Pastor, Surf. Sci. 497, 275 (2002)

    Article  ADS  Google Scholar 

  18. L.I. Candia, J. Carbonetti, G.D. Garcia, F.O. Sanchez-Varretti, Int. J. Mod. Phys. C 26, 1550136 (2015)

  19. M. Nazzarro, F. Nieto, A.J. Ramirez-Pastor, Phys. A 331, 517 (2004)

    Article  Google Scholar 

  20. X. Guo, J. Wang, J. Mol. Liq. 324, 114692 (2021)

    Article  Google Scholar 

  21. D. Nicholson, N.G. Parsonage, Computer Simulation and the Statistical Mechanics of Adsorption (Academic Press, London, 1982)

    Google Scholar 

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

    Google Scholar 

  23. N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, E. Teller, J. Chem. Phys. 21, 1087 (1953)

    Article  ADS  Google Scholar 

  24. A.J. Ramirez-Pastor, F. Bulnes, Phys. A 283, 198 (2000)

    Article  Google Scholar 

  25. F. Bulnes, A.J. Ramirez-Pastor, Phys. A 295, 71 (2001)

    Article  Google Scholar 

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This work was supported in part by CONICET (Argentina) under project number PIP 112-201701-00673CO; Universidad Nacional de San Luis (Argentina) under project No. 03-0816; and Universidad Tecnológica Nacional, Facultad Regional San Rafael, under projects PID UTN UTI4914 and UTI5154.

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All the authors were involved in the preparation of the manuscript. All the authors have read and approved the final manuscript.

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Correspondence to Fabricio Orlando Sanchez-Varretti.

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Sanchez-Varretti, F.O., Ramirez-Pastor, A.J. Adsorption of interacting particles on bivariate diffusion-limited aggregates. Eur. Phys. J. E 44, 44 (2021).

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