Critical wetting in the two-dimensional Ising ferromagnet confined between inhomogeneous walls

Regular Article

Abstract

We present a numerical study of the critical wetting behavior of an Ising magnet confined between two walls, separated by a distance L, where short-range inhomogeneous surface magnetic fields act. So, samples are assumed to have a size L × M, L being the width and M the length, respectively. By considering surface fields varying spatially with a given wavelength or period (λ), H 1(x,λ) with 1 ≤ xM, we found that the wetting temperature is given by the exact result of Abraham [D.B. Abraham, Phys. Rev. Lett. 44, 1165 (1980)] provided that an effective field given by the spacial average value \(\left( {H_{eff} \equiv \tfrac{1} {\lambda }\int_0^\lambda {H_1 (x,\lambda )dx > 0} } \right)\) is considered. The above results hold in the low wavelength regime, while for λ → ∞ and a bivaluated surface field (i.e., H max for xM/ 2, and δ H max for x>M/ 2, with 0 <δ< 1), one observes two almost independent wetting transitions, both being compatible with Abraham’s exact results corresponding to H max and δ H max, respectively. On the other hand, for H 1(x,λ) ≠ 0 but H eff = 0 bulk standard critical behavior results is observed.

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    J.S. Rowlinson, B. Widom, Molecular Theory of Capillarity (Oxford University Press, Oxford, 1982)Google Scholar
  2. 2.
    D.E. Sullivan, M.M. Telo da Gama, in Fluid Interfacial Phenomena, edited by C. Croxton (Wiley, New York, 1986), p. 45Google Scholar
  3. 3.
    S. Dietrich, in Phase Transitions and Critical Phenomena, edited by C. Domb, J.L. Lebowitz (Academic, London, 1988), Vol. 12, p. 1Google Scholar
  4. 4.
    M. Schick, in Liquids at Interfaces, edited by J. Charvolin, J.-F. Joanny, J. Zinn-Justin (Elsevier, Amsterdam, 1990), p. 415Google Scholar
  5. 5.
    D. Bonn, D. Ross, Rep. Progr. Phys. 64, 1085 (2001)ADSCrossRefGoogle Scholar
  6. 6.
    P.G. De Gennes, F. Brochard-Wyart, D. Quéré, Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves (Springer, Berlin, 2003)Google Scholar
  7. 7.
    M. Schön, S. Klapp, Nanoconfined Fluids: Soft Matter Between Two and Three Dimensions (J. Wiley & Sons, New York, 2006)Google Scholar
  8. 8.
    Low and High Temperature Wetting: State of the Art, Ann. Revs. Mater. Res., edited by D.R. Clarke, M. Rühle, A.P. Tomsia (Ann. Revs., Palo Alto, 2008), Vol. 38Google Scholar
  9. 9.
    D. Bonn, J. Eggers, J.O. Indekeu, J. Meunier, E. Rolley, Rev. Mod. Phys. 81, 739 (2009)ADSCrossRefGoogle Scholar
  10. 10.
    Multilayer Thin Films: Sequential Assembly of Nanocomposite Materials, edited by G. Decker, J.B. Schlenoff (Wiley-VCH, Weinheim, 2002)Google Scholar
  11. 11.
    Nano-Architectured and Nano-Structured Materials, edited by Y. Champion, H.-J. Fecht (Wiley-VCH, Weinheim, 2004)Google Scholar
  12. 12.
    Handbook of Nanostructured Thin Films and Coatings, edited by S. Zhang (CRC Press, Boca Raton, 2010), Vols. 1–3Google Scholar
  13. 13.
    S. Dietrich, M.N. Popescu, M. Rauscher, J. Phys.: Condens. Matter 17, 577 (2005)ADSGoogle Scholar
  14. 14.
    D. Quéré, Rep. Prog. Phys. 68, 2495 (2005)ADSCrossRefGoogle Scholar
  15. 15.
    C. Borgs, J. De Coninck, R. Kotecky, M. Zinque, Phys. Rev. Lett. 74, 2292 (1995)ADSCrossRefGoogle Scholar
  16. 16.
    P. Swain, R. Lipowsky, Langmuir 14, 6772 (1998)CrossRefGoogle Scholar
  17. 17.
    J. De Coninck, J. Ruiz, S. Miracle-Sole, Phys. Rev. E 65, 036139 (2002)ADSCrossRefGoogle Scholar
  18. 18.
    K. Grabowski, A. Patrykiejew, S. Sokolowsky, E.V. Albano, A. de Virgiliis, Surf. Sci. 448, 11 (2000)ADSCrossRefGoogle Scholar
  19. 19.
    P.R. Pandey, S. Roy, J. Phys. Chem. Lett. 4, 3692 (2013)CrossRefGoogle Scholar
  20. 20.
    B. Zhang, J. Wang, X. Zhang, Langmuir 29, 6652 (2013)CrossRefGoogle Scholar
  21. 21.
    M. Trobo, E.V. Albano, Phys. Rev. E 88, 052407 (2013)ADSCrossRefGoogle Scholar
  22. 22.
    K. Binder, D.P. Landau, M. Müller, J. Stat. Phys. 110, 1411 (2003)CrossRefMATHGoogle Scholar
  23. 23.
    E.V. Albano, K. Binder, D.W. Heermann, W. Paul, Surf. Sci. 223, 151 (1989)ADSCrossRefGoogle Scholar
  24. 24.
    E.V. Albano, K. Binder, Phys. Rev. E 85, 061601 (2012)ADSCrossRefGoogle Scholar
  25. 25.
    E.V. Albano, K. Binder, Phys. Rev. Lett. 109, 036101 (2012)ADSCrossRefGoogle Scholar
  26. 26.
    E.V. Albano, K. Binder, W. Paul, J. Phys.: Condens. Matter 12, 2701 (2000)ADSGoogle Scholar
  27. 27.
    F. Parisen Toldin, M. Tröndle, S. Dietrich, Phys. Rev. E 88, 052110 (2013)ADSCrossRefGoogle Scholar
  28. 28.
    F. Parisen Toldin, S. Dietrich, J. Stat. Mech. 2010, P11003 (2010)CrossRefGoogle Scholar
  29. 29.
    N.G. Fytas, W. Selke, Eur. Phys. J. B 86, 365 (2013)ADSCrossRefGoogle Scholar
  30. 30.
    D.B. Abraham, Phys. Rev. Lett. 44, 1165 (1980)ADSCrossRefMathSciNetGoogle Scholar
  31. 31.
    L.W. Bruch, R.D. Diehl, J.A. Venables, Rev. Mod. Phys. 79, 1381 (2007)ADSCrossRefGoogle Scholar
  32. 32.
    H.-J. Elmers, Int. J. Mod. Phys. B 9, 3115 (1995)ADSCrossRefGoogle Scholar
  33. 33.
    J. Bandlow, P. Kaghazchi, T. Jacob, C. Papp, B. Tränkenschuh, R. Streber, M.P.A. Lorenz, T. Fuhrmann, R. Denecke, H.-P. Steinrück Phys. Rev. B 83, 174107 (2011)ADSCrossRefGoogle Scholar
  34. 34.
    P. Zeppenfeld, S. Horch, G. Comsa, Phys. Rev. Lett. 73, 1259 (1994)ADSCrossRefGoogle Scholar
  35. 35.
    S. Horch, P. Zeppenfeld, G. Comsa, Appl. Phys. A 60, 147 (1995)ADSCrossRefGoogle Scholar
  36. 36.
    M. Dienwiebel, P. Zeppenfeld, J. Einfeld, G. Comsa, F. Picaud, C. Ramseyer, C. Girardet, Surf. Sci. 446, L113 (2000)ADSCrossRefGoogle Scholar
  37. 37.
    H. Hövel, B. Grimm, B. Reihl, Surf. Sci. 477, 43 (2001)ADSCrossRefGoogle Scholar
  38. 38.
    J.-Y. Park, S.-J. Kahng, U.D. Ham, Y. Kuk, K. Miyake, K. Hata, H. Shigekawa, Phys. Rev. B 60, 16934 (1999)ADSCrossRefGoogle Scholar
  39. 39.
    P.W. Davis, M.A. Quinlau, G. Somorjai, Surf. Sci. 121, 290 (1982)ADSCrossRefGoogle Scholar
  40. 40.
    V. Marsico, M. Blanc, K. Kuhnke, K. Kern, Phys. Rev. Lett. 78, 94 (1997)ADSCrossRefGoogle Scholar
  41. 41.
    V. Pouthier, C. Ramseyer, C. Girardet, K. Kuhnke, V. Marsico, M. Blanc, R. Schuster, K. Kern, Phys. Rev. B 56, 4211 (1997)ADSCrossRefGoogle Scholar
  42. 42.
    W. Widdra, P. Trischberger, W. Friess, D. Menzel, S.H. Payne, H.J. Kreuzer, Phys. Rev. B 57, 4111 (1998)ADSCrossRefGoogle Scholar
  43. 43.
    F. Picaud, V. Pouthier, C. Ramseyer, C. Girardet, Surf. Rev. Lett. 6, 669 (1999)CrossRefGoogle Scholar
  44. 44.
    M. Wagner, F.R. Negreiros, L. Sementa, G. Barcaro, S. Surnev, A. Fortunelli, F.P. Netzer, Phys. Rev. Lett. 110, 216101 (2013)ADSCrossRefGoogle Scholar
  45. 45.
    J.J. Zhang, G. Katsaros, F. Montalenti, D. Scopece, R.O. Rezaev, C. Mickel, B. Rellinghaus, L. Miglio, S. De Franceschi, A. Rastelli, O.G. Schmidt Phys. Rev. Lett. 109, 085502 (2012)ADSCrossRefGoogle Scholar
  46. 46.
    J. Guo, Y. Mo, E. Kaxiras, Z. Zhang, H.H. Weitering, Phys. Rev. B 73, 193405 (2006)ADSCrossRefGoogle Scholar
  47. 47.
    N.N. Negulyaev, V.S. Stepanyuk, W. Hergert, P. Bruno, J. Kirschner, Phys. Rev. B 77, 085430 (2008)ADSCrossRefGoogle Scholar
  48. 48.
    R. Zdyb, E. Bauer, Phys. Rev. Lett. 100, 155704 (2008)ADSCrossRefGoogle Scholar
  49. 49.
    S.R. Lu, R. Yu, J. Zhu, Phys. Rev. B 87, 165436 (2013)ADSCrossRefGoogle Scholar
  50. 50.
    M. Krawiec, M. Jaochowski, Phys. Rev. B 82, 195443 (2010)ADSCrossRefGoogle Scholar
  51. 51.
    L. Li, L. Luo, J. Ciston, W.A. Saidi, E.A. Stach, J.C. Yang, G. Zhou1, Phys. Rev. Lett. 113, 136104 (2014)ADSCrossRefGoogle Scholar
  52. 52.
    M. Godoy, A.J. Moreno, G.A. Jorge, H.J. Ferrari, P.S. Antonel, J.L. Mietta, M. Ruiz, R.M. Negri, M.J. Pettinari, V. Bekeris, J. Appl. Phys. 111, 044905 (2012)ADSCrossRefGoogle Scholar
  53. 53.
    E.V. Albano, K. Binder. J. Stat. Phys. 157, 436 (2014)ADSCrossRefGoogle Scholar
  54. 54.
    A. Maciolek, J. Stecki, Phys. Rev. B 54, 1128 (1996)ADSCrossRefGoogle Scholar
  55. 55.
    P. Nowakowski, M. Napiórkowski, Phys. Rev. E 78, 060602(R) (2008)ADSCrossRefGoogle Scholar
  56. 56.
    L. Onsager, Phys. Rev. 65, 117 (1944)ADSCrossRefMathSciNetMATHGoogle Scholar
  57. 57.
    K. Binder, J.S. Wang, J. Stat. Phys. 55, 87 (1989)ADSCrossRefMathSciNetGoogle Scholar
  58. 58.
    K. Binder, in Finite Size Scaling and Numerical Simulation of Statistical Systems, edited by V. Privman (World Scientific, Singapore, 1990), p. 173Google Scholar
  59. 59.
    K. Binder, Phys. Rev. Lett. 47, 693 (1981)ADSCrossRefGoogle Scholar
  60. 60.
    K. Binder, Rep. Prog. Phys. 60, 487 (1997)ADSCrossRefGoogle Scholar
  61. 61.
    O. Dillmann, W. Janke, M. Müller, K. Binder, J. Chem. Phys. 114, 5823 (2001)ADSCrossRefGoogle Scholar
  62. 62.
    E.V. Albano, K. Binder, Dieter W. Heermann, W. Paul, Z. Phys. B 77, 445 (1989)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Instituto de Física de Líquidos y Sistemas Biológicos (IFLYSIB), CCT La PlataCONICET, UNLPLa PlataArgentina
  2. 2.Departamento de Ciencias Básicas, Facultad de IngenieríaUniversidad Nacional de La Plata (UNLP)La PlataArgentina
  3. 3.Departamento de Física, Facultad de Ciencias ExactasUniversidad Nacional de La Plata (UNLP)La PlataArgentina

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