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Profile and Width of Rough Interfaces

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Abstract

In the context of Landau theory and its field theoretical refinements, interfaces between coexisting phases are described by intrinsic profiles. These intrinsic interface profiles, however, are neither directly accessible by experiment nor by computer simulation as they are broadened by long-wavelength capillary waves. In this paper we study the separation of the small scale intrinsic structure from the large scale capillary wave fluctuations in the Monte Carlo simulated three-dimensional Ising model. To this purpose, a blocking procedure is applied, using the block size as a variable cutoff, and a translationally invariant method to determine the interface position of strongly fluctuating profiles on small length scales is introduced. While the capillary wave picture is confirmed on large length scales and its limit of validity is estimated, an intrinsic regime is, contrary to expectations, not observed.

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References

  • B. Widom, in Phase Transitions and Critical Phenomena, Vol. 2, C. Domb and M. Green, eds. (Academic Press, 1972).

  • J. Rowlinson and S. Widom, Molecular Theory of Capillarity(Clarendon Press, 1982).

  • K. Binder, in Phase Transitions and Critical Phenomena, Vol. 8, C. Domb and J. Lebowitz, eds. (Academic Press, 1983).

  • D. Jasnow (1984) ArticleTitleCritical phenomena at interfaces Rep. Prog. Phys. 47 1059–1132

    Google Scholar 

  • J. van der Waals, The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density, Verhandel Konink. Akad. Weten. 1 (1893). English translation: J.Rowlinson, J. Stat. Phys. 20:97–244 (1979).

  • J. Cahn J. Hillard (1958) ArticleTitleFree energy of a nonuniform system J.Chem. Phys. 28 258–267

    Google Scholar 

  • S. Fisk B. Widom (1960) ArticleTitleStructure and free energy of the interface between fluid phases in equilibrium near the critical point J. Chem. Phys. 50 3219–3227

    Google Scholar 

  • F. Buff R. Lovett F. Stillinger (1965) ArticleTitleInterfacial density profile for fluids in the critical region Phys. Rev. Lett. 15 621–623

    Google Scholar 

  • M. Gelfand M. Fisher (1990) ArticleTitleFinite-size effects in fluid interfaces. Physica A 166 1–74

    Google Scholar 

  • M. Sanyal, S. Sinha, K. Huang, and B. Ocko, X-ray-scattering study of capillary-wave fluctuations at a liquid surface, Phys. Rev.Lett. 66:628–631 (1991); I. Tidswell, T. Rabedeau, P. Pershan, and S. Kosowsky, Complete Wetting of a rough surface: An X-ray study,Phys. Rev. Lett. 66:2108–2111 (1991).

    Google Scholar 

  • M. Tolan, O. Seeck, J. Schlomka, W. Press, J. Wang, S. Sinha, Z. Li, M.Rafailovich, and J. Sokolov, Evidence for capillary waves on dewetted polymer film surfaces: A combined X-ray and atomic force microscopy study, Phys. Rev. Lett. 81:2731–2734 (1998); K.Shull, A. Mayes, and T. Russell, Segment distributions in lamellardiblock copolymers, Macromolecules 26:3929–3936 (1993); M. Sferrazza, C. Xiao, R. Jones, D. Bucknall, J. Webster, and J.Penfold, Evidence for capillary waves at immiscible polymer/polymer-interfaces, Phys. Rev. Lett.78:3693–3696 (1997); J. Scherble, B. Stark, B. Stuhn, J.Kressler, H. Budde, S. Horing, D. Schubert, P. Simon, and M. Stamm, Comparison of interfacial width of block copolymers of dg-poly(methyl methacrylate) with various poly(n-alkyl methacrylate)s and the respective homopolymer pairs as measured by neutron reflection,Macromolecules 32:1859–1864 (1999).

  • A. Werner, F. Schmid, M. Müller, and K. Binder, Anomalous size-dependence of interfacial profiles between coexisting phases of polymer mixtures in thin film geometry: A Monte-Carlo simulation, J. Chem. Phys. 107:8175–8188 (1997); A. Werner, F. Schmid, M. Müller, and K. Binder, ‘‘Intrinsic’’ profiles and capillary waves at homopolymer interfaces: A Monte Carlo study, Phys. Rev. E 59:728–738 (1999).

    Google Scholar 

  • E. Bürkner D. Stauffer (1983) ArticleTitleMonte Carlo study of surface roughening in the three-dimensional Ising model. Z. Phys. B 53 241–243

    Google Scholar 

  • K. Mon D. Landau D. Stauffer (1990) ArticleTitleInterface roughening in the three-dimensional Ising model Phys. Rev. B 42 545–547

    Google Scholar 

  • M. Hasenbusch K. Pinn (1992) ArticleTitleSurface tension, surface stiffness, and surface width of the 3-dimensional Ising model on a cubic lattice Physica A 192 342–374

    Google Scholar 

  • J. Weeks (1977) ArticleTitleStructure and thermodynamics of the liquid–vapor interface J. Chem. Phys. 67 3106–3121

    Google Scholar 

  • M. Le Bellac, Quantum and Statistical Field Theory (Clarendon Press, 1991).

  • J. Küster and G. Münster, in preparation.

  • N. J. Günther D. A. Nicole D. J. Wallace (1980) ArticleTitleGoldstone modes in vacuum decay and first-order phase transitions J. Phys. A 13 1755–1767

    Google Scholar 

  • M. Hasenbusch K. Pinn (1997) ArticleTitleThe interface tension of the three-dimensional Ising model in the scaling region Physica A 245 366–378

    Google Scholar 

  • P. Hoppe G. Münster (1998) ArticleTitleThe interface tension of the three-dimensional Ising model in two-loop order Phys. Lett. A. 238 265–269

    Google Scholar 

  • U. Wolff (1989) ArticleTitleCollective Monte Carlo updating for spin systems Phys. Rev. Lett. 62 361–364 Occurrence Handle10.1103/PhysRevLett.62.361

    Article  Google Scholar 

  • M. Hasenbusch S. Meyer M. Pütz (1996) ArticleTitleThe roughening transition of the 3d Ising Interface: A Monte Carlo study J. Stat. Phys. 85 383–401

    Google Scholar 

  • D. Stauffer (1997) ArticleTitleOil–water interfaces in the Ising model Prog.Colloid Polym. Sci. 103 60–66

    Google Scholar 

  • M. Müller, Fluktuationen kritischer Grenzflächen auf verschiedenen Größenskalen, Diploma thesis, University of Münster, Jan. 2004.

  • F. Schmid K. Binder (1992) ArticleTitleRough interfaces in a bcc-based binary alloy Phys. Rev. B 46 13553–13564

    Google Scholar 

  • R. Guida J. Zinn-Justin (1998) ArticleTitleCritical exponents of the N-vector model J. Phys. A 31 8103–8121 Occurrence Handle10.1088/0305-4470/31/40/006 Occurrence Handle99e:82039 Occurrence Handle0978.82037

    Article  MathSciNet  MATH  Google Scholar 

  • M. Caselle F. Gliozzi U. Magnea S. Vinti (1996) ArticleTitleWidth of long colour flux tubes in lattice gauge systems Nucl. Phys. B 460 397–412

    Google Scholar 

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  1. Institut für Theoretische Physik, Universität Münster, Wilhelm-Klemm-Str. 9, Münster, Germany, D-48149

    Melanie Müller & Gernot Münster

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  1. Melanie Müller
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  2. Gernot Münster
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Correspondence to Gernot Münster.

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Müller, M., Münster, G. Profile and Width of Rough Interfaces. J Stat Phys 118, 669–686 (2005). https://doi.org/10.1007/s10955-004-8824-2

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