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Phase Transitions of Model Colloids in External Fields

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Computer Simulations in Condensed Matter Systems: From Materials to Chemical Biology Volume 2

Part of the book series: Lecture Notes in Physics ((LNP,volume 704))

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Abstract

The nature of the melting transition for a system of hard disks with translational degrees of freedom in two spatial dimensions has been analyzed by a combination of computer simulation methods and a finite size scaling technique. The behavior of the system is consistent with the predictions of the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory.

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References

  1. D. P. Landau and K. Binder (2000) A Guide to Monte Carlo Simulations in Statistical Physics. Cambridge University Press

    Google Scholar 

  2. Bridging Time Scales: Molecular Simulations for the Next Decade. edited by P. Nielaba, M. Mareschal, G. Ciccotti, Springer, Berlin (2002)

    Google Scholar 

  3. S. Sengupta, P. Nielaba, M. Rao, and K. Binder (2000) Elastic constants from microscopic strain fluctuations. Phys. Rev. E61, pp. 1072–1080

    ADS  Google Scholar 

  4. P. M. Chaikin and T. C. Lubensky (1995) Principles of condensed matter physics. Cambridge University Press, Cambridge

    Google Scholar 

  5. D. C. Wallace (1958) in Solid state physics, eds. H. Ehrenreich, F. Seitz and D. Turnbull, Academic Press, New York; J. H. Weiner (1983), Statistical mechanics of elasticity. Wiley, New York

    Google Scholar 

  6. K. W. Wojciechowski and A. C. Brańka (1988) Elastic moduli of a perfect hard disc crystal in two dimensions. Phys. Lett. 134A, pp. 314–318

    ADS  Google Scholar 

  7. S. Sengupta, P. Nielaba, and K. Binder (2000) Elastic moduli, dislocation core energy, and melting of hard disks in two dimensions. Phys. Rev. E61, pp. 6294–6301

    ADS  Google Scholar 

  8. F. Seitz (1940) Modern Theory of Solids, McGaraw-Hill, New York; M. Born and K. Huang (1954) Dynamical Theory of Crystal Lattices, Oxford University Press, Oxford; For experimental temperature dependent elastic constants of solid argon see: H. Meixner, P. Leiderer, P. Berberich and E. Lüscher (1972) The elastic constants of solid argon determined by stimulated brillouin scattering. Phys. Lett. 40A, pp. 257–258

    Google Scholar 

  9. V. N. Ryzhov and E. E. Tareyeva (1995) Two-stage melting in two dimensions: first principles approach. Phys. Rev. B51, pp. 8789–8794

    ADS  Google Scholar 

  10. K. Franzrahe, Ph.D. thesis (in work)

    Google Scholar 

  11. P. Henseler, Ph.D. thesis (in work)

    Google Scholar 

  12. P. Nielaba, K. Binder, D. Chaudhuri, K. Franzrahe, P. Henseler, M. Lohrer, A. Ricci, S. Sengupta, and W. Strepp (2004) Elastic properties, structures and phase transitions in model colloids. J. Phys.: Cond. Mat. 16, pp. S4115–S4136

    Article  ADS  Google Scholar 

  13. K. Franzrahe, P. Henseler, A. Ricci, W. Strepp, S. Sengupta, M. Dreher, Chr. Kircher, M. Lohrer, W. Quester, K. Binder, and P. Nielaba (2005) Twodimensional model colloids and nano-wires: phase transitions, effects of external potentials and quantum effects. Comp. Phys. Commun. 169, pp. 197–202

    Article  ADS  Google Scholar 

  14. A. Ricci (2006) Ph.D. thesis (U. Mainz)

    Google Scholar 

  15. K. Zahn, A. Wille, G. Maret, S. Sengupta, and P. Nielaba (2003) Elastic properties of 2D colloidal crystals from video microscopy. Phys. Rev. Lett. 90, pp. 155506-1–155506-4

    Article  ADS  Google Scholar 

  16. B. J. Alder and T. E. Wainwright (1962) Phase transition in elastic disks. Phys. Rev. 127, pp. 359–361

    Article  ADS  Google Scholar 

  17. J. Lee and K. Strandburg (1992) First-order melting transition of the hard-disk system. Phys. Rev. B46, pp. 11190–11193

    ADS  Google Scholar 

  18. J. A. Zollweg and G. V. Chester (1992) Melting in two dimensions. Phys. Rev. B46, pp. 11186–11189

    ADS  Google Scholar 

  19. T. V. Ramakrishnan (1982) Density-wave theory of first-order freezing in two dimensions. Phys. Rev. Lett. 48, pp. 541–545; X. C. Zeng and D. W. Oxtoby (1990) Applications of modified weighted density functional theory: freezing of simple liquids. J. Chem. Phys. 93, pp. 2692–2700; Y. Rosenfeld (1990) Freeenergy model for the inhomogeneous hard-sphere fluid in D dimensions: structure factors for the hard-disk (D=2) mixtures in simple explicit form. Phys. Rev. A42, pp. 5978–5989

    Google Scholar 

  20. A. Jaster (1999) Computer simulations of the two-dimensional melting transition using hard disks. Phys. Rev. E 59, pp. 2594–2602; A. Jaster (2000) Shorttime behaviour of the two-dimensional hard-disk model. Physica A 277, pp. 106–114

    Google Scholar 

  21. J. M. Kosterlitz and D. J. Thouless (1973) Ordering, metastability and phase transitions in two-dimensional systems. J. Phys. C 6, pp. 1181–1203; B. I. Halperin and D. R. Nelson (1978) Theory of two-dimensional melting, Phys. Rev. Lett. 41, pp. 121–124; D. R. Nelson and B. I. Halperin (1979) Dislocationmediated melting in two dimensions. Phys. Rev. B 19, pp. 2457–2484; A. P. Young (1979) Melting and the vector Coulomb gas in two dimensions. Phys. Rev. B 19, pp. 1855–1866

    Google Scholar 

  22. K. Zahn, R. Lenke, and G. Maret (1999) Two-stage melting of paramagnetic colloidal crystals in two dimensions. Phys. Rev. Lett. 82, pp. 2721–2724

    Article  ADS  Google Scholar 

  23. M. Bates and D. Frenkel (2000) In.uence of vacancies on the melting transition of hard disks in two dimensions. Phys. Rev. E61, pp. 5223–5227

    ADS  Google Scholar 

  24. K. Binder, S. Sengupta, and P. Nielaba (2002) The liquid-solid transition of hard-discs: first order transition or Kosterlitz-Thouless-Halperin-Nelson-Young scenario? J. Phys.: Condens. Matter 14, pp. 2323–2333

    Article  ADS  Google Scholar 

  25. N. A. Clark, B. J. Ackerson, and A. J. Hurd (1983) Multidetector scattering as a probe of local structure in disordered phases. PRL 50, pp. 1459–1462

    Article  ADS  Google Scholar 

  26. A. Chowdhury, B. J. Ackerson, and N. A. Clark (1985) Laser-induced freezing. PRL 55, pp. 833–836

    Article  ADS  Google Scholar 

  27. K. Loudiyi and B. J. Ackerson (1992) Direct observation of laser induced freezing. Physica A 184, 1–25; Monte Carlo simulation of laser induced freezing. ibid pp. 26–41

    Google Scholar 

  28. Q.-H. Wei, C. Bechinger, D. Rudhardt, and P. Leiderer (1998) Experimental study of laser-induced melting in two-dimensional colloids. PRL 81, pp. 2606–2609

    Article  ADS  Google Scholar 

  29. C. Bechinger, Q. H. Wei, and P. Leiderer (2000) Reentrant melting of twodimensional colloidal systems. J. Phys.: Cond. Mat. 12, pp. A425–A430

    Article  ADS  Google Scholar 

  30. C. Bechinger, M. Brunner, and P. Leiderer (2001) Phase behavior of twodimensional colloidal systems in the presence of periodic light fields. PRL 86, pp. 930–933

    Article  ADS  Google Scholar 

  31. J. Chakrabarti, H. R. Krishnamurthy, and A. K. Sood (1994) Density functional theory of laser-induced freezing in colloidal suspensions. PRL 73, pp. 2923–2926

    Article  ADS  Google Scholar 

  32. L. L. Rasmussen and D. W. Oxtoby (2002) Induced freezing and re-entrant melting in the hard-disc fluid; applications of the fundamental measure functional. J. Phys.: Cond. Mat. 14, pp. 12021–12030

    Article  ADS  Google Scholar 

  33. E. Frey, D. R. Nelson, and L. Radzihovsky (1999) Light-induced melting of colloidal crystals in two dimensions. PRL 83, pp. 2977–2980; L. Radzihovsky, E. Frey, D. R. Nelson (2001) Novel phases and reentrant melting of two-dimensional colloidal crystals. Phys. Rev. E63, pp. 031503-1–031503-34

    Google Scholar 

  34. J. Chakrabarti, H. R. Krishnamurthy, A. K. Sood, and S. Sengupta (1995) Reentrant melting in laser field modulated colloidal suspensions. PRL 75, pp. 2232–2235

    Article  ADS  Google Scholar 

  35. C. Das and H. R. Krishnamurthy (1998) Laser-induced quasicrystalline order in charge-stabilized colloidal systems. PRB 58, pp. R5889–R5892

    Article  ADS  Google Scholar 

  36. C. Das, A. K. Sood, and H. R. Krishnamurthy (1999) Bond-orientational ordering and shear rigidity in modulated colloidal liquids. Physica A 270, pp. 237–244

    ADS  Google Scholar 

  37. C. Das, P. Chaudhuri, A. Sood, and H. Krishnamurthy (2001) Current Science 80(8), p. 959

    Google Scholar 

  38. D. Chaudhuri and S. Sengupta (2004) A numerical renormalization group study of laser-induced freezing. Europhys. Lett. 67, pp. 814–819; (2006) Direct test of defect-mediated laser-induced melting theory for two-dimensional solids. Phys. Rev. E73, pp. 011507-1–011507-12

    Google Scholar 

  39. For an introduction to phase transitions in colloids see, A. K. Sood (1991) in Solid State Physics, E. Ehrenfest and D. Turnbull Eds., Academic Press, New York; 45, 1; P. N. Pusey in Liquids (1991) Freezing and the Glass Transition, J. P. Hansen and J. Zinn-Justin Eds. (North Holland, Amsterdam)

    Google Scholar 

  40. W. Strepp, S. Sengupta, and P. Nielaba (2001) Phase transitions of hard disks in external periodic potentials: a Monte Carlo study. Phys. Rev. E63, pp. 046106-1–046106-10

    ADS  Google Scholar 

  41. W. Strepp, S. Sengupta, and P. Nielaba (2002) Phase transitions of soft disks in external periodic potentials: a Monte Carlo study. Phys. Rev. E66, pp. 056109-1–056109-13

    ADS  Google Scholar 

  42. W. Strepp, S. Sengupta, M. Lohrer, and P. Nielaba (2002) Phase transitions of hard and soft disks in external periodic potentials: A Monte Carlo study. Comput. Phys. Commun. 147, pp. 370–373

    Article  MATH  ADS  Google Scholar 

  43. W. Strepp, S. Sengupta, M. Lohrer, and P. Nielaba (2003) Phase transitions in model colloids in reduced geometry. Mathematics and Computers in Simulation 62, pp. 519–527

    Article  MATH  MathSciNet  Google Scholar 

  44. K. Binder (1981) Finite size scaling analysis of Ising model block distribution functions. Z. Phys. B43, pp. 119–140; K. Binder (1981) Critical properties from Monte Carlo coarse graining and renormalization. PRL 47, pp. 693–696

    Google Scholar 

  45. K. Vollmayr, J. D. Reger, M. Scheucher, and K. Binder (1993) Finite size effects at thermally-driven first order transitions: a phenomenological theory of the order parameter distribution. Z. Phys. B 91, pp. 113–125

    Article  ADS  Google Scholar 

  46. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller and E. Teller (1953) Equation of state calculations by fast computing machines. J. Chem. Phys. 21, pp. 1087–1092

    Article  ADS  Google Scholar 

  47. W. Strepp. M. Lohrer, S. Sengupta, and P. Nielaba, Phase transitions of hard and soft disks in external periodic potentials: a Monte Carlo study of the effect of the interaction range, preprint

    Google Scholar 

  48. M. Brunner, C. Bechinger, W. Strepp, V. Lobaskin, and H. H. von Gruenberg (2002) Density-dependent pair interaction in 2D colloidal suspensions. Europhys. Lett. 58, pp. 926–932

    Article  ADS  Google Scholar 

  49. W. Quester (2003) Diplomarbeit (U. Konstanz)

    Google Scholar 

  50. Chr. Kircher (2004) Diplomarbeit (U. Konstanz)

    Google Scholar 

  51. W. Strepp (2003) Ph.D-thesis (U. Konstanz)

    Google Scholar 

  52. W. Strepp and P. Nielaba, in preparation

    Google Scholar 

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Author information

Authors and Affiliations

  1. Physics Department, University of Konstanz, 78457, Konstanz, Germany

    P. Nielaba & W. Strepp

  2. S.N. Bose National Center for Basic Sciences, 700098, Calcutta, India

    S. Sengupta

Authors
  1. P. Nielaba
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  2. S. Sengupta
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  3. W. Strepp
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Editor information

Editors and Affiliations

  1. Dipartimento di Fisica, Università di Modena e Reggio Emilia, Via Campi, 213/A, 41100, Modena, Italy

    Mauro Ferrario Professor

  2. Dipartimento di Fisica, INFN, Università di Roma La Sapienza, Piazzale Aldo Moro 2, 00185, Roma, Italy

    Giovanni Ciccotti Professor

  3. Institut für Physik, Universität Mainz, Staudinger Weg 7, 55128, Mainz, Germany

    Kurt Binder Professor

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Nielaba, P., Sengupta, S., Strepp, W. (2006). Phase Transitions of Model Colloids in External Fields. In: Ferrario, M., Ciccotti, G., Binder, K. (eds) Computer Simulations in Condensed Matter Systems: From Materials to Chemical Biology Volume 2. Lecture Notes in Physics, vol 704. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-35284-8_8

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