Entropic sampling of the flexible polyelectrolyte with the Wang-Landau algorithm

Authors

Keywords:

методы Монте-Карло, статистическая термодинамика, полиэлектролиты, энтропическое моделирование, численные методы, статистические ансамбли

Abstract

We consider a flexible polyelectrolyte model on a lattice. The Coulomb potential and the excluded volume condition between different ions/beads are taken into account. We use the entropic sampling method implemented within an efficient numerical algorithm presented by Wang and Landau in 2001 to study thermodynamic properties of the system. The obtained energy distributions provide the calculation of canonical properties such as conformational energy, heat capacity, entropy, and free energy by numerical integration. Entropic sampling with the Wang-Landau algorithm allows us to obtain statistics for the states with extremely low probabilities of realization in the statistical ensemble, down to 10&circ(-285). We also compare the results of entropic sampling with the data obtained by the standard Monte Carlo method.

Author Biographies

N.A. Volkov

St Petersburg University,
Faculty of Physics

P.N. Vorontsov-Velyaminov

St Petersburg University,
Faculty of Physics

A.P. Lyubartsev

St Petersburg University,
Faculty of Physics

References

  1. Lyubartsev A.P., Nordenskiöld L. Computer simulation of polyelectrolytes // Handbook of Polyelectrolytes and Their Applications. Stevenson Ranch (California, USA): American Scientific Publishers, 2002. 309-326.
  2. Любарцев А.П., Воронцов-Вельяминов П.Н. Моделирование гибких полиэлектролитов методом Монте-Карло // Высокомол. Соедин. A. 1990. 32. 721-726.
  3. Severin M. Thermal maximum in the size of short polyelectrolyte chains. A Monte Carlo study // J. Chem. Phys. 1993. 99. 628-633.
  4. Stevens M.J., Kremer K. The nature of flexible linear polyelectrolytes in salt free solution: A molecular dynamics study // J. Chem. Phys. 1995. 103. 1669-1690.
  5. Stevens M.J., Plimpton S.J. The effect of added salt on polyelectrolyte structure // Eur. Phys. J. B. 1998. 2. 341-345.
  6. Hsiao P.-Y. Linear polyelectrolytes in tetravalent salt solutions // J. Chem. Phys. 2006. 124. 044904-1- 044904-10.
  7. Klos J., Pakula T. Lattice Monte Carlo simulations of three-dimensional charged polymer chains // J. Chem. Phys. 2004. 120. 2496-2501.
  8. Klos J., Pakula T. Lattice Monte Carlo simulations of three-dimensional charged polymer chains. II. Added salt // J. Chem. Phys. 2004. 120. 2502-2506.
  9. Klos J., Pakula T. Lattice Monte Carlo simulations of a charged polymer chain: Effect of valence and concentration of the added salt // J. Chem. Phys. 2005. 122. 134908-1- 134908-7.
  10. Metropolis N., Rosenbluth A.W., Rosenbluth M.N., Teller A.H., Teller E. Equation of state calculations by fast computing machines // J. Chem. Phys. 1953. 21. 1087-1092.
  11. Binder K. Monte Carlo methods in statistical physics. Berlin- Heidelberg- New York: Springer-Verlag, 1979.
  12. Allen M.P., Tildesley D.J. Computer Simulations of Liquids. Oxford, 1987.
  13. Iba Y. Extended ensemble Monte Carlo // Int. J. Modern Physics C. 2001. 12. 623-656.
  14. Mitsutake A., Sugita Y., Okamoto Y. Generalized-ensemble algorithms for molecular simulations of biopolymers // Biopolymers (Peptide Science). 2001. 60. 96-123.
  15. Lyubartsev A.P., Vorontsov-Velyaminov P.N. Generalized-ensemble Monte Carlo methods in chemical physics // Recent Res. Devel. Chem. Phys. 2003. 4. 63-78.
  16. Lyubartsev A.P., Martsinovskii A.A., Shevkunov S.V., Vorontsov-Velyaminov P.N. New approach to Monte Carlo calculation of the free energy: Method of expanded ensembles // J. Chem. Phys. 1992. 96. 1776-1783.
  17. Berg B.A., Neuhaus T. Multicanonical ensemble: A new approach to simulate first-order phase transitions // Phys. Rev. Lett. 1992. 68. 9-12.
  18. Lee J. New Monte Carlo algorithm: Entropic sampling // Phys. Rev. Lett. 1993. 71. 211-214.
  19. Hukushima K., Nemoto K. Exchange Monte Carlo method and application to spin glass simulations // J. Phys. Soc. Japan. 1996. 65. 1604-1608.
  20. Wang F., Landau D.P. Efficient, multiple-range random walk algorithm to calculate the density of states // Phys. Rev. Lett. 2001. 86. 2050-2053.
  21. Wang F., Landau D.P. Determining the density of states for classical statistical models: A random walk algorithm to produce a flat histogram // Phys. Rev. E. 2001. 64. 056101-1- 056101-16.
  22. Yan Q., Faller R., dePablo J.J. Density-of-states Monte Carlo method for simulation of fluids // J. Chem. Phys. 2002. 116. 8745-8749.
  23. Shell M.S., Debenedetti P.G., Panagiotopoulos A.Z. Generalization of the Wang- Landau method for off-lattice simulations // Phys. Rev. E. 2002. 66. 056703-1- 056703-9.
  24. Faller R., dePablo J.J. Density of states of a binary Lennard- Jones glass // J. Chem. Phys. 2003. 119. 4405-4408.
  25. Rampf F., Paul W., Binder K. On the first-order collapse transition of a three-dimensional, flexible homopolymer chain model // Europhys. Lett. 2005. 70. 628-634.
  26. Rathore N., dePablo J.J. Monte Carlo simulation of proteins through a random walk in energy space // J. Chem. Phys. 2002. 116. 7225-7230.
  27. Rathore N., Knotts T.A., dePablo J.J. Density of states simulations of proteins // J. Chem. Phys. 2003. 118. 4285-4290.
  28. Rathore N., Yan Q., dePablo J.J. Molecular simulation of the reversible mechanical unfolding of proteins // J. Chem. Phys. 2005. 120. 5781-5788.
  29. Kim E.B., Faller R., Yan Q., Abbott N.L., dePablo J.J. Potential of mean force between a spherical particle suspended in a nematic liquid crystal and a substrate // J. Chem. Phys. 2002. 117. 7781-7787.
  30. Calvo F. Sampling along reaction coordinates with the Wang- Landau method // Molecular Physics. 2002. 100. 3421-3427.
  31. Schulz B.J., Binder K., Muller M. Flat histogram method of Wang- Landau and N-fold way // Int. J. Mod. Phys. 2002. 13. 477-494.
  32. Vorontsov-Velyaminov P.N., Volkov N.A., Yurchenko A.A. Entropic sampling of simple polymer models within Wang- Landau algorithm // Journ. Phys. A: Math. Gen. 2004. 37. 1573-1588.
  33. Volkov N.A., Yurchenko A.A., Lyubartsev A.P., Vorontsov-Velyaminov P.N. Entropic sampling of free and ring polymer chains // Macromol. Theory Simul. 2005. 14. 491-504.
  34. Douglas J., Guttman C.M., Mah A., Ishinabe T. Spectrum of self-avoiding walk exponents // Phys. Rev. E. 1997. 55. 738-749.
  35. Grassberger P., Hegger R. Simulations of three-dimensional heta polymers // J. Chem. Phys. 1995. 102. 6881-6899.
  36. Ewald P. Die Berechnung optischer und elektrostatischer Gitterpotentiale // Ann. Phys. 1921. 64. 253-287.
  37. de Gennes P.G. Scaling concepts in polymer science. Itaca: Cornell University Press, 1979.
  38. Zhao D., Huang Y., He Z., Qian R. Monte Carlo simulation of the conformational entropy of polymer chains // J. Chem. Phys. 1996. 104. 1672-1674.
New computational technologies

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Published

21-11-2006

How to Cite

Волков Н., Воронцов-Вельяминов П., Любарцев А. Entropic Sampling of the Flexible Polyelectrolyte With the Wang-Landau Algorithm // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2006. 7. 300-309

Issue

Vol. 7 (2006): Issue 4.

Section

Section 1. Numerical methods and applications