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Partially Annealed Disorder and Collapse of Like-Charged Macroions

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Abstract

Charged systems with partially annealed charge disorder are investigated using field-theoretic and replica methods. Charge disorder is assumed to be confined to macroion surfaces surrounded by a cloud of mobile neutralizing counterions in an aqueous solvent. A general formalism is developed by assuming that the disorder is partially annealed (with purely annealed and purely quenched disorder included as special cases), i.e., we assume in general that the disorder undergoes a slow dynamics relative to fast-relaxing counterions making it possible thus to study the stationary-state properties of the system using methods similar to those available in equilibrium statistical mechanics. By focusing on the specific case of two planar surfaces of equal mean surface charge and disorder variance, it is shown that partial annealing of the quenched disorder leads to renormalization of the mean surface charge density and thus a reduction of the inter-plate repulsion on the mean-field or weak-coupling level. In the strong-coupling limit, charge disorder induces a long-range attraction resulting in a continuous disorder-driven collapse transition for the two surfaces as the disorder variance exceeds a threshold value. Disorder annealing further enhances the attraction and, in the limit of low screening, leads to a global attractive instability in the system.

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References

  1. Schena, M., Shalon, D., Davis, R.W., Brown, P.O.: Science 270, 467 (1995)

    Article  ADS  Google Scholar 

  2. Halperin, A., Buhot, A., Zhulina, E.B.: Biophys. J. 86, 718 (2004)

    ADS  Google Scholar 

  3. Meyer, E.E., Lin, Q., Hassenkam, T., Oroudjev, E., Israelachvili, J.N.: Proc. Natl. Acad. Sci. USA 102, 6839 (2005)

    Article  ADS  Google Scholar 

  4. Perkin, S., Kampf, N., Klein, J.: Phys. Rev. Lett. 96, 038301 (2006)

    Article  ADS  Google Scholar 

  5. Perkin, S., Kampf, N., Klein, J.: J. Phys. Chem. B 109, 3832 (2005)

    Article  Google Scholar 

  6. Meyer, E.E., Rosenberg, K.J., Israelachvili, J.: Proc. Natl. Acad. Sci. USA 103, 15739 (2006)

    Article  ADS  Google Scholar 

  7. Kantor, Y., Li, H., Kardar, M.: Phys. Rev. Lett. 69, 61 (1992)

    Article  ADS  Google Scholar 

  8. Borukhov, I., Andelman, D., Orland, H.: Eur. Phys. J. B 5, 869 (1998)

    ADS  Google Scholar 

  9. Lipowsky, R., Sackmann, E. (eds.): Handbook of Biological Physics: Structure and Dynamics of Membranes. Elsevier, Amsterdam (1995)

    MATH  Google Scholar 

  10. Ninham, B.W., Parsegian, V.A.: J. Theor. Biol. 31, 405 (1971)

    Article  Google Scholar 

  11. Chan, D., Perram, J.W., White, L.R., Healy, T.W.: J. Chem. Soc. Faraday Trans. I 71, 1046 (1975)

    Article  Google Scholar 

  12. Chan, D., Healy, T.W., White, L.R.: J. Chem. Soc. Faraday Trans. I 72, 2844 (1976)

    Article  Google Scholar 

  13. Verwey, E.J.W., Overbeek, J.Th.G.: Theory of the Stability of Lyophobic Colloids. Elsevier, Amsterdam (1948)

    Google Scholar 

  14. Israelachvili, J.N.: Intermolecular and Surface Forces. Academic Press, London (1990)

    Google Scholar 

  15. Parsegian, V.A.: Van der Waals Forces. Cambridge University Press, Cambridge (2005)

    Google Scholar 

  16. Andelman, D.: In: Lipowsky, R., Sackmann, E. (eds.) Handbook of Biological Physics: Structure and Dynamics of Membranes, vol. 1B. Elsevier, Amsterdam (1995). Chap. 12

    Google Scholar 

  17. Podgornik, R., Žekš, B.: J. Chem. Soc. Faraday Trans. II 84, 611 (1988)

    Article  Google Scholar 

  18. Podgornik, R.: J. Chem. Phys. 91, 5840 (1989)

    Article  ADS  Google Scholar 

  19. Podgornik, R.: J. Phys. A: Math. Gen. 23, 275 (1990)

    Article  MATH  ADS  Google Scholar 

  20. Boroudjerdi, H., Kim, Y.W., Naji, A., Netz, R.R., Schlagberger, X., Serr, A.: Phys. Rep. 416, 129 (2005)

    Article  ADS  Google Scholar 

  21. Naji, A., Jungblut, S., Moreira, A.G., Netz, R.R.: Physica A 352, 131 (2005)

    Article  ADS  Google Scholar 

  22. Netz, R.R.: Eur. Phys. J. E 5, 557 (2001)

    Google Scholar 

  23. Grosberg, A.Yu., Nguyen, T.T., Shklovskii, B.I.: Rev. Mod. Phys. 74, 329 (2002)

    Article  ADS  Google Scholar 

  24. Levin, Y.: Rep. Prog. Phys. 65, 1577 (2002)

    Article  ADS  Google Scholar 

  25. Moreira, A.G., Netz, R.R.: Europhys. Lett. 57, 911 (2002)

    Article  ADS  Google Scholar 

  26. Lukatsky, D.B., Safran, S.A.: Europhys. Lett. 60, 629 (2002)

    Article  ADS  Google Scholar 

  27. Kanduč, M., Trulsson, M., Naji, A., Burak, Y., Forsman, J., Podgornik, R.: Phys. Rev. E (2008, in press)

  28. Naji, A., Podgornik, R.: Phys. Rev. E 72, 041402 (2005)

    Article  ADS  Google Scholar 

  29. Podgornik, R., Naji, A.: Europhys. Lett. 74, 712 (2006)

    Article  ADS  Google Scholar 

  30. Fleck, C., Netz, R.R.: Europhys. Lett. 70, 341 (2005)

    Article  ADS  Google Scholar 

  31. Fleck, C., Netz, R.R.: Eur. J. Phys. E 22, 261 (2007)

    Google Scholar 

  32. Fleck, C., Netz, R.R., von Grünberg, H.H.: Biophys. J. 82, 76 (2002)

    Article  ADS  Google Scholar 

  33. Nguyen, T.T., Grosberg, A.Yu., Shklovskii, B.I.: J. Chem. Phys. 113, 1110 (2000)

    Article  ADS  Google Scholar 

  34. Foret, L., Kühn, R., Würger, A.: Phys. Rev. Lett. 89, 156102 (2002)

    Article  ADS  Google Scholar 

  35. Russ, C., Heimburg, T., von Grünberg, H.H.: Biophys. J. 84, 3730 (2003)

    Google Scholar 

  36. Harries, D., Podgornik, R., Parsegian, V.A., Mar-Or, E., Andelman, D.: J. Chem. Phys. 124, 224702 (2006)

    Article  ADS  Google Scholar 

  37. Gelbart, W.M., Bruinsma, R.: Phys. Rev. E 55, 831 (1997)

    Article  ADS  Google Scholar 

  38. Kim, Y.W., Sung, W.: Phys. Rev. Lett. 91, 118101 (2003)

    Article  ADS  Google Scholar 

  39. Hed, G., Safran, S.A.: Phys. Rev. Lett. 93, 138101 (2004)

    Article  ADS  Google Scholar 

  40. Kanduč, M., Podgornik, R.: Eur. Phys. J. E 23, 265 (2007)

    Google Scholar 

  41. Jho, Y.S., Kanduč, M., Naji, A., Podgornik, R., Kim, M.W., Pincus, P.A.: Phys. Rev. Lett. (2008, in press)

  42. Punkkinen, O., Naji, A., Podgornik, R., Vattulainen, I., Hansen, P.-L.: Europhys. Lett. 82, 48001 (2008)

    Article  ADS  Google Scholar 

  43. Dotsenko, V.: Introduction to the Replica Theory of Disordered Statistical Systems. Cambridge University Press, New York (2001)

    MATH  Google Scholar 

  44. Dotsenko, V.: An Introduction to the Theory of Spin Glasses and Neural Networks. World Scientific, Singapore (1994)

    MATH  Google Scholar 

  45. Manne, S., Cleveland, J.P., Gaub, H.E., Stucky, G.D., Hansma, P.K.: Langmuir 10, 4409 (1994)

    Article  Google Scholar 

  46. Manne, S., Gaub, H.E.: Science 270, 1480 (1995)

    Article  ADS  Google Scholar 

  47. Zhang, G., Marie, P., Maaloum, M., Muller, P., Benoit, N., Krafft, M.P.: J. Am. Chem. Soc. 127, 10412 (2005)

    Article  Google Scholar 

  48. Haken, H.: Synergetics, an Introduction. Springer, Berlin (1983)

    MATH  Google Scholar 

  49. Risken, H.: The Fokker-Planck Equation. Springer, Berlin (1989)

    MATH  Google Scholar 

  50. Kaneko, K.: Prog. Theor. Phys. 66, 129 (1981)

    Article  ADS  Google Scholar 

  51. Landauer, R., Woo, J.W.F.: Phys. Rev. A 6, 2204 (1972)

    Article  ADS  Google Scholar 

  52. Allahverdyan, A.E., Petrosyan, K.G.: Phys. Rev. Lett. 96, 065701 (2006)

    Article  ADS  Google Scholar 

  53. Allahverdyan, A.E., Nieuwenhuizen, Th.M.: Phys. Rev. Lett. 85, 232 (2000)

    Article  ADS  Google Scholar 

  54. Allahverdyan, A.E., Nieuwenhuizen, Th.M.: Phys. Rev. E 62, 845 (2000)

    ADS  Google Scholar 

  55. Coolen, A.C.C., Penney, R.W., Sherrington, D.: Phys. Rev. B 48, 16116 (1993)

    Article  ADS  Google Scholar 

  56. Penney, R.W., Coolen, A.C.C., Sherrington, D.: J. Phys. A: Math. Gen. 26, 3681 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  57. Dotsenko, V., Franz, S., Mézard, M.: J. Phys. A: Math. Gen. 27, 2351 (1994)

    Article  MATH  ADS  Google Scholar 

  58. Penney, R., Sherrington, D.: J. Phys. A: Math. Gen. 27, 4027 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  59. Caticha, N.: J. Phys. A: Math. Gen. 27, 5501 (1994)

    Article  MATH  ADS  Google Scholar 

  60. Feldman, D.E., Dotsenko, V.S.: J. Phys. A: Math. Gen. 27, 4401 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  61. Jogen, G., Bolle, D., Coolen, A.C.C.: J. Phys. A: Math. Gen. 31, L737 (1998)

    Article  ADS  Google Scholar 

  62. Jongen, G., Anemüller, J., Bolle, D., Coolen, A.C.C., Perez-Vicente, C.: J. Phys. A: Math. Gen. 34, 3957 (2001)

    Article  MATH  ADS  Google Scholar 

  63. Kondor, I.: J. Phys. A: Math. Gen. 16, L127 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  64. Allahverdyan, A.E., Nieuwenhuizen, Th.M., Saakian, D.B.: Eur. Phys. J. B 16, 317 (2000)

    ADS  Google Scholar 

  65. Dean, D.S.: J. Phys. A: Math. Gen. 29, L613 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  66. Archer, A.J., Rauscher, M.: J. Phys. A: Math. Gen. 37, 9325 (2004)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  67. Marconi, U.M.B., Tarazona, P.: J. Chem. Phys. 110, 8032 (1999)

    Article  ADS  Google Scholar 

  68. Hohenberg, P.C., Halperin, B.I.: Rev. Mod. Phys. 49, 435 (1977)

    Article  ADS  Google Scholar 

  69. Ma, S.-K.: Modern Theory of Critical Phenomena. Benjamin, Massachusetts (1976)

    Book  Google Scholar 

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Authors and Affiliations

  1. Dept. of Molecular Physics, Yerevan State University, 1 Al. Manougian str., Yerevan, 375025, Armenia

    Yevgeni S. Mamasakhlisov

  2. Materials Research Laboratory, University of California, Santa Barbara, CA, 93106, USA

    Ali Naji

  3. Dept. of Chemistry and Biochemistry, University of California, Santa Barbara, CA, 93106, USA

    Ali Naji

  4. Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA, 93106, USA

    Ali Naji & Rudolf Podgornik

  5. Dept. of Physics, Faculty of Mathematics and Physics, University of Ljubljana, 1000, Ljubljana, Slovenia

    Rudolf Podgornik

  6. Dept. of Theoretical Physics, J. Stefan Institute, 1000, Ljubljana, Slovenia

    Rudolf Podgornik

  7. Lab. of Physical and Structural Biology, National Institutes of Health, Bethesda, MD, 20892, USA

    Rudolf Podgornik

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  1. Yevgeni S. Mamasakhlisov
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  2. Ali Naji
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  3. Rudolf Podgornik
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Correspondence to Ali Naji.

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Mamasakhlisov, Y.S., Naji, A. & Podgornik, R. Partially Annealed Disorder and Collapse of Like-Charged Macroions. J Stat Phys 133, 659–681 (2008). https://doi.org/10.1007/s10955-008-9635-7

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  • DOI: https://doi.org/10.1007/s10955-008-9635-7

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