Surface fractals probed by adsorbate spin-lattice relaxation dispersion

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 59, Issue 5, 1999, Pages 5848-5854

  Zavada, Tatiana ^a   Kimmich, Rainer ^a  

^a UNIVERSITY OF ULM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE;

EID: 0005150591     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.59.5848     Document Type: Article

References (34)

1. P. Pincus and S.A. Safran, Europhys. Lett. 42, 103 (1998).
2. S.A. Safran, Phys. Rev. Lett. 81, 4768 (1998).
3. A.W.C. Lau and P. Pincus, Phys. Rev. Lett. 81, 1338 (1998).
4. J.N. Israelachvili and G.E. Adams, Nature (London) 262, 774 (1976)
5. J.N. IsraelachviliG.E. AdamsJ. Chem. Soc., Faraday Trans. 1 74, 975 (1978).
6. J.C. Crocker and D.G. Grier, Phys. Rev. Lett. 77, 1897 (1996).
7. D. Sentenac and J.J. Benattar, Phys. Rev. Lett. 81, 160 (1998).
8. N. Gronbech-Jensen, R.J. Mashl, R.F. Bruinsma, and W.M. Gelbart, Phys. Rev. Lett. 78, 2477 (1997)
9. Phys. Rev. Lett.B.-Y. Ha and A.J. Liu, 79, 1289 (1997).
10. I. Rouzina and V.A. Bloomfield, J. Phys. Chem. 100, 9977 (1996)
11. B.I. Shklovskii, Phys. Rev. Lett. 82, 3268 (1999).
12. L. Guldbrand, B. Jonsson, H. Wennerstrom, and P. Linse, J. Chem. Phys. 80, 2221 (1984).
13. R. Kjellander and S. Marcelja, Chem. Phys. Lett. 112, 49 (1984)
14. R. KjellanderS. MarceljaJ. Chem. Phys. 82, 2122 (1985).
15. S. Marcelja, Biophys. J. 61l, 1117 (1992)
16. P. Attard, R. Kjellander, and J. Mitchel, Chem. Phys. Lett. 139, 219 (1987).
17. P. Attard, D.J. Mitchell, and B.W. Ninham, J. Chem. Phys. 88, 4987 (1988).
18. P. Attard, D.J. Mitchell, and B.W. Ninham, J. Chem. Phys. 89, 4358 (1988).
19. R. Podgornik and B. Zeks, J. Chem. Soc., Faraday Trans. 2 84, 611 (1988).
20. R. Podgornik, Chem. Phys. Lett. 156, 71 (1989)
21. R. PodgornikJ. Chem. Phys. 91, 5840 (1989).
22. M. Kardar and R. Golestanian, Rev. Mod. Phys. 71, 1233 (1999); see Appendix II of this reference.
23. We stress that by condensed charges we mean layer charges in the limit (Formula presented), and layer charges plus condensed counterions in the opposite limit (Formula presented). By delocalized charges we mean counterions in the limit (Formula presented) and delocalized counterions in the limit (Formula presented).
24. The counterions are assumed to be confined to the volume between the planes which are taken to have infinitely large area; this is also applicable to a system consisting of a lamellar stack of many such membranes where there is no reservoir to which charges can escape. The other interesting case is where the counterions can escape; this case is beyond the scope of the present work (see, however, Ref. 28).
25. S.A. Safran, Statistical Thermodynamics of Surfaces, Interfaces, and Membranes (Addison-Wesley, Reading, MA, 1994), pp. 158–159.
26. Monte Carlo simulations providing mean-field results for (Formula presented) were performed by B. Jonsson, H. Wennerstrom, and B. Halle, J. Phys. Chem. 84, 2179 (1980); see also
27. S.A. Safran, P.A. Pincus, M.E. Cates, and F.C. MacKintosh, J. Phys. (Paris) 51, 503 (1990) and references therein, where a variational calculation for the counterion distribution around a cylinder showed that splitting up the charge into 2D and 3D components gives results comparable with the exact results.
28. H. Li and M. Kardar, Phys. Rev. Lett. 67, 3275 (1991);see also the review in Ref. 17.
29. L.D. Landau and E.M. Lifshitz, Statistical Physics, 3rd ed. (Pergamon, New York, 1980), reviewed and enlarged by E.M. Lifshitz and L.P. Pitaevskii.
30. The result for the fluctuation free energy of classical plasma is obtained in, e.g., Ref. 23 in Chap. 78.
31. Textbook explanations of the definition of (Formula presented) may be found in, e.g., Ref. 23, Eqs. (116.2) and (116.3), p. 351.
32. J. Marra, Biophys. J. 50, 815 (1986).
33. O. Krichevsky and J. Stavans, Phys. Rev. E 55, 7260 (1997).
34. Note that in the case where the counterions can be squeezed out of the surfaces [in this case (Formula presented) instead of (Formula presented) where the counterions are confined, in the limit (Formula presented)], the mean-field repulsive PB pressure (Formula presented) is weaker and scales as (Formula presented) [this is obtained in, e.g., V.A. Parsegian and D. Gingell, Biophys. J. 12, 1192 (1972); see the Appendix], instead of (Formula presented). However, in distinction to (Formula presented), the layer-charge fluctuation pressure (Formula presented) will not change its scaling behavior even in the case where the counterions can escape because it is determined exclusively by the surface concentration of the mobile layer charges (Formula presented), while (Formula presented) and (Formula presented) do depend on (Formula presented) and will be smaller than (Formula presented) in this case; thus the total fluctuation pressure (Formula presented) will have the same scaling (Formula presented), but reduced amplitude compared to the case where the counterions are confined within the volume between the surfaces.