Scaling behavior of self-avoiding tethered vesicles

Z. Zhang; H. T. Davis; D. M. Kroll

doi:10.1103/PhysRevE.48.R651

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Scaling behavior of self-avoiding tethered vesicles

Z. Zhang and H. T. Davis

D. M. Kroll

Department of Chemical Engineering and Materials Science and Center for Interfacial Engineering, University of Minnesota, Minneapolis, Minnesota 55455

Institut für Festkörperforforschung, KFA Jülich, Postfach 1913, 5170 Jülich, Germany

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Phys. Rev. E 48, R651(R) – Published 1 August, 1993

DOI: https://doi.org/10.1103/PhysRevE.48.R651

Abstract

The scaling behavior of self-avoiding tethered vesicles is analyzed using shell theory and scaling arguments. For closed networks, there is a linear coupling between the out-of-plane undulation modes and the in-plane phonon modes that causes a strong suppression of out-of-plane fluctuations at long length scales. This leads to new scaling behavior, which has important consequences for the analysis of experimental and simulation data. Molecular-dynamics simulation data for tethered vesicles are also presented and analyzed using these results. We find that the exponent η, which describes the scale dependence of the bending rigidity, has the value η=0.81±0.03.

References (31)

Present address: Laboratoire de Physique Statistique, L'ecole Normale Superieure, 24, rue L'homond, 75231 Paris Cedex 05, France.
T. Hwa, E. Kokufuta and E. Tanaka, Phys. Rev. A 44, 2235 (1991); X. Wen, C.W. Garland, T. Hwa, M. Kardar, E. Kokufuta, Y. Li, M. Orkisz and T. Tanaka, Nature 355, 426 (1992).
C.F. Schmidt, K. Svoboda, N. Lei, C.R. Safinya, S.M. Block, and D. Branton, in The Structure and Conformation of Amphiphilic Membranes, edited by R. Lipowsky, D. Richter, and K. Kremer, Springer Proceedings in Physics Vol. 66 (Springer Verlag, Berlin, 1992), p. 128.
K. Szoboda, C.F. Schmidt, D. Branton and S.M. Block, Biophys. J. 63, 784 (1992).
C. Schmidt, K. Szoboda, N. Lei, I.B. Petsche, L.E. Berman, C.R. Safinya and G. Grest, Science 259, 952 (1993).
M. Plischke and D.H. Boal, Phys. Rev. A 38, 4943 (1988); F.F. Abraham, W.E. Rudge and M. Plischke, Phys. Rev. Lett. 62, 1757 (1989); J. S. Ho and A. Baumgärtner, ibid. 63, 1324 (1989); D.H. Boal, E. Levinson, D. Liu and M. Plischke, Phys. Rev. A 40, 3292 (1989).
G. Gompper and D.M. Kroll, Europhys. Lett. 15, 783 (1991); , J. Phys. I France 1, 1411 (1991).
F.F. Abraham and M. Goulian, Europhys. Lett. 19, 293 (1992); D.M. Kroll and G. Gompper, J. Phys. I France 3, 1131 (1993).
D.R. Nelson and L. Peliti, J. Phys. (Paris) 48, 1085 (1987).
J.A. Aronovitz and T.C. Lubensky, Phys. Rev. Lett. 60, 2634 (1988).
L.D. Landau and E.M. Lifshitz, Theory of Elasticity (Pergamon, Oxford, 1959).
J.H. Jellet, Roy. Irish Acad. Trans. 22, 343 (1855).
F.I. Niordson, Shell Theory (North Holland, New York, 1985).
Two exceptions are Refs. [14] and [15].
M.A. Peterson, H. Strey and E. Sackmann, J. Phys. II France 2, 1273 (1992).
S. Komura and R. Lipowsky, J. Phys. II France 2, 1563 (1992).
P. Le Doussal and L. Radzihovsky, Phys. Rev. Lett. 69, 1209 (1992).
W. Helfrich, Z. Naturforsch. 28C, 693 (1973).
There are no edge contributions to F because of the spherical topology.
We choose the normalization ${int}_{S}$ dΩ ( $Y_{l}$ sup m $)^{2}$ = 1.
A. Zilker, H. Engelhardt and E. Sackmann, J. Phys. (Paris) 48, 2139 (1987).
R. Waugh and E.A. Evans, Biophys. J. 26, 115 (1979).
H. Engelhardt and E. Sackmann, Biophys. J. 54, 495 (1988).
There will still be logarithmic corrections; we ignore these effects here.
R. Lipowsky, Europhys. Lett. 7, 255 (1988).
F.F. Abraham and D.R. Nelson, Science 249, 4393 (1990); , J. Phys. (Paris) 51, 2653 (1990).
S. Komura and A. Baumgärtner, Phys. Rev. A 44, 3511 (1991).
I.B. Petsche and G.S. Grest (unpublished).
G.S. Grest, J. Phys. I France 1, 1695 (1991).
The factor $k_{B}$ T has been absorbed in our definition of the elastic constants so that kappa is dimensionless and K has the dimension (length) ${}^{- 2}$ .
M. Goulian, N. Lei, J. Miller and S.K. Sinha, Phys. Rev. A 46, R6170 (1992).

[c1] Present address: Laboratoire de Physique Statistique, L'ecole Normale Superieure, 24, rue L'homond, 75231 Paris Cedex 05, France.

[c2] T. Hwa, E. Kokufuta and E. Tanaka, Phys. Rev. A 44, 2235 (1991); X. Wen, C.W. Garland, T. Hwa, M. Kardar, E. Kokufuta, Y. Li, M. Orkisz and T. Tanaka, Nature 355, 426 (1992).

[c3] C.F. Schmidt, K. Svoboda, N. Lei, C.R. Safinya, S.M. Block, and D. Branton, in The Structure and Conformation of Amphiphilic Membranes, edited by R. Lipowsky, D. Richter, and K. Kremer, Springer Proceedings in Physics Vol. 66 (Springer Verlag, Berlin, 1992), p. 128.

[c4] K. Szoboda, C.F. Schmidt, D. Branton and S.M. Block, Biophys. J. 63, 784 (1992).

[c5] C. Schmidt, K. Szoboda, N. Lei, I.B. Petsche, L.E. Berman, C.R. Safinya and G. Grest, Science 259, 952 (1993).

[c6] M. Plischke and D.H. Boal, Phys. Rev. A 38, 4943 (1988); F.F. Abraham, W.E. Rudge and M. Plischke, Phys. Rev. Lett. 62, 1757 (1989); J. S. Ho and A. Baumgärtner, ibid. 63, 1324 (1989); D.H. Boal, E. Levinson, D. Liu and M. Plischke, Phys. Rev. A 40, 3292 (1989).

[c7] G. Gompper and D.M. Kroll, Europhys. Lett. 15, 783 (1991); , J. Phys. I France 1, 1411 (1991).

[c8] F.F. Abraham and M. Goulian, Europhys. Lett. 19, 293 (1992); D.M. Kroll and G. Gompper, J. Phys. I France 3, 1131 (1993).

[c9] D.R. Nelson and L. Peliti, J. Phys. (Paris) 48, 1085 (1987).

[c10] J.A. Aronovitz and T.C. Lubensky, Phys. Rev. Lett. 60, 2634 (1988).

[c11] L.D. Landau and E.M. Lifshitz, Theory of Elasticity (Pergamon, Oxford, 1959).

[c12] J.H. Jellet, Roy. Irish Acad. Trans. 22, 343 (1855).

[c13] F.I. Niordson, Shell Theory (North Holland, New York, 1985).

[c14] Two exceptions are Refs. [14] and [15].

[c15] M.A. Peterson, H. Strey and E. Sackmann, J. Phys. II France 2, 1273 (1992).

[c16] S. Komura and R. Lipowsky, J. Phys. II France 2, 1563 (1992).

[c17] P. Le Doussal and L. Radzihovsky, Phys. Rev. Lett. 69, 1209 (1992).

[c18] W. Helfrich, Z. Naturforsch. 28C, 693 (1973).

[c19] There are no edge contributions to F because of the spherical topology.

[c20] We choose the normalization ${int}_{S}$ dΩ ( $Y_{l}$ sup m $)^{2}$ = 1.

[c21] A. Zilker, H. Engelhardt and E. Sackmann, J. Phys. (Paris) 48, 2139 (1987).

[c22] R. Waugh and E.A. Evans, Biophys. J. 26, 115 (1979).

[c23] H. Engelhardt and E. Sackmann, Biophys. J. 54, 495 (1988).

[c24] There will still be logarithmic corrections; we ignore these effects here.

[c25] R. Lipowsky, Europhys. Lett. 7, 255 (1988).

[c26] F.F. Abraham and D.R. Nelson, Science 249, 4393 (1990); , J. Phys. (Paris) 51, 2653 (1990).

[c27] S. Komura and A. Baumgärtner, Phys. Rev. A 44, 3511 (1991).

[c28] I.B. Petsche and G.S. Grest (unpublished).

[c29] G.S. Grest, J. Phys. I France 1, 1695 (1991).

[c30] The factor $k_{B}$ T has been absorbed in our definition of the elastic constants so that kappa is dimensionless and K has the dimension (length) ${}^{- 2}$ .

[c31] M. Goulian, N. Lei, J. Miller and S.K. Sinha, Phys. Rev. A 46, R6170 (1992).

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Scaling behavior of self-avoiding tethered vesicles

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