Abstract
The large-scale behavior of surface-interacting self-avoiding polymer chains placed on finitely ramified fractal lattices is studied using exact recursion relations. It is shown how to obtain surface susceptibility critical indices and how to modify a scaling relation for these indices in the case of fractal lattices. We present the exact results for critical exponents at the point of adsorption transition for polymer chains situated on a class of Sierpinski gasket-type fractals. We provide numerical evidence for a critical behavior of the type found recently in the case of bulk self-avoiding random walks at the fractal to Euclidean crossover.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
E. Bouchaud, L. Auvray, J. Cotton, M. Daoud, B. Farnoux, and G. Jannink,Prog. Surf. Sci. 27:5 (1988).
P. G. de Gennes,Adv. Colloid Interface Sci. 27:189 (1987).
K. Binder and K. Kremer, inScaling Phenomena in Disordered Systems, R. Pynn and A. Skjeltrop, eds. (Plenum Press, New York, 1985), p. 525.
D. Napper,Polymeric Stabilization of Colloidal Dispersions (Academic Press, New York, 1983).
E. Eisenriegler, K. Kremer, and K. Binder,J. Chem. Phys. 77:6296 (1982).
K. Binder, inPhase Transitions and Critical Phenomena, Vol. 8, C. Domb and J. L. Lebowitz, eds. (Academic Press, New York, 1983).
H. Meirovitch and S. Livne,J. Chem. Phys. 88:4507 (1988).
F. Seno and A. L. Stella,Europhys. Lett. 7:605 (1989).
T. Ishinabe,J. Chem. Phys. 76:5589 (1982).
K. De'Bell, T. Lookman, and S. G. Whittington,Phys. Rev. A 41:682 (1990).
I. Guim and T. Burkhardt,J. Phys. A 22:1131 (1989).
A. R. Veal, J. M. Yeomans, and G. J. Jug,J. Phys. A 24:827 (1991).
K. Kremer,J. Phys. A 16:4333 (1983).
M. Benhamou and G. Mahoux,J. Phys. (Paris)49:577 (1988), and references therein.
B. Duplantier and H. Saleur,Phys. Rev. Lett. 57:3179 (1986).
T. W. Burkhardt, E. Eisenriegler, and I. Guim,Nucl. Phys. B 316:559 (1989).
G. H. Weiss and R. J. Rubin,Adv. Chem. Phys. 52:363 (1983).
V. Privman, G. Forgacs, and H. L. Frisch,Phys. Rev. B 37:9897 (1988).
E. Bouchaud and J. Vannimenus,J. Phys. (Paris)50:2931 (1989).
J. Vannimenus,Physica D 38:351 (1989).
S. Elezović, M. Knežević, and S. Milošević,J. Phys. A 20:1215 (1987).
D. Dhar,J. Phys. (Paris)49:397 (1988).
S. Milošević and I. Živić,J. Phys. A 24:L833 (1991).
B. Nienhuis,Phys. Rev. Lett. 49:1062 (1982).
D. Dhar,J. Math. Phys. 18:577 (1977).
D. Dhar,J. Math. Phys. 19:5 (1978).
B. Duplantier,J. Stat. Phys. 54:581 (1989).
M. Knežević, unpublished.
J. A. Given and B. B. Mandelbrot,J. Phys. A 16:L56 (1983).
B. Derrida and H. Herrmann,J. Phys. (Paris)44:1365 (1984).
B. Bonnier, Y. Leroyer, and C. J. Meyers,J. Phys. (Paris)48:533 (1987).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bubanja, V., Knežević, M. & Vannimenus, J. Adsorption of a flexible self-avoiding polymer chain: Exact results on fractal lattices. J Stat Phys 71, 1–21 (1993). https://doi.org/10.1007/BF01048085
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01048085