Abstract
We study the diffusion of polymers through quenched short-range correlated random media by renormalization group (RG) methods, which allow us to derive universal predictions in the limit of long chains and weak disorder. We take local quenched random potentials with second momentv and the excluded-volume interactionu of the chain segments into account. We show that our model contains the relevant features of polymer diffusion in random media in the RG sense if we focus on the local entropic effects rather than on the topological constraints of a quenched random medium. The dynamic generating functional and the general structure of its perturbation expansion inu andv are derived. The distribution functions for the center-of-mass motion and the internal modes of one chain and for the correlation of the center of mass motions of two chains are calculated to one-loop order. The results allow for sufficient cross-checks to have trust in the one-loop renormalizability of the model. The general structure as well as the one-loop results of the integrated RG flow of the parameters are discussed. Universal results can be found for the effective static interactionw≔u−v≥0 and for small effective disorder coupling\(\bar v(l)\) on the intermediate length scalel. As a first physical prediction from our analysis, we determine the general nonlinear scaling form of the chain diffusion constant and evaluate it explicitly as
for\(\bar v(l) \ll 1\).
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References
J. des Cloizeaux and G. Jannink,Les Polymeres en Solution (Les Ulis-France, 1987, in English: Clarendon Press, Oxford 1990).
U. Ebert and L. Schäfer,Makromol. Chem./Macromol. Symp. 81:31 (1994).
L. Schäfer, Private communication.
Y. Oono,Adv. Chem. Phys. 61:301 (1985).
B. Schaub, D. B. Creamer, and H. Johannesson,J. Phys. A 21:1431 (1988) and references therein.
M. Doi and S. F. Edwards,The Theory of Polymer Dynamics (Clarendon Press, Oxford, 1986).
A. Baumgärtner and M. Muthukumar,J. Chem. Phys. 87:3082 (1987); M. Muthukumar and A. Baumgärtner,Macromolecules 22:1937, 1941 (1989).
J. Machta,Phys. Rev. A 40:1720 (1989).
T. P. Lodge, N. A. Rotstein, and S. Prager,Adv. Chem. Phys. 79:1 (1990).
G. C. Martinez-Mekler and M. A. Moore,J. Phys. Lett. (Paris)42:L 413 (1981).
U. Ebert and L. Schäfer,Europhys. Lett. 21:741 (1993); L. Schäfer and U. Ebert,Makromol. Chem./Macromol. Symp. 81:17 (1994).
U. Ebert, A. Baumgärtner, and L. Schäfer,Phys. Rev. E [to appear].
B. Duplantier,Phys. Rev. A 38:364 (1988).
A. B. Harris,Z. Phys. B 49:347 (1983).
R. Bausch, H. K. Janssen, and H. Wagner,Z. Phys. B 24:113 (1976).
H. K. Janssen,Kritische Dynamik, Lecture notes, University of Düsseldorf (1985).
P.-G. de Gennes,Physics 3:37 (1967).
B. J. Berne and R. Pecora,Dynamic Light Scattering (Wiley, New York, 1976).
A. A. Vladimirov, D. I. Kazakov, and O. V. Tarasov,Sov. Phys. JETP 50:521 (1979).
K. G. Chetyrkin, S. G. Gorischny, S. A. Larin, and F. V. Tkachov,Phys. Lett. B 132:351 (1983).
H. Kleinert, J. Neu, V. Schulte-Frohlinde, K. G. Chetyrkin, and S. A. Larin,Phys. Lett. B 272:39 (1991).
R. Schloms and V. Dohm,Nucl. Phys. B 328:639 (1989).
B. Krüger and L. Schäfer,J. Phys. I. France 4:757 (1994).
L. Schäfer, U. Lehr, and Ch. Kapeller,J. Phys. I France 1:211 (1991).
L. Schäfer and C. Kappeler,J. Chem. Phys. 99:6135 (1993).
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Ebert, U. Polymer diffusion in quenched disorder: A renormalization group approach. J Stat Phys 82, 183–265 (1996). https://doi.org/10.1007/BF02189230
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DOI: https://doi.org/10.1007/BF02189230