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Acta Physica Slovaca 65, No.1, 1 – 64 (2015) (64 pages)
GENERALIZED LANGEVIN THEORY OF THE BROWNIAN MOTION AND THE DYNAMICS OF POLYMERS IN SOLUTION Jana Tóthová1 and Vladimír Lisý1,2 1Department of Physics, Technical University of Košice, Park Komenského 2, 042 00 Košice, Slovakia 2Laboratory of Radiation Biology, Joint Institute of Nuclear Research, 141 980 Dubna, Moscow Region, Russia Full text: ::pdf :: (Received 12 May 2015, accepted 14 May 2015) Abstract: The review deals with a generalization of the Rouse and Zimm bead-spring models of the dynamics of flexible polymers in dilute solutions. As distinct from these popular theories, the memory in the polymer motion is taken into account. The memory naturally arises as a consequence of the fluid and bead inertia within the linearized Navier-Stokes hydrodynamics. We begin with a generalization of the classical theory of the Brownian motion, which forms the basis of any theory of the polymer dynamics. The random force driving the Brownian particles is not the white one as in the Langevin theory, but “colored”, i.e., statistically correlated in time, and the friction force on the particles depends on the history of their motion. An efficient method of solving the resulting generalized Langevin equations is presented and applied to the solution of the equations of motion of polymer beads. The memory effects lead to several peculiarities in the time correlation functions used to describe the dynamics of polymer chains. So, the mean square displacement of the polymer coils contains algebraic long-time tails and at short times it is ballistic. It is shown how these features reveal in the experimentally observable quantities, such as the dynamic structure factors of the scattering or the viscosity of polymer solutions. A phenomenological theory is also presented that describes the dependence of these quantities on the polymer concentration in solution. DOI: PACS: 05.40.Jc, 05.10.Gg, 61.25.he, 82.35.Lr Keywords: Brownian motion, Generalized Langevin equation, Polymer solutions, Polymer dynamics, Bead-spring models, Memory effects, Scattering of light and neutrons, Viscosity of polymer solutions |
ISSN 1336-040X (online) ISSN 0323-0465 (printed) For authors: ActaStyle.cls |
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