Long-time tails in the dynamics of Rouse polymers

Abstract

The Rouse model of the dynamics of polymers in solution is generalized by taking into account the hydrodynamic memory during the motion of the polymer monomers in an incompressible liquid. This leads to new peculiarities in the behavior of the time correlation functions describing the polymer motion. It is demonstrated by the appearance of long-time tails of these functions. The mean square displacement of the polymer coil as a whole contains, in addition to the Einstein term ∼t, other contributions, the leading of which is ∼t1/2. The behavior of the correlation functions for internal modes differs from the traditional exponential relaxation: as t→∞, they consist of tails decaying like t−n/2, the longest-lived being ∼t−3/2.

The joint Rouse-Zimm theory of the dynamics of polymers in dilute solutions

“…This expression holds in the case of steady flow and takes into account the hydrodynamic interaction. In a more general case, with the hydrodynamic memory [9,12,15] the force (2) should be replaced by the Boussinesq force and equation (1) has to be solved together with the nonstationary hydrodynamic equations for the macroscopic velocity of the solvent. To take into account the presence of other polymers in solution, we use the Brinkman's work [13] (see also [14]) in which a polymer is considered as a porous medium.…”

“…The considered time scales are t τ R = R 2 ρ/η, where R is the hydrodynamic radius of the polymer, ρ is the density and η is the viscosity of the solvent. This means that the effects of hydrodynamic memory (or the viscous aftereffect) are neglected [9,12,15]. The distribution of the coils in solution is considered to be stationary (this is justified at least for the times t τ D ; the choice of this time scale is possible since always τ p τ D , where τ D = R 2 /D is the characteristic time of the coil diffusion with the diffusion coefficient D).…”

“…Next, the internal modes are distributed discretely (the assumption of their continuous distribution with respect to p is true only in a restricted time domain and often leads to incorrect interpretation of experimental data [11]. The formalism from our theory with the time-dependent hydrodynamics of polymers has been adopted [9,12] and, finally, the Brinkman's theory [13,14] for the flow in porous media is used in order to take into account the effect of other coils on the test polymer. The presented theory has the following limitations.…”

The effects of hydrodynamic noise on the diffusion of polymers in dilute solutions

“…In the next section we briefly summarize the approach used in our previous papers [10,11,20]. Then we derive the generalized RZ equation taking into account the effects of hydrodynamic noise, with random fluctuations of the hydrodynamic stress tensor being responsible for the noise.…”

“…In our previous papers [10,11], a generalization of the RZ theory that can be called the hydrodynamic RZ model has been proposed. The main idea of this generalization comes from the theory of the Brownian motion, which lies in the basis of the RZ model.…”