The Rouse model with harmonic springs and the Langevin equation (Langevin-Rouse model) is widely used to describe the linear viscoelasticity of unentangled polymer melts. A similar model, in which the Langevin equation is replaced by discrete local jump dynamics (the jump-Rouse model), is also used to describe the dynamics of some systems such as entangled polymer melts. Intuitively, we expect that the Langevin- and jump-Rouse models give similar linear viscoelastic behaviors. However, the Langevin- and jump-Rouse models are not equivalent, and their linear viscoelastic behaviors can be different. In this work, we compare the shear relaxation moduli of the Langevin- and jump-Rouse model in detail. We develop a jump rate model in which the resampling ratio is tunable. By using this jump rate model, we can smoothly connect the jump-Rouse model and the Langevin-Rouse model. We perform kinetic Monte Carlo simulations to calculate the shear relaxation modulus data of the jump-Rouse model. We compare the simulation results with various numbers of beads and resampling ratios, and show that the shear relaxation moduli of the Langevin- and jump-Rouse models are similar but slightly different. We analyze the short-time relaxation behavior of the jump-Rouse model, and show that the local jumps give a single Maxwell type relaxation in the short-time region.
We investigate the nature of the effective dynamics and statistical forces obtained after integrating out nonequilibrium degrees of freedom. To be explicit, we consider the Rouse model for the conformational dynamics of an ideal polymer chain subject to steady driving. We compute the effective dynamics for one of the many monomers by integrating out the rest of the chain. The result is a generalized Langevin dynamics for which we give the memory and noise kernels and the effective force, and we discuss the inherited nonequilibrium aspects.
Linear viscoelastic properties for a dilute polymer solution are predicted by modeling the solution as a suspension of non-interacting bead-spring chains. The present model, unlike the Rouse model, can describe the solution's rheological behavior even when the solvent quality is good, since excluded volume effects are explicitly taken into account through a narrow Gaussian repulsive potential between pairs of beads in a bead-spring chain. The use of the narrow Gaussian potential, which tends to the more commonly used delta-function repulsive potential in the limit of a width parameter "d" goin…
The Rouse model has recently been modified to take into account the excluded volume interactions that exist between various parts of a polymer chain by incorporating a narrow Gaussian repulsive potential between pairs of beads on the Rouse chain (cond-mat/0002448). The narrow Gaussian potential is characterized by two parameters: z* - which accounts for the strength of the interaction, and d* - which accounts for the extent of the interaction. In the limit of d* going to zero, the narrow Gaussian potential tends to the more commonly used delta-function repulsive potential. The influence of the…
We theoretically investigate the looping dynamics of a linear polymer immersed in a viscoelastic fluid. The dynamics of the chain is governed by a Rouse model with a fractional memory kernel recently proposed by Weber et al. (S. C. Weber, J. A. Theriot, and A. J. Spakowitz, Phys. Rev. E 82, 011913 (2010)). Using the Wilemski-Fixman (G. Wilemski and M. Fixman, J. Chem. Phys. 60, 866 (1974)) formalism we calculate the looping time for a chain in a viscoelastic fluid where the mean square displacement of the center of mass of the chain scales as t^(1/2). We observe that the looping time is faster…
The presence of a viscoelastic mechanism distinctly different from the segmental a-relaxation and the Rouse modes within the glass-rubber transition zone of polymers had been justified by theoretical considerations, and subsequently experimentally verified in different bulk polymers by various techniques, and in several laboratories. Referred to in the literature as the sub-Rouse modes, they were also found in polymer thin films by the creep compliance measurements of McKenna and co-workers Established by experiment and theoretical considerations is the enhanced mobility of sub-Rouse modes in …
We study the dynamical response of a single semiflexible polymer chain based on the theory developed by Hallatschek et al. for the wormlike-chain model. The linear viscoelastic response under oscillatory forces acting at the two chain ends is derived analytically as a function of the oscillation frequency . We shall show that the real part of the complex compliance in the low frequency limit is consistent with the static result of Marko and Siggia whereas the imaginary part exhibits the power-law dependence +1/2. On the other hand, these compliances decrease as the power law -7/8 for the high …
In polymer melts, the interaction between segments are considered to be screened and the ideal Gaussian chain statistics is recovered. The experimental fact that linear viscoelasticity of unentangled polymers can be well described by the Rouse model is naively considered as due to this screening effect. Although various theoretical models are based on the screening effect and the screening effect is believed to be reasonable, the screening effect cannot be fully justified on a solid theoretical basis. In this work, we study the screening effect by utilizing a simple dumbbell type model. We per…
The overdamped (inertialess) dumbbell model is widely utilized to study rheological properties of polymers or other soft matters. In most cases, the effect of inertia is merely neglected because the momentum relaxation is much faster than the bond relaxation. We theoretically analyze the effect of inertia on the linear viscoelasticity of the harmonic dumbbell model. We show that the momentum and bond relaxation modes are kinetically coupled and the inertia can affect the bond relaxation if the momentum relaxation is not sufficiently fast. We derive an overdamped Langevin equation for the dumbb…
The local dynamical features of a PEO melt studied by MD simulations are compared to two model chain systems, namely the well-known Rouse model as well as the semiflexible chain model (SFCM) that additionally incorporates chain stiffness. Apart from the analysis of rather general quantities such as the mean square displacement (MSD), we present a new statistical method to extract the local bead mobility from the simulation data on the basis of the Langevin equation, thus providing a complementary approach to the classical Rouse-mode analysis. This allows us to check the validity of the Langevi…
Anomalous diffusion in coupled viscoelastic media: A fractional Langevin equation approach
Pohang University of Science and Technology（浦项科技大学）；Institute for Theoretical Science, Pohang University of Science and Technology（浦项科技大学理论科学研究所）；Asia Pacific Center for Theoretical Physics（亚太理论物理中心）
For reproducing the anomalous -- i.e., sub- or super-diffusive -- behavior in some stochastic dynamical systems, the Generalized Langevin Equation (GLE) has gained considerable popularity in recent years. Motivated by the question whether or not a system with anomalous dynamics can have the GLE formulation, here I consider polymer physics, where sub-diffusive behavior is commonplace. I provide an exact derivation of the GLE for phantom Rouse polymers, andby identifying polymeric response to local strains, I argue the case for the GLE formulation for self-avoiding polymers and polymer transloca…
Viscoelastic properties of polymer melts are particularly challenging to compute due to the intrinsic stress fluctuations in molecular dynamics (MD). We compared equilibrium and non-equilibrium MD approaches for extracting the storage (G') and loss moduli (G") over a wide frequency range from a bead-spring chain model, in both unentangled and entangled regimes. We found that, with properly chosen data processing and noise reduction procedures, different methods render quantitatively equivalent results. In equilibrium MD (EMD), applying the Green-Kubo relation with a multi-tau correlator method…
Linear Viscoelasticity of Semiflexible Polymers with Hydrodynamic Interactions
IITB-Monash Research Academy, Indian Institute of Technology Bombay（印度理工学院孟买分校 IITB-莫纳什研究院）；Department of Chemical Engineering, Indian Institute of Technology Bombay（印度理工学院孟买分校化学工程系）；Department of Chemical and Biological Engineering, Monash University（莫纳什大学化学与生物工程系）
Stress Relaxation in Monodisperse Entangled Polymer Melts: Correlation Between Viscoelastic Response and Single-Chain Relaxation via Molecular Dynamics Simulations
Johannes Gutenberg-Universität Mainz（约翰内斯·古腾堡美因茨大学）
Polydispersity is inevitable in industrially produced polymers. Established theories of polymer dynamics and rheology, however, were mostly built on monodisperse linear polymers. Dynamics of polydisperse polymers is yet to be fully explored -- especially how chains of different lengths affect the dynamics of one another in a mixture. This study explored the dynamics of bidisperse polymer melts using molecular dynamics and a bead-spring chain model. Binary mixtures between a moderately entangled long-chain species and an unentangled or marginally entangled short-chain species were investigated.…
Complexation between anionic and cationic polyelectrolytes results in solid-like precipitates or liquid-like coacervate depending on the added salt in the aqueous medium. However, the boundary between these polymer-rich phases is quite broad and the associated changes in the polymer relaxation in the complexes across the transition regime are poorly understood. In this work, the relaxation dynamics of complexes across this transition is probed over a wide timescale by measuring viscoelastic spectra and zero-shear viscosities at varying temperatures and salt concentrations for two different sal…
