Search

A quantitative theory of hydrodynamic interactions in unentangled polymer melts and concentrated solutions is presented. The study is focussed on the pre-Rouse transient time regimes (t < τR, the Rouse relaxation time) where the hydrodynamic response is governed mainly by the viscoelastic effects. It is shown that transient viscoelastic hydrodynamic interactions are not suppressed (screened) at large distances and are virtually independent of polymer molecular mass. A number of transient regimes of unusual and qualitatively different behavior of isotropic and anisotropic hydrodynamic response functions are elucidated. The regimes are characterized in terms of two main length-scale dependent characteristic times: momentum spreading time τi ∝ r4/3 and viscoelastic time τ* ∝ r4. It is shown that for t > τi the viscoelastic hydrodynamic interactions can be described in terms of the time or length scale dependent effective viscosity which, for t < τR and/or for r < Rcoil, turns out to be much lower than the macroscopic 'polymer' viscosity ηm. The theory also involves a quantitative analysis of the length-scale dependent stress relaxation in polymer melts. The general predictions for hydrodynamic interactions in thermostated systems with Langevin friction are obtained as well. [ABSTRACT FROM AUTHOR]

By Monte Carlo simulations of a variant of the bond-fluctuation model without topological constraints, we examine the center-of-mass (COM) dynamics of polymer melts in d = 3 dimensions. Our analysis focuses on the COM displacement correlation function CN(t)≈∂t2hN(t)/2, measuring the curvature of the COM mean-square displacement hN(t). We demonstrate that CN(t) ≈ -(RN/TN)2(ρ*/ρ) f(x = t/TN) with N being the chain length (16 <= N <= 8192), RN ∼ N1/2 is the typical chain size, TN ∼ N2 is the longest chain relaxation time, ρ is the monomer density, ρ*≈N/RNd is the self-density, and f(x) is a universal function decaying asymptotically as f(x) ∼ x-ω with ω = (d + 2) × α, where α = 1/4 for x < 1 and α = 1/2 for x > 1. We argue that the algebraic decay NCN(t) ∼ -t-5/4 for t < TN results from an interplay of chain connectivity and melt incompressibility giving rise to the correlated motion of chains and subchains. [ABSTRACT FROM AUTHOR]

We present the derivation of coarse-grained force fields for two types of polymers, polyethylene (PE), and cis-polybutadiene (cis-PB), using the concept of potential of mean force. Coarse-grained force fields were obtained from microscopic simulations for several coarse-graining levels, i.e., different number of monomers &grave; per mesoscopic unit called "bead." These force fields are then used in dissipative particle dynamics (DPD) simulations to study structural and dynamical properties of polymer melts of PE and cis-PB. The radial distribution functions g(R), the end-to-end distance R0, the end-to-end vector relaxation time τ, and the chain center of mass self-diffusion DCM are computed for different chain lengths at different coarse-graining factor τ. Scaling laws typical of the Rouse regime are obtained for both polymers for chain lengths ranging from 6 to 50 beads. It is found that the end-to-end distance R0 obtained from DPD simulations agree well with values obtained from both microscopic simulations and experiments. The dependence of the friction coefficient used in DPD simulations versus the coarse-graining level is discussed in view of the overall scaling of the dynamical properties. [ABSTRACT FROM AUTHOR]

We quantitatively assess the effect of density fluctuation modes on the dynamics of a tagged polymer in an unentangled melt. To this end, we develop a density-based mode-coupling theory (dMCT) using the Mori-Zwanzig approach and projecting the fluctuating force onto pair-density fluctuation modes. The effect of dynamical density fluctuations on the center-of-mass (cm.) dynamics is also analyzed based on a perturbative approach and we show that dMCT and perturbation techniques yield identical results. The cm. velocity autocorrelation function (cm. VAF) exhibits a slow power law relaxation in the time range between the monomer time t1 and the Rouse relaxation time tN. We obtain an analytical expression for the cm. VAF in terms of molecular parameters. In particular, the cm. VAF scales as -- N-1t5/4 (where N is the number of monomer units per chain) in the relevant time regime. The results are qualitatively accounted for by the dynamical correlation hole effect. The predicted --t5/4 dependence of the cm. VAF is supported by data of non-momentum-conserving computer simulations. However, the comparison shows that the theory significantly underestimates the amplitude of the effect. This issue is discussed and an alternative approach is addressed in the second part of this series [Farago et al., Phys. Rev. E 85, 051807 (2012), the following paper]. [ABSTRACT FROM AUTHOR]

A mode-coupling theory (MCT) version (called hMCT thereafter) of a recently presented theory [Farago, Meyer, and Semenov, Phys. Rev. Lett. 107, 178301 (2011)] is developed to describe the diffusional properties of a tagged polymer in a melt. The hMCT accounts for the effect of viscoelastic hydrodynamic interactions (VHIs), that is, a physical mechanism distinct from the density-based MCT (dMCT) described in the first paper of this series. The two versions of the MCT yield two different contributions to the asymptotic behavior of the center-of-mass velocity autocorrelation function (cm. VAF). We show that in most cases the VHI mechanism is domiijant; for long chains and prediffusive times it yields a negative tail ∝--N-1/2t-3/2 for the cm. VAF. The case of non-momentum-conserving dynamics (Langevin or Monte Carlo) is discussed as well. It generally displays a distinctive behavior with two successive relaxation stages: first --N-15/4t-5/4 (as in the dMCT approach), then --N-1/2t-3/2. Both the amplitude and the duration of the first t-5/4 stage crucially depend on the Langevin friction parameter y. All results are also relevant for the early time regime of entangled melts. These slow relaxations of the cm. VAF, thus account for the anomalous subdiffusive regime of the cm. mean square displacement widely observed in numerical and experimental works. [ABSTRACT FROM AUTHOR]

Contrary to common belief, hydrodynamic interactions in polymer melts are not screened beyond the monomer length and are important in transient regimes. We show that viscoelastic hydrodynamic interactions (VHIs) lead to anomalous dynamics of a tagged chain in an unentangled melt at t < tN, the Rouse time. The center-of-mass (c.m.) mean-square displacement is enhanced by a large factor increasing with chain length. We develop a theory of VHI-controlled chain dynamics yielding a negative c.m. velocity autocorrelation function which agrees with our molecular dynamics simulations without any fitting parameter. It is also shown that Langevin friction strongly affects the short-t c.m. dynamics, also captured by our theory. The transient VHI effects thus provide the dominant contribution to the subdiffusive c.m. motion universally observed in simulations and experiments. [ABSTRACT FROM AUTHOR]

We introduce a theoretical model of simple fluid, whose interactions, defined in terms of the Voronoi cells of the configurations, are local and many-body. The resulting system is studied both theoretically and numerically. We show that the fluid, though sharing the global features of other models of fluids with soft interactions, has several unusual characteristics, which are investigated and discussed. [ABSTRACT FROM AUTHOR]

The continuous-time random walk (CTRW) describes the single-particle dynamics as a series of jumps separated by random waiting times. This description is applied to analyze trajectories from molecular dynamics (MD) simulations of a supercooled polymer melt. Based on the algorithm presented by Helfferich et al. [Phys. Rev. E 89,042603 (2014)], we detect jump events of the monomers. As a function of temperature and chain length, we examine key distributions of the CTRW: the jump-length distribution (JLD), the waiting-time distribution (WTD), and the persistence-time distribution (PTD), i.e., the distribution of waiting times for the first jump. For the equilibrium (polymer) liquid under consideration, we verify that the PTD is determined by the WTD. For the mean-square displacement (MSD) of a monomer, the results for the CTRW model are compared with the underlying MD data. The MD data exhibit two regimes of subdiffusive behavior, one for the early a process and another at later times due to chain connectivity. By contrast, the analytical solution of the CTRW yields diffusive behavior for the MSD at all times. Empirically, we can account for the effect of chain connectivity in Monte Carlo simulations of the CTRW. The results of these simulations are then in good agreement with the MD data in the connectivity-dominated regime, but not in the early a regime where they systematically underestimate the MSD from the MD. [ABSTRACT FROM AUTHOR]

Single-particle trajectories in supercooled liquids display long periods of localization interrupted by "fast moves." This observation suggests a modeling by a continuous-time random walk (CTRW). We perform molecular dynamics simulations of equilibrated short-chain polymer melts near the critical temperature of mode-coupling theory Fc and extract "moves" from the monomer trajectories. We show that not all moves comply with the conditions of a CTRW. Strong forward-backward correlations are found in the supercooled state. A refinement procedure is suggested to exclude these moves from the analysis. We discuss the repercussions of the refinement on the jump-length and waiting-time distributions as well as on characteristic time scales, such as the average waiting time ("exchange time") and the average time for the first move ("persistence time"). The refinement modifies the temperature (F) dependence of these time scales. For instance, the average waiting time changes from an Arrhenius-type to a Vogel-Fulcher-type T dependence. We discuss this observation in the context of the bifurcation of the a process and (Johari) ß process found in many glass-forming materials to occur near Fc. Our analysis lays the foundation for a study of the jump-length and waiting-time distributions, their temperature and chain-length dependencies, and the modeling of the monomer dynamics by a CTRW approach in the companion paper [J. Helfferich et al., Phys. Rev. E 89, 042604 (2014)]. [ABSTRACT FROM AUTHOR]