Longest Polymer Relaxation Time Research Articles

Hydrodynamic correlations of viscoelastic fluids by multiparticle collision dynamics simulations.

The emergent fluctuating hydrodynamics of a viscoelastic fluid modeled by the multiparticle collision dynamics (MPC) approach is studied. The fluid is composed of flexible, Gaussian phantom polymers that interact by local momentum-conserving stochastic MPCs. For comparison, the analytical solution of the linearized Navier-Stokes equation is calculated, where viscoelasticity is taken into account by a time-dependent shear relaxation modulus. The fluid properties are characterized by the transverse velocity autocorrelation function in Fourier space as well as in real space. Various polymer lengths are considered-from dumbbells to (near-)continuous polymers. Viscoelasticity affects the fluid properties and leads to strong correlations, which overall decay exponentially in Fourier space. In real space, the center-of-mass velocity autocorrelation function of individual polymers exhibits a long-time tail, independent of the polymer length, which decays as t-3/2, similar to a Newtonian fluid, in the asymptotic limit t → ∞. Moreover, for long polymers, an additional power-law decay appears at time scales shorter than the longest polymer relaxation time with the same time dependence, but negative correlations, and the polymer length dependence L-1/2. Good agreement is found between the analytical and simulation results.

Internal dynamics of semiflexible polymers with active noise.

The intramolecular dynamics of flexible and semiflexible polymers in response to active noise is studied theoretically. The active noise may either originate from interactions of a passive polymer with a bath of active Brownian particles or the polymer itself is comprised of active Brownian particles. We describe the polymer by the continuous Gaussian semiflexible-polymer model, taking into account the finite polymer extensibility. Our analytical calculations predict a strong dependence of the polymer dynamics on the activity. In particular, active semiflexible polymers exhibit a crossover from a bending elasticity-dominated dynamics at weak activity to that of flexible polymers at strong activity. The end-to-end vector correlation function decays exponentially for times longer than the longest polymer relaxation time. Thereby, the polymer relaxation determines the decay of the correlation function for long and flexible polymers. For shorter and stiffer polymers, the relaxation behavior of individual active Brownian particles dominates the decay above a certain activity. The diffusive dynamics of a polymer is substantially enhanced by the activity. Three regimes can be identified in the mean square displacement for sufficiently strong activities: an activity-induced ballistic regime at short times, followed by a Rouse-type polymer-specific regime for any polymer stiffness, and free diffusion at long times, again determined by the activity.

Shear thinning behavior of linear polymer melts under shear flow via nonequilibrium molecular dynamics.

The properties of both untangled and entangled linear polymer melts under shear flow are studied by nonequilibrium molecular dynamics simulations. The results reveal that the dependence of shear viscosity η on shear rate γ, expressed by n ~ γ(-n), exhibits three distinct regimes. The first is the well-known Newtonian regime, namely, η independent of shear rate at small shear rates γ < τ0(-1) (where τ0 is the longest polymer relaxation time at equilibrium). In the non-Newtonian regime (γ > τ0(-1)) the shear dependence of viscosity exhibits a crossover at a critical shear rate γc dividing this regime into two different regimes, shear thinning regime I (ST-I) and II (ST-II), respectively. In the ST-I regime (τ0(-1) < γ < γc), the exponent n increases with increasing chain length N, while in the ST-II regime (γ > γc) a universal power law n ~ γ(-0.37) is found for considered chain lengths. Furthermore, the longer the polymer chain is, the smaller the shear viscosity for a given shear rate in the ST-II regime. The simulation also shows that a characteristic chain length, below which γc will be equal to τ0(-1), lies in the interval 30 < N < 50. For all considered chain lengths in the ST-II regime, we also find that the first and second normal stress differences N1 and N2 follow power laws of N1 ~ γ(2/3) and N2 ~ γ(0.82), respectively; the orientation resistance parameter mG follows the relation mG ~ γ(0.75) and the tumbling frequency ftb follows ftb ~ γ(0.75). These results imply that the effects of entanglement on the shear dependences of these properties may be negligible in the ST-II regime. These findings may shed some light on the nature of shear thinning in flexible linear polymer melts.

Renormalization group analysis of polymer cyclization with non-equilibrium initial conditions

We develop a renormalization group approach for cyclizing polymers for the case when chain ends are initially close together (ring initial conditions). We analyze the behavior at times much shorter than the longest polymer relaxation time. In agreement with our previous work (Europhys. Lett. 73, 621 (2006)) we find that the leading time dependence of the reaction rate k(t) for ring initial conditions and equilibrium initial conditions are related, namely k (ring)(t) proportional, variant t (-delta) and k (eq)(t) proportional, variant t (1-delta) for times less than the longest polymer relaxation time. Here delta is an effective exponent which approaches delta = 5/4 for very long Rouse chains. Our present analysis also suggests a "sub-leading" term proportional to (ln t)/t which should be particularly significant for smaller values of the renormalized reaction rate and early times. For Zimm dynamics, our RG analysis indicates that the leading time dependence for the reaction rate is k(t) approximately 1/t for very long chains. The leading term is again consistent with the expected relation between ring and equilibrium initial conditions. We also find a logarithmic correction term which we "exponentiate" to a logarithmic form with a Landau pole. The presence of the logarithm is particularly important for smaller chains and, in the Zimm case, large values of the reaction rate.

Shear Thinning and Tumbling Dynamics of Single Polymers in the Flow-Gradient Plane

The conformational changes imparted on single, flexible DNA polymers by a steady, simple shear flow were directly visualized in the flow-gradient plane. Two fluorescently stained DNA double-strand sizes of 22 μm and 80 μm in contour length were employed, and Wi values of up to 584 were probed (Wi = shear rate × longest polymer relaxation time). By exploitation of the linear proportionality between polymer density and its recorded image, the accessible radius of gyration tensor elements (Gij) were measured. Of those, the ensemble-averaged 〈G22〉 and 〈G12〉 were related to the bulk shear viscosity and first normal stress coefficient, respectively, via the Giesekus stress tensor. We found their respective behaviors to follow power-law decays of Wi -0.52 and Wi -1.28 at large Wi. Polymer dynamics were also investigated. Like rigid ellipsoids of revolution, polymers displayed a constant partition between positive and negative orientations irrespective of shear rate at Wi ≫ 1. Unlike them, however, polymers prefe...

Reactive Polymer Interfaces: How Reaction Kinetics Depend on Reactivity and Density of Chemical Groups

We present a systematic theory of polymer reaction kinetics at an interface separating two immiscible melts, A and B, in each of which a fraction of chains carry reactive end groups. We consider arbitrary values of local group reactivity, Qb, and reactive group densities in either bulk, n A and n B , with the convention nA e nB . At short times reaction kinetics are second order in bulk densities. Initially, kinetics are of simple mean field type, with surface density of reaction product after time t given by R t Qbha 3 tnA nB where h is the interface width and a reactive group size. If Qb exceeds a density-dependent threshold a transition occurs, at a time less than the longest polymer relaxation time U, to second order diffusion-controlled (DC) kinetics with R t xt 4nA nB . Here xt is the rms monomer displacement. Logarithmic corrections arise in marginal cases. This leads to R t t/(ln t) for unentangled chains, while for entangled melts consecutive regimes R t t/(ln t), R t t . At a certain time scale the interface saturates with AB copolymer product and reactions are strongly suppressed. This prevents the onset of the long time first-order DC regime if the reactivity is very small, Qb < Qb † with Qb † 1/N 1/2 (unentangled melts) or Qb † 1/N 3/2 (entangled).

Reaction kinetics in polymer melts

We study the reaction kinetics of end-functionalized polymer chains dispersed in an unreactive polymer melt. Starting from an infinite hierarchy of coupled equations for many-chain correlation functions, a closed equation is derived for the 2nd order rate constant $k$ after postulating simple physical bounds. Our results generalize previous 2-chain treatments (valid in dilute reactants limit) by Doi, de Gennes, and Friedman and O'Shaughnessy, to arbitrary initial reactive group density $n_0$ and local chemical reactivity $Q$. Simple mean field (MF) kinetics apply at short times, $k \sim Q$. For high $Q$, a transition occurs to diffusion-controlled (DC) kinetics with $k \approx x_t^3/t$ (where $x_t$ is rms monomer displacement in time $t$) leading to a density decay $n_t \approx n_0 - n_0^2 x_t^3$. If $n_0$ exceeds the chain overlap threshold, this behavior is followed by a regime where $n_t \approx 1/x_t^3$ during which $k$ has the same power law dependence in time, $k \approx x_t^3/t$, but possibly different numerical coefficient. For unentangled melts this gives $n_t \sim t^{-3/4}$ while for entangled cases one or more of the successive regimes $n_t \sim t^{-3/4}$, $t^{-3/8}$ and $t^{-3/4}$ may be realized depending on the magnitudes of $Q$ and $n_0$. Kinetics at times longer than the longest polymer relaxation time $\tau$ are always MF. If a DC regime has developed before $\tau$ then the long time rate constant is $k \approx R^3/\tau$ where $R$ is the coil radius. We propose measuring the above kinetics in a model experiment where radical end groups are generated by photolysis.