Considerations on the multiple scattering representation of the concentration dependence of the viscoelastic properties of polymer systems

Review: Kirkwood-Riseman Model in Non-Dilute Polymeric Fluids

In two prior articles, I demonstrated from extensive simulational studies by myself and others that the Rouse model of polymer dynamics is invalid in polymer melts and in dilute solution. However, the Rouse model is the foundational basis for most modern theories of polymeric fluid dynamics, such as reptation/scaling models. One therefore rationally asks whether there is a replacement. There is, namely by extending the Kirkwood-Riseman model. Here, I present a comprehensive review of one such set of extensions, namely the hydrodynamic scaling model. This model assumes that polymer dynamics in dilute and concentrated solution is dominated by solvent-mediated hydrodynamic interactions; chain crossing constraints are taken to create only secondary corrections. Many other models assume, contrariwise, that in concentrated solutions, the chain crossing constraints dominate the dynamics. An extended Kirkwood-Riseman model incorporating interchain hydrodynamic interactions is developed. It yields pseudovirial series for the concentration and molecular weight dependencies of the self-diffusion coefficient Ds and the low-shear viscosity η. To extrapolate to large concentrations, rationales based on self-similarity and on the Altenberger-Dahler positive-function renormalization group are presented. The rationales correctly predict how Ds and η depend on polymer concentration and molecular weight. The renormalization group approach leads to a two-parameter ansatz that correctly predicts the functional forms of the frequency dependencies of the storage and loss moduli. A short description is given of each of the papers that led to the hydrodynamic scaling model. Experiments supporting the aspects of the model are noted.

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.

Rotational and translational diffusion of fluorocarbon tracer spheres in semidilute xanthan solutions

We report an experimental study of rotational and translational diffusion and sedimentation of colloidal tracer spheres in semidilute solutions of the nonadsorbing semiflexible polymer xanthan. The tracers are optically anisotropic, permitting depolarized dynamic light scattering measurements without interference from the polymer background. The xanthan solutions behave rheologically like model semidilute polymeric solutions with long-lived entanglements. On the time scale of tracer motion the xanthan solutions are predominantly elastic. The generalized Stokes-Einstein relation describing the polymer solution as a continuous viscous fluid therefore severely overestimates the tracer hindrance. Instead, effective medium theory, describing the polymer solution as a homogeneous Brinkman fluid with a hydrodynamic screening length equal to the concentration-dependent static correlation length, is in excellent agreement with the tracer sedimentation and rotational diffusion coefficients. Rotational diffusion, however, is at the same time in good agreement with a simple model of a rotating sphere in a concentric spherical depletion cavity. Translational diffusion is faster than predicted for a Brinkman fluid, likely due to polymer depletion.

Screening of hydrodynamic interactions in semidilute polymer solutions: a computer simulation study

We study single-chain motion in semidilute solutions of polymers of length N=1000 with excluded-volume and hydrodynamic interactions by a novel algorithm. The crossover length of the transition from Zimm (short lengths and times) to Rouse dynamics (larger scales) is proportional to the static screening length. The crossover time is the corresponding Zimm time. Our data indicate Zimm behavior at large lengths but short times. There is no hydrodynamic screening until the chains feel constraints, after which they resist the flow: "Incomplete screening" occurs in the time domain.