ABSTRACT
We consider the spatiotemporal fluctuation of slip-link positions via the implementation of elastic slip-links. The level of description is similar to our previously proposed slip-link model, wherein we use the entanglement position in space as dynamic variables, and the number of Kuhn steps between entanglements. However, since it is a mean-field, single-chain description it has some relevance to the slip-spring simulations of Likhtman, and the phantom chain model for cross-linked networks. It might also provide a connection between slip-links and tubes. Two implementations are possible, depending on whether or not the slip-links are allowed to pass through one another. If a boundary condition on the dynamics preventing such passage is imposed, then the plateau modulus is unchanged from perfectly rigid slip-links. Only the dynamics is changed. On the other hand, for phantom slip-links the distribution of the number of entanglements changes from Poisson. Furthermore, requiring normalization of the distribution function sets a constraint on how loose the virtual springs for the elastic slip-link are. These restrictions appear to be in agreement with parameter values used for the slip-spring simulations, although nonphantom slip-links were used there. The results are completely analogous to what was found by James and Guth for ideal elastic networks, whose derivation is repeated here. Our earlier rigid slip-link model is recovered as a limiting case.
ABSTRACT
Molecular theories for polymer rheology are based on conformational dynamics of the polymeric chain. Hence, measurements directly related to molecular conformations appear more appealing than indirect ones obtained from rheology. In this study, primitive chain network simulations are compared to experimental data of entangled DNA solutions [Teixeira et al., Macromolecules 40, 2461 (2007)]. In addition to rheological comparisons of both linear and nonlinear viscoelasticities, a molecular extension measure obtained by Teixeira et al. through fluorescent microscopy is compared to simulations, in terms of both averages and distributions. The influence of flow on conformational distributions has never been simulated for the case of entangled polymers, and how DNA molecular individualism extends to the entangled regime is not known. The linear viscoelastic response and the viscosity growth curve in the nonlinear regime are found in good agreement with data for various DNA concentrations. Conversely, the molecular extension measure shows significant departures, even under equilibrium conditions. The reason for such discrepancies remains unknown.
Subject(s)
Computer Simulation , DNA/chemistry , Elasticity , Models, Chemical , Molecular Structure , Local Area Networks , Polymers/chemistry , Shear Strength , Solutions/chemistry , Surface Properties , ViscosityABSTRACT
We propose a simple dynamic model of polymers under shear with an anisotropic mobility tensor. We calculate the shear viscosity, the rheo-dielectric response function, and the parallel relaxation modulus under shear flow deduced from our model. We utilize recently developed linear response theories for nonequilibrium systems to calculate linear response functions. Our results are qualitatively consistent with experimental results. We show that our anisotropic mobility model can reproduce essential dynamical nature of polymers under shear qualitatively. We compare our model with other models or theories such as the convective constraint release model or nonequilibrium linear response theories.