Addressing Unsolved Mysteries of Polymer Viscoelasticity

摘要

By using coarse-grained bead-spring and entanglement tube models, much progress has been made over the past 50 years in understanding and modeling the dynamics and rheology of polymers, both in dilute solution state and in entangled solutions and melts. However, several major issues have remained unresolved, and these are now being addressed using microscopic simulations resolved at the level of the monomer. In the dilute solution state, the dynamics can be described by a coarse-grained bead-spring model, with each spring representing around 100 backbone bonds, even at frequencies high enough that one expects to see modes of relaxation associated with local motions of smaller numbers of bonds. The apparent absence of these local modes has remained a mystery, but microscopic simulations now indicate that these modes are slowed down by torsional barriers to the extent that they are coincident with much longer ranged spring-like modes. Other mysteries of dilute solution rheology include extension-thinning behavior observed at very high extension rates, an apparent lack of complete stretching of polymers in fast extensional flows as measured by light scattering experiments, and the unusual molecular weight dependence of polymer scission in fast flows. In entangled solutions, it is still not entirely clear how, or even if, the rheology can be mapped onto that of a “dynamically equivalent” melt, and, if so, what the scaling laws are for choosing the appropriate renormalized monomer size and renormalized time and modulus scales. It is also not yet clear to what extent “dynamic dilution” can be used to simplify and organize constraint release effects in the relaxation of monodisperse and polydisperse linear and long-chain branched polymers. For multiply-branched polymers, the motion of the branch point is critical in determining the rate of relaxation of the molecule, and theories for this motion have not been adequately tested. As with dilute solutions, simulations resolved at the level of the monomer are now helping to settle these issues. For example, molecular dynamics simulations of branched polymers show that ideas of hierarchical relaxation, introduced by McLeish and coworkers, appear to be valid. Similar simulations indicate that the effective “tube diameter” increases gradually starting at times as short as the “equilibration time” at which the polymer first “feels” the presence of the tube, and that this slow increase in effective tube diameter can help explain some anomalies in the relaxation of asymmetric star branched polymers.