A new implementation of constraint dynamics for the discrete slip-link model (DSM), which is statistically consistent with sliding dynamics of the chain, is proposed. The DSM agrees with linear viscoelastic (LVE) data for linear monodisperse entangled polymer melts at least as well as state-of-the-art tube models. The agreement with data can be obtained by fitting only two parameters, β and τ K that are independent of the molecular weight of the polymer. However, because the theory exists on a more-detailed level of description, it contains fewer assumptions than do existing tube models and assumptions of the latter may be examined. Several fundamental differences between DSM and tube models are revealed. For example, Rouse motion is an inappropriate realization of constraint dynamics in the slip-link picture. Moreover, the chain relaxation by sliding dynamics for the DSM is significantly different from the fraction of survived entanglements multiplied by the plateau modulus, whereas the tube model assumes that these are equivalent at long times. These two differences effectively cancel one another. Moreover, they could result in different bidisperse LVE predictions. On the other hand, several other assumptions made in tube theories are confirmed by the DSM results. Finally, model comparisons with experimental data exposed some limitations in the experiments.

To ensure timely cytokinesis, the equatorial actomyosin contractile ring constricts at a relatively constant rate despite its progressively decreasing size. Thus, the per-unit-length constriction rate increases as ring perimeter decreases. To understand this acceleration, we monitored cortical surface and ring component dynamics during the first cytokinesis of the Caenorhabditis elegans embryo. We found that, per unit length, the amount of ring components (myosin, anillin) and the constriction rate increase with parallel exponential kinetics. Quantitative analysis of cortical flow indicated that the cortex within the ring is compressed along the axis perpendicular to the ring, and the per-unit-length rate of cortical compression increases during constriction in proportion to ring myosin. We propose that positive feedback between ring myosin and compression-driven flow of cortex into the ring drives an exponential increase in the per-unit-length amount of ring myosin to maintain a high ring constriction rate and support this proposal with an analytical mathematical model.

The discrete slip-link model (DSM) was developed to describe the dynamics of flexible polymer melts. The model is able to predict linear viscoelasticity of monodisperse linear, polydisperse linear, and branched systems. The model also shows good agreement with dielectric relaxation experiments, except for the single data set available for bidisperse linear systems with a small volume fraction of long chains. In this work, both shear and elongational flow predictions obtained using the DSM without parameter adjustment are shown. Model predictions for shear flow agree very well with experimental results. The DSM is able to capture the transient response as well as the steady-state viscosity. However, for elongational flow, agreement is unsatisfactory at large strains. The DSM captures the onset of strain hardening, but after a Hencky strain between 2 and 3, it predicts transient strain softening, whereas experiments show only monotonic growth. We explore a number of assumptions and approximations of the model and their effect on flow predictions. The approximations are related to the neglect of these phenomena, which are expected to be more sensitive in elongational flow: finite extensibility, convective constraint

An analytic expression is proposed for the primitive-path length of entangled polymer chains. The expression is derived from statistical mechanics of a chain that is a random walk with randomly scattered entanglements. The only parameters are the number of Kuhn steps in the chain and a dimensionless parameter beta that contains information about the entanglement density and Kuhn step size. The expression is found to compare very favorably with numerical results recently found from examining topological constraints in microscopic simulations. The comparison also predicts well the plateau modulus of polyethylene, suggesting that the slip-link model is a viable intermediate in the search for true ab initio rheology predictions. Since the expression is analytic, it can be used to make predictions where the simulations cannot reach, and hence is applicable for coarse graining.