The problem of stress relaxation in entangled, reversibly breakable polymers (e.g., wormlike micelles) is considered. In the case where the dominant diffusive mode for the polymers is reptation, this problem has been treated in earlier numerical work by coupling the full reaction kinetics of scissions and recombinations to the dynamics of reptation (represented by a one-dimensional stochastic process). Here we study a simplified renewal model, which replaces the exact reaction kinetics by a Poisson jump process that neglects temporal correlations in the chain length experienced by a particular monomer or tube segment. Between jumps in chain length, the stress relaxation is presumed to follow that of an equivalent unbreakable chain. We apply the solution to the case of reptating flexible polymers and compare the resulting complex modulus with the earlier numerical treatments. It is found that agreement is very good. The renewal model is then used to analyze in detail, for the first time, the crossover to a rapid-scission regime in which chain diffusion between scission events is dominated by breathing modes. A third regime, in which the motion between scission events is Rouse-like, remains unsuitable for study with this model, for reasons that we explain. Various implications of the renewal model for the interpretation of experimental results are discussed. We also provide explicit estimates for chain lengths in CTAC/NaSal/NaCl systems using experimental Cole–Cole plots.

We show that within a living eukaryotic cell, mean square displacement of an engulfed microsphere shows enhanced diffusion scaling as t(3/2) at short times, with a clear crossover to subdiffusive or ordinary diffusion scaling at longer times. The motion, observed nearby the nucleus, is due to interactions with microtubule-associated motor proteins rather than thermal Brownian motion. We propose that time-dependent friction introduced by the intracellular polymer networks leads to sub-ballistic motion, analogous to subdiffusion observed in passive networks of semiflexible biopolymers.

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projected length (area) of the polymer (membrane). We demonstrate how, at long times, these fluctuations lead to reptation motion of the polymer (membrane) in the longitudinal direction. We generalize this approach to investigate the motion of a membrane between two plates and a polymer in a tube. The latter problem is used as a model for polymer motion in semi-dilute solutions in which the persistence length is longer than the entanglement length. Such systems are not suitable for the classical reptation model of de-Gennes and of Doi and Edwards, which was designed for chains that are flexible on the entanglement distance. The reptation diffusion coefficient and relaxation times that we obtain have the same scaling with chain length L as in the classical reptation model, but differ greatly in factors that are dependent on the ratio of persistence length to entanglement length. We also discuss the diffusion of a tagged "monomer" under imposed tension and liquid crystalline order. 1. both in melts and in semi-dilute or concentrated solutions, the chainsegments between two consecutive entanglement points (along a tagged chain) are flexible. The classical reptation model thus assumes that L~» Lp, where L~is the (real space) distance between two suchentanglement points, and Lp is the persistence (Kuhn) length. The reptation is viewed as resulting from the motion of loop-like defects along the tube contour (the so-called "primitive path" ). This motion is described by the "bead and spring" Rouse model, because the chain is rather flexible between its nearest entanglement points.

We study the motion of a probe driven by microtubule-associated motors within a living eukaryotic cell. The measured mean square displacement, of engulfed 2 and 3 microm diameter microspheres shows enhanced diffusion scaling as t(3/2) at short times, with a clear crossover to ordinary or subdiffusive scaling, i.e., t(gamma) with gamma less than or equal to 1, at long times. Using optical tweezers we tried to move the engulfed bead within the cell in order to relate the anomalous diffusion scaling to the density of the network in which the bead is embedded. Results show that the larger beads, 2 and 3 microm diameter, must actively push the cytoskeleton filaments out of the way in order to move, whereas smaller beads of 1 microm diameter can be "rattled" within a cage. The 1 microm beads also perform an enhanced diffusion but with a smaller and less consistent exponent 1.2 approximately t(3/4). In the case of small beads, there may also be a Brownian contribution to the motion that results in a smaller exponent.