Multi-scale modeling of diffusion-controlled reactions in polymers: Renormalisation of reactivity parameters

The quantitative description of polymeric systems requires hierarchical modeling schemes, which bridge the gap between the atomic scale, relevant to chemical or biomolecular reactions, and the macromolecular scale, where the longest relaxation modes occur. Here, we use the formalism for diffusion-controlled reactions in polymers developed by Wilemski, Fixman, and Doi to discuss the renormalisation of the reactivity parameters in polymer models with varying spatial resolution. In particular, we show that the adjustments are independent of chain length. As a consequence, it is possible to match reactions times between descriptions with different resolution for relatively short reference chains and to use the coarse-grained model to make quantitative predictions for longer chains. We illustrate our results by a detailed discussion of the classical problem of chain cyclization in the Rouse model, which offers the simplest example of a multi-scale descriptions, if we consider differently discretized Rouse models for the same physical system. Moreover, we are able to explore different combinations of compact and non-compact diffusion in the local and large-scale dynamics by varying the embedding dimension. Z9

Multiscale equilibration of highly entangled isotropic model polymer melts

We present a computationally efficient multiscale method for preparing equilibrated, isotropic long chain model polymer melts. As an application we generate Kremer-Grest melts of $1000$ chains with $200$ entanglements and $25000$-$2000$ beads per chain, which cover the experimentally relevant bending rigidities up to and beyond the limit of the isotropic-nematic transition. In the first step, we employ Monte Carlo simulations of a lattice model to equilibrate the large-scale chain structure above the tube scale while ensuring a spatially homogeneous density distribution. We then use theoretical insight from a constrained mode tube model to introduce the bead degrees of freedom together with random walk conformational statistics all the way down to the Kuhn scale of the chains. This is followed by a sequence of simulations with carefully parameterized force-capped bead-spring models, which slowly introduce the local bead packing while reproducing the larger scale chain statistics of the target Kremer-Grest system at all levels of force-capping. Finally we can switch to the full Kremer-Grest model without perturbing the structure. The resulting chain statistics is in excellent agreement with literature results on all length scales accessible in brute-force simulations of shorter chains.Comment: Revised manuscript. Submitted to Journal of Chemical Physic

Stress Relaxation of Entangled Polymer Networks

The non-linear stress-strain relation for crosslinked polymer networks is studied using molecular dynamics simulations. Previously we demonstrated the importance of trapped entanglements in determining the elastic and relaxational properties of networks. Here we present new results for the stress versus strain for both dry and swollen networks. Models which limit the fluctuations of the network strands like the tube model are shown to describe the stress for both elongation and compression. For swollen networks, the total modulus is found to decrease like (V_0/V)^{2/3} and goes to the phantom model result only for short strand networks.Comment: 9 pages, 3 figures, RevTe

Strain-dependent localization, microscopic deformations, and macroscopic normal tensions in model polymer networks

We use molecular dynamics simulations to investigate the microscopic and macroscopic response of model polymer networks to uniaxial elongations. By studying networks with strands lengths ranging from $N_s=20$ to 200 we cover the full crossover from cross-link to entanglement dominated behavior. Our results support a recent version of the tube model which accounts for the different strain dependence of chain localization due to chemical cross-links and entanglements

DNA nano-mechanics: how proteins deform the double helix

It is a standard exercise in mechanical engineering to infer the external forces and torques on a body from its static shape and known elastic properties. Here we apply this kind of analysis to distorted double-helical DNA in complexes with proteins. We extract the local mean forces and torques acting on each base-pair of bound DNA from high-resolution complex structures. Our method relies on known elastic potentials and a careful choice of coordinates of the well-established rigid base-pair model of DNA. The results are robust with respect to parameter and conformation uncertainty. They reveal the complex nano-mechanical patterns of interaction between proteins and DNA. Being non-trivially and non-locally related to observed DNA conformations, base-pair forces and torques provide a new view on DNA-protein binding that complements structural analysis.Comment: accepted for publication in JCP; some minor changes in response to review 18 pages, 5 figure + supplement: 4 pages, 3 figure

Topological versus rheological entanglement length in primitive path analysis protocols

Primitive path analysis algorithms are now routinely employed to analyze entanglements in computer simulations of polymeric systems, but different analysis protocols result in different estimates of the entanglement length, N_e. Here we argue that standard PPA measures the rheological entanglement length, typically employed by tube models and relevant to quantitative comparisons with experiment, while codes like Z or CReTA also determine the topological entanglement length. For loosely entangled systems, a simple analogy between between phantom networks and the mesh of entangled primitive paths suggests a factor of two between the two numbers. This result is in excellent agreement with reported values for poly-ethylene, poly-butadiene and bead-spring polymer melts.Comment: 3 pages, no figure