Comparing equilibration schemes of high-molecular-weight polymer melts with topological indicators

Topological comparison of flexible and semiflexible chains in polymer melts with θ-chains

A central paradigm of polymer physics states that chains in melts behave like random walks as intra- and interchain interactions effectively cancel each other out. Likewise, θ-chains, i.e., chains at the transition from a swollen coil to a globular phase, are also thought to behave like ideal chains, as attractive forces are counterbalanced by repulsive entropic contributions. While the simple mapping to an equivalent Kuhn chain works rather well in most scenarios with corrections to scaling, random walks do not accurately capture the topology and knots, particularly for flexible chains. In this paper, we demonstrate with Monte Carlo and molecular dynamics simulations that chains in polymer melts and θ-chains not only agree on a structural level for a range of stiffnesses but also topologically. They exhibit similar knotting probabilities and knot sizes, both of which are not captured by ideal chain representations. This discrepancy comes from the suppression of small knots in real chains, which is strongest for very flexible chains because excluded volume effects are still active locally and become weaker with increasing semiflexibility. Our findings suggest that corrections to ideal behavior are indeed similar for the two scenarios of real chains and that the structure and topology of a chain in a melt can be approximately reproduced by a corresponding θ-chain.

Topology-Based Detection and Tracking of Deadlocks Reveal Aging of Active Ring Melts

Connecting the viscoelastic behavior of stressed ring melts to the various forms of entanglement that can emerge in such systems is still an open challenge. Here, we consider active ring melts, where stress is generated internally, and introduce a topology-based method to detect and track consequential forms of ring entanglements, namely, deadlocks. We demonstrate that, as stress accumulates, more and more rings are co-opted in a growing web of deadlocks that entrap many other rings by threading, bringing the system to a standstill. The method ought to help the study of topological aging in more general polymer contexts.

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 25 000-2000 beads/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.

Knot formation of dsDNA pushed inside a nanochannel

Recent experiments demonstrated that knots in single molecule dsDNA can be formed by compression in a nanochannel. In this manuscript, we further elucidate the underlying molecular mechanisms by carrying out a compression experiment in silico, where an equilibrated coarse-grained double-stranded DNA confined in a square channel is pushed by a piston. The probability of forming knots is a non-monotonic function of the persistence length and can be enhanced significantly by increasing the piston speed. Under compression knots are abundant and delocalized due to a backfolding mechanism from which chain-spanning loops emerge, while knots are less frequent and only weakly localized in equilibrium. Our in silico study thus provides insights into the formation, origin and control of DNA knots in nanopores.

Facile equilibration of well-entangled semiflexible bead-spring polymer melts

The widely used double-bridging hybrid (DBH) method for equilibrating simulated entangled polymer melts [Auhl et al., J. Chem. Phys. 119, 12718-12728 (2003)] loses its effectiveness as chain stiffness increases into the semiflexible regime because the energy barriers associated with double-bridging Monte Carlo moves become prohibitively high. Here we overcome this issue by combining DBH with the use of core-softened pair potentials. This reduces the energy barriers substantially, allowing us to equilibrate melts with N ≃ 40N_e and chain stiffnesses all the way up to the isotropic-nematic transition using simulations of no more than 100 × 10⁶ time steps. For semiflexible chains, our method is several times faster than the standard DBH; we exploit this speedup to develop improved expressions for Kremer-Grest melts' chain-stiffness-dependent Kuhn length ℓ_K and entanglement length N_e.