No Arabic abstract
Dynamics of various biological filaments can be understood within the framework of active polymer models. Here we consider a bead-spring model for a flexible polymer chain in which the active interaction among the beads is introduced via an alignment rule adapted from the Vicsek model. Following a quench from the high-temperature coil phase to a low-temperature state point, we study the coarsening kinetics via molecular dynamics (MD) simulations using the Langevin thermostat. For the passive polymer case the low-temperature equilibrium state is a compact globule. Results from our MD simulations reveal that though the globular state is also the typical final state in the active case, the nonequilibrium pathways to arrive at such a state differ from the passive picture due to the alignment interaction among the beads. We notice that deviations from the intermediate pearl-necklace-like arrangement, that is observed in the passive case, and the formation of more elongated dumbbell-like structures increase with increasing activity. Furthermore, it appears that while a small active force on the beads certainly makes the coarsening process much faster, there exists nonmonotonic dependence of the collapse time on the strength of active interaction. We quantify these observations by comparing the scaling laws for the collapse time and growth of pearls with the passive case.
We study analytically and by means of an off-lattice bead-spring dynamic Monte Carlo simulation model the adsorption kinetics of a single macromolecule on a structureless flat substrate in the regime of strong physisorption. The underlying notion of a ``stem-flower polymer conformation, and the related mechanism of ``zipping during the adsorption process are shown to lead to a Fokker-Planck equation with reflecting boundary conditions for the time-dependent probability distribution function (PDF) of the number of adsorbed monomers. The theoretical treatment predicts that the mean fraction of adsorbed segments grows with time as a power law with a power of $(1+ u)^{-1}$ where $ uapprox 3/5$ is the Flory exponent. The instantaneous distribution of train lengths is predicted to follow an exponential relationship. The corresponding PDFs for loops and tails are also derived. The complete solution for the time-dependent PDF of the number of adsorbed monomers is obtained numerically from the set of discrete coupled differential equations and shown to be in perfect agreement with the Monte Carlo simulation results. In addition to homopolymer adsorption, we study also regular multiblock copolymers and random copolymers, and demonstrate that their adsorption kinetics may be considered within the same theoretical model.
We investigate, using numerical simulations, the conformations of isolated active ring polymers. We find that the their behaviour depends crucially on their size: short rings ($N lesssim$ 100) are swelled whereas longer rings ($N gtrsim$ 200) collapse, at sufficiently high activity. By investigating the non-equilibrium process leading to the steady state, we find a universal route driving both outcomes; we highlight the central role of steric interactions, at variance with linear chains, and of topology conservation. We further show that the collapsed rings are arrested by looking at different observables, all underlining the presence of an extremely long time scales at the steady state, associated with the internal dynamics of the collapsed section. Finally, we found that is some circumstances the collapsed state spins about its axis.
In capillary-driven fluid dynamics, simple departures from equilibrium offer the chance to quantitatively model the resulting relaxations. These dynamics in turn provide insight on both practical and fundamental aspects of thin-film hydrodynamics. In this work, we describe a model trilayer dewetting experiment elucidating the effect of solid, no-slip confining boundaries on the bursting of a liquid film in a viscous environment. This experiment was inspired by an industrial polymer processing technique, multilayer coextrusion, in which thousands of alternating layers are stacked atop one another. When pushed to the nanoscale limit, the individual layers are found to break up on time scales shorter than the processing time. To gain insight on this dynamic problem, we here directly observe the growth rate of holes in the middle layer of the trilayer films described above, wherein the distance between the inner film and solid boundary can be orders of magnitude larger than its thickness. In otherwise identical experimental conditions, thinner films break up faster than thicker ones. This observation is found to agree with a scaling model that balances capillary driving power and viscous dissipation with, crucially, a no-slip boundary condition at the solid substrate/viscous environment boundary. In particular, even for the thinnest middle-layers, no finite-size effect is needed to explain the data. The dynamics of hole growth is captured by a single master curve over four orders of magnitude in the dimensionless hole radius and time, and is found to agree well with predictions including analytic expressions for the dissipation.
We study the driven translocation of a semi-flexible polymer through a nanopore by means of a modified version of the iso-flux tension propagation theory (IFTP), and extensive molecular dynamics (MD) simulations. We show that in contrast to fully flexible chains, for semi-flexible polymers with a finite persistence length $tilde{ell}_p$ the {it trans} side friction must be explicitly taken into account to properly describe the translocation process. In addition, the scaling of the end-to-end distance $R_N$ as a function of the chain length $N$ must be known. To this end, we first derive a semi-analytic scaling form for $R_N$, which reproduces the limits of a rod, an ideal chain, and an excluded volume chain in the appropriate limits. We then quantitatively characterize the nature of the {it trans} side friction based on MD simulations of semi-flexible chains. Augmented with these two factors, the modified IFTP theory shows that there are three main regimes for the scaling of the average translocation time $tau propto N^{alpha}$. In the stiff chain (rod) limit $N/tilde{ell}_p ll 1$, {$alpha = 2$}, which continuously crosses over in the regime $ 1 < N/tilde{ell}_p < 4$ towards the ideal chain behavior with {$alpha = 3/2$}, which is reached in the regime $N/tilde{ell}_p sim 10^2$. Finally, in the limit $N/tilde{ell}_p gg 10^6$ the translocation exponent approaches its symptotic value $1+ u$, where $ u$ is the Flory exponent. Our results are in good agreement with available simulations and experimental data.
Self-assembling, semi-flexible polymers are ubiquitous in biology and technology. However, there remain conflicting accounts of the equilibrium kinetics for such an important system. Here, by focusing on a dynamical description of a minimal model in an overdamped environment, I identify the correct kinetic scheme that describes the system at equilibrium in the limits of high bonding energy and dilute concentration.