We investigate mixtures of ring and linear polymers in solution at various number ratios, ranging from pure chains to pure rings, and at densities around the overlap concentration. In bulk and at rest, we find a shrinking of both topologies with increasing polymer content of the solution. At the same time, we observe an increase in the solution viscosity with a concomitant reduction of the polymer diffusivity. When exposing ring-chain mixtures of any composition to a pressure-driven flow in a slit channel, we find that ring polymers always migrate toward the center, whereas chains populate the regions of high local shear close to the channel walls. Interestingly, in a pure chain solution, this cross-stream migration toward the walls is absent. This phenomenon could be used to iteratively separate chains and rings at high mass throughput in simple microfluidic devices using pressure-driven flows. Furthermore, we show how pressure-driven flow can be used as a computationally efficient approach for determining the shear viscosity of (complex) liquids.

The separation of polymers based on their size, rigidity, and topology is an essential but also highly challenging task for nanoscience and engineering. Using hybrid Molecular Dynamics simulations that correctly take into account hydrodynamics, we have designed microfluidic channels for separating linear from ring polymers in dilute solutions. We establish that the transport velocity of the polymers is independent of their topology and rigidity when the channel walls are smooth and repulsive. However, when the walls are decorated with attractive spots arranged on lines parallel to the flow, ring polymers exhibit an order of magnitude higher transport velocity compared to linear chains. The spots induce a homeotropic-like reorientation of ring polymers close to walls leading to a tank-treading motion along them, whereas linear chains are immobilized upon adsorption. This mechanism becomes more enhanced with increasing polymer rigidity. The presented technique holds thus promise for reliably separating nanoparticles based on their topology.

We study the hydrodynamic transport of knotted ring polymers through modulated channels, establishing that the transport velocity is strongly dependent on the ring topology for Peclet numbers smaller than unity. As soon as convection dominates, transport properties become insensitive to the presence and type of knots. We identify two distinct modes of transport, corresponding to the motion being led by the knotted or unknotted portions of the ring, most surprisingly without impact on separation efficiency. The modes can be selected by the channel geometry and this could be harnessed to design nanofluidic devices for the continuous topological sorting of entangled biopolymers. 1 Introduction Channel confinement is increasingly used as the method of choice for examining the impact of topology on the physical behavior of polymers. In recent breakthrough experiments, linear 1 DNA filaments were trapped inside a channel and their metric properties were monitored, while their knotted state was changed by compression or elongation. 1-3 The measurements, together with models and simulations, helped establish how the knotting and unknotting kinetics is coupled to the global dynamics of the chain, 1-5 how knot size fluctuates in and out-of-equilibrium, 6-8 and how the motion of knots along the confined chains responds to an externally-imposed flow or elongational field. 2,3 Besides the relevance to polymer physics, these aspects have bearings in applicative contexts such as genomic barcoding, where erroneous readouts can be caused by the backfolded contour of knotted DNA. 9 Channel confinement has been applied to ring polymers as well. These systems have been mostly studied for their static properties, and particularly for the non-monotonic dependence of knotting probability on channel width, 6,8 which has been associated to the free energy balance between the knotted and unknotted portions. 6,10 By contrast, the rich kinetic behavior of confined knotted rings is still underexplored and basic properties, such as transport, have remained unclarified. In this work, we examine the unique mobility properties resulting from the combined action of hydrodynamic flow and channel geometry. We use hydrodynamic simulations to study how differently-knotted rings flow through channels with a periodic hourglass topography, where chambers, which entropically trap the polymers, and narrowings, which hinder knot passage, appear in alternation. This, as we show, realizes a minimalistic system where the diffusive and convective transport components of different knot types can be competitively adjusted via the flow strength or channel geometry. It also allows us to test the hypothesis of 11 that channel shape can be optimized to make possible the separation of rings with same length but different knot types, as needed, e.g., for topological profiling of viral DNA. Up to now, filtering mechanisms for chains and rings have been proposed, 12,13 which however are not aimed at discriminating rings by knot type. We demonstrate that the mobility of ...

We have used nonequilibrium molecular dynamics to simulate the flow of water molecules around a charged nanoparticle described at the atomic scale. These nonequilibrium simulations allowed us to compute the friction coefficient of the nanoparticle and then to deduce its hydrodynamic radius. We have compared two different strategies to thermostat the simulation box, since the low symmetry of the flow field renders the control of temperature non trivial. We show that both lead to an adequate control of the temperature of the system. To deduce the hydrodynamic radius of the nanoparticle we have employed a partial thermostat, which exploits the cylindrical symmetry of the flow field. Thereby, only a part of the simulation box far from the nanoparticle is thermostated. We have taken into account the finite concentration of the nanoparticle when calculating the friction force acting on it. We have focused on the case of polyoxometalate ions, which are inorganic charged nanoparticles. It appears that, for a given structure of the nanoparticle at the atomic level, the hydrodynamic radius significantly increases with the nanoparticles charge, a phenomenon that had not been quantified so far using molecular dynamics. The presence of an added salt only slightly modifies the hydrodynamic radius.