1,721,160 research outputs found
Topological and physical links in soft matter systems
No full textLinking, or multicomponent topological entanglement, is ubiquitous in soft matter systems, from mixtures of polymers and DNA filaments packed in vivo to interlocked line defects in liquid crystals and intertwined synthetic molecules. Yet, it is only relatively recently that theoretical and experimental advancements have made it possible to probe such entanglements and elucidate their impact on the physical properties of the systems. Here, we review the state-of-the-art of this rapidly expanding subject and organize it as follows. First, we present the main concepts and notions, from topological linking to physical linking and then consider the salient manifestations of molecular linking, from synthetic to biological ones. We next cover the main physical models addressing mutual entanglements in mixtures of polymers, both linear and circular. Finally, we consider liquid crystals, fluids and other non-filamentous systems where topological or physical entanglements are observed in defect or flux lines. We conclude with a perspective on open challenges
Torsion of polygons in Z3
No full textTesi, M.C.; Janse van Rensburg, E.J.; Orlandini, E.; Whittington, S.G.. (1997). Torsion of polygons in Z3. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/3056
Translocation of links through a pore: Effects of link complexity and size
No full textWe have used Langevin dynamics to simulate the forced translocation of linked polymer rings through a narrow pore. For fixed size (i.e. fixed number of monomers) the translocation time depends on the link type and on whether the rings are knotted or unknotted. For links with two unknotted rings the crossings between the rings can slow down the translocation and are responsible for a delay as the crossings pass through the pore. The results fall on a set of relatively smooth curves for different link families with the translocation time not always increasing with crossing number within the same family. When one ring is knotted the results depend on whether the link is prime or composite and, for the composite case, they depend on whether the knotted or unknotted ring enters the pore first. We find a similar situation for 3-component links where the results depend on whether the link is prime or composite. These results contribute to our understanding of how the entanglement complexity between filaments impacts their translocation dynamics and should be useful for extending nanopore-sensing techniques to probe the topological properties of these systems
Upsurge of Spontaneous Knotting in Polar Diblock Active Polymers
No full textSpontaneous formation of knots in long polymers at equilibrium is inevitable but becomes rare in sufficiently short chains. Here, we show that knotting increases by orders of magnitude in diblock polymers having a fraction p of self-propelled monomers. Remarkably, this enhancement is not monotonic in p with an optimal value independent of the monomer's activity. By monitoring the knot's size and position we elucidate the mechanisms of its formation, diffusion, and untying and ascribe the nonmonotonic behavior to the competition between the rate of knot formation and the knot's lifetime. These findings suggest a nonequilibrium mechanism to generate entangled filaments at the nano- and microscales
Asymptotics of linked polygons
No full textThe asymptotic (i.e. large n) behaviour of pairs of ring polymers can depend on whether or not they are topologically linked and on the link complexity. We study this problem for pairs of linked polygons on the simple cubic lattice using a Monte Carlo method that, by keeping the link type fixed, can sample pairs of polygons whose individual lengths can fluctuate. By considering different prime links and linked pairs with knotted components we study how the link complexity affects the connective constant and the entropic exponent of these systems. We present numerical evidence that, in the large n limit, the entropically favoured situation corresponds to one component growing with n while the second component (and so the linked portion) has contour length o(n)
Formation of Topological Bigels in Mixtures of Colloidal Rings and Polymers
No full textWe study a spherically confined mixture of polymers and colloidal rings. Unlike in standard colloidpolymer mixtures, the polymers interact topologically with the rings by threading them. We find that, above a critical value of the ring radius, threading yields a topological transition from a fluid to a gel-like phase characterized by a space-spanning network of interlocked polymers and rings, which we refer to as a bicomponent gel, or bigel. By exploiting the mixture dual character (rings and polymers), we predict analytically the value of the critical radius. We also show that the mobility of entanglements in the mixture slows down upon entering the gel phase, due to topological hindrance arising from threadings, while the transition rates between topological states of the colloidal probes provide another strong dynamical signature of the gel phase
The rise and fall of branching: A slowing down mechanism in relaxing wormlike micellar networks
Full text linkA mean-field kinetic model suggests that the relaxation dynamics of wormlike micellar networks is a long and complex process due to the problem of reducing the number of free end-caps (or dangling ends) while also reaching an equilibrium level of branching after an earlier overgrowth. The model is validated against mesoscopic molecular dynamics simulations and is based on kinetic equations accounting for scission and synthesis processes of blobs of surfactants. A long relaxation time scale is reached with both thermal quenches and small perturbations of the system. The scaling of this relaxation time is exponential with the free energy of an end cap and with the branching free energy. We argue that the subtle end-recombination dynamics might yield effects that are difficult to detect in rheology experiments, with possible underestimates of the typical time scales of viscoelastic fluids
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