Bulletin of the American Physical Society
APS March Meeting 2021
Volume 66, Number 1
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session S04: Topological Effects in Soft MatterFocus Live
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Sponsoring Units: DPOLY DSOFT DBIO DCOMP Chair: Petro Maksymovych; Rajeev Kumar, Oak Ridge National Lab |
Thursday, March 18, 2021 11:30AM - 11:42AM Live |
S04.00001: Diblock Copolymer Melts of Linear Chains, Rings and Trefoil Knots in Lamellar Morphology: A Molecular Dynamics Simulations Study Jan-Michael Carrillo, Rajeev Kumar, Bobby G Sumpter We present results of coarse-grained molecular dynamics simulations of phase separating diblock copolymer melts having different chain topologies. Specifically, we investigated the self-assembly of 50-50 AB lamella structures composed of linear chains, rings or trefoil knots having the same molecular weights. The lamellar-disordered phase transition stays first order, while the order-disorder temperature (ODT) and the domain sizes, both, follow the sequence: linear chains > rings > trefoil knots. This behavior correlates with the size of the polymer chain in the disordered and ordered (lamellar) melts. Investigation of the polymer chain structures shows that chains are perturbed relative to the homopolymer melt with structures being stretched and compressed in the normal and lateral dimensions of the lamella domains, respectively. |
Thursday, March 18, 2021 11:42AM - 11:54AM Live |
S04.00002: Topological Tuning of Polymer and DNA Dynamics Davide Michieletto Understanding the dynamics of dense solutions of polymers with non-trivial topologies remains an outstanding challenge in polymer physics. In this talk, I will discuss how subtle architecture-specific topological interactions called “threadings” can be identified using persistence homology [1] and present numerical evidence of how they can drive the onset of a "topological glass" in systems of ring polymers [2,3]. Then, I will discuss how the same principles can be applied to higher-order "chimeric" polymers that display fused linear and ring topologies, such as tadpole-shaped polymers [4]. I will finally show numerical and experimental evidence of how the rheology of the bulk can be finely tuned by smart design of chimeric architectures via DNA origami and by dynamic altering of DNA topology. This work represents a signifcant advancement of our understanding of the fascinating relationship between polymer topology and bulk rheology. |
Thursday, March 18, 2021 11:54AM - 12:30PM Live |
S04.00003: Nonlinear Dynamics of Nonconcatenated Entangled Ring Polymers Invited Speaker: Michael Rubinstein The steady-state shear viscosity of nonconcatenated ring polymer melts is studied by a combination of experiments, simulations, and theory. Experiments using polystyrenes with Z≈5 and Z≈11 entanglements indicate weaker shear thinning for rings compared to linear polymers and observe power-law dependence of ring shear viscosity on shear rate with exponent -0.56±0.02 up to Weissenberg number Wi~100. Non-equilibrium molecular dynamics simulations reveal a similar shear thinning behavior with exponent -0.57±0.08 for a wider range of the number of entanglements per ring 4≤Z≤57. If the shear rate exceeds a certain threshold, shear-thinning becomes non-universal, chain length-dependent. In our experiments, we see the onset of this regime at the largest accessed Wi, and in simulations, which we extended up to Wi~10,000, it is fully developed. In this regime, viscosity decreases with increasing chain length. A simple scaling theory predicts universal regime in the sheared melt of rings with viscosity decreasing with the shear rate with exponent -0.57, in good agreement with both experiments and simulations. We develop a shear slit model explaining many subtle details of observed conformations and dynamics as well as the chain length-dependent behavior of viscosity in the non-universal regime at large shear rates. The signature feature of the model is the presence of two distinct length scales: each chain is confined in the velocity gradient direction to a shear slit of thickness dictated by the size of chain section with relaxation time on the order of reciprocal shear rate, while chains are strongly stretched in the flow velocity direction, with much smaller tension blobs. In this model, the chain length-dependent onset of non-universal behavior is set by tension blob getting as small as about one Kuhn segment. |
Thursday, March 18, 2021 12:30PM - 12:42PM Live |
S04.00004: Free Energy of a Knotted Polymer Confined to Narrow Cylindrical and Conical Channels James Polson, Cameron Hastie Monte Carlo simulations are used to study the conformational behavior of a semiflexible polymer confined to cylindrical and conical channels in the Odijk regime. For cylindrical confinement, we examine polymers with a single knot of topology 31, 41, or 51, as well as unknotted polymers that are capable of forming S-loops. We measure the variation of the free energy F with the polymer extension length X and examine the effect of varying the polymer topology, persistence length P and cylinder diameter D on the free energy functions and the knot span. We find that increasing the knot complexity increases the typical size of the knot. In addition, the scaling properties of the free energy and knot span are in agreement with predictions from a theoretical model constructed using known properties of interacting polymers in the Odijk regime. We also examine the variation of F with position of a knot in conical channels for various values of the cone angle. The behavior is in agreement with predictions from a theoretical model in which the dominant contribution to the change in F is the change in the size of the hairpins as the knot moves to the wider region of the channel. |
Thursday, March 18, 2021 12:42PM - 12:54PM Live |
S04.00005: The many faces of topological defects in smectic liquid crystals Paul Arne Monderkamp, Rene Wittmann, Frank Smallenburg, Hartmut Loewen Liquid crystal structures in confined space inevitably feature topological defects through the requirements set by the boundary conditions. The Euler characteristic of the shape of the cavity imposes the total contained topological charge. |
Thursday, March 18, 2021 12:54PM - 1:06PM Live |
S04.00006: Topological entanglement of polymers and viscoelasticity Eleni Panagiotou Polymer entanglement is closely related to polymeric material viscoelastic response. However, the notion of entanglement in polymers remains elusive. In this talk we will see how rigorous measures of topological complexity from Knot Theory can be applied to quantify polymer entanglement. In particular, we use the Gauss linking integral, the periodic linking number [1] and the Jones polynomial [2] to mathematically characterize polymer entanglement of linear chains. Next, we use Molecular Dynamics Simulations to examine how these mathematical measures of complexity capture entanglement effects related to material properties [3,4]. Our results confirm that mathematical entanglement complexity reflects material properties. If time permits, we will also see a new topology user package for physicists and engineers [5]. |
Thursday, March 18, 2021 1:06PM - 1:18PM Live |
S04.00007: Predicting Degeneracy and Topological Properties in 2D Phononic Band Diagrams Tejas Dethe, Siddhartha Sarkar, Matevz Marincic, Polina Zhilkina, Andrej Kosmrlj Phononic crystals are macroscopic elastic structures that have periodic modulations in material properties like shear modulus and density. We can draw analogies between band diagrams in phononic crystals that describe wave propagation and electronic band diagrams using the well-established tools in hard condensed matter theory. By applying representation theory to the symmetry properties of 2D phononic crystals, we can predict the existence or absence of degenerate wavemodes that correspond to intersections in the phononic band diagrams. Numerical calculations of these phononic band diagrams confirmed theoretical predictions for all seventeen 2D crystallographic groups. As in electronic systems, we also investigate the topological nature of phononic bands. Using band representations, which can be expressed as linear combinations of Wannier functions, we infer whether a phononic band has trivial or non-trivial topology. Using the above approach, we can design phononic crystals with target band structure properties. |
Thursday, March 18, 2021 1:18PM - 1:54PM Live |
S04.00008: Topological-Order Beyond 2D U(1) Systems: A Novel Perspective on Solidification and Curvature in Crystals and Glassy Solids Invited Speaker: Caroline Gorham This work illuminates the importance of topology in providing a description of the formation and structure of solid states, with SO(3) symmetries, beyond perfect crystals. We view crystallization as a “flattening transition,” in which complementary curvature-carrying topological defects (disclinations and 3rd homotopy group) bind in a 4D XYZW model – via a Kosterlitz-Thouless mechanism. This minimizes misorientational fluctuations of the relevant SU(2) quaternion orientational order parameter in the crystalline solid state. The ordered network of permanent defects (e.g., major skeleton) that stabilizes topologically-close-packed crystals, with icosahedral short-range orientational order that is geometrically-frustrated from filling space, is viewed as an uncharged analogue to the Abrikosov flux lattice that characterizes the ground state of Josephson junction arrays in the presence of a frustrating applied transverse magnetic field. |
Thursday, March 18, 2021 1:54PM - 2:06PM Live |
S04.00009: When Do Polyelectrolytes Entangle? Michael Jacobs, Andrey Dobrynin Entanglements in polyelectrolyte solutions is a controversial issue in polymer science. Here, we develop an approach based on a scaling relationship between solution correlation length ξ≈lgν/B and number of monomers per correlation blob g for polymers with monomer projection length l. Numerical coeffiecients B are obtained from plateaus of normalized specific viscosity ηsp(c)cα/N as a function of monomer concentration c with degree of polymerization N. Exponent α=1/(1-3ν) describes the concentration dependence of the number of monomers per correlation blob, g∼cα. Knowledge of B-parameters allow for the universal representation of specific viscosity and relaxation time data in terms of the number of correlation blobs per chain, N/g. Applying this approach to viscosity data for polyelectrolyte solutions, we establish that in solutions of chains with DP up to 104, polyelectrolytes only entangle in the concentrated solution regime. Thus, in order to observe entanglements in polyelectrolyte solutions in a concentration range where their properties are controlled by electrostatic interactions, one has to study polyelectrolyte chains with DP of at least an order in magnitude longer than studied so far. |
Thursday, March 18, 2021 2:06PM - 2:18PM Live |
S04.00010: Disentangling the Dynamics of Prime Knots Hyo Jung Park, Lakshminarayanan Mahadevan, Anna Lappala Many areas of physics describe entanglements— from vortex- to molecular knots, there is interest in understanding knots as dynamic objects. Formally, knots are defined as closed curves embedded in R3 that cannot be untangled without a cut. A subset of these curves, the prime knots, cannot be decomposed (i. e., expressed as a connected sum of two non-trivial knots). We investigate the dynamics of prime knots, capturing events like periodic breathing and other correlated motions, and relate these events to knot complexity, curvature, torsion and linking numbers. With the help of Molecular Dynamics simulations, we build a framework to analyze correlated motions in prime knots modeled as polymer chains, and study how these motions relate to their local structural properties. We investigate the link between dynamical arrest and local geometry in knotted polymers and present and characterize a novel type of motion discovered in knots that may have applications to nanoscale materials and machines. |
Thursday, March 18, 2021 2:18PM - 2:30PM Live |
S04.00011: Discovering Topological Invariants in Inhomogeneous Polymeric Systems Rajeev Kumar In this talk, I will present our work related to understanding topological invariants in melts of linear and ring polymers. In particular, issue of Gauge invariance in the field theory of polymers will be discussed and it will be shown that Gauge fixing can be used to discover topological invariants. A specific example using the Coulomb gauge will be used to demonstrate that the helicity is one of the topological invariants for both, linear and ring polymers. Furthermore, a numerical recipe to generate knotted vector fields will be presented for studying topological configurations near equilibrium using the self-consistent field theory of polymers. |
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