Ring Polymer Dynamics Are Governed by a Coupling between Architecture and Hydrodynamic Interactions

The behavior of linear polymer chains in dilute solution flows has an established history. Polymers often possess more complex architectures, however, such as branched, dendritic, or ring structures. A major challenge lies in understanding how these nonlinear chain topologies affect the dynamic properties in nonequilibrium conditions, in both dilute and entangled solutions. In this work, we interrogate the single-chain dynamics of ring polymers using a combination of simulation, theory, and experiment. Inspired by recent experimental results by Li et al., we demonstrate that the presence of architectural constraints has surprising and pronounced effects on the dynamic properties of polymers as they are driven out of equilibrium. Ring constraints lead to two behaviors that contrast from linear chains. First, the coil−stretch transition occurs at larger values of the dimensionless flow strength (Weissenberg number) compared to linear chains, which is driven by coupling between intramolecular hydrodynamic interactions (HI) and chain architecture. Second, a large loop conformation is observed for ring polymers in extensional flow at intermediate to large Weissenberg numbers, and we show that this open loop conformation is driven by intramolecular HI. Our results reveal the emergence of new paradigms in chain architecture− hydrodynamic coupling that may be relevant for solution-based processing of polymeric materials and could provide new opportunities for precise flow-based polymer conformation control to guide material properties. ■ INTRODUCTION Ring polymers are intensely studied in polymer physics, primarily due to their status as a model system for understanding the role of chain topology. Circular (or ring) polymers provide the opportunity to probe some of the most fundamental features of long-chain macromolecules. For example, the absence of chain ends leads to compelling questions with regards to entanglements: how does an entangled melt of rings relieve stress, given the absence of free chain ends? How does this affect the flow properties of ring-based materials? Over the past several years, a large amount of literature has been devoted to these questions. The essence of the question lies in understanding how a polymer that has similar local random walk statistics compared to a linear polymer is altered by the constraint that the overall chain must return to its starting point. These fundamental questions in ring polymer dynamics are typically considered in the context of concentrated systems; however, recent work has begun to probe the dynamic behavior of single ring polymer chains in dilute solution. Such systems are motivated by the success of single-chain dynamics, which has informed polymer dynamics for a half century. This field stemmed from pioneering work by Rouse and Zimm that established the language of polymer relaxation and dynamics in the linear regime. Moving forward, additional work by others including Peterlin and De Gennes established the theoretical principles of how polymers stretch in fluid flows. The fundamental competition relevant for nonequilibrium polymer dynamics is between hydrodynamic flow fields that stretch a polymer and the entropic forces that drive a polymer to relax back to a random coil. This competition leads to a coil−stretch transition in extension-dominated flows and a weaker second-order transition in simple shear flows. The details of this transition are sensitive to hydrodynamic interactions (HI) between polymer segments in solution. In essence, intramolecular HI leads to hydrodynamic screening in the coiled state, with hydrodynamic friction or drag increasing as a polymer chain unravels in flow. This conformation-dependent drag ultimately gives rise to a first-order-like coil-to-stretch transition for chains in elongation flows. From this perspective, the single-chain problem has contributed substantially to our understanding of polymer dynamics and rheology, both as a limiting case that informs concentrated polymer dynamics and as a technologically relevant physical description of polymers useful for solution processing or for flow-based polymer manipulation. Bulk rheological and rheooptical techniques such as birefringence and light scattering have provided a wealth of information regarding polymer chain dynamics. Bulk-level techniques, however, can only indirectly infer molecular features of polymer stretching dynamics by measuring bulk Received: October 29, 2015 Revised: February 11, 2016 Published: February 19, 2016 Article pubs.acs.org/Macromolecules © 2016 American Chemical Society 1961 DOI: 10.1021/acs.macromol.5b02357 Macromolecules 2016, 49, 1961−1971 materials properties. In recent years, single molecule fluorescence microscopy has enabled direct imaging of polymer chains and visualization of dynamic conformational evolution in nonequilibrium fluid flow. This approach has led to the ability to directly probe the fundamental predictions of polymer dynamics: single-chain diffusivity, conformational relaxation, flow-driven chain stretching in both elongation and shear flows, chain tumbling, confinement effects, and conformational chain hysteresis predicted decades earlier. New experimental and theoretical efforts have focused on nonlinear architectures, collapsed polymers, knotted polymers, and nondilute solutions. Compared to linear chains, ring polymers have received less attention in the context of single-chain dynamics, despite substantial literature considering their melt properties. Nevertheless, the fundamental question of topological constraints in ring polymers remains important in the case of single-chain dynamics. This article exposes surprising results that arise in the elongational flow-induced stretching of ring polymers in strong flows. In particular, we observe a coupling between chain architecture of ring polymers and intramolecular HI between polymer segments, which becomes highly nontrivial and leads to changes in the critical flow strength at the onset of the coil−stretch transition. Interestingly, these interactions also lead to a transient looped conformation in the fully stretched polymer ring. This work addresses recent observations in the literature regarding ring polymers in dilute solution flows and suggests that the coupling between hydrodynamics and chain connectivity is an area with rich phenomenology in the context of polymers with nonlinear topologies. ■ METHODS Simulation. We use standard Brownian dynamics (BD) methods to model a single ring polymer in an implicit solvent undergoing an elongational flow. The model considers the polymer chain to be composed of N beads of index i at positions ri. We follow the trajectory of these beads in a potential U given by