Linear and Nonlinear Shear Rheology of a Marginally Entangled Ring Polymer

Abstract

We present systematic, unique linear and nonlinear shear rheology data of an experimentally pure ring polystyrene and its linear precursor. This polymer was synthesized anionically and characterized by interaction chromatography and fractionation at the critical condition. Its weight-average molar mass is 84 kg/mol; i.e., it is marginally entangled (entanglement number Z ≈ 5). Its linear viscoelastic response appears to be better described by the Rouse model (accounting for ring closure) rather than the lattice-animal-based model, suggesting a transition from unentangled to entangled ring dynamics. The failure of both models in the terminal region may reflect the remaining unlinked linear contaminants and/or ring–ring interpenetration. The viscosity evolution at different shear rates was measured using a homemade cone-partitioned plate fixture in order to avoid edge fracture instabilities. Our findings suggest that rings are much less shear thinning compared to their linear counterparts, whereas both obey the Cox–Merz rule. The shear stress (or viscosity) overshoot is much weaker for rings compared to linear chains, pointing to the fact that their effective deformation is smaller. Finally, step strain experiments indicate that the damping function data of ring polymers clearly depart from the Doi–Edwards prediction for entangled linear chains, exhibiting a weak thinning response. These findings indicate that these marginally entangled rings behave like effectively unentangled chains with finite extensibility and deform much less in shear flow compared to linear polymers. They can serve as guideline for further investigation of the nonlinear dynamics of ring polymers and the development of constitutive equations.

Detailed Molecular Dynamics Simulation of the Structure and Self‐Diffusion of Linear and Cyclic n‐Alkanes in Melt and Blends

“…Due to the absence of chain ends and their closed‐loop structure, cyclic polymers exhibit material properties that differ considerably from those of the two other classes of polymers, linear and branched, of the same molecular length. The origin of many of these differences remains still poorly understood even after many years of intense theoretical, computational, and experimental research . Given, in particular, the success of the reptation model in describing the dynamics of linear entangled polymers, particular emphasis has been given recently on understanding the conformational and viscoelastic properties of melts of nonconcatenated ring polymers in the crossover region from unentangled to entangled.…”

Single polymer dynamics of topologically complex DNA

“…The introduction of a single topological constraint via ring closure drastically changes the dynamic response of circular polymers in flow [7,[38][39][40].…”

“…Moreover, the rheological behavior of melts of circular polymers are highly sensitive to linear contaminants, leading to conflicting experimental reports from bulk-scale techniques [7,38]. For these reasons, several open questions remain regarding the physical mechanisms in these systems.…”

“…Furthermore, trace quantities of linear polymers are known to drastically change the rheological behavior of entangled ring polymers. Even with recent advances in synthesis and purification, bulk measurement techniques lack the molecular resolution needed to fully understand ring polymer mechanisms [7,38]. Enzymatic transformations enable topological control over DNA molecules [41,49], which further emphasizes the suitability of DNA as a suitable system for studying entangled ring polymers.…”

“…To this end, new capabilities in experiments and simulations will extend the reach of single polymer dynamics, and these techniques will be leveraged to study contested assumptions in the field, ranging from the nature of molecular entanglements to polymer crystallization. As one example, single polymer dynamics have already clarified inconsistencies in rheological measurements of circular polymers due to threading of rings by linear chains [7,38,47]. An additional area of interest includes the proposed relaxation A C C E P T E D M A N U S C R I P T…”