Linear and Nonlinear Shear Rheology of a Marginally Entangled Ring Polymer

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 <i>Z</i> ≈ 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

Comparison of Critical Adsorption Points of Ring Polymers with Linear Polymers

The critical adsorption points (CAP) for ring and linear polymers are determined and compared using Monte Carlo simulations and liquid chromatography experiments. The CAP is defined as the coelution point of ring or linear polymers with different molecular weights (MW). Computational studies show that the temperature at the CAP, <i>T</i>_CAP, for rings is higher than <i>T</i>_CAP for linear polymers regardless of whether the chains are modeled as random walks or self-avoiding walks. The difference in the CAP can be attributed only to the architectural difference. Experimentally, four pairs of linear and ring polystyrenes (PS) of different MW were synthesized and purified. Care was taken to account for the difference between the end-groups in linear polymers and the linkage unit in ring polymers. Elution of these polymers using a C18 bonded silica stationary phase and a CH₂Cl₂/CH₃CN mixed eluent were studied. The temperature at the coelution point, <i>T</i>_CAP, and the coelution time at the CAP, <i>t</i>_E,CAP, were determined for both ring and linear polymers. Experimentally, it was found that <i>T</i>_CAP of linear PS is lower than <i>T</i>_CAP of cyclic PS and <i>t</i>_E,CAP of linear PS is shorter than <i>t</i>_E,CAP of ring PS. Therefore, at the CAP of linear polymers, ring polymers elute later in order of increasing MW while, at the CAP of ring polymers, linear polymers elute earlier in order of decreasing MW. This is in excellent agreement with the Monte Carlo computer simulation results. We also found that the functionality effect can interfere in the LCCC separation of ring polymers from their linear precursors