Abstract
We present results for the steady state shear rheology of non-concatenated, unentangled and marginally entangled ring poly(ethylene oxide) (PEO) melts from detailed, atomistic nonequilibrium molecular dynamics (NEMD) simulations, and compare them to the behavior of the corresponding linear melts. The applied flow field spans a wide range of shear rates, from the linear (Newtonian) to the highly non-linear (described by a power law) regime. For all melts studied, rings are found to exhibit shear thinning but to a lesser degree compared to linear counterparts, mostly due to their reduced deformability and stronger resistance to alignment in the direction of flow. These features are attributed to the more compact structure of ring molecules compared to linear chains; the latter are capable of adopting wider and more open conformations even under shear due to the freedom provided by the free ends. Similar to linear melts, rings also exhibit a first and a second normal stress coefficient; the latter is negative. The ratio of the magnitude of the two coefficients remains practically constant with shear rate and is systematically higher than the corresponding one for linear melts. Emphasis was also given to the statistics of terminal (re-orientational) relaxation times which we computed by analyzing all chains in the simulated systems one by one; it was demonstrated that long time dynamics are strongly heterogeneous both for rings and (especially) linears. Repeating the analysis under flow conditions, and as expected, we found that the applied flow field significantly suppresses dynamic heterogeneity, especially for high shear rates well beyond the Newtonian plateau. Finally, a detailed geometrical analysis revealed that the average population of ring–ring threading events in the longest melt studied here (the PEO-5k ring) remains practically unaffected by the imposed flow rate even at strong shear rates, except for multi-threadings which disappear. To further analyze this peculiar and rather unexpected effect, we computed the corresponding survival times and penetration lengths, and found that the overwhelming majority of threadings under shear are extremely weak constraints, as they are characterized by very small penetration lengths, thus also by short survival times. They are expected therefore to play only a minor (if any) role on chain dynamics.
Highlights
Due to their molecular architecture, ring polymers exhibit distinct dynamics, and rheological behavior that differs substantially from that of linear analogues.The work of Kapnistos et al [1] revealed that highly purified entangled ring melts do not exhibitPolymers 2019, 11, 1194; doi:10.3390/polym11071194 www.mdpi.com/journal/polymersPolymers 2019, 11, 1194 the well-known plateau modulus, but an extended power law regime where the shear modulus of relaxation G(t) scales with time t as G(t) ~ t0.4 followed by the terminal relaxation zone
For example, the work of Halverson et al [8] who carried out coarse-grained equilibrium molecular dynamics (MD) simulations of fully entangled pure ring and linear melts and showed that entangled rings do not exhibit a plateau in the stress relaxation modulus, in accordance with experiments [1], and are characterized by a zero shear rate viscosity that scales rather weakly with chain length (η0 ∼ N1.4±0.2 ) compared to what is predicted by the reptation theory for linear melts (η0 ∼ N3.4±0.2 )
Melts simulated, we observe the typical characteristic behavior of the shear viscosity with shear rate already known for linear polymer melts: (a) At low shear rates (WiC ≤ 1), the viscosity is practically constant defining what we know as the Newtonian plateau. (b) At higher shear rates, the viscosity starts decreasing, exhibiting what we know from the corresponding behavior of linear polymers as shear thinning. (c) At even higher shear rates, we enter the highly nonlinear regime where the viscosity drops rapidly with applied shear rate
Summary
Due to their molecular architecture (absence of free ends, looped structure), ring polymers exhibit distinct dynamics, and rheological behavior that differs substantially from that of linear analogues. For example, the work of Halverson et al [8] who carried out coarse-grained equilibrium MD simulations of fully entangled pure ring and linear melts and showed that entangled rings do not exhibit a plateau in the stress relaxation modulus, in accordance with experiments [1], and are characterized by a zero shear rate viscosity that scales rather weakly with chain length (η0 ∼ N1.4±0.2 ) compared to what is predicted by the reptation theory for linear melts (η0 ∼ N3.4±0.2 ). In a more recent work, Yoon et al [14] conducted atomistic NEMD simulations in shear and planar elongational flow with unentangled and marginally entangled pure ring and pure linear PE melts, and found that rings exhibit shear thinning but to a smaller degree compared to linears Their simulation results for the response of chain size to the applied flow field showed that rings exhibit a stronger resistance and deform less by the flow than linear polymers.
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