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Nanorheology of Entangled Polymer Melts.

ABSTRACT: We use molecular simulations to probe the local viscoelasticity of an entangled polymer melt by tracking the motion of embedded nonsticky nanoparticles (NPs). As in conventional microrheology, the generalized Stokes-Einstein relation is employed to extract an effective stress relaxation function G_{GSE}(t) from the mean square displacement of NPs. G_{GSE}(t) for different NP diameters d are compared with the stress relaxation function G(t) of a pure polymer melt. The deviation of G_{GSE}(t) from G(t) reflects the incomplete coupling between NPs and the dynamic modes of the melt. For linear polymers, a plateau in G_{GSE}(t) emerges as d exceeds the entanglement mesh size a and approaches the entanglement plateau in G(t) for a pure melt with increasing d. For ring polymers, as d increases towards the spanning size R of ring polymers, G_{GSE}(t) approaches G(t) of the ring melt with no entanglement plateau.

SUBMITTER: Ge T

PROVIDER: S-EPMC5896298 | biostudies-literature | 2018 Feb

REPOSITORIES: biostudies-literature

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Nanorheology of Entangled Polymer Melts.

Ge Ting T Grest Gary S GS Rubinstein Michael M

Physical review letters 20180201 5

We use molecular simulations to probe the local viscoelasticity of an entangled polymer melt by tracking the motion of embedded nonsticky nanoparticles (NPs). As in conventional microrheology, the generalized Stokes-Einstein relation is employed to extract an effective stress relaxation function G_{GSE}(t) from the mean square displacement of NPs. G_{GSE}(t) for different NP diameters d are compared with the stress relaxation function G(t) of a pure polymer melt. The deviation of G_{GSE}(t) from ...[more]

PMID: 29481209

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Project description: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.

Project description:A scaling model of self-similar conformations and dynamics of nonconcatenated entangled ring polymers is developed. Topological constraints force these ring polymers into compact conformations with fractal dimension df = 3 that we call fractal loopy globules (FLGs). This result is based on the conjecture that the overlap parameter of subsections of rings on all length scales is the same and equal to the Kavassalis-Noolandi number OKN ≈ 10-20. The dynamics of entangled rings is self-similar and proceeds as loops of increasing sizes are rearranged progressively at their respective diffusion times. The topological constraints associated with smaller rearranged loops affect the dynamics of larger loops through increasing the effective friction coefficient but have no influence on the entanglement tubes confining larger loops. As a result, the tube diameter defined as the average spacing between relevant topological constraints increases with time t, leading to "tube dilation". Analysis of the primitive paths in molecular dynamics simulations suggests a complete tube dilation with the tube diameter on the order of the time-dependent characteristic loop size. A characteristic loop at time t is defined as a ring section that has diffused a distance equal to its size during time t. We derive dynamic scaling exponents in terms of fractal dimensions of an entangled ring and the underlying primitive path and a parameter characterizing the extent of tube dilation. The results reproduce the predictions of different dynamic models of a single nonconcatenated entangled ring. We demonstrate that traditional generalization of single-ring models to multi-ring dynamics is not self-consistent and develop a FLG model with self-consistent multi-ring dynamics and complete tube dilation. This selfconsistent FLG model predicts that the longest relaxation time of nonconcatenated entangled ring polymers scales with their degree of polymerization N as τrelax ~ N7/3, while the diffusion coefficient of these rings scales as D3d ~ N-5/3. For the entangled solutions and melts of rings, we predict power law stress relaxation function G(t) ~ t-3/7 at t < τrelax without a rubbery plateau and the corresponding viscosity scaling with the degree of polymerization N as η ~ N4/3. These theoretical predictions are in good agreement with recent computer simulations and are consistent with experiments of melts of nonconcatenated entangled rings.

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Nanorheology of Entangled Polymer Melts.

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Nanorheology of Entangled Polymer Melts.

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