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1. Nonlinear rheology of entangled wormlike micellar solutions predicted by a micelle-slip-spring model

   https://doi.org/10.1122/8.0000426  

   Sato, Takeshi; Larson, Ronald G. (May 2022, Journal of Rheology)

   We examine linear and nonlinear shear and extensional rheological properties using a “micelle-slip-spring model” [T. Sato et al., J. Rheol. 64, 1045–1061 (2020)] that incorporates breakage and rejoining events into the slip-spring model originally developed by Likhtman [Macromolecules 38, 6128–6139 (2005)] for unbreakable polymers. We here employ the Fraenkel potential for main chain springs and slip-springs to address the effect of finite extensibility. Moreover, to improve extensional properties under a strong extensional flow, stress-induced micelle breakage (SIMB) is incorporated into the micelle-slip-spring model. Thus, this model is the first model that includes the entanglement constraint, Rouse modes, finite extensibility, breakage and rejoining events, and stress-induced micelle breakage. Computational expense currently limits the model to micellar solutions with moderate numbers of entanglements ([Formula: see text]), but for such solutions, nearly quantitative agreement is attained for the start-up of the shearing flow. The model in the extensional flow cannot yet be tested owing to the lack of data for this entanglement level. The transient and steady shear properties predicted by the micelle-slip-spring model for a moderate shear rate region without significant chain stretch are fit well by the Giesekus model but not by the Phan–Thien/Tanner (PTT) model, which is consistent with the ability of the Giesekus model to match experimental shear data. The extensional viscosities obtained by the micelle-slip-spring model with SIMB show thickening followed by thinning, which is in qualitative agreement with experimental trends. Additionally, the extensional rheological properties of the micelle-slip-spring model with or without SIMB are poorly predicted by both the Giesekus and the PTT models using a single nonlinear parameter. Thus, future work should seek a constitutive model able to capture the behavior of the slip-spring model in shear and extensional flows and so provide an accurate, efficient model of micellar solution rheology. 

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2. A critical and constructive analysis of nonstretching approximations in a family of Rolie-Poly models

   https://doi.org/10.1122/8.0000941  

   Chen, Vickie; Wang, Brandon; Drucker, Charles T; Peterson, Joseph D (July 2025, Journal of Rheology)

   Entangled polymers are an important class of materials for their toughness, processability, and functionalizability. During processing, deformation introduces elastic stresses due to a combination of polymer orientation and polymer stretching. For many flows, however, the elastic contribution from chain stretching is not significant, and so-called “nonstretching” approximations have been developed to help explain and interpret experimental observations. Unfortunately, these nonstretching models tend to be limited to simple polymer formulations (linear and monodisperse) and are not useful for understanding any effects from marginal chain stretching that may be present. In this paper, we show that nonstretching approximations can be formally constructed as a perturbation expansion starting from a fully stretching constitutive equation. We apply this framework to the Rolie-Poly model, deriving the existing nonstretching variation and expanding to the second order. The second-order continuation provides quantitatively improved accuracy for both steady and unsteady flows and prevents a pathological/nonphysical blowup that can occur when effects from marginal chain stretching are ignored. We also derive and discuss leading order nonstretching approximations for more complex models of entangled polymers, accounting for disentanglement dynamics, polydispersity, and reversible scission reactions. Alternatives to the formal perturbation framework are also discussed, with potential trade-offs between accuracy, versatility, and computational cost. 

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3. Cooperative Polymer Dynamics at the Crossover between the Unentangled and the Entangled Regimes: Theoretical Predictions of Scattering and Linear Shear Relaxation for Polyethylene Melts

   https://doi.org/10.1021/acs.macromol.4c01442  

   Guenza, M G (October 2024, Macromolecules)

   The dynamics of polymer melts at the crossover between unentangled and entangled regimes is formalized here through an extension of the Cooperative Dynamics Generalized Langevin Equation (CDGLE) (J. Chem. Phys. 1999, 110, 7574), by including the constraint to the dynamics due to entanglements through an effective intermonomer potential that confines the motion of the chains. As one polymer chain in a melt interpenetrates with a N other chains, with N the degree of chain polymerization, their dynamics is coupled through their potential of mean-force, leading to chains’ cooperative motion and center-of-mass subdiffusive dynamics. When increasing the degree of polymerization, the extended CDGLE approach describes the dynamical behavior of unentangled to weakly entangled systems undergoing cooperative dynamics. By direct comparison of the CDGLE with data of Neutron Spin Echo (NSE) experiments on polyethylene melts, we find that the cooperative dynamics in entangled systems are confined in the region delimited by entanglements. We extend the CDGLE to describe linear dynamical mechanical measurements and use it to calculate shear relaxation for the polyethylene samples investigated by NSE. The effects of cooperative dynamics, local flexibility, and entanglements in the shear relaxation are discussed. It is noteworthy that the theoretical approach describes with accuracy the crossover from unentangled to entangled-global dynamics for polyethylene melts of increasing chain length, covering the regimes of unentangled and weakly entangled (up to 12 entanglements) dynamics in one approach. 

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4. Probing the nonequilibrium dynamics of stress, orientation, and entanglements in polymer melts with orthogonal interrupted shear simulations

   https://doi.org/10.1122/8.0000407  

   Galvani Cunha, Marco A.; Olmsted, Peter D.; Robbins, Mark O. (May 2022, Journal of Rheology)

   Both entangled and unentangled polymer melts exhibit stress overshoots when subject to shearing flow. The size of the overshoot depends on the applied shear rate and is related to relaxation mechanisms such as reptation, chain stretch, and convective constraint release. Previous experimental work shows that melts subjected to interrupted shear flows exhibit a smaller overshoot when sheared after partial relaxation. This has been shown to be consistent with predictions by constitutive models. Here, we report molecular dynamics simulations of interrupted shear of polymer melts where the shear flow after the relaxation stage is orthogonal to the originally applied flow. We observe that, for a given relaxation time, the size of the stress overshoot under orthogonal interrupted shear is larger than observed during parallel interrupted shear, which is not captured by constitutive models. Differences in maxima are also observed for overshoots in the first normal stress and chain end-to-end distance. We also show that measurements of the average number of entanglements per chain and average orientation at different scales along the chain are affected by the change in shear direction, leading to nonmonotonic relaxation of the off-diagonal components of orientation and an appearance of a “double peak” in the average number of entanglements during the transient. We propose that such complex behavior of entanglements is responsible for the increase in the overshoots of stress components and that models of the dynamics of entanglements might be improved upon by considering a tensorial measurement of entanglements that can be coupled to orientation. 

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5. Modeling of Entangled Polymer Diffusion in Melts and Nanocomposites: A Review

   https://doi.org/10.3390/polym11050876  

   Karatrantos, Argyrios; Composto, Russell J.; Winey, Karen I.; Kröger, Martin; Clarke, Nigel (May 2019, Polymers)

   This review concerns modeling studies of the fundamental problem of entangled (reptational) homopolymer diffusion in melts and nanocomposite materials in comparison to experiments. In polymer melts, the developed united atom and multibead spring models predict an exponent of the molecular weight dependence to the polymer diffusion very similar to experiments and the tube reptation model. There are rather unexplored parameters that can influence polymer diffusion such as polymer semiflexibility or polydispersity, leading to a different exponent. Models with soft potentials or slip-springs can estimate accurately the tube model predictions in polymer melts enabling us to reach larger length scales and simulate well entangled polymers. However, in polymer nanocomposites, reptational polymer diffusion is more complicated due to nanoparticle fillers size, loading, geometry and polymer-nanoparticle interactions. 

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