An official website of the United States government
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.
more »
« less
Probing the nonequilibrium dynamics of stress, orientation, and entanglements in polymer melts with orthogonal interrupted shear simulations
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.
more »
« less
- Award ID(s):
- 1628974
- PAR ID:
- 10323008
- Date Published:
- Journal Name:
- Journal of Rheology
- Volume:
- 66
- Issue:
- 3
- ISSN:
- 0148-6055
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Polymer synthesis routes result in macromolecules with molecular weight dispersity ĐM that depends on the polymerization mechanism. The lowest dispersity polymers are those made by anionic and atom-transfer radical polymerization, which exhibit narrow distributions ĐM = Mw/Mn ∼ 1.02–1.04. Even for small dispersity, the chain length can vary by a factor of two from the average. The impact of chain length dispersity on the viscoelastic response remains an open question. Here, the effects of dispersity on stress relaxation and shear viscosity of entangled polyethylene melts are studied using molecular dynamics simulations. Melts with chain length dispersity, which follow a Schulz–Zimm (SZ) distribution with ĐM = 1.0–1.16, are studied for times up to 800 μs, longer than the terminal time. These systems are compared to those with binary and ternary distributions. The stress relaxation functions are extracted from the Green–Kubo relation and from stress relaxation following a uniaxial extension. At short and intermediate time scales, both the mean squared displacement and the stress relaxation function G(t) are independent of ĐM. At longer times, the terminal relaxation time decreases with increasing ĐM. In this time range, the faster motion of the shorter chains results in constraint release for the longer chains.more » « less
-
Poole, Robert J (Ed.)The FENE-P (Finitely-Extensible Nonlinear Elastic) dumbbell constitutive equation is widely used in simulations and stability analyses of free and wall-bounded viscoelastic shear flows due to its relative simplicity and accuracy in predicting macroscopic properties of dilute polymer solutions. The model contains three independent material parameters, which expressed in dimensionless form correspond to a Weissenberg number (Wi), i.e., the ratio of the dumbbell relaxation time scale to a characteristic flow time scale, a finite extensibility parameter (L), corresponding to the ratio of the fully extended dumbbell length to the root mean square end-to-end separation of the polymer chain under equilibrium conditions, and a solvent viscosity ratio. An exact solution for the rheological predictions of the FENE-P model in steady simple shear flow is available [Sureshkumar et al., Phys Fluids (1997)], but the resulting nonlinear and nested set of equations do not readily reveal the key shear-thinning physics that dominates at high Wi as a result of the finite extensibility of the polymer chain. In this note we review a simple way of evaluating the steady material functions characterizing the nonlinear evolution of the polymeric contributions to the shear stress and first normal stress difference as the shear rate increases, provide asymptotic expansions as a function of Wi , and show that it is in fact possible to construct universal master curves for these two material functions as well as the corresponding stress ratio. Steady shear flow experiments on three highly elastic dilute polymer solutions of different finite extensibilities also follow the identified master curves. The governing dimensionless parameter for these master curves is Wi/L and it is only in strong shear flows exceeding Wi/L > 1 that the effects of finite extensibility of the polymer chains dominate the evolution of polymeric stresses in the flow field. We suggest that reporting the magnitude of Wi/L when performing stability analyses or simulating shear-dominated flows with the FENE-P model will help clarify finite extensibility effects.more » « less
-
Mud is a suspension of fine-grained particles (sand, silt, and clay) in water. The interaction of clay minerals in mud gives rise to complex rheological behaviors, such as yield stress, thixotropy, and viscoelasticity. Here, we experimentally examine the flow behaviors of kaolinite clay suspensions, a model mud, using steady shear rheometry. The flow curves exhibit both yield stress and rheological hysteresis behaviors for various kaolinite volume fractions (ϕk). Further understanding of these behaviors requires fitting to existing constitutive models, which is challenging due to numerous fitting parameters. To this end, we employ a Bayesian inference method, Markov chain Monte Carlo, to fit the experimental flow curves to a microstructural viscoelastic model. The method allows us to estimate the rheological properties of the clay suspensions, such as viscosity, yield stress, and relaxation time scales. The comparison of the inherent relaxation time scales suggests that kaolinite clay suspensions are strongly viscoelastic and weakly thixotropic at relatively low ϕk, while being almost inelastic and purely thixotropic at high ϕk. Overall, our results provide a framework for predictive model fitting to elucidate the rheological behaviors of natural materials and other structured fluids.more » « less
-
Abstract Dielectric spectroscopy measures the dynamics of polymer melts over a broad frequency range. Developing a theory for the spectral shape can extend the analysis of dielectric spectra beyond determining relaxation times from the peak maxima and adds physical meaning to shape parameters determined with empirical fit functions. Toward this goal, we use the experimental results on unentangled poly(isoprene), and unentangled poly(butylene oxide), polymer melts, to test whether the concept of end blocks could be one reason for the Rouse model deviating from experimental data. These end blocks have been suggested by simulations and neutron spin echo spectroscopy and are a consequence of the monomeric friction coefficient depending on the position of the bead in the chain. The concept of an end block is an approximation which partitions the chain in a middle and two end blocks to avoid overparameterization by a continuous position dependent change of the friction parameter. Analysis of dielectric spectra shows that the deviations of the calculated from the experimental normal mode cannot be related to the end block relaxation. However, the results do not contradict an end block hiding below the segmental relaxation peak. It seems that the results are compatible with an end block being the specific part of the sub-Rouse chain interpretation close to the chain ends.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1122/8.0000407
