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
End block dynamics in unentangled polymers by dielectric spectroscopy
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
- PAR ID:
- 10501436
- Publisher / Repository:
- IOPScience
- Date Published:
- Journal Name:
- Journal of Physics: Condensed Matter
- Volume:
- 35
- Issue:
- 37
- ISSN:
- 0953-8984
- Page Range / eLocation ID:
- 375101
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
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
-
Broadband dielectric spectroscopy is employed to probe dynamics in low molecular weight poly(cis-1,4-isoprene) (PI) confined in unidirectional silica nanopores with mean pore diameter, D, of 6.5nm. Three molecular weights of PI (3, 7 and 10kg/mol) were chosen such that the ratio of D to the polymer radius of gyration, Rg, is varied from 3.4, 2.3 to 1.9, respectively. It is found that the mean segmental relaxation rate remains bulk-like but an additional process arises at lower frequencies with increasing molecular weight (decreasing D/Rg). In contrast, the mean relaxation rates of the end-to-end dipole vector corresponding to chain dynamics are found to be slightly slower than that in the bulk for the systems approaching D/Rg ∼ 2, but faster than the bulk for the polymer with the largest molecular weight. The analysis of the spectral shapes of the chain relaxation suggests that the resulting dynamics of the 10 kg/mol PI confined at length-scales close to that of the Rg are due to non-ideal chain conformations under confinement decreasing the chain relaxation times. The understanding of these faster chain dynamics of polymers under extreme geometrical confinement is necessary in designing nanodevices that contain polymeric materials within substrates approaching the molecular scale.more » « less
-
Abstract Dielectric spectroscopy is extremely powerful to study molecular dynamics, because of the very broad frequency range. Often multiple processes superimpose resulting in spectra that expand over several orders of magnitude, with some of the contributions partially hidden. For illustration, we selected two examples, (i) normal mode of high molar mass polymers partially hidden by conductivity and polarization and (ii) contour length fluctuations partially hidden by reptation using the well-studied polyisoprene melts as example. The intuitive approach to describe experimental spectra and to extract relaxation times is the addition of two or more model functions. Here, we use the empirical Havriliak-Negami function to illustrate the ambiguity of the extracted relaxation time, despite an excellent agreement of the fit with experimental data. We show that there are an infinite number of solutions for which a perfect description of experimental data can be achieved. However, a simple mathematical relationship indicates uniqueness of the pairs of the relaxation strength and relaxation time. Sacrificing the absolute value of the relaxation time enables to find the temperature dependence of the parameters with a high accuracy. For the specific cases studied here, the time temperature superposition (TTS) is very useful to confirm the principle. However, the derivation is not based on a specific temperature dependence, hence, independent from the TTS. We compare new and traditional approaches and find the same trend for the temperature dependence. The important advantage of the new technology is the knowledge of the accuracy of the relaxation times. Relaxation times determined from data for which the peak is clearly visible are the same within the experimental accuracy for traditional and new technology. However, for data where a dominant process hides the peak, substantial deviations can be observed. We conclude that the new approach is particularly helpful for cases in which relaxation times need to be determined without having access to the associated peak position.more » « less
-
null (Ed.)Recent findings that the association bond lifetimes τ α* in associating polymers diverge from their supramolecular network relaxation times τ c challenge past theories. The bond lifetime renormalization proposed by Rubinstein and coworkers [Stukalin et al. , Macromolecules , 2013, 46 , 7525] provides a promising explanation. To examine systematically its applicability, we employ shear rheology and dielectric spectroscopy to study telechelic associating polymers with different main chain (polypropylene glycol and polydimethylsiloxane), molecular weight (below entanglement molecular weight) and end groups (amide, and carboxylic acid) which form dimeric associations by hydrogen bonding. The separation between τ c (probed by rheology) and τ α* (probed by dielectric spectroscopy) strongly increases with chain length as qualitatively predicted by the model. However, to describe the increase quantitatively, a transition from Rouse to reptation dynamics must be assumed. This suggests that dynamics of super-chains must be considered to properly describe the transient network.more » « less
An official website of the United States government
