Dielectric Relaxation of Monodisperse Linear Polyisoprene: Contribution of Constraint Release

Constraint Release Rouse Mechanisms in Bidisperse Linear Polymers: Investigation of the Release Time of a Short-Long Entanglement

Despite a wide set of experimental data and a large number of studies, the quantitative description of the relaxation mechanisms involved in the disorientation process of bidisperse blends is still under discussion. In particular, while it has been shown that the relaxation of self-unentangled long chains diluted in a short chain matrix is well approximated by a Constraint Release Rouse (CRR) mechanism, there is no consensus on the value of the average release time of their entanglements, τobs, which fixes the timescale of the CRR relaxation. Therefore, the first objective of the present work is to discuss the different approaches proposed to determine this time and compare them to a large set of experimental viscoelastic data, either newly measured (poly(methyl-)methacrylate and 1,4-polybutadiene blends) or coming from the literature (polystyrene and polyisoprene blends). Based on this large set of data, it is found that with respect to the molar mass of the short chain matrix, τobs follows a power law with an exponent close to 2.5, rather than 3 as previously proposed. While this slight change in the power law exponent does not strongly affect the values of the constraint release times, the results obtained suggest the universality of the CRR process. Finally, we propose a new description of τobs, which is implemented in a tube-based model. The accurate description of the experimental data obtained provides a good starting point to extend this approach to self-entangled binary blends.

Uniqueness of relaxation times determined by dielectric spectroscopy

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.

Slip-spring simulations of different constraint release environments for linear polymer chains

The constraint release (CR) mechanism has important effects on polymer relaxation and the chains will show different relaxation behaviour in conditions of monodisperse, bidisperse and other topological environments. By comparing relaxation data of linear polyisoprene (PI) chains dissolved in very long matrix and monodisperse melts, Matsumiya et al. showed that CR mechanism accelerates both dielectric and viscoelastic relaxation (Matsumiya et al. 2013 Macromolecules 46, 6067. (doi:10.1021/ma400606n)). In this work, the experimental data reported by Matsumiya et al. are reproduced using the single slip-spring (SSp) model and the CR accelerating effects on both dielectric and viscoelastic relaxation are validated by simulations. This effect on viscoelastic relaxation is more pronounced. The coincidence for end-to-end relaxation and the viscoelastic relaxation has also been checked using probe version SSp model. A variant of SSp with each entanglement assigning a characteristic lifetime is also proposed to simulate various CR environment flexibly. Using this lifetime version SSp model, the correct relaxation function can be obtained with equal numbers of entanglement destructions by CR and reptation/contour length fluctuation (CLF) for monodisperse melts. Good agreement with published experiment data is also obtained for bidisperse melts, which validates the ability to correctly describe the CR environment of the lifetime version model.

ENTANGLEMENT-LOOSENING DYNAMICS RESOLVED THROUGH COMPARISON OF DIELECTRIC AND VISCOELASTIC DATA OF TYPE-A POLYMERS: A REVIEW

For so-called type-A polymer chains having electrical dipoles aligned parallel along their backbone, the large-scale chain motion over the end-to-end distance results in not only viscoelastic but also dielectric relaxation. These two relaxation processes detect the same motion but with different averaging moments, which enables us to experimentally resolve some details of the chain dynamics through comparison of viscoelastic and dielectric data of type-A polymers. For a typical type-A polymer, high-cis polyisoprene (PI), results of such an experimental approach are summarized to discuss characteristic features of an entanglement-loosening process (constraint release and/or dynamic tube dilation process) resolved from the data comparison.

Comparative Analysis of Different Tube Models for Linear Rheology of Monodisperse Linear Entangled Polymers

The aim of the present paper is to analyse the differences between tube-based models which are widely used for predicting the linear viscoelasticity of monodisperse linear polymers, in comparison to a large set of experimental data. The following models are examined: Milner–McLeish, Likhtman–McLeish, the Hierarchical model proposed by the group of Larson, the BoB model of Das and Read, and the TMA model proposed by the group of van Ruymbeke. This comparison allows us to highlight and discuss important questions related to the relaxation of entangled polymers, such as the importance of the contour-length fluctuations (CLF) process and how it affects the reptation mechanism, or the contribution of the constraint release (CR) process on the motion of the chains. In particular, it allows us to point out important approximations, inherent in some models, which result in an overestimation of the effect of CLF on the reptation time. On the contrary, by validating the TMA model against experimental data, we show that this effect is underestimated in TMA. Therefore, in order to obtain accurate predictions, a novel modification to the TMA model is proposed. Our current work is a continuation of earlier research (Shchetnikava et al., 2014), where a similar analysis is performed on well-defined star polymers.

A strain-controlled RheoSANS instrument for the measurement of the microstructural, electrical, and mechanical properties of soft materials

In situ measurements are an increasingly important tool to inform the complex relationship between nanoscale properties and macroscopic material measurements. Knowledge of these phenomena can be used to develop new materials to meet the performance demands of next generation technologies. Conductive complex fluids have emerged as an area of research where the electrical and mechanical properties are key design parameters. To study the relationship between microstructure, conductivity, and rheology, we have developed a small angle neutron scattering (SANS) compatible Couette rheological geometry capable of making impedance spectroscopy measurements under continuous shear. We have also mounted this geometry on a commercial strain controlled rheometer with a modified forced convection oven. In this manuscript, we introduce the simultaneous measurement of impedance spectroscopy, rheological properties and SANS data. We describe the validation of this dielectric RheoSANS instrument and demonstrate its operation using two systems-an ion gel comprising Pluronic® surfactant and ionic liquid, ethyl-ammonium nitrate, and poly(3-hexylthiophene) organogel prepared in a mixture of hexadecane and dichlorobenzene. In both systems, we use this new measurement capability to study the microstructural state of these materials under two different protocols. By monitoring their dielectric rheology at the same time as the SANS measurement, we demonstrate the capacity to directly probe structure-property relationships inherent to the macroscopic material response.

Primitive chain network simulations of probe rheology

Probe rheology experiments, in which the dynamics of a small amount of probe chains dissolved in immobile matrix chains is discussed, have been performed for the development of molecular theories for entangled polymer dynamics. Although probe chain dynamics in probe rheology is considered hypothetically as single chain dynamics in fixed tube-shaped confinement, it has not been fully elucidated. For instance, the end-to-end relaxation of probe chains is slower than that for monodisperse melts, unlike the conventional molecular theories. In this study, the viscoelastic and dielectric relaxations of probe chains were calculated by primitive chain network simulations. The simulations semi-quantitatively reproduced the dielectric relaxation, which reflects the effect of constraint release on the end-to-end relaxation. Fair agreement was also obtained for the viscoelastic relaxation time. However, the viscoelastic relaxation intensity was underestimated, possibly due to some flaws in the model for the inter-chain cross-correlations between probe and matrix chains.

Dynamic dilution exponent in monodisperse entangled polymer solutions

We study and model the linear viscoelastic properties of several entangled semi-dilute and concentrated solutions of linear chains of different molar masses and at different concentrations dissolved in their oligomers. We discuss the dilution effect of the oligomers on the entangled long chains. In particular, we investigate the influence of both concentration and molar mass on the value of the effective dynamic dilution exponent determined from the level of the storage plateau at low and intermediate frequencies. We show that the experimental results can be quantitatively explained by considering the tension re-equilibration process along the chains, in agreement with van Ruymbeke et al. (Macromol., 2014), i.e. by considering that the real dilution exponent α is always equal to 1, while larger values of the dilution exponent (1 < α < 1.3) found experimentally are attributed to the enhanced relaxation of the long chain extremities. Then we discuss the influence of the polymer concentration on the terminal relaxation time of the solutions and how this can be modelled by the enhanced contour length fluctuation process (CR-CLF). We point out that this larger dilution effect is not only a function of concentration but also depends on the molar mass of the chains. While the proposed approach successfully explains the viscoelastic properties of a large number of semi-dilute solutions of polymers in their own oligomers, important discrepancies are found for semi-dilute entangled polymers in small-molecule theta or good solvents. Possible explanations for the differences between these sample sets are proposed, based on the comparison of their viscoelastic behavior.

Chain Dynamics on Crossing the Glass Transition: Nonequilibrium Effects and Recovery of the Temperature Dependence of the Structural Relaxation

In this paper we report thermally stimulated depolarization current results on the chain and segmental dynamics of two monodisperse polyisoprenes accessing both dynamics at ultralow frequency range and exploring the relationship between segmental and chain time scales when crossing the glass transition. In this range, we have recorded experimental evidence of nonequilibrium effects on the slowest chain mode dynamics. The nonequilibrium effects seem to occur simultaneously for both chain and α-relaxation. Moreover, detailed analysis strongly indicates the recovery of an even T-dependence for the chain and α-relaxation dynamics on crossing glass transition and in the glassy state. The obtained results can be understood taking into account the different temperature dependences of the length scales involved in the segmental and chain relaxations.

Polymer chain dynamics: evidence of nonexponential mode relaxation using thermally stimulated depolarization current techniques

The slowest (p=1) mode relaxation of several polyisoprenes has been experimentally isolated by thermally stimulated depolarization current techniques. Close to the glass transition the p=1 mode deviates from the exponential behavior assumed by Rouse and tube-reptation theories. This effect is found to be a consequence of the closeness of τ_{p=1} and α-relaxation time scales. The scenario resembles that of broadened fast component dynamics in polymer blends with high dynamic asymmetry and suggests a possible general interpretation in terms of the effect of local density fluctuations (α relaxation) on chain dynamics.