From Rouse to Fully Established Entanglement Dynamics: A Study of Polyisoprene by Dielectric Spectroscopy

The effect of chemical constitution on polyisoprene dynamics

Polyisoprene (PI) melts have been studied, with most reports focusing on systems with high 1,4-cis content. In contrast, 1,4-trans PI homopolymers or random copolymers have seldom been examined, despite a handful of investigations suggesting a distinct dynamic behavior. Herein, we employ all-atom simulations to investigate the effect of chemical architecture on the dynamics of cis and trans-PI homopolymers, as well as copolymers. We examine the thermodynamic, conformational, and structural properties of the polymers and validate the performance of the models. We probe chain dynamics, revealing that cis-PI presents accelerated translation and reorientation modes relative to trans as recorded by the mean square displacement of the chain center-of-mass as well as by the characteristic times of the lower modes in a Rouse analysis. Interestingly, progressing to higher modes, we observe a reversal with trans units exhibiting faster dynamics. This was further confirmed by calculations of local carbon-hydrogen vector reorientation dynamics, which offer a microscopic view of segmental mobility. To obtain insight into the simulation trajectories, we evaluate the intermediate incoherent scattering function that supports a temperature-dependent crossover in relative mobility that extends over separations beyond the Kuhn-length level. Finally, we analyzed the role of non-Gaussian displacements, which demonstrate that cis-PI exhibits increased heterogeneity in dynamics over short-timescales in contrast to trans-PI, where deviations persist over times extending to terminal dynamics. Our all-atom simulations provide a fundamental understanding of PI dynamics and the impact of microstructure while providing important data for the design and optimization of PI-based materials.

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.

Toward strong self-healing polyisoprene elastomers with dynamic ionic crosslinks

To compromise high mechanical strength and efficient self-healing capability in an elastomer with dynamic crosslinks, optimization of the molecular structure is crucial in addition to the tuning of the dynamic properties of the crosslinks. Herein, we studied the effects of molecular weight, content of carboxy groups, and neutralization level of ionically crosslinked polyisoprene (PI) elastomers on their morphology, network rearrangement behavior, and self-healing and mechanical properties. In this PI elastomer, nanosized sphere-shaped ionic aggregates are formed by both neutralized and non-neutralized carboxy groups that act as stickers. The number density of the ionic aggregates that act as physical crosslinks increased with increase in the stickers' concentration, although the size of the ionic aggregates was independent of the molecular weight and the stickers' concentration. The ionic network was dynamically rearranged by the stickers' hopping between the ionic aggregates, and the rearrangement was accelerated by decreasing the neutralization level. We found that the 2Rg of the PI must be significantly larger than the average distance between the ionic aggregates to obtain a mechanically strong PI elastomer. We also found that further increase in the molecular weight is effective to enhance the dimensional stability of the elastomer. However, this approach reduced the elastomer's self-healing rate at the same time because the diffusion and randomization of the polymer chains between the damaged faces were reduced. In this work, we clearly demonstrated the principle in the optimization of the molecular structure for the ionically crosslinked PI elastomers to tune the mechanical and autonomous self-healing properties.

Elucidating the impact of extreme nanoscale confinement on segmental and chain dynamics of unentangled poly(cis-1,4-isoprene)

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 6.5 nm. Three molecular weights of PI (3, 7 and 10 kg/mol) were chosen such that the ratio of D to the polymer radius of gyration, R_g, 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/R_g. 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/R_g ∼ 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 10kg/mol PI confined at length-scales close to that of the R_g 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.

Studies on the molecular dynamics of acetylated oligosaccharides of different topologies (linear versus cyclic)

In this paper, the molecular dynamics and thermal properties of representative acetylated linear and cyclic oligosaccharides: acTRE, acRAF, acSTA, ac-α-CD, ac-β-CD, ac-γ-CD, have been investigated by using broadband dielectric spectroscopy and differential scanning calorimetry. We found that there are marked differences in the dynamics of the structural and secondary relaxation processes in both groups of materials. Just to mention a variation in the distribution of the structural relaxation times as well as different evolutions of the glass transition temperature (T_g) and fragility (m) versus molecular weight (M_w), which seem to be affected by the shape of the molecule, strain in the carbohydrate ring and mobility of side acetyl moieties.

Scaling analysis of the viscoelastic response of linear polymers

Viscoelastic response in terms of the complex shear modulus G^*(ω) of the linear polymers poly(ethylene-alt-propylene), poly(isoprene), and poly(butadiene) is studied for molar masses (M) from 3k up to 1000k and over a wide temperature range starting from the glass transition temperature T_g (174 K-373 K). Master curves G'(ωτ_α) and G″(ωτ_α) are constructed for the polymer-specific relaxation. Segmental relaxation occurring close to T_g is independently addressed by single spectra. Altogether, viscoelastic response is effectively studied over 14 decades in frequency. The structural relaxation time τ_α used for scaling is taken from dielectric spectra. We suggest a derivative method for identifying the different power-law regimes and their exponents along G″(ωτ_α) ∝ ω^ε″. The exponent ε″ = ε″(ωτ_α) ≡ d ln G″(ωτ_α)/d ln(ωτ_α) reveals more details compared to conventional analyses and displays high similarity among the polymers. Within a simple scaling model, the original tube-reptation model is extended to include contour length fluctuations (CLFs). The model reproduces all signatures of the quantitative theory by Likhtman and McLeish. The characteristic times and power-law exponents are rediscovered in ε″(ωτ_α). The high-frequency flank of the terminal relaxation closely follows the prediction for CLF (ε″ = -0.25), i.e., G″(ω) ∝ ω^-0.21±0.02. At lower frequencies, a second regime with lower exponent ε″ is observed signaling the crossover to coherent reptation. Application of the full Likhtman-McLeish calculation provides a quantitative interpolation of ε″(ωτ_α) at frequencies below those of the Rouse regime. The derivative method also allows identifying the entanglement time τ_e. However, as the exponent in the Rouse regime (ωτ_e > 1) varies along ε_eRouse = 0.66 ± 0.04 (off the Rouse prediction ε_Rouse = 0.5) and that at ωτ_e < 1 is similar, only a weak manifestation of the crossover at τ_e is found at highest M. Yet, calculating τ_e/τ_α= (M/M_o)², we find good agreement among the polymers when discussing ε″(ωτ_e). The terminal relaxation time τ_t is directly read off from ε″(ωτ_α). Plotting τ_t/τ_e as a function of Z = M/M_e, we find universal behavior as predicted by the TR model. The M dependence crosses over from an exponent significantly larger than 3.0 at intermediate M to an exponent approaching 3.0 at highest M in agreement with previous reports. The frequency of the minimum in G″(ωτ_α) scales as τ_min ∝ M^1.0±0.1. An M-independent frequency marks the crossover to glassy relaxation at the highest frequencies. Independent of the amplitude of G″(ω), which may be related to sample-to-sample differences, the derivative method is a versatile tool to provide a detailed phenomenological analysis of the viscoelastic response of complex liquids.

Molecular dynamic heterogeneity in relation to free volume and relaxation dynamics in organic glass-formers: oligomeric cis-1,4-poly(isoprene)

Herein, a combined study of the molecular rotation dynamics and free volume in cis-1,4-poly(isoprene) using two external probing techniques via ESR and PALS together with relaxation dynamics of the host medium via BDS is presented. The spectral evolution of the spin probe TEMPO from simulations over a wide range from 100 K up to 300 K exhibits three different regions of its correlation time consisting of a slow regime at low temperatures followed by the molecular dynamic heterogeneity zone from T = T = 155 K = 0.82 × T up to T_c ≅ 236 K = 1.26 × T and ending with a fast regime at high temperatures with the further characteristic ESR temperatures, T = 186 K ≅ T and T = 260 K. These are in close coincidence with four characteristic PALS temperatures: T = 160 K, T = 190 K, T = 227 K, and T = 263 K. Finally, using BDS, we revealed that the high-frequency features of the structural relaxation of 1,4-PIP 0.8k were related to the observed effects in the ESR and PALS response of the liquid state.

HORIZONS FOR DESIGN OF FILLED RUBBER INFORMED BY MOLECULAR DYNAMICS SIMULATION

Fillers such as carbon black provide a long-standing and essential strategy for the mechanical reinforcement of rubber in tires and other load-bearing applications. Despite their technological importance, however, the microscopic mechanism of this reinforcement remains a matter of considerable debate. A predictive understanding of filler-based reinforcement could catalyze the design of new rubber-filler composites with enhanced performance. Molecular dynamics simulations of rubber mechanical response in the presence of structured fillers offer a new strategy for resolving the origins of filler-based reinforcement and guiding filler design. Results of for ideal rubber-filler dispersions over a range of filler structures suggest that neither hydrodynamic effects nor non-deformable “bound rubber domains” are necessary to achieve high reinforcement. Moreover, simulations show that particle surface area is a poor predictor of reinforcement. Instead, simulated reinforcement correlates strongly with filler structure, with more rarified filler structure predicting much greater reinforcement at fixed loading. Simulation results are consistent with a scenario in which reinforcement at industrially relevant loadings is dominated by formation of a jammed network of filler particles, suggesting that reinforced rubber can be understood as a superposition of two materials: a rubbery solid, and a jammed granular solid. This perspective points to an opportunity to improve filler-reinforced rubber design by leveraging concepts and expertise developed over many decades in the fields of jamming and granular media.

Effect of Low-Concentration Polymers on Crystal Growth in Molecular Glasses: A Controlling Role for Polymer Segmental Mobility Relative to Host Dynamics

Low-concentration polymers can strongly influence crystal growth in small-molecule glasses, a phenomenon important for improving physical stability against crystallization. We measured the velocity of crystal growth in two molecular glasses, nifedipine (NIF) and o-terphenyl (OTP), each doped with four or five different polymers. For each polymer, the concentration was fixed at 1 wt % and a wide range of molecular weights was tested. We find that a polymer additive can strongly alter the rate of crystal growth, from a 10-fold reduction to a 10-fold increase. For a given polymer, increasing molecular weight slows down crystal growth and the effect saturates around DP = 100, where DP is the degree of polymerization. For all the systems studied, the polymer effect on crystal growth rate forms a master curve in the variable (T_g,polymer - T_g,host)/T_cryst, where T_g is the glass transition temperature and T_cryst is the crystallization temperature. These results support the view that a polymer's effect on crystal growth is controlled by its segmental mobility relative to the host-molecule dynamics. In the proposed model, crystal growth rejects impurities and creates local polymer-rich regions, which must be traversed by host molecules to sustain crystal growth at rates determined by polymer segmental mobility. Our results do not support the view that host-polymer hydrogen bonding plays a controlling role in crystal growth inhibition.

Qualitative change in structural dynamics of some glass-forming systems

Analysis of the temperature dependence of the structural relaxation time τ(α)(T) in supercooled liquids revealed a qualitatively distinct feature-a sharp, cusplike maximum in the second derivative of logτ(α)(T)at some T(max). It suggests that the super-Arrhenius temperature dependence of τ(α)(T) in glass-forming liquids eventually crosses over to an Arrhenius behavior at T<T(max), and there is no divergence of τ(α)(T) at nonzero T. T(max) can be above or below T(g), depending on the sensitivity of τ(T) to a change in the liquid's density quantified by the exponent γ in the scaling τ(α)(T)∼exp(A/Tρ(-γ)). These results might turn the discussion of the glass transition in a different direction-toward the origin of the limiting activation energy for structural relaxation at low T.

The segmental and chain relaxation modes in high-cis-polyisoprene as studied by thermally stimulated currents

The technique of Thermally Stimulated Currents is used to study the slow molecular mobility in a series of poly (1,4-cis-isoprene) samples with different molecular weights, Mw, and low polydispersity. The technique revealed a high resolution power, particularly useful in the study of the lower molecular weight samples where the chain and the segmental relaxations strongly overlap. The dynamic crossover that is reported for the normal mode by varying the molecular weight is clearly revealed by the thermally stimulated depolarization currents results through the temperature location, TMn, of the normal mode peak, the values of the relaxation time at TMn, τ(TMn), and the value of the fragility index of the normal mode, mn. The kinetic features of the glass transition relaxation of polyisoprene have also been determined.

Intermolecular spin relaxation and translation diffusion in liquids and polymer melts: insight from field-cycling 1H NMR relaxometry

With the advent of commercial field-cycling (FC) spectrometers, NMR relaxometry has gained new momentum as a method of investigating dynamics in liquids and polymers. The outcome of FC NMR experiments is spin-lattice relaxation time versus frequency (relaxation dispersion). In the case of protons, due to the intra- and intermolecular origin of dipolar interactions, the relaxation dispersion reflects rotational as well as translational dynamics. The latter shows a universal dispersion law at low frequencies, which allows determination of the diffusion coefficient D(T) in addition to the rotational correlation time τ(rot)(T), that is, FC (1)H NMR becomes an alternative to field-gradient NMR spectroscopy. Subdiffusive translation found in polymers can be accessed by singling out the intermolecular relaxation through isotope dilution experiments, and the mean square displacement can then be revealed as a function of time, thus complementing neutron scattering experiments. Likewise, information on reorientational dynamics is provided by the intramolecular relaxation. Assuming frequency-temperature superposition the corresponding correlation functions can be monitored up to eight decades in amplitude and time, which allows thorough testing of current polymer theories.

Hydrodynamic and viscoelastic effects in polymer diffusion

We develop a fluctuating hydrodynamics approach to study the impact of the hydrodynamic and viscoelastic interactions on the motion of the center of mass of a polymer as well as on the relaxation of Rouse modes, either in a Θ solvent or in a melt of identical unentangled chains. We show that this method allows us to describe the effect of hydrodynamic interactions beyond the Zimm (for a single chain in a Θ solvent) or the Rouse models (for an unentangled melt). In the latter case, we recover the same important effect of the viscoelastic hydrodynamic interactions on the center-of-mass diffusion, first described in Farago et al (2011 Phys. Rev. Lett. 107 178301).

Mode-coupling approach to polymer diffusion in an unentangled melt. I. The effect of density fluctuations

We quantitatively assess the effect of density fluctuation modes on the dynamics of a tagged polymer in an unentangled melt. To this end, we develop a density-based mode-coupling theory (dMCT) using the Mori-Zwanzig approach and projecting the fluctuating force onto pair-density fluctuation modes. The effect of dynamical density fluctuations on the center-of-mass (c.m.) dynamics is also analyzed based on a perturbative approach and we show that dMCT and perturbation techniques yield identical results. The c.m. velocity autocorrelation function (c.m. VAF) exhibits a slow power law relaxation in the time range between the monomer time t_{1} and the Rouse relaxation time t_{N}. We obtain an analytical expression for the c.m. VAF in terms of molecular parameters. In particular, the c.m. VAF scales as -N^{-1}t^{-5/4} (where N is the number of monomer units per chain) in the relevant time regime. The results are qualitatively accounted for by the dynamical correlation hole effect. The predicted -t^{-5/4} dependence of the c.m. VAF is supported by data of non-momentum-conserving computer simulations. However, the comparison shows that the theory significantly underestimates the amplitude of the effect. This issue is discussed and an alternative approach is addressed in the second part of this series [Farago et al., Phys. Rev. E 85, 051807 (2012), the following paper].