Rouse Modes Research Articles

Viscoelastic Relaxation of Rouse Chains undergoing Head-to-Head Association and Dissociation: Motional Coupling through Chemical Equilibrium

For nonentangled Rouse chains undergoing head-to-head association and dissociation reaction, the viscoelastic relaxation functions g1(t) and g2(t) were formulated for a case that a given dissociated unimer chain rapidly reassociates with its original partner unimer. The relaxation of the unimer and dimer was essentially determined by ratios ra and rd of the Rouse relaxation time (in the absence of reaction) to the association and dissociation times. For small ra and rd, the reaction was slow so that the unimer and dimer relaxed through respective pure Rouse modes, as naturally expected. However, for most cases in wide ranges of ra and rd, the dimer relaxation was accelerated with increasing rd (>1), and g2 of the dimer was indistinguishable from the pure Rouse relaxation function of the unimer, g1,Rouse. For those cases, g1 of the unimer also coincided with g1,Rouse. These results demonstrate that the motional coupling between the unimer and dimer, occurring through the association/dissociation reaction, strongly affects the relaxation. The Rouse modes of the unimer and dimer were found to split in two series due to this coupling, and new relaxation modes due to the coupling emerged as well. Those new modes largely contribute to g1 and g2 for the cases of ra, rd > 1, thereby compensating the difference between the split modes (involved in gj) and the pure Rouse modes (in g1,Rouse) to provide the unimer and dimer with the superficial coincidence between their gj and g1,Rouse. In addition, in limited cases of moderately small rd, the relaxation of odd modes of the dimer was accelerated by the dissociation but remained still slower than the relaxation of g1,Rouse. For this case, the unimer relaxation was slower than its pure Rouse relaxation (namely, the unimer relaxation was retarded by the reaction), because of the coupling with the dimer odd modes. This result confirmed the significant effect of motional coupling on the relaxation of the unimer and dimer.

Chain end mobilities in polymer melts--a computational study.

The Rouse model can be regarded as the standard model to describe the dynamics of a short polymer chain under melt conditions. In this contribution, we explicitly check one of the fundamental assumptions of this model, namely, that of a uniform friction coefficient for all monomers, on the basis of MD simulation data of a poly(ethylene oxide) (PEO) melt. This question immediately arises from the fact that in a real polymer melt, the terminal monomers have on average more intermolecular neighbors than the central monomers, and one would expect that exactly these details affect the precise value of the friction coefficient. The mobilities are determined by our recently developed statistical method, which provides detailed insights into the local polymer dynamics. Moreover, it yields complementary information to that obtained from the mean square displacement (MSD) or the Rouse mode analysis. It turns out that the Rouse assumption of a uniform mobility is fulfilled to a good approximation for the PEO melt. However, a more detailed analysis reveals that the underlying microscopic dynamics are highly affected by different contributions from intra- and intermolecular excluded volume interactions, which cannot be taken into account by a modified friction coefficient. Minor deviations occur only for the terminal monomers on larger time scales, which can be attributed to the presence of two different escape mechanisms from their first coordination sphere. These effects remain elusive when studying the dynamics with the MSD only.

Rouse mode analysis of chain relaxation in polymer nanocomposites

Rouse mode analysis of chain relaxation in polymer nanocomposites

Rouse mode analysis of chain relaxation in polymer nanocomposites.

Large-scale molecular dynamics simulations are used to study the internal relaxations of chains in nanoparticle (NP)/polymer composites. We examine the Rouse modes of the chains, a quantity that is closest in spirit to the self-intermediate scattering function, typically determined in an (incoherent) inelastic neutron scattering experiment. Our simulations show that for weakly interacting mixtures of NPs and polymers, the effective monomeric relaxation rates are faster than in a neat melt when the NPs are smaller than the entanglement mesh size. In this case, the NPs serve to reduce both the monomeric friction and the entanglements in the polymer melt, as in the case of a polymer-solvent system. However, for NPs larger than half the entanglement mesh size, the effective monomer relaxation is essentially unaffected for low NP concentrations. Even in this case, we observe a strong reduction in chain entanglements for larger NP loadings. Thus, the role of NPs is to always reduce the number of entanglements, with this effect only becoming pronounced for small NPs or for high concentrations of large NPs. Our studies of the relaxation of single chains resonate with recent neutron spin echo (NSE) experiments, which deduce a similar entanglement dilution effect.

The universal trend of the non-exponential Rouse mode relaxation in polymer systems: a theoretical interpretation based on a generalized Langevin equation

We show that the universal behavior of the Rouse-mode relaxation in polymer systems - which has been recently reported from experimental data [S. Arrese-Igor, et al., Phys. Rev. Lett., 2014, 113, 078302] - can be quantitatively explained in the framework of a theoretical approach based on: (i) a generalized Langevin equation formalism and (ii) a memory function which takes into account the coupling between intra-chain dynamics and collective dynamics. This approach opens the way for generalizing the magnitudes probing chain dynamics in polymer systems.

Thermo-Rheological, Piezo-Rheological, and TVγ-Rheological Complexities of Viscoelastic Mechanisms in Polymers

Experimental evidence are collected together to show in general the viscoelastic mechanisms of low and high molecular weight polymers have different dependences on temperature T, pressure P, and the same scaling product variable, TVγ, where V is the specific volume and γ is a material constant. The viscoelastic mechanisms include the Johari–Goldstein β-relaxation, the segmental α-relaxation, the sub-Rouse modes, the Rouse modes, and the terminal relaxation if the polymer chains are entangled. Appropriately called the thermo-, piezo-, and TVγ-rheological complexity of polymers, these viscoelastic anomalies are fundamental and deserve attention from the polymer physics community. Although we show that the coupling model can rationalize the origin of the complexity and explain some of the data quantitatively, the objective of this paper is to stimulate others to construct a theory that can do even better.

Non-exponential Rouse correlators and generalized magnitudes probing chain dynamics

Inspired by the generalized Langevin equation (GLE) formalism with some approximations, we have proposed a method to generalize the Rouse expression of the magnitudes probing chain dynamics, taking into account the non-exponential character of the Rouse mode correlators. In this way, generalized expressions for the incoherent neutron scattering function and for the End-to-End relaxation – which give rise in the frequency domain to the dielectric ‘normal mode’ relaxation – have been obtained. These magnitudes have been checked by means of fully atomistic molecular dynamics (MD) simulations corresponding to pure poly(ethylene oxide) (PEO) and to PEO in an asymmetric blend with poly(methyl methacrylate) (PMMA). Moreover, the results obtained also seem to give support to the unified scenario recently proposed for explaining the non-exponential relaxation of the long-wavelength Rouse modes in polymer systems in terms of the effect of density fluctuations (α-process) on chain dynamics.

Origin of the crossover in dynamics of the sub-Rouse modes at the same temperature as the structural α-relaxation in polymers.

The nature of the liquid-glass transition remains an unsolved fundamental problem. One aspect is the striking change in dynamics of the structural α-relaxation generally observed at a temperature T(B) above Tg in all glass-formers. More intriguing in the case of polymers is that the change of dynamics occurs not only in the structural α-relaxation but also in the sub-Rouse modes, i.e. chain modes in between the α-relaxation and the Rouse modes. However, the nature of the dynamic crossover of the sub-Rouse modes remains unclear. In this paper, the dynamics of a series of poly(n-alkyl methacrylates) with different molecular weights and microstructures studied by mechanical spectroscopy are reported. We demonstrate that the sub-Rouse modes exhibit a similar crossover of dynamics at the same T(B) as the α-relaxation. This property shared by the two viscoelastic mechanisms is remarkable. By invoking the results from the studies using positron annihilation spectroscopy and adiabatic calorimetry, we show that both viscoelastic mechanisms are coupled to density, correlated with the change of the configuration entropy, and are intermolecularly cooperative. The time scale of sub-Rouse modes at T(B) of the polymers studied is approximately independent of molecular weight and micro-structure of the polymers studied. The findings enhance the understanding of the sub-Rouse modes and their manifestation in the viscoelasticity of polymers in the glass-rubber transition region.

Detecting the Rouse and Sub-Rouse Modes in Poly(Butyl Acrylate) and Poly(Ethyl Acrylate) Through Two-Dimensional Dynamic Mechanical Spectra

The difficulties of observing sub-Rouse modes (SRM) and Rouse modes (RM) in acrylate polymers has resulted in many arguments and disputes concerning the nature of their glass-rubber transition. Because different modes have different sensitivity to external perturbations, the two-dimensional dynamic analysis mechanical spectra (2D-DMS) was introduced to detect the local segments motion (LSM), SRM, and RM in poly(butyl acrylate) (PBA) and poly(ethyl acrylate) (PEA). The results of the asynchronous spectra showed the LSM, SRM, and RM of PBA and PEA are located, respectively, at about (−46 ∼ −29°C), (−28 ∼ −10°C), (−4 ∼ 27°C), and about (−12 ∼ −5°C), (−3 ∼ 6°C), and (10 ∼ 44°C). Furthermore, the LSM and SRM of PBA and PEA have an overlap in the synchronous spectra. This is suggested to be caused by the higher coupling effect in PBA and PEA when compared with strong glass formation polymers, like polyisobutylene (PIB).

Rouse Mode Analysis of Chain Relaxation in Homopolymer Melts.

We use molecular dynamics simulations of the Kremer–Grest (KG) bead–spring model of polymer chains of length between 10 and 500, and a closely related analogue that allows for chain crossing, to clearly delineate the effects of entanglements on the length-scale-dependent chain relaxation in polymer melts. We analyze the resulting trajectories using the Rouse modes of the chains and find that entanglements strongly affect these modes. The relaxation rates of the chains show two limiting effective monomeric frictions, with the local modes experiencing much lower effective friction than the longer modes. The monomeric relaxation rates of longer modes vary approximately inversely with chain length due to kinetic confinement effects. The time-dependent relaxation of Rouse modes has a stretched exponential character with a minimum of stretching exponent in the vicinity of the entanglement chain length. None of these trends are found in models that allow for chain crossing. These facts, in combination, argue for the confined motion of chains for time scales between the entanglement time and their ultimate free diffusion.

Structure and dynamics of confined flexible and unentangled polymer melts in highly adsorbing cylindrical pores.

Coarse-grained molecular dynamics simulations are used to probe the dynamic phenomena of polymer melts confined in nanopores. The simulation results show excellent agreement in the values obtained for the normalized coherent single chain dynamic structure factor, S(Q,Δt)/S(Q,0). In the bulk configuration, both simulations and experiments confirm that the polymer chains follow Rouse dynamics. However, under confinement, the Rouse modes are suppressed. The mean-square radius of gyration ⟨R(g)(2)⟩ and the average relative shape anisotropy ⟨κ(2)⟩ of the conformation of the polymer chains indicate a pancake-like conformation near the surface and a bulk-like conformation near the center of the confining cylinder. This was confirmed by direct visualization of the polymer chains. Despite the presence of these different conformations, the average form factor of the confined chains still follows the Debye function which describes linear ideal chains, which is in agreement with small angle neutron scattering experiments (SANS). The experimentally inaccessible mean-square displacement (MSD) of the confined monomers, calculated as a function of radial distance from the pore surface, was obtained in the simulations. The simulations show a gradual increase of the MSD from the adsorbed, but mobile layer, to that similar to the bulk far away from the surface.

Scaling of the dynamics of flexible Lennard-Jones chains.

The isomorph theory provides an explanation for the so-called power law density scaling which has been observed in many molecular and polymeric glass formers, both experimentally and in simulations. Power law density scaling (relaxation times and transport coefficients being functions of ρ(γ(S)), where ρ is density, T is temperature, and γ(S) is a material specific scaling exponent) is an approximation to a more general scaling predicted by the isomorph theory. Furthermore, the isomorph theory provides an explanation for Rosenfeld scaling (relaxation times and transport coefficients being functions of excess entropy) which has been observed in simulations of both molecular and polymeric systems. Doing molecular dynamics simulations of flexible Lennard-Jones chains (LJC) with rigid bonds, we here provide the first detailed test of the isomorph theory applied to flexible chain molecules. We confirm the existence of isomorphs, which are curves in the phase diagram along which the dynamics is invariant in the appropriate reduced units. This holds not only for the relaxation times but also for the full time dependence of the dynamics, including chain specific dynamics such as the end-to-end vector autocorrelation function and the relaxation of the Rouse modes. As predicted by the isomorph theory, jumps between different state points on the same isomorph happen instantaneously without any slow relaxation. Since the LJC is a simple coarse-grained model for alkanes and polymers, our results provide a possible explanation for why power-law density scaling is observed experimentally in alkanes and many polymeric systems. The theory provides an independent method of determining the scaling exponent, which is usually treated as an empirical scaling parameter.

Multilayered damping composites with damping layer/constraining layer prepared by a novel method

The alternating multilayered damping composites, chlorinated butyl rubber (CIIR) as damping layer and polymethyl methacrylate (PMMA) as constraining layer, were first prepared through novel multilayered co-extrusion. The damping properties of the CIIR/PMMA multilayered damping composites were investigated by dynamic mechanical analysis (DMA). The results showed that the damping peak moved to high temperature and the efficient damping temperature range was broaden with the layer number increasing. The shift of the loss peak was ascribed to the move of Rouse mode of CIIR, which was attributed to the motion of longer chain segment, but the local segmental motion was not changed. Finite element analysis (FEA) was used to simulate the distribution of shear strain in the multilayered damping composites. The FEA results exhibited that, in the temperature range between Tg-CIIR and Tg-PMMA, the shear strain occurred in the CIIR layer under vibration field, since the storage modulus ( E ′) of PMMA was much higher than that of CIIR. Furthermore, the average shear strain was increased with the layer number increasing.

Enhance Slower Relaxation Process of Poly(ethyl acrylate) through Internal Plasticization

Abstract In this paper, we report a chemical way to resolve longer motions units in the glass-rubber transition region of poly (ethyl acrylate) (PEA), so called internal plasticization. The ethyl acrylate (EA) monomers were copolymerized with little amount of isoprene (IP) monomers. We propose that the single bonds adjunct to double bonds would have better flexible activity than usual single bonds, so the motion units located between two adjunct double bonds would be enhanced. The dynamic mechanical spectra of internally plasticized PEA (IPPEA) and PEA show that the tan δ of IPPEA is asymmetric, while the tan δ of PEA is symmetric. Furthermore, the results of 2D-DMAS show that the LSM, SRM and RM of IPPEA are located at 7 °C, 12 °C and 36 °C. The shoulder peak of tan δ of IPPEA at higher temperature side was confirmed that it contains sub-rouse mode (SRM) and rouse mode (RM). Thus, internal plasticization is an effective way to resolve modes above Tg.

A mesoscopic simulation method for predicting the rheology of semi-dilute wormlike micellar solutions

We present a fast “pointer” simulation method that extends the model of Cates and coworkers for the rheology of entangled wormlike micelles. Our method includes not only reptation, breakage/rejoining, contour length fluctuations, and Rouse modes, which were included in Cates' model, but also constraint release, bending modes, and a cross-over to the tight entanglement regime, which had not been previously considered. Our method also contains correlations in micelle length across multiple breakage/rejoining cycles, not included in previous approaches. Our method uses “pointers” that track the ends of unrelaxed regions along each micelle, thereby allowing efficient simulations of relaxation dynamics for ensembles containing thousands of micelles, to obtain accurate results without preaveraging or neglecting correlations. A modified genetic algorithm is applied to transform the simulation data from the time to the frequency domain. The method can span several regimes of behavior depending on the relative rat...

Origins of the two simultaneous mechanisms causing glass transition temperature reductions in high molecular weight freestanding polymer films

From ellipsometry measurements, Pye and Roth [Phys. Rev. Lett. 107, 235701 (2011)] presented evidence of the presence of two glass transitions originating from two distinctly different and simultaneous mechanisms to reduce the glass transition temperature within freestanding polystyrene films with thickness less than 70 nm. The upper transition temperature T(u)(g)(h) is higher than the lower transition temperature T(l)(g)(h) in the ultrathin films. After comparing their data with the findings of others, using the same or different techniques, they concluded that new theoretical interpretation is needed to explain the two transitions and the different dependences of T(u)(g)(h) and T(l)(g)(h) on film thickness and molecular weight. We address the problem based on advance in delineating the different viscoelastic mechanisms in the glass-rubber transition zone of polymers. Theoretical considerations as well as experiments have shown in time-scales immediately following the segmental α-relaxation are the sub-Rouse modes with longer length scale but shorter than that of the Rouse modes. The existence of the sub-Rouse modes in various polymers including polystyrene has been repeatedly confirmed by experiments. We show that the sub-Rouse modes can account for the upper transition and the properties observed. The segmental α-relaxation is responsible for the lower transition. This is supported by the fact that the segmental α-relaxation in ultrathin freestanding PS films had been observed by dielectric relaxation measurements and photon correlation spectroscopy. Utilizing the temperature dependence of the segmental relaxation times from these experiments, the glass transition temperature T(α)(g)associated with the segmental relaxation in the ultrathin film is determined. It turns out that T(α)(g) is nearly the same as T(l)(g)(h) of the lower transition, and hence definitely segmental α-relaxation is the mechanism for the lower transition. Since it is unlikely that the segmental α-relaxation can give rise to two very different transitions simultaneously, a new mechanism for the upper transition is needed, and the sub-Rouse modes provide the mechanism.

Compact structure and non-Gaussian dynamics of ring polymer melts

We present a neutron scattering analysis of the structure and dynamics of PEO polymer rings with a molecular weight 2.5 times higher than the entanglement mass. The melt structure was found to be more compact than a Gaussian model would suggest. With increasing time the center of mass (c.o.m.) diffusion undergoes a transition from sub-diffusive to diffusive behavior. The transition time agrees well with the decorrelation time predicted by a mode coupling approach. As a novel feature well pronounced non-Gaussian behavior of the c.o.m. diffusion was found that shows surprising analogies to the cage effect known from glassy systems. Finally, the longest wavelength Rouse modes are suppressed possibly as a consequence of an onset of lattice animal features as hypothesized in theoretical approaches.

Rouse Mode Analysis of Chain Relaxation in Homopolymer Melts

Rouse Mode Analysis of Chain Relaxation in Homopolymer Melts

The molecular dynamics of different relaxation modes in asymmetric chlorinated butyl rubber/petroleum resin blends

The PR plays a role like an anti-plasticizer in decreasing the free volume fraction of the CIIR/PR blend. The mobility of Rouse modes is confined significantly more than that of local segmental motion.

The proper glass transition temperature of amorphous polymers on dynamic mechanical spectra

Glass transition is crucial to the thermal and dynamical properties of polymers. Thus, it is important to detect glass transition temperature (T g) with a sensitive and proper method. Dynamic mechanical analysis (DMA) is one of the most frequently used methods to determine T g due to its advantage of high sensibility. However, there is controversy in the past literatures to determine the proper glass transition temperature among three transition temperatures, i.e., T g1, T g2 and T g3 in the dynamic mechanical spectra, which correspond to the temperature abscissa of intersect value of two tangent lines on storage modulus (E′), the peak of the loss modulus (E″) and the peak of the loss tangent (tan δ). In this work, these three transition temperatures were compared with the glass transition temperature determined by DSC (T gDSC). Based on the discussion of different modes of molecular motion around the glass transition region, it is demonstrated that T g1 and T g2 have the same molecular mechanism as T gDSC, i.e., local segmental motion which is enthalpic in nature and determines the proper glass transition temperature, while T g3 is assigned to the transition temperature of entropic Rouse modes, thus cannot be used as the proper glass transition temperature.