Softening Dispersion Research Articles

Deconvolution of the segmental and chain modes in amorphous polymers: Do the short-chain modes affect the bulk relaxation?

A new method for calculating the retardation spectra for linear viscoelastic materials is presented. The method uses the analytical expressions among the viscoelastic functions through the numerical evaluation of the Inverse Laplace Transform (ILT) with the Gaver–Wynn–Rho (GWR) algorithm. It is applied to study three polymers' relaxation mechanisms: a star Polystyrene and two Polycyanurate networks with two different crosslink densities. The shear spectrum is de-convoluted to separate the segmental and the chain modes responsible for the softening dispersion. The retardation mechanisms extracted from the shear response are then compared with the volumetric bulk response. The results show that the shear segmental contribution is narrower than the volumetric bulk response and finishes about two decades before the shoulder's appearance in the shear retardation spectrum. Thus, the volumetric bulk response, mainly exerted by the segmental mode, is also affected at long times by the short time chain mechanism, usually claimed to be Sub-Rouse modes. • A new method for evaluating the spectra of viscoelastic materials is proposed. • The molecular mechanisms contributing to the shear response of polymers are de-convoluted. • The de-convolution allows the quantitative comparison of the volumetric and shear mechanisms. • Sub-Rouse modes affect the long-time tail of the volumetric bulk response.

Abnormal segmental dynamics of poly(methyl methacrylate)/poly(vinylidene fluoride) blends by mechanical spectroscopy

The molecular relaxation dynamics of PMMA/PVDF blends above the glass transition temperature (Tg) over a wide composition range are studied by mechanical spectroscopy combined with differential scanning calorimetry (DSC) and Fourier transform infrared spectroscopy (FTIR) measurements. The mechanical spectra of the blends reveal the existence of two relaxation modes: α, ascribed to the glass transition, and α′, related to the softening dispersion composed of the sub-Rouse modes and the Rouse modes. At ϕPVDF = 40%, both the α and α′ relaxation processes shift to low-temperatures and are accelerated, which is due to the formation of the interphase and unfavourable interchain entanglements in the intermediate composition. The abnormal dynamics of the blend at ϕPVDF = 40% is further confirmed by the observed weak interaction between PMMA and PVDF from FTIR measurements and an obvious drop of the intermolecular coupling from the Coupling Model. However, the longer α′ relaxation shows a different dynamic behavior from the α relaxation for the blends with increasing the PVDF content at ϕPVDF ≤ 40%, which is due to the structure evolution and the change of chains entanglement with heating. This work enriches the understanding of the complex relaxation dynamics and the structure evolution in PMMA/PVDF blends.

Nonlinear Bloch waves and balance between hardening and softening dispersion.

The introduction of nonlinearity alters the dispersion of elastic waves in solid media. In this paper, we present an analytical formulation for the treatment of finite-strain Bloch waves in one-dimensional phononic crystals consisting of layers with alternating material properties. Considering longitudinal waves and ignoring lateral effects, the exact nonlinear dispersion relation in each homogeneous layer is first obtained and subsequently used within the transfer matrix method to derive an approximate nonlinear dispersion relation for the overall periodic medium. The result is an amplitude-dependent elastic band structure that upon verification by numerical simulations is accurate for up to an amplitude-to-unit-cell length ratio of one-eighth. The derived dispersion relation allows us to interpret the formation of spatial invariance in the wave profile as a balance between hardening and softening effects in the dispersion that emerge due to the nonlinearity and the periodicity, respectively. For example, for a wave amplitude of the order of one-eighth of the unit-cell size in a demonstrative structure, the two effects are practically in balance for wavelengths as small as roughly three times the unit-cell size.

Effect of some inorganic particles on the softening dispersion of the dynamics of butyl rubber

Inorganic particles have been common fillers for processing butyl rubber (IIR). Studying the effect of inorganic particles on the molecular motions of IIR was important to both relevant theory and applications. In this paper, the morphology and dynamics of IIR/silica, IIR/carbon black and IIR/Fe3O4 blends were studied. It was found that silica was homogenously dispersed in IIR and it suppressed the molecular motions of IIR at all loads. In addition, the carbon black with a low load averagely dispersed in IIR and suppressed the molecular motions of IIR; however, it agglomerated and the suppression was weakened as the load was increased. Moreover, Fe3O4 had nearly no influence on the molecular motions of IIR.

Changes in the Viscoelastic Mechanisms of Polyisobutylene by Plasticization

Our dynamic mechanical measurements in the glass–rubber transition zone of polyisobutylene (PIB), expressed in terms of the relaxation spectrum H(τ) and loss tangent (tan δ), have found an additional shoulder. Following the interpretation of previous works, the shoulder is attributed to the sub-Rouse modes, which account for motions intermediate in length scale to the Rouse and local segmental modes. The fact that the sub-Rouse modes are well resolved in PIB and not in other amorphous polymers was traced to its weak intermolecular coupling, which ultimately originates from the compact and symmetrical structure of its repeat unit. We test this interpretation further by studying the change on adding liquid paraffin (LP) to PIB, which should disrupt the effective chain packing of undiluted PIB. We found on adding LP to PIB that the softening dispersion becomes narrower, and eventually the disappearance of the shoulder. The effect is due to the mobility of entropic Rouse modes enhanced significantly more than...

Kinetics of a Bioactive Compound (Caffeine) Mobility at the Vicinity of the Mechanical Glass Transition Temperature Induced by Gelling Polysaccharide

An investigation of the diffusional mobility of a bioactive compound (caffeine) within the high-solid (80.0% w/w) matrices of glucose syrup and κ-carrageenan plus glucose syrup exhibiting distinct mechanical glass transition properties is reported. The experimental temperature range was from 20 to -60 °C, and the techniques of modulated differential scanning calorimetry, small deformation dynamic oscillation in shear, and UV spectrometry were employed. Calorimetric and mechanical measurements were complementary in recording the relaxation dynamics of high-solid matrices upon controlled heating. Predictions of the reaction rate theory and the combined WLF/free volume framework were further utilized to pinpoint the glass transition temperature (T(g)) of the two matrices in the softening dispersion. Independent of composition, calorimetry yielded similar T(g) predictions for both matrices at this level of solids. Mechanical experimentation, however, was able to detect the effect of adding gelling polysaccharide to glucose syrup as an accelerated pattern of vitrification leading to a higher value of T(g). Kinetic rates of caffeine diffusion within the experimental temperature range were taken with UV spectroscopy. These demonstrated the pronounced effect of the gelling κ-carrageenan/glucose syrup mixture to retard diffusion of the bioactive compound near the mechanical T(g). Modeling of the diffusional mobility of caffeine produced activation energy and fractional free-volume estimates, which were distinct from those of the carbohydrate matrix within the glass transition region. This result emphasizes the importance of molecular interactions between macromolecular matrix and small bioactive compound in glass-related relaxation phenomena.

Longer-scale segmental dynamics of amorphous poly(ethylene oxide)/poly(vinyl acetate) blends in the softening dispersion

To study the influence of poly(ethylene oxide) (PEO) on the relaxation process of poly(vinyl acetate) (PVAc) in the glass to rubber softening dispersion, the mechanical loss behaviour of PEO/PVAc blends (with PEO contents up to 20 wt%) were measured as a function of temperature and frequency. It is shown that the PEO component has a plasticizing effect on the α and α′ relaxation modes of PVAc, where the α mode is ascribed to the local segmental mode and the α′ mode is related to the motion of longer chain segments in the softening dispersion, composed of the sub-Rouse modes and the Rouse modes. Both the α and α′ modes shifted to lower temperatures with increase of PEO concentration. Time–temperature superposition breaks down for PEO/PVAc blends in the entire temperature range due to the different friction coefficients of the α and α′ modes. A single master curve of the α′ mode for pure PVAc and the PEO/PVAc blends is obtained, suggesting that the size of chain segments containing on the order of 10 to 50 or more backbone bonds does not change upon blending. Furthermore, the dynamics of the α′ mode of the PVAc component in the blends is found to show a characteristic crossover through the temperature dependence of relaxation time and relaxation strength. The crossover temperature TB decreases with increasing PEO content, while the crossover relaxation time for the blends is constant with a value about 0.08 s, much longer than 10−7 ± 1 s for the α mode. According to the coupling model, the crossover is suggested to be due to the variation of intermolecular coupling at TB.

Detecting different modes of molecular motion in polyisobutylene and chlorinated butyl rubber by using dielectric probes

To explore the complex molecular dynamics of glass-forming substances in the softening dispersion region from the glassy state to the rubbery state, polyisobutylene (PIB) and chlorinated butyl rubber (CIIR), representives of an amorphous polymer with effective chain packing and low intermolecular cooperativity, were doped with low molecular weight brominated para-tert-octyl phenolic resin (PR) and then tested using dielectric spectroscopy. The results show that the PR molecules, having little effect on the overall molecular dynamics of PIB and CIIR, can be used as the dielectric probes to successfully monitor local segmental motion, sub-Rouse modes and Rouse modes in the dielectric spectra simultaneously. The relaxation times of the local segmental motion and the Rouse modes can be directly obtained from the dielectric spectra. It is found that the Rouse modes have weaker temperature-dependence than the local segmental motion, indicating the thermorheological complexity of PIB and CIIR. Consequently, the local segmental motion superposes the Rouse modes at a temperature near Tg. This study suggests that the dielectric probes have the capability to detect and study different modes of molecular motion around the softening dispersion region.

Unexpected Phase Behavior of Amylose in a High Solids Environment

The purpose of this paper is to present and rationalize data concerning the structural behavior of amylose in the presence of glucose syrup. Observations were obtained by the experimental methods of small-deformation dynamic oscillation on shear, modulated differential scanning calorimetry, and scanning electron microscopy. In contrast to industrial polysaccharides that undergo readily a coil-to-helix transition (e.g., agarose, deacylated gellan, and kappa-carrageenan), amylose holds its structural characteristics unaltered at low and intermediate levels of glucose syrup. This is followed by an early phase inversion from a polysaccharide to cosolute dominated system at levels of solids above 70.0%, as compared to industrial polysaccharides that can dictate kinetics of vitrification at a solid content as high as 90.0% in the formulation. Additional viscoelastic "anomalies" include a clear breakdown of thermorheological simplicity with data exhibiting two tan delta peaks in the passage from the softening dispersion to the glassy state. Besides phenomenological evidence, mechanistic modeling using the combined framework of the free volume/reaction rate theories argue for two distinct glass transition temperatures in the mixture. It is proposed that the amylose/glucose syrup/water system does not reach a state of molecular mixing, with the morphological features being those of a micro phase-separated material.

Dynamic Crossover of α′ Relaxation in Poly(vinyl acetate) above Glass Transition via Mechanical Spectroscopy

The molecular relaxation dynamics of poly(vinyl acetate) (PVAc) has been studied by mechanical spectroscopy above the glass transition temperature (T(g)) within a frequency range from 1 mHz to 100 Hz. The temperature-dependent mechanical spectra reveal the existence of two relaxation modes: alpha, ascribed to the glass transition, and alpha', which may be related to the softening dispersion, composed of the sub-Rouse modes and the Rouse modes. The alpha' mode has a weaker temperature dependence than the alpha mode. Furthermore, the alpha' mode from the frequency-domain spectra exhibits a similar dynamic crossover at temperature T(B) approximately 387 K as the alpha mode through the temperature dependence of relaxation time, relaxation strength, and shape parameter. However, the crossover of the alpha' mode occurs at a time of about 0.08 s, longer than 10(-6)-10(-7) s for the alpha mode by dielectric spectroscopy. According to the coupling model, the crossover is suggested to be caused by the strong increase of intermolecular cooperativity below T(B).

Beyond the free volume theory: Introduction of the concept of cooperativity to the chain dynamics of biopolymers during vitrification

Abstract It is accepted in the literature that the viscoelastic properties of amorphous synthetic polymers in the rubber-to-glass dispersion relate to different modes in the time/temperature domain. The protocol of thermorheological simplicity as manifest through the combined WLF/free volume theory constitutes an early attempt to understand the nature of vitrification in spite of its obvious drawback of considering that all molecular retardation and relaxation processes have the same temperature dependence. Increasingly, thermorheological complexity is being recorded in the superposition of mechanical spectra in the viscoelastic master or composite curve, which is an observation that cannot be readily addressed. The newly proposed coupling theory aims to emphasize the distinct temperature dependence of molecular processes within the rubber-to-glass softening dispersion, thus identifying the local segmental motions as the main contributor to the viscoelastic spectrum at the vicinity of the glass transition temperature. Predictions of the coupling theory have explained the “anomalous” experimental facts in the viscoelasticity of amorphous synthetic materials, and the recently established relaxation time—intensity of intermolecular interaction correlations in the vitrification of the gelatin/co-solute mixture.

Resolution of Sub-Rouse Modes of Polystyrene by Dissolution

The properties of the softening “glass to rubber” dispersion of two archetypal amorphous polymers, polystyrene and polyisobutylene, appear to differ greatly. Previously, these differences have been explained by the larger intermolecular coupling between the repeat units in executing the local segmental motions in polystyrene than polyisobutylene. Dissolution of polystyrene into a solvent with a lower glass temperature certainly diminishes the intermolecular coupling and could make the softening dispersion of the polystyrene solution resemble bulk polyisobutylene. Creep compliance measurements of solutions of polystyrene in tri-m-tolyl phosphate are used to show that this expectation is the case. At 17% polystyrene, the properties of the softening dispersion of the solution are nearly identical to that of bulk polyisobutylene, including the appearance of a resolved sub-Rouse mode.

Fine Structure and Thermorheological Complexity of the Softening Dispersion in Styrene-Based Copolymers

The segmental and terminal relaxation processes of polystyrene, styrene−acrylonitrile, and α-methylstyrene−acrylonitrile copolymers have been investigated by means of both dynamic-mechanical and dielectric spectroscopy in the linear response region. The temperature dependence of the average relaxation time τ of the two processes follows a Vogel−Tamman−Fulcher (VTF) equation: τ ∝ exp[B/(T − T∞)]. Nevertheless, the segmental and terminal relaxations exhibit appreciably different VTF parameters. This vitiates time−temperature superpositioning in the segmental relaxation temperature region, giving rise to complex thermorheological behavior. As first shown by Plazek et al., this finding further confirms the Donth and Ngai models. Peculiar relationships between the VTF parameters of the segmental and terminal relaxation of the same polymer and of the same relaxation process of different polymers are pointed out. These relationships reveal general features of the VTF equation. A comparison between dynamic-mecha...

Anomalous stability behavior of a properly invariant constitutive equation which generalises fractional derivative models

Viscoelastic materials like amorphous polymers or organic glasses show a complex relaxation behavior in the softening dispersion region, i.e. from glass transition to the α relaxation zone. It is known that a uni-dimensional Maxwell model, modified within the conceptual framework of fractional calculus, has been found to predict experimental data in this range of temperatures. After developing a fully objective constitutive relation for an incompressible fluid, it is shown here that the fractional derivative Maxwell model results from the linearization of this objective equation about the state of rest, when some assumptions about the memory kernels are made. Next, it is demonstrated that the three dimensional, linearized version of the frame indifferent equation exhibits anomalous stability characteristics, namely that the rest state is neither stable nor unstable under exponential disturbances. Also, the material cannot support purely harmonic excitations either. Consequently, it appears that fractional derivative constitutive equations may be used to study a very limited category of flows in rheology rather than the whole spectrum.

Viscoelastic properties of amorphous polymers. 5. A coupling model analysis of the thermorheological complexity of polyisobutylene in the glass-rubber softening dispersion

Isothermal data of high molecular weight polyisobutylene obtained by mechanical measurements with a spectral range over eight decades and additional photon correlation measurements have found that there are three distinct viscoelastic mechanisms in the glass-rubber transition zone. Theoretical considerations have helped to identify these three mechanisms to originate separately from local segmental (α) modes, sub-Rouse (sR) modes, and Rouse (R) modes. The temperature dependences of the shift factors of these mechanisms, aT,α, aT,sR and aT,R, determined over a common temperature range are found to be all different. The differences in temperature dependences are explained quantitatively by the coupling model. The local segmental motion contributes to compliances ranging from the glassy compliance, Jg, up to 10−8.5 Pa−1. The sub-Rouse modes contribute in the compliance range, 10−8.5 ≤ J(t) ≤ 10−7 Pa−1. The Rouse modes account for the compliances in the range of 10−7 Pa−1 ≤ J(t) ≤ Jplateau, where Jplateau is the plateau compliance. The magnitudes of the bounds given here are only rough estimates. Shift factors, aT, obtained by time-temperature superpositioning of viscoelastic data taken in the softening transition over a limited experimental window are shown to be a combination of the three individual shifts factors, aT,α, aT,sR, and aT,R. Consequently, care must be exercised in interpreting or using the WLF equation that fits the shift factors of the entire softening dispersion, because the latter do not describe the temperature dependence of any one of the three viscoelastic mechanisms. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys, 35: 599–614, 1997

General Applicability of the Coupling Model to Viscoelasticity of Polymers : from Local Segmental Motion to Terminal Flow

We survey the important problems in polymer viscoelasticity that impede progress in this field. These problems manifest themselves as spectacular anomalies in the viscoelastic data that have been reproduced in different polymers and in different laboratories, but have largely been put aside for lack of explanation. Without solving these difficult problems, there can be no satisfactory understanding of the viscoelastic properties of polymers spanning across the local segmental motion, the glass-rubber softening dispersion, the rubbery plateau and the terminal dispersion. The coupling model, which has general applicablity to various relaxation mechanisms of polymers and beyond polymers, is able to resolve all these problems.

Viscoelastic Properties of Amorphous Polymers. 6. Local Segmental Contribution to the Recoverable Compliance of Polymers

A prominent shoulder exhibited in the shear retardation spectrum of a high molecular weight polystyrene enables the local segmental contribution to the recoverable compliance to be isolated and determined for the first time. The prominence of this shoulder depends on the time/frequency window of the viscoelastic measurements. This interesting dependence is explained by the thermorheological complexity of the glass−rubber softening dispersion.

Viscoelastic properties of polymers. 4. Thermorheological complexity of the softening dispersion in polyisobutylene

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTViscoelastic properties of polymers. 4. Thermorheological complexity of the softening dispersion in polyisobutyleneD. J. Plazek, I.-C. Chay, K. L. Ngai, and C. M. RolandCite this: Macromolecules 1995, 28, 19, 6432–6436Publication Date (Print):September 1, 1995Publication History Published online1 May 2002Published inissue 1 September 1995https://doi.org/10.1021/ma00123a007RIGHTS & PERMISSIONSArticle Views832Altmetric-Citations176LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (595 KB) Get e-Alerts Get e-Alerts

Identification of Different Modes of Molecular Motion in Polymers That Cause Thermorheological Complexity

Abstract The viscoelastic properties of amorphous polymers are reviewed with emphasis on the glass to rubber dispersion (often referred to as the transition zone). Deviations from thermorheologieal simplicity (where molecular retardation and relaxation mechanisms have the same temperature dependence) are identified. Most theories and models of polymer chain dynamics do not address or acknowledge thermorheological complexities and correlations, such as that between the temperature dependence and the breadth of viscoelastic and dielectric dispersions of the local segmental motion. Without successful theories of these phenomena the understanding of polymer chain dynamics must be considered incomplete. In this review, old and new experimental data are used to identify the different modes of molecular motions and the domains of their contributions to the time and frequency dependence of the mechanical response of amorphous polymers. The different modes are then shown generally to have their own dependence on temperature. Thus the viscoelastic spectrum, including local segmental motions which dominate the onset of glassy behavior and largely determine the glass temperature, Tg, the glass to rubber softening dispersion, the rubbery plateau and the terminal zone, is thermorheologically complex. A coupling theory, with the physics of intermolecular interactions and cooperativity built into it, describes well the many-body dynamics of densely packed molecular systems such as polymers. The many predictions of the coupling theory are applied to the different viscoeleatic modes to explain the observed anomalous experimental facts and established correlations. The theoretical understanding has been improved to the extent that now a connection can be made between the chemical structure of the monomer and the viscoelastic properties of the polymer.

Breakdown of time-temperature superposition in miscible polymer blends and the coupling scheme

The coupling theoretical scheme has been used to describe the terminal as well as the softening dispersion of a miscible blend of 20 wt % poly(ethylene oxide) in poly(methyl methacrylate). Compared with the pure states, the blend has a drastically reduced number of kinetic couplings of PEO chains but a slightly increased number for PMMA chains. This modification of kinetic coupling provides insight into the breakdown of time-temperature superposition in the blend as observed by Colby