Volume relaxation and related dynamic mechanical property changes during physical aging of poly-ether-ether-ketone (peek)

Non-equilibrium glasses, including polymer glasses, spontaneously tend to approach the equilibrium state. The time-dependent phenomena occurring in glassy polymers below the glass transition are commonly referred to as physical aging. Since the physical aging results primarily in a volume relaxation (or densification), our efforts have been focused on the measurements of the time-dependent behavior of the specific volume. The dependence of the storage and loss moduli upon aging have been related to the progressive loss of mobility associated with the volume relaxation. A Williams-Watts type equation has been adopted to model the volume relaxation data at different temperatures, and a numerical procedure has been developed in order to predict the kinetics of volume relaxation subjected to complex thermal histories.     

Aging of the Johari-Goldstein relaxation in the glass-forming liquids sorbitol and xylitol

Employing frequency-dependent dielectric susceptibility we characterize the aging in two supercooled liquids, sorbitol and xylitol, below their calorimetric glass transition temperatures. In addition to the alpha relaxation that tracks the structural dynamics, the susceptibility of both liquids possesses a secondary Johari-Goldstein relaxation at higher frequencies. Following a quench through the glass transition, the susceptibility slowly approaches the equilibrium behavior. For both liquids, the magnitude of the Johari-Goldstein relaxation displays a dependence on the time since the quench, or aging time, that is quantitatively very similar to the age dependence of the alpha peak frequency. The Johari-Goldstein relaxation time remains constant during aging for sorbitol while it decreases slightly with age for xylitol. Hence, one cannot sensibly assign a fictive temperature to the Johari-Goldstein relaxation. This behavior contrasts with that of liquids lacking distinct Johari-Goldstein peaks for which the excess wing of the alpha peak tracks the main part of the peak during aging, enabling the assignment of a single fictive temperature to the entire spectrum. The aging behavior of the Johari-Goldstein relaxation time further calls into question the possibility that the relaxation time possesses stronger temperature dependence in equilibrium than is observed in the out-of-equilibrium state below the glass transition.     

Fundamental relationship between the nonequilibrium glassy state and yield stress of amorphous polymers

This paper reports the theoretical prediction and experimental verification of the connection between the yield stress of amorphous polymers and the physical aging phenomenon. The analysis reveals the existence of a fundamental relationship between the nonequilibrium glassy state and the thermally activated process controlling viscoelastic and plastic deformation. The results show that the volume relaxation and deformation kinetics share the same relaxation times, and that the activation energy for deformation below T_g is much smaller than previously mentioned in the literature. This indicates that the phenomenon of physical aging plays a very important role in the deformation and processing of polymers at low temperatures. The effect of quenching and annealing on the yield stress is described in terms of the mean energy of hole formation, the departure of volume from its equilibrium state, the distribution of hole energies, and lattice volume. The same set of molecular parameters obtained from the molecular kinetic theory of the glass transition and volume relaxation predicts the yield stress as a function of cooling rate, annealing time, temperature, and strain rate.     

聚芳醚酮高温长时间下的断裂行为──2．物理老化的影响

研究了聚芳醚酮在２００℃下长时间放置过程中的密度，热焓，屈服及应力松弛行为随时间的变化规律．结果表明，随放置时间的增长，材料的结构形态与物性随时间的变化速率在１０小时后急剧减慢．文中对物性变化的时间依赖性进行了讨论．在应力松弛过程中出现银纹的现象可归结为物理老化过程中分子链间排列逐渐紧密的结果．     

Primary and secondary relaxations in supercooled eugenol and isoeugenol at ambient and elevated pressures: dependence on chemical microstructure

Dielectric loss spectra of two glass-forming isomers, eugenol and isoeugenol, measured at ambient and elevated pressures in the normal liquid, supercooled, and glassy states are presented. The isomeric chemical compounds studied differ only by the location of the double bond in the alkyl chain. Above the glass transition temperature T(g), the dielectric loss spectra of both isomers exhibit an excess wing on the high frequency flank of the loss peak of the alpha relaxation and an additional faster gamma process at the megahertz frequency range. By decreasing temperature below T(g) at ambient pressure or by elevating pressure above P(g), the glass transition pressure, at constant temperature, the excess wing of isoeugenol shifts to lower frequencies and is transformed into a secondary beta-loss peak, while in eugenol it becomes a shoulder. These spectral features enable the beta-relaxation time tau(beta) to be determined in the glassy state. These changes indicate that the excess wings in isoeugenol and eugenol are similar and both are secondary beta relaxations that are not resolved in the liquid state. While in both isoeugenol and eugenol the loss peak of the beta relaxation in the glassy state and the corresponding excess wing in the liquid state shifts to lower frequencies on elevating pressure, the locations of their gamma relaxation show little change with increasing pressure. The different pressure sensitivities of the excess wing and gamma relaxation are further demonstrated by the nearly perfect superposition of the alpha-loss peak together with excess wing from the data taken at ambient pressure and at elevated pressure (and higher temperature so as to have the same alpha-peak frequency), but not the gamma-loss peak in both isoeugenol and eugenol. On physical aging isoeugenol, the beta-loss peak shifts to lower frequencies, but not the gamma relaxation. Basing on these experimental facts, the faster gamma relaxation is a local intramolecular process involving a side group and the slower beta relaxation mimics the structural alpha relaxation in behavior, involves the entire molecule and satisfies the criteria for being the Johari-Goldstein beta relaxation. Analysis and interpretation of the spectra utilizing the coupling model further demonstrate that the excess wings seen in the equilibrium liquid states of these two isomers are their genuine Johari-Goldstein beta relaxation.     

Dynamic shear modulus of glycerol: corrections due to instrument compliance

A recent article by Shi et al. [J. Chem. Phys.123, 174507 (2005)] reports results from mechanical measurements on three simple inorganic glass formers: glycerol, m-toluidine, and sucrose benzoate. The experiments carried out were stress relaxation, aging, and dynamic (all in shear) using a torsional rheometer, an advanced rheometric expansion system (TA Instruments). The original force rebalance transducer (2KFRT) supplied with the system was replaced with a custom-made load cell (Sensotec) that had a capacity of 20 000 g cm in torque and 5000 g in normal force. The replacement of the load cell was done due to the belief that the main source of compliance in this instrument was from the 2KFRT. With this assumption, the authors published their results for the three materials of interest and compared their results with the techniques of Schroter and Donth [J. Chem. Phys.113, 9101 (2000)] for the measurements on glycerol and reported important differences. These differences were disputed by one of the present authors (Schroter), and the present report shows that the results from Schroter and Donth are correct. We show that the reasons have to do with the instrument compliance being greater than originally thought by Shi et al. Here we examine the effects of platen diameter/geometry on the glycerol dynamic moduli, describe a means to correct dynamic data, present a revised comparison of the corrected data with that of Schroter and Donth, and provide a discussion of future work and conclusions.     

Structural relaxation and rheological response of a driven amorphous system

The interplay between the structural relaxation and the rheological response of a simple amorphous system {a 80:20 binary Lennard-Jones mixture [W. Kob and H. C. Andersen, Phys. Rev. Lett. 73, 1376 (1994)]} is studied via molecular dynamics simulations. In the quiescent state, the model is well known for its sluggish dynamics and a two step relaxation of correlation functions at low temperatures. An ideal glass transition temperature of Tc=0.435 has been identified in the previous studies via the analysis of the system's dynamics in the framework of the mode coupling theory of the glass transition [W. Kob and H. C. Andersen, Phys. Rev. E 51, 4626 (1995)]. In the present work, we focus on the question whether a signature of this ideal glass transition can also be found in the case where the system's dynamics is driven by a shear motion. Indeed, the following distinction in the structural relaxation is found: In the supercooled state, the structural relaxation is dominated by the shear at relatively high shear rates gamma, whereas at sufficiently low gamma the (shear-independent) equilibrium relaxation is recovered. In contrast to this, the structural relaxation of a glass is always driven by shear. This distinct behavior of the correlation functions is also reflected in the rheological response. In the supercooled state, the shear viscosity eta decreases with increasing shear rate (shear thinning) at high shear rates, but then converges toward a constant as the gamma is decreased below a (temperature-dependent) threshold value. Below Tc, on the other hand, the shear viscosity grows as eta proportional, etax 1/gamma, suggesting a divergence at gamma=0. Thus, within the accessible observation time window, a transition toward a nonergodic state seems to occur in the driven glass as the driving force approaches zero. As to the flow curves (stress versus shear rate), a plateau forms at low shear rates in the glassy phase. A consequence of this stress plateau for Poiseuille-type flows is demonstrated.     

Theory of relaxation and elasticity in polymer glasses

The recently developed activated barrier hopping theory of deeply supercooled polymer melts [K. S. Schweizer and E. J. Saltzman, J. Chem. Phys. 121, 1984 (2004)] is extended to the nonequilibrium glass state. Below the kinetic glass temperature T(g), the exact statistical mechanical relation between the dimensionless amplitude of long wavelength density fluctuations, S(0), and the thermodynamic compressibility breaks down. Proper extension of the theory requires knowledge of the nonequilibrium S(0) which x-ray scattering experiments find to consist of a material specific and temperature-independent quenched disorder contribution plus a vibrational contribution which varies roughly linearly with temperature. Motivated by these experiments and general landscape concepts, a simple model is proposed for S(0)(T). Deep in the glass state the form of the temperature dependence of the segmental relaxation time is found to depend sensitively on the magnitude of frozen in density fluctuations. At the (modest) sub-T(g) temperatures typically probed in experiment, an effective Arrhenius behavior is generically predicted which is of nonequilibrium origin. The change in apparent activation energy across the glass transition is determined by the amplitude of frozen density fluctuations. For values of the latter consistent with experiment, the theory predicts a ratio of effective activation energies in the range of 3-6, in agreement with multiple measurements. Calculations of the shear modulus for atactic polymethylmethacrylate above and below the glass transition temperature have also been performed. The present work provides a foundation for the formulation of predictive theories of physical aging, the influence of deformation on the alpha relaxation process, and rate-dependent nonlinear mechanical properties of thermoplastics.     

Theory of aging in structural glasses

The random first-order transition theory of the dynamics of supercooled liquids is extended to treat aging phenomena in nonequilibrium structural glasses. A reformulation of the idea of "entropic droplets" in terms of libraries of local energy landscapes is introduced which treats in a uniform way the supercooled liquid (reproducing earlier results) and glassy regimes. The resulting microscopic theory of aging makes contact with the Nayaranaswamy-Moynihan-Tool nonlinear relaxation formalism and the Hodge-Scherer extrapolation of the Adam-Gibbs formula, but deviations from both approaches are predicted and shown to be consistent with experiment. The nonlinearity of glassy relaxation is shown to quantitatively correlate with liquid fragility. The residual non-Arrhenius temperature dependence of relaxation observed in quenched glasses is explained. The broadening of relaxation spectra in the nonequilibrium glass with decreasing temperature is quantitatively predicted. The theory leads to the prediction of spatially fluctuating fictive temperatures in the long-aged glassy state, which have non-Gaussian statistics. This can give rise to "ultraslow" relaxations in systems after deep quenches.     

Relaxation processes in room temperature ionic liquids: the case of 1-butyl-3-methyl imidazolium hexafluorophosphate

A detailed investigation on the nature of the relaxation processes occurring in a typical room temperature ionic liquid (RTIL), namely, 1-butyl-3-methyl imidazolium hexafluorophosphate ([bmim][PF(6)]), is reported. The study was conducted using both elastic and inelastic neutron scattering over a wide temperature range from 10 to 400 K, accessing the dynamic features of both the liquid and glassy amorphous states. In this study, the inelastic fixed energy scan technique has been applied for the first time to this class of materials. Using this technique, the existence of two relaxation processes below the glass transition and a further diffusive process occurring above the glass-liquid transition are observed. The low temperature processes are associated with methyl group rotation and butyl chain relaxation in the glassy state and have been modeled in terms of two Debye-like, Arrhenius activated processes. The high temperature process has been modeled in terms of a Kohlraush-Williams-Watts relaxation, with a distinct Vogel-Fulcher-Tamman temperature dependence. These results provide novel information that will be useful in rationalizing the observed structural and dynamical behavior of RTILs in the amorphous state.     

The Adam-Gibbs equation and the out-of-equilibrium alpha relaxation of glass forming systems

The temperature dependence of the alpha-relaxation time out of equilibrium has been investigated by means of dielectric relaxation in a series of fragile glass formers including several polymers. The influence of physical aging on this behavior has also been studied. The experimental results have been quantitatively compared with the predictions of the Adam-Gibbs equation. It has been found that, whereas for small molecule glass formers the experimental values of the apparent activation energy agree quite well with the prediction of the Adam-Gibbs equation, for polymers the experimental activation energy values are systematically higher. Moreover, whereas for small molecule glass formers the experimental values of the apparent activation energy remains essentially unaffected by physical aging, for polymers a pronounced reduction of the experimental apparent activation energy is observed. These results are found to be consistent with the Adam-Gibbs equation if a significant temperature variation of the configurational entropy in the investigated temperature range would occur for nonannealed polymers, being the possible variation hardly noticeable for the small molecules. With this assumption, all the obtained results would support the validity of the Adam-Gibbs equation for describing the temperature dependence of the time scale of the alpha-relaxation also out of equilibrium, at least for fragile glass formers.     

The influence of surface phenomena on molecular mobility in glassy polymers

Literature data on molecular mobility in glassy polymers have been analyzed. It has been shown that, in the temperature range corresponding to the glassy state of a polymer, a large-scale (segmental) molecular motion is possible, with this motion being responsible for the physical (thermal) aging of the polymer. Heating of an aged polymer restores its initial state, and the aging process begins again (effect of “rejuvenation”). At the same time, aging processes may be initiated by a mechanical action on a glassy polymer. It is sufficient to subject an aged polymer to a mechanical action to transfer it to a state characteristic of a polymer heated above the glass-transition temperature. It should be noted that deformation of a glassy polymer is nonuniform over its volume and occurs in local zones (shear bands and/or crazes). It is of importance that these zones contain an oriented fibrillized polymer with fibril diameters of a few to tens of nanometers, thereby giving rise to the formation of a developed interfacial surface in the polymer. The analysis of the published data leads to a conclusion that the aging of a mechanically “rejuvenated” polymer is, as a matter of fact, the coalescence of nanosized structural elements (fibrils), which fill the shear bands and/or crazes and have a glasstransition temperature decreased by tens of degrees.     

Experimental evidence and theoretical analysis of physical aging in thin and thick amorphous glassy polymer films

Through time‐dependent gas transport properties, we have investigated the physical aging process of amorphous glassy polymer films made from a polynorbornene. By combining the concepts of free volume and the kinetic theory of glass stabilization, it was found that the time dependence of the gas permeability could be rationalized through the thickness dependence of the glass transition temperature. A mathematical relationship was developed that directly relates polymer physical aging (tracked by the gas permeability decay) and sample thickness. It was confirmed by permeation measurements with nitrogen and helium that the aging process is accelerated for thin glassy polymer films (about 8000 Å). The theoretical results show that accelerated aging for thin films compared to thick films can be qualitatively predicted, based on the decrease in the glass transition temperature when the film thickness decreases. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2239–2251, 1999     

Temperature Dependence of the Back-Stress in Shear for Glassy Polycarbonate

Summary: Back-stress is the equilibrium stress and represents conditions under which relaxation events in the material stop and the material can carry an applied load indefinitely without a change in strain. In most models for glassy polymers, back-stress plays a central role since relaxation in materials is closely related to the distance of the current conditions from equilibrium. A number of these models that are commonly used for modeling glassy polymers use a modeling structure similar to large deformation plasticity. The flow rule for the plastic strain in these models are directly connected to the “over-stress,” a properly invariant difference between the stress and the back-stress. The importance of correctly evaluating the back-stress to use in these models is clear. For this class of models, the authors have recently developed a method for directly calculating the back-stress under shear deformations. This method is based on evaluating the slope of the stress-strain response under conditions of similar elastic and plastic strain, but different strain rates. Since plastic flow goes to zero at equilibrium, the back-stress can be found by locating points of zero plastic strain rate. Using the proposed method, the back-stress in glassy polycarbonate has been evaluated under shear in isothermal tests going from room temperature to 120 °C, just below the glass transition temperature for polycarbonate. The proposed method provided a full map of the back-stress for polycarbonate over a large range of shear strain and temperature.     

Dielectric relaxation in two liquid crystalline polyacrylates under high hydrostatic pressure

For two polyacrylates with p-cyano-phenyl benzoate side groups and different spacer lengths the dielectric relaxation was measured in the nematic and isotropic phase at pressures up to 5000 bar. The relaxation of the cyano groups was observed as a separate relaxation process; it seems to be closely correlated with the glass relaxation. The pressure dependence of the glass temperature and of the clearing temperature could be derived from the experiments.     

A quantitative model for the specific volume of polymer–diluent mixtures in the glassy state

A mathematical model to describe the specific volume of glassy mixtures of a polymer and a low molecular weight diluent or additive is presented. The model is based on understandable physical assumptions and relies on parameters that can be determined experimentally or estimated from methods available in the literature. The predictions of the model show good agreement with the experimental data for mixtures of four polymers with diluents that in the pure state are liquid, glassy, or crystalline. The observed negative departure from volume additivity, as defined by simple additivity of the specific volume of the pure glassy polymer and the pure amorphous diluent, is the result of the relaxation of the excess volume of the glassy mixture relative to the equilibrium state caused by mixing two components with different glass transition temperatures. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1037–1050, 1998     

Sheared polymer glass and the question of mechanical rejuvenation

There has been much recent debate as to whether mechanical deformation reverses the aging of a material, and returns it to a structure characteristic of the system at a higher temperature. We use molecular dynamics simulation to address this problem by carrying out shear and temperature increase simulation on atactic glassy polystyrene. Our results show explicitly that the structure (as quantified by the torsion population) changes associated with shear and temperature increase are quantitatively--and in some cases qualitatively--different. This is due to the competition between rejuvenation and physical aging, and we show this by carrying out a relaxation simulation. The conclusion agrees with those from previous experiments and simulations, which were suggestive of mechanical deformation moving the system to structures distinct from those reached during thermal treatment.     

Antiplasticization and local elastic constants in trehalose and glycerol mixtures

We have performed molecular dynamics simulations of glassy trehalose with various amounts of glycerol in order to explore the tendency for glycerol to antiplasticize the glass. We find that below a temperature of 300 K, the average density of the system containing 5%(wt) glycerol is larger than that of the pure trehalose system; the glass transition temperature is decreased, and the elastic constants are essentially unchanged. Taken together, these phenomena are indicative of mild antiplasticization, a type of behavior generally observed in polymeric systems. We have calculated the local elastic constants in our glassy materials and, consistent with previous simulations on a coarse-grained polymer, we find evidence of domains having negative elastic moduli. We have explored the ability of various measures of the Debye-Waller factor u(2) to predict the stiffness of our systems in terms of their elastic constants. We find that u(2) is indeed correlated with the behavior of the bulk elastic constants. On a local level, a correlation exists between the local moduli and u(2); however, that correlation is not strong enough to arrive at conclusive statements about the local elastic properties.     

Comment on “optical homogeneous linewidths of resorufin in ethanol glass: an apparent contradiction between hole-burning and photon-echo results?”

Inaccurate speculations (Chem. Phys. Letters 137 (1987) 201) that photon-echo measurements on resorufin in ethanol glass (Chem. Phys. Letters 120 (1986) 6; J. Chem. Phys. 86 (1987) 77) were performed on the glassy plastic crystal phase of ethanol and were systematically in error are corrected. Control experiments reported in the original papers and recent results on resorufin in glycerol, which does not form multiple phases, are cited. The original conclusion that photon-echo and hole-burning experiments measure different physical properties in these systems is confirmed. Recent theoretical work has shown that the difference between the two experiments results from slow relaxation processes known to exist in glasses and that the comparison of the two experiments is a valuable means of studying these processes.     

从溶胀平衡研究玻璃态高聚物的凝聚缠结网络

在13~15℃室温条件下对聚苯乙烯(PS)颗粒在二氧六环/水混合溶剂中的溶胀情况进行目视观察,可以看到,当减小混合溶剂二氧六环/水中的水含量时,PS颗粒从玻璃态到溶胀的玻璃态、溶胀的高弹态、流体态的转变,与PS颗粒升温时从玻璃态到高弹态、流体态的转变相对应.选定混合溶剂二氧六环/水(水6·8wt%)对一个单分散PS试样(Mw=1·68×105)在30℃进行分相平衡和溶胀平衡的测定.分相平衡是先将PS/二氧六环/水(混合溶剂水含量6·8wt%)体系加热到130℃使PS溶解成一均相溶液,然后在冷却过程中分相,在30℃达分相平衡(30天)时,浓相高分子体积浓度p″=0·304,稀相几乎为纯溶剂.从Flory-Huggins相平衡理论得出此体系的高分子-溶剂相互作用参数χ=0·63.本工作使用的单分散PS试样在选定的混合溶剂,即二氧六环/水(水6·8wt%)中,30℃时不能溶解只能溶胀,单分散PS颗粒淬冷试样(密度ρp=1·0451g/mL)到达溶胀平衡(80天)时浓相高分子体积浓度p″=0·308.而此淬冷试样经在80℃热处理100h后的老化试样(ρp=1·0470g/mL)达溶胀平衡(70天)时p″=0·312.从溶胀过程中浓相体积变化曲线可知试样经在80℃热处理过程中凝聚网络趋向于更均一,更接近热处理温度下的平衡态,试样密度增大,网络产生了新的链间凝聚,物理交联密度增大(凝聚点间分子量减小).从溶胀平衡理论并取χ=0·63(分相平衡)可得到淬冷试样的物理交联点间分子量Mc=11·6×104,老化试样的物理交联点间分子量Mc=6·9×104.实验结果说明溶胀过程及溶胀平衡的测定可以反映玻璃态高聚物中的凝聚网络结构的细节,而且非常敏感.