Time-aging Time Superposition Research Articles

Structural relaxation of nanocrystalline PdAu alloy: Probing the spectrum of potential barriers

A commonality between nanocrystalline metals and metallic glasses is their dependence of structure and properties upon preparation history and postprocessing. Depending on preparation conditions, stored excess enthalpy and volume—relative to the crystalline ground state—can vary significantly. Annealing of material states of elevated enthalpy or volume induces structural relaxation and concomitant depletion of excess energy and volume. We analyzed the kinetics of volume relaxation in nanocrystalline PdAu alloys by partitioning the overall process into a set of independent and parallel reactions for arbitrary time-temperature protocols. The obtained spectra of kinetic parameters imply a complex relaxation behavior that violates time-temperature superposition and time aging-time superposition. The analysis will enable to reconstruct the effective energy landscape underlying the relaxation dynamics.

Characterization of physical aging by time-resolved rheometry: fundamentals and application to bituminous binders

Physical aging is a ubiquitous phenomenon in glassy materials and it is reflected, for example, in the time evolution of rheological properties under isothermal conditions. In this paper, time-resolved rheometry (TRR) is used to characterize this time-dependent rheological behavior. The fundamentals of TRR are briefly reviewed, and its advantages over the traditional Struik’s physical aging test protocol are discussed. In the experimental section, the TRR technique is applied to study physical aging in bituminous binders. Small-diameter parallel plate (SDPP) rheometry is employed to perform cyclic frequency sweep (CFS) experiments over extended periods of time (from one to 8.6 days). The results verify that the mutation of rheological properties is relatively slow during physical aging (mutation number N′mu << 1), thus allowing rheological measurements on a quasi-stable sample. The effects of temperature, crystallinity, and styrene-butadiene-styrene (SBS) polymer modification on the physical aging of bitumen are evaluated. The time-aging time superposition is found to be valid both for unmodified and for polymer-modified bitumen. Vertical shifts are necessary, in addition to horizontal time-aging time shifts, to generate smooth master curves for highly SBS-modified bitumen.

Aging of polymers of intrinsic microporosity tracked by methanol vapour permeation

The initially very promising transport properties of glassy high free volume polymers deteriorate rapidly over time. In this work, we focused on this aging phenomenon in two polymers of intrinsic microporosity (PIMs), namely PIM-1 and PIM-EA-TB. To identify the main mechanisms involved, we studied the time-declines of permeability and diffusivity of methanol vapours in flat membranes with approximately equal thicknesses. The permeation measurements were carried out using a continuous flow permeation method with carrier gas, where the methanol vapours were held at constant activity 0.2 at 25°C. Two different experimental modes were used: (i) continuous experiments that consisted of one long experiment with a duration of over 650h for each polymer and (ii) momentary experiments that consisted of a vast number of short (ca. 6h) consecutive measurements of transient permeation. The observed decreases of methanol permeability due to aging were more intense in the case of continuous mode for both polymers. In other words, the aging was ca. 1.3 times faster in the continuous mode in comparison with the momentary mode. Using time-aging time superposition, we successfully predicted the continuous experiments from the momentary experiments.

Prediction of Long and Short Time Rheological Behavior in Soft Glassy Materials

We present an effective time approach to predict long and short time rheological behavior of soft glassy materials from experiments carried out over practical time scales. Effective time approach takes advantage of relaxation time dependence on aging time that allows time-aging time superposition even when aging occurs over the experimental time scales. Interestingly, experiments on a variety of soft materials demonstrate that the effective time approach successfully predicts superposition for diverse aging regimes ranging from subaging to hyperaging behaviors. This approach can also be used to predict behavior of any response function in molecular as well as spin glasses.

Physical Aging and Heterogeneous Dynamics

Physical aging appears consistent with homogeneous models that are based upon a single "inner clock", but incompatible with the established heterogeneous nature of relaxation in glass-forming materials and the concomitant dispersion of aging rates. This work demonstrates that aging follows the conceptually simpler model of heterogeneous dynamics that differs from the homogeneous case in the rate at which equilibrium is approached. However, the very fast modes within the relaxation time dispersion age according to a common inner clock, because their fictive temperatures are slaved to macroscopic softening. Evidence is provided for such a transition to homogeneous aging as the frequency is increased into the excess wing. The results explain why aging of glasses appears homogeneous and consistent with time aging-time superposition in cases where observations are based on the high frequency behavior.

Theory of physical aging in polymer glasses

A statistical segment scale theory for the physical aging of polymer glasses is proposed and applied. The approach is based on a nonlinear stochastic Langevin equation of motion and the concept of an effective free energy which quantifies temporary localization, collective barriers, and the activated segment hopping process. The key collective structural variable that plays the role of the dynamic order parameter for aging is the experimentally measurable nanometer and longer wavelength amplitude of density fluctuations, S0 . The degree of local cooperativity, and the bare activation energy of the high-temperature Arrhenius process, are determined in the molten state by utilizing experimental measurements of the glass temperature and dynamic crossover time, respectively. A first-order kinetic equation with a time varying rate is proposed for the temporal evolution of S0 which is self-consistently and nonlinearly coupled with the mean segmental relaxation time. The theory has been applied to study physical aging of the alpha relaxation time, shear relaxation modulus, amplitude of density fluctuations, cohesive energy, absolute yield stress, and fictive temperature of polymethylmethacrylate and other glasses over a range of temperatures. Temperature-dependent logarithmic and effective power-law aging is predicted at intermediate times. Time-aging time superposition is found for the mechanical relaxation function. A strongly asymmetric aging response is predicted for up and down temperature jump experiments. Comparison of the approach with the classic phenomenological model is presented.

Physical Aging and Creep Behavior of Poly(Methyl Methacrylate)

In this work, the physical aging and its effect on nonlinear creep behavior of poly(methyl methacrylate) are presented. After annealing above Tg to release the previous thermal and stress history, the samples were quenched to 60oC, aged for various times, and were then tested at three different stress levels (22MPa, 26MPa and 30MPa) at room temperature of 27oC. At each stress level, the creep strain was converted to compliance and measured as a function of test time and aging time. The test results show that higher stress accelerates creep rate of the material while physical aging plays a reverse role. The time-aging time superposition is applicable to build a master creep compliance curve at each stress level, and it is demonstrated that the shift rate deceases with increasing stress. Moreover, based on the time-stress superposition principle, a unified master curve was constructed by further shifting the sub-master curves at 30MPa and 26 MPa to a reference stress level of 22MPa.

Effect of Isothermal Physical Aging on Creep Behavior of Stainless-Fiber/PPE Composites

In this research, the effect of isothermal physical aging on creep behavior of stainless-fiber/poly-phenylene ether (PPE) composites was investigated. Metal-fiber/PPE composites are non-crystalline thermoplastics and often used in engineering plastics, which have been developed for Electro-Magnetic-Interference (EMI) shielding. The results showed creep compliance curves to shift towards both the longer physical time and lower compliance sides with an increase in pre-aging treatment time, and it was established that creep deformation is arrested due to the progression of physical aging. Thus it was clarified that pre-aged composites can withstand higher temperature and longer time. The time-aging time superposition was established in creep of stainlessfiber/PPE composite. It was also observed that within the aging-time range, the shift rate is constant at all temperatures. The results showed that the shift rate is smaller at lower temperature and greater at higher temperature, and it reaches its maximum value at a wide range of temperature.

Physical aging of an amorphous polyimide: Enthalpy relaxation and mechanical property changes

The physical aging behavior of an isotropic amorphous polyimide possessing a glass transition temperature of approximately 239°C was investigated for aging temperatures ranging from 174 to 224°C. Enthalpy recovery was evaluated as a function of aging time following sub-Tg annealing in order to assess enthalpy relaxation rates, and time-aging time superposition was employed in order to quantify mechanical aging rates from creep compliance measurements. With the exception of aging rates obtained for aging temperatures close to Tg, the enthalpy relaxation rates exhibited a significant decline with decreasing aging temperature while the creep compliance aging rates remained relatively unchanged with respect to aging temperature. Evidence suggests distinctly different relaxation time responses for enthalpy relaxation and mechanical creep changes during aging. The frequency dependence of dynamic mechanical response was probed as a function of time during isothermal aging, and failure of time-aging time superposition was evident from the resulting data. Compared to the creep compliance testing, the dynamic mechanical analysis probed the shorter time portion of the relaxation response which involved the additional contribution of a secondary relaxation, thus leading to failure of superposition. Room temperature stress-strain behavior was also monitored after aging at 204°C, with the result that no discernible embrittlement due to physical aging was detected despite aging-induced increases in yield stress and modulus. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1931–1946, 1999

Study of the Effect of Aging Progression on Creep Behavior of PPE Composites

In this study, creep behavior of stainless fiber-PPE composites was analyzed in an oil environment at elevated temperatures, and the effects of physical aging on creep behavior were intensively investigated. The results showed that the creep phenomena of metal fiber-PPE composite with pre-aging treatment correlated with the Arrhenius time-temperature reciprocation law and within the aging range; time-aging time superposition also held good. Thus, prediction of short-term creep behavior for any pre-aging time was possible, based on the grand master curve of the creep compliance master curves and the shift factor for aging progression. It was clarified that a pre-aged composite can withstand higher temperatures and longer times. It was also observed that the energy of activation during creep decreased with an increase in pre-aging treatment time.

Viscoelastic Responses of Polyhedral Oligosilsesquioxane Reinforced Epoxy Systems.

The properties of nanostructured plastics are determined by complex relationships between the type and size of the nanoreinforcement, the interface, and the chemical interaction between the nanoreinforcement and the polymeric chain, along with macroscopic processing and microstructural effects. Recently, families of mono- and difunctionalized polyhedral oligomeric silsesquioxane (POSS) macromers bearing epoxide groups have been developed. This paper presents an investigation of the thermal and viscoelastic property enhancements in commonly used model epoxy resins reinforced with monofunctional POSS-epoxy macromers. The glass transitions of these POSS-epoxy nanocomposites were studied using differential scanning calorimetry. Small-strain stress relaxations under uniaxial deformation were examined to provide insight into the time-dependent viscoelastic behavior of these nanocomposites. The POSS-epoxy macromers utilized in this study were monofunctional and hence occupied chain terminus points within the network. Nevertheless, they were effective at hindering the molecular motion of the epoxy network junctions. Thus the glass transition temperature, Tg, was observed to increase with increasing weight fraction of the monofunctional POSS-epoxy. The viscoelastic response at temperatures below Tg was examined and was found to correlate to a stretched exponential relaxation function. Time-aging time-superposition was found to be applicable to the data under all test conditions and for all of the materials used in this study. Surprisingly, the instantaneous modulus was not observed to be affected by incorporation of the POSS nanoreinforcement. This suggests that while POSS cages influence polymer chain motions, including the motion of the molecular junctions, these nanoreinforcements did not participate in the overall deformation of the chains. Experiments performed under identical thermodynamic states, revealed that the molecular level reinforcement provided by the POSS cages also retarded the physical aging process in the glassy state. Therefore, the time required to reach structural equilibrium was longer for samples reinforced with POSS-epoxy than for those of the neat resins.

Physical Aging of Thin Films of Nylon and PET

The physical aging of nylon 66 and PET [poly(ethylene terephthalate)] films as a function of aging temperature, magnitude of applied stress, and aging time was investigated. One hundred micron thick nylon films and 5μm and 190 μm films of PET were investigated in temperature ranges that extended from below the glass transition temperature to well above it. Creep experiments were performed to probe the evolution of the material response after quenching from a "stabilization" temperature to the aging temperature and it was found that the classical time-aging time superposition could be applied to both the nylon and PET materials in the temperature range from 25 to 60°C. The behaviors at higher temperature could not be superposed using time-aging time shifting. The rate of aging of the nylon films was found to be significantly different from that found for a similar nylon that had been injection molded.

Anomalous aging in two-phase systems: Creep and stress relaxation differences in rubber-toughened epoxies

From time-aging time superposition principles, similar to time-temperature superposition, one would expect similar shifting or superposition behaviors for both creep and stress relaxation responses. In particular, for isotropic homogeneous systems, in the linear viscoelastic regime, consideration of superposition in rheology by Markowitz or the discussion by Ferry from the Kramers-Kronig relation would seem to demand that creep and stress relaxation shift in the same way. Here we report on results from creep and stress relaxation measurements in two-phase, rubber-toughened epoxies that exhibit Boltzman additivity of creep or relaxation behaviors and follow the time-aging time superposition behavior in creep, but not in stress relaxation. While the lack of superposition in stress relaxation is, perhaps, not surprising, the finding that the creep responses at different aging times superimpose while the stress relaxation responses do not, presents an anomalous behavior that has not been previously reported. In addition, our findings show that the stress relaxation responses show short time softening upon aging. Possible reasons for the anomalous behaviors are briefly considered.

Dynamics of Structural Recovery and Mechanical Response of Polymeric Liquids Near to the Glass Transition

ABSTRACTResults from the NIST torsional dilatometer have indicated that after a temperature step from equilibrium, the volume (structure) and mechanical response (physical aging) can evolve at different rates, depending on the temperature history. The torsional dilatometer results have been modeled in two ways. First, it was assumed that the volume and mechanical response are governed by different clocks, with the principle of time-aging time superposition employed to evaluate an aging time shift factor atc from the torsional response, which was then compared to a structural shift factor aδ calculated from the evolution of the volume. These results were also investigated using a thermoviscoelastic model based on rational thermodynamics and configurational entropy; this model does not include an explicit assumption of separate time scales, but different time scales for the structure and mechanical properties appear to arise naturally from the formulation. The results from the thermoviscoelastic model show good qualitative agreement with the torsional dilatometer results, although more material data is needed to make an exact comparison.

Generalized stress relaxation behaviour and physical aging in heterogeneous amorphous polyblends

The influence of physical aging on viscoelastic behaviour of heterogeneous amorphous polyblends of ABS and polycarbonate was studied by means of stress relaxation experiments at different temperatures. The stress relaxation data of the constituent phases ABS and PC are found to be in agreement with the universal description of relaxation behaviour of amorphous polymers at the onset of the glass-rubber transition. The regimes where master curve construction by time-temperature and time-aging time superposition is permitted could be deduced for the thermorheologically complex polyblends. It is shown that the relaxation curves of the ABS/PC blends can be calculated by means of a quasi-elastic extension of the van der Poel-model using the stress relaxation data of the constituent phases and their volume fractions.