Structural relaxation of stacked ultrathin polystyrene films

The T_g depression and kinetic behavior of stacked polystyrene ultrathin films is investigated by differential scanning calorimetry (DSC) and compared with the behavior of bulk polystyrene. The fictive temperature (T_f) was measured as a function of cooling rate and as a function of aging time for aging temperatures below the nominal glass transition temperature (T_g). The stacked ultrathin films show enthalpy overshoots in DSC heating scans which are reduced in height but occur over a broader temperature range relative to the bulk response for a given change in fictive temperature. The cooling rate dependence of the limiting fictive temperature, T_f′, is also found to be higher for the stacked ultrathin film samples; the result is that the magnitude of the T_g depression between the ultrathin film sample and the bulk is inversely related to the cooling rate. We also find that the rate of physical aging of the stacked ultrathin films is comparable with the bulk when aging is performed at the same distance from T_g; however, when conducted at the same aging temperature, the ultrathin film samples show accelerated physical aging, that is, a shorter time is required to reach equilibrium for the thin films due to their depressed T_g values. The smaller distance from T_g also results in a reduced logarithmic aging rate for the thin films compared with the bulk, although this is not indicative of longer relaxation times. The DSC heating curves obtained as a function of cooling rate and aging history are modeled using the Tool-Narayanaswamy-Moynihan model of structural recovery; the stacked ultrathin film samples show lower β values than the bulk, consistent with a broader distribution of relaxation times. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2741–2753, 2008     

Physical aging studies in epoxy resins. I. Kinetics of the enthalpy relaxation process in a fully cured epoxy resin

The physical aging of an epoxy resin based on diglycidyl ether of bisphenol-A cured by a hardener derived from phthalic anhydride has been studied by differential scanning calorimetry. The isothermal curing of the epoxy resin was carried out in one step at 130°C for 8 h, obtaining a fully cured resin whose glass transition was at 98.9°C. Samples were aged at temperatures between 50 and 100°C for periods of time from 15 min to a maximum of 1680 h. The extent of physical aging has been measured by the area of the endothermic peak which appears below and within the glass transition region. The enthalpy relaxation was found to increase gradually with aging time to a limiting value where structural equilibrium is reached. However, this structural equilibrium was reached experimentally only at an aging temperature of T_g-10°C. The kinetics of enthalpy relaxation was analysed in terms of the effective relaxation time τ_eff. The rate of relaxation of the system given by 1/τ_eff decreases as the system approaches equilibrium, as the enthalpy relaxation tends to its limiting value. Single phenomenological approaches were applied to enthalpy relaxation data. Assuming a separate dependence of temperature and structure on τ, three characteristic parameters of the enthalpic relaxation process were obtained (In A = ?333, E_H = 1020 kJ/mol, C = 2.1 g/J). Comparisons with experimental data show some discrepancies at aging temperatures of 50 and 60°C, where sub-T_g peaks appears. These discrepancies probably arise from the fact that the model assumes a single relaxation time. A better fit to aging data was obtained when a Williams-Watts function was applied. The values of the nonexponential parameter β were slightly dependent on temperature, and the characteristic time was found to decrease with temperature. © 1994 John Wiley & Sons, Inc.     

Features of structural relaxation in diblock copolymers

Time- and temperature-dependent structural relaxation (physical aging) of poly (styrene-b-methyl methacrylate) (PS-b-PMMA) block copolymers was investigated by calorimetry. Our study reveals the interplay of the relaxation responses of the two components of the copolymer in an intermediate temperature regime. That is, when the testing temperature is closely below the glass transition temperatures of PS and PMMA, structural relaxation in these polymer phases takes place concurrently, the corresponding thermogram displays partially superposed dual endothermic peaks as a feature of physical aging in the diblock copolymers. The aging response for each component is identified from a curve fitting method and analyzed by the relaxation of enthalpy. Comparing with the homopolymer analogs, the PS and PMMA in diblock copolymers show enhanced aging rate.     

Frequency and molecular-mass-dependent nonexponential proton NMR relaxation in polymer melts

A theoretical treatment of the nonexponential relaxation behavior of the different proton nuclear magnetic resonance (NMR) relaxation processes in polymer melts is presented. Formulas are derived for a three-component model given by two versions and a homogeneous distribution of correlation times. The theoretical results were tested with measurements of T₁, T_2e, and T₂ as functions of frequency and molecular mass in linear fractionated polyethylene samples. While the T₁ relaxation always yields exponential magnetization decays, the T_2e and T₂ measurements show biexponential relaxation behavior. From the calculations it was found that the correlation time of the local motion is independent of the molecular mass, whereas the correlation time of the slowest motional process increases with M^2.8_w for the three-component model and with M^2.2_w for the distribution of correlation times, respectively. © 1992 John Wiley & Sons, Inc.     

Dynamic processes in polymeric networks as studied by NMR relaxation methods

By means of NMR pulse methods molecular motions of polymer subchains in crosslinked polystyrene gels are studied. The temperature dependence of the effective transverse relaxation timeT _{2 eff} is explained by a local reorientation process. The local configuration of the elastic chains of the network is shown to be mainly determined by polymer-solvent interaction. The results are compared with those of concentrated solutions. The influence of static-like contributions to the 2nd moments is discussed.     

Enthalpy relaxation in a partially cured epoxy resin

The enthalpy relaxation of a partially cured (70%) epoxy resin, derived from diglycidyl ether of bisphenol-A cured by methyl-tetrahydrophthalic anhydride with accelerator, has been investigated. The key parameters of the structural relaxation (the apparent activation energy Δh*, the nonlinearity parameter x, and the nonexponentiality parameter β) are compared with those of the fully cured epoxy resin. The aging rates, characterized by the dependences of the enthalpy loss and peak temperature on log(annealing time), are greater in the partially cured epoxy than they are in the fully cured resin at an equivalent aging temperature (T_a = T_g − 20°C). There is a significant reduction in Δh*, from 1100 kJ mol⁻¹ for the fully cured system to 615 kJ mol⁻¹, as the degree of cure is reduced. The parameter x determined by the peak-shift method appears essentially independent of the degree of cure (x = 0.41 ± 0.03 for the partially cured resin compared with 0.42 ± 0.03 obtained previously for the fully cured resin), and does not follow the usually observed correlation of increasing x as Δh* decreases. This invariability of the parameter x seems to indicate that it is determined essentially by the local chemical structure of the backbone chain, and rather little by the supramolecular structure. On the other hand, the estimated nonexponentiality parameter β lies between 0.3 and 0.456, which is significantly lower than in the fully cured epoxy (β ≅ 0.5), indicative of a broadening of the distribution of relaxation times as the degree of cross-linking is reduced. Like the parameter x, this also does not follow the usual correlation with Δh*. These results are discussed in the framework of strong and fragile behavior of glass-forming systems, but it is difficult to reconcile these results in any simple way with the concept of strength and fragility. © 1996 John Wiley & Sons, Inc.     

Influence of the chemical structure on the kinetics of the structural relaxation process of acrylate and methacrylate polymer networks

The enthalpy relaxation of poly(hydroxyethyl methacrylate) (PHEMA), poly(ethyl methacrylate) (PEMA) and poly(ethyl acrylate) (PEA) networks, obtained by DSC, are compared. The temperature interval of the glass transition broadens in the sequence PEA-PEMA-PHEMA. The plots of the enthalpy loss during the annealing for 200 min at different temperatures below T_g show that the structural relaxation process also takes place in PHEMA in a broader temperature interval than in PEA or PEMA. The modelling of the structural relaxation process using a phenomenological model allows determining the temperature dependence of the relaxation times concluding that the fragility in PHEMA is significantly lower than in PEMA. Both features are ascribed to the connectivity of the polymer chains in PHEMA via hydrogen bonding. The role of the presence of the methyl group bonded to the main chain is analysed by comparing the results obtained in PEA and PEMA.     

Structural relaxation of glass-forming polymers based on an equation for configurational entropy, 4. Structural relaxation in styrene-acrylonitrile copolymer

The structural relaxation process in styrene-acrylonitrile copolymer has been characterized by means of differential scanning calorimetry (DSC) experiments. The results in the form of heat capacity, c_p(T), curves are analyzed using a model for the evolution of the configurational entropy during the process recently proposed by the authors.^11,12 The model simulation allows one to determine the enthalpy (or entropy) structural relaxation times and the β parameter of the Kohlrausch-Williams-Watts equation characterizing the width of the distribution of relaxation times. This material parameters are compared with their analogues determined from the dielectric and dynamic-mechanical relaxation processes. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2201–2217, 1997     

Nuclear spin relaxation dynamics of 13CO2 sorbed in polyisobutene rubber

Recently we presented the dynamics of ¹³CO₂ molecules sorbed in silicone rubber (PDMS) ascertained from spin relaxation experiments. Results of a similar investigation for ¹³CO₂ sorbed in polyisobutene (PIB) are presented in this report. The spin-lattice and spin-spin relaxation times as well as nuclear Overhauser enhancements (NOE) were determined as a function of temperature and Larmor frequency. The relaxation mechanisms found to be important for ¹³CO₂/PIB system are intermolecular dipole-dipole relaxation and chemical shift anisotropy with a minor contribution from spin rotation relaxation. We have determined the parameters which characterize correlation times for ¹³CO₂ collisional motion, rotational motion, and translational motions in the PIB. The self-diffusion coefficient of 5.15 × 10^?8 cm²/s obtained from the nuclear magnetic resonance (NMR) data is close to the literature value of the mutual diffusion coefficient of CO₂ in PIB at 300 K obtained from permeability measurements. In contrast to the case of CO₂/PDMS in which a broad distribution (characterized by a fractional exponential correlation function of the Williams-Watts type with α = 0.58) is observed, a sharp distribution with a fractional exponent, α, of 0.99 is found for the CO₂/PIB system. Instead of assuming an Arrhenius type temperature dependence, we used a Williams-Landel-Ferry type temperature dependence and found it to be better suited to describe the behavior of this system. PIB is a densely packed “strong” chain polymer which responds gradually to the temperature variation and gas sorption. In contrast PDMS is a relatively loosely packed “fragile” polymer with a propensity to exhibit rapid dynamic responses to the temperature change and gas sorption. © 1993 John Wiley & Sons, Inc.     

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‐T_g 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 T_g, 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     

Volume and enthalpy relaxation response after combined temperature history in polycarbonate

Summary Volume and enthalpy relaxation in polycarbonate subjected to double temperature jumps in the T_g region has been analysed. It concerns both initial T_down-jump from equilibrium above T_g to consolidation temperature below T_g and fina1 T_up-jump to relaxation temperature, also below T_g. The measured H and V data after T_up-jump were compared with respect to aging time calculating (dH/dV) ratio denoted as aging bulk modulus, K_a. According this new methodology H and V relaxation response after T_up-jump demonstrates differences in relaxation responses.     

Comparison of enthalpy relaxation between two different molecular masses of a bisphenol-A polycarbonate

Summary The present work is an extension of an earlier study that compared the stress relaxation between two molecular masses of a bisphenol-A polycarbonate due to thermal aging. The enthalpy relaxation of the same materials has been characterized. First, by measuring the change in enthalpy loss (ΔH_a) and fictive temperature (T_f) as a function of aging temperature (T_a) ranging from -25 to 120°C, using differential scanning calorimetry. For the limited aging time of 120 h, ΔH_a and T_f changes were only appreciable for (T_g -70 K)<T_a<T_g . While the influence of molecular mass was somewhat discernible, enthalpy measurements were not as sensitive as stress relaxation tests in differentiating molecular mass effects. In a second investigation, the kinetics of enthalpy relaxation upon isothermal aging at 130°C was evaluated using the peak shift method and found to be comparable to literature values. The plot of ΔH_a as a function of log (aging time) showed two distinct regions: a brief non-linear portion (less than 1 h aging) which is followed by a linear relationship as typically reported in the literature. In contrast to the linear region, the non-linear relaxation behaviour of the poorly aged state does not appear to be dependent on molecular mass.     

Enthalpy relaxation of an epoxy–anhydride resin by temperature‐modulated differential scanning calorimetry

The enthalpy relaxation of an epoxy–anhydride resin was studied by physical aging and frequency‐dependence experiments with alternating differential scanning calorimetry (ADSC), which is a temperature‐modulated differential scanning calorimetry technique. The samples were aged at 80 °C, about 26 K below the glass‐transition temperature, for periods up to 3800 h and then scanned under the following modulation conditions: underlying heating rate of 1 K min⁻¹, amplitude of 0.5 K, and period of 1 min. The enthalpy loss was calculated by the total heat‐flow signal, and its variation with the log (aging time) gives a relaxation rate (per decade), this value being in good agreement with that calculated by conventional DSC. The enthalpy loss was also analyzed in terms of the nonreversing heat flow, revealing that this property is not suitable for calculating enthalpy loss. The effect of aging on the modulus of the complex heat capacity, |Cp*|, is shown by a sharper variation on the low side of the glass transition and an increase in the inflexional slope of |Cp*|. Likewise, the phase angle also becomes sharper in the low‐temperature side of the relaxation. The area under the corrected out‐phase heat capacity remains fairly constant with aging. The dependence of the dynamic glass transition, measured at the midpoint of the variation of |Cp*|, on ln(frequency) allows one to determine an apparent activation energy, Δh*, which gives information about the temperature dependence of the relaxation times in equilibrium over a range close to the glass transition. The values of Δh*, determined from ADSC experiments in a range of frequencies between 4.2 and 33 mHz and at an amplitude of 0.5 K, and an underlying heating rate of 1 K min⁻¹, were analyzed and compared with that obtained by conventional DSC from the dependence of the fictive temperature on the cooling rate. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2272–2284, 2000     

Nuclear magnetic relaxation in aqueous solutions of vinylpyrrolidone and polyvinylpyrrolidone

Deuteron magnetic spin-lattice relaxation times have been measured in D₂O solutions of vinylpyrrolidone and polyvinylpyrrolidone as a function of concentration and temperature. For the monomer the results are interpreted in terms of a hydrophobic hydrations effect in which 42 D₂O molecules per solute molecule have a correlation time of 3.2 psec at 298°K. Application of the transition state theory to the temperature dependence gave H^*=21 kJ mole^–1 for the relaxation process. In the case of the polymer it is argued that a hydrophilic hydration effect dominates the observed relaxation. These activation enthalpy at 298°K is 24 kJ-mole^–1. Assuming a hydration number of one D₂O per polymer unit, the correlation time for the bound water is 77 psec at 298°K. Polymer proton spin-lattice relaxation times were measured as a function of frequency, and the results are analyzed in terms of a log normal distribution of correlation times. The median value at 296°K is 1.2 nsec.     

Physical aging in polycarbonate nanocomposites containing grafted nanosilica particles: A comparison between enthalpy and yield stress evolution

Understanding and controlling physical aging below the glass transition temperature (T_g) is very important for the long‐term performance of plastic parts. In this article, the effect of grafted silica nanoparticles on the physical aging of polycarbonate (PC) below the T_g is studied by using the evolution of the enthalpy relaxation and the yield stress. The nanocomposites were found to reach a thermodynamic equilibrium faster than unfilled PC, implying that physical aging is accelerated in presence of grafted nanosilica particles. The Tool‐Narayanaswamy‐Moynihan model shows that the aging is accelerated by the grafted silica nanoparticles, but the molecular mechanism responsible for physical aging remains unaltered. Furthermore, dynamic mechanical analysis shows that the kinetics of physical aging can be related to a free volume distribution or a local attraction‐energy distribution as a result of the change in mobility of the polymer chain. Finally, a qualitative equivalence is observed in the physical aging followed by both the enthalpy relaxation and yield stress. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2069–2081     

Physical aging of a polyetherimide: Creep and DSC measurements

Creep and differential scanning calorimetry (DSC) measurements have been used to study the physical aging behavior of a polyetherimide. Isothermal aging temperatures ranged from 160°C to T_g with aging times ranging from 10 min to 8 days. The only measurable effect of physical aging on the short-time creep curves is a shift of the creep compliance to longer times. Andrade plots of the compliance versus the cube root of time are linear at short times with the slope β decreasing with increasing aging time to a constant value once equilibrium is reached. Log β³ is related directly to the degree to which the creep curves shift to longer times with physical aging, and is used in this work as a measure of physical aging. A reduced curve of log β³ versus log aging time is obtained for the aging temperatures investigated by appropriate vertical and horizontal shifts. The enthalpy change during aging increases linearly with the logarithm of the aging time, t_a, leveling off at equilibrium at values which increase with decreasing aging temperature. Hence, both nonequilibrium and equilibrium temperature shift factors can be calculated from the DSC data. Good agreement is observed between the equilibrium temperature shift factors obtained from the creep and DSC data. The temperature dependence of the nonequilibrium temperature shift factors is found to be an order of magnitude smaller than that of the equilibrium shift factors. The time scales to reach equilibrium for enthalpy and for mechanical measurements are found to be the same within experimental error. © 1995 John Wiley & Sons, Inc.     

Molecular relaxation in the blends of polystyrene/poly(2,6-dimethyl-1,4-phenylene oxide) at low temperature

Molecular relaxation behavior in terms of the α, β, and γ transitions of miscible PS/PPO blends has been studied by means of DMTA and preliminary work has been carried out using DSC. From DSC and DMTA (by tan δ), the observed α relaxation (T_α or T_g) of PS, PPO, and the blends, which are intermediate between the constituents, are in good agreement with earlier reports by others. In addition, the β transition (T_β) of PS at 0.03 Hz and 1 Hz is observed at −30 and 20°C, respectively, while the γ relaxation (T_γ) is not observed at either frequency. The T_β of PPO is 30°C at 0.03 Hz and is not observed at 1 Hz, while the T_γ is −85°C at 0.03 Hz and −70°C at 1 Hz. On the other hand, blend composition-independent β or γ relaxation observed in the blends may be a consequence of the absence of intra- or intermolecular interaction between the constituents at low temperature. Thus it is suggested that at low temperature, the β relaxation of PS be influenced solely by the local motion of the phenylene ring, and that the β or γ relaxation of PPO be predominated by the local cooperative motions of several monomer units or the rotational motion of the methyl group in PPO. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1981–1986, 1998     

Unexpected proton spin‐lattice relaxation in the solutions of polyolefin and tetrachloroethane

‘Unexpected’ proton spin‐lattice relaxation (T₁) times are reported for the solutions of poly(ethylene‐co‐1‐octene) and tetrachloroethane‐d₂. For the residual protons of the deuterated solvent and the methyl and vinyl protons at the polymer chain ends, their T₁ relaxation times vary significantly with both the polymer concentration and molecular weight over a wide range. The T₁s also decrease with increasing temperature at relative high temperatures. Such behaviors are in contrast to most reported polymer solutions in which the T₁ has nearly no concentration or molecular weight dependence in the dilute and semi‐dilute regime, and normal dependence on temperature. Further investigation revealed that the paramagnetic oxygen effect did shorten the measured proton T₁s, but cannot account for the unexpected T₁ dependences. Spin rotation is proposed to provide a reasonable explanation. Copyright © 2010 John Wiley & Sons, Ltd.     

Studies of the enthalpy relaxation and the “multiple melting” behavior of semicrystalline poly(arylene ether ether ketone) (PEEk)

We report the results of an investigation by differential scanning calorimetry (DSC) of two mobility controlled processes in the amorphous phas e of semicrystalline PEEK — enthalpy relaxation below the glass transition (T _g) and secondary crystallization aboveT _g. Both result in the observation of an endothermic peak just above the annealing temperature in the DSC scan of the polymer — the enthalpy recovery peak and the low temperature melting peak, respectively. There is a striking similarity in the time and temperature dependence of the endothermic peak for these two processes. These results are reminiscent of those obtained from small strain creep studies of physical aging of semicrystalline PEEK below and aboveT _g.We gratefully acknowledge support of this work by the National Science Foundation, Science and Technology Center for High Performance Polymeric Adhesives and Composites under DMR grant 91-2004 and by an NSF Young Investigator Award (DMR 93-57512).     

Stress relaxation of PVC below the yield point

Stress relaxation of commercial poly(vinyl chloride) (PVC) is measured at strains below 3% and at different temperatures below the glass transition temperature. First it is shown that below the yield point the material follows a linear viscoelastic behavior. Then the data at a fixed deformation level (0.03) are fitted by considering a lognormal distribution function of relaxation times. Furthermore, from the measured stress-strain curves, the temperature dependence of the elastic tensile modulus is determined. The temperature dependence of the elastic modulus, the relaxation strength, and the parameters of the distribution: mean relaxation time, τ_m, and half-width, β, are given. Moreover, the distribution function and the temperature dependence of its characteristic parameters are discussed in terms of a cooperative model of the mechanisms involved in the mechanical relaxation of glassy polymers. Finally, the relationship proposed between the tensile modulus and the free volume helps explain the temperature dependence of the relaxation strength. © 1996 John Wiley & Sons, Inc.