Viscoelastic properties of amorphous polymers 3: low molecular weight poly(methylphenylsiloxane)

By making creep and recoverable creep measurements of a nearly monodisperse low molecular weight poly(methyl phenyl siloxane) sample, we have found on decreasing temperature towardsT _g that there is continuously a change in the viscoelastic spectrum concomitant with a decrease of the steadystate recoverable compliance. This behavior is exactly the same as previously observed in low molecular weight poly(styrene), proving that this spectacular anomaly in the viscoelasticity of low molecular weight polymers is general and deserves an explanation. Photon correlation spectroscopic measurements performed on the same sample have extended the observation of the viscoelastic response to shorter times and the result corroborates the trend of variation established by the creep data.Dedicated to Prof.Dr. E. W. Fischer on his 65th Birthday. Prof.Dr. Fischer is known for his valuable contribution to fosterine, international collaboration of research in polymer science. This work is an example of his contribution because it would not be possible without him bringing us together. One of us (KLN) would like to take this opportunity to thank Prof. Dr. Fischer for his unwaiving support of the 1st (Crete) and the 2nd (Alicante) International Discussion Meeting on Relaxations in Complex Systems     

The evolution of the viscoelastic retardation spectrum during the development of an epoxy resin network

The evolution of the viscoelastic behavior of an epoxy resin at various stages of curing has been followed with the changes in the retardation spectrum. The creep J(t) and recoverable creep compliance J_r(t) curves of the neat epoxy resin Epon l00lF (Shell) were determined at temperatures between 30 and 77°C. The viscosity decreased over 8 orders of magnitude as the temperature was increased. Specimens with eight stages of network development were prepared by reacting all of the epoxy resin's oxirane rings with amine hydrogens from varying ratios of a monofunctional amine (methyl aniline) and a tetrafunctional amine 4,4′-diamino diphenyl sulfone (DDS). Preparations in which 25, 35, and 40% DDS were used did not result in a molecular network, so they were viscoelastic liquids. With 45% DDS, the product had a nascent network and was judged to be just beyond the point of incipient gelation. The remaining preparations from 0.50, 0.60, 0.70, and 1.0 DDS yielded tighter less compliant molecular networks. The creep and recoverable compliance curves were measured over a range of temperatures above the glass transition temperature, T_g. They were reduced to T_g, and retardation spectra L(ln τ) were calculated.     

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.     

Rebuttal to “comments on ‘some evidence against the existence of the liquid–liquid transition. IV. The temperature dependence of shear viscosity’”

Data on the temperature dependence of viscosity obtained on three different polystyrenes with narrow molecular weight distributions are fitted to the Vogel, Fulcher, Tamman, and Hesse (VTFH) equation as well as to two intersecting Arrhenius lines. Both fits are optimized by means of computer programs. The data were chosen to fit the requirements stated by Boyer. The results of the analyses support the earlier conclusions that temperature-dependent viscosity data do not indicate the presence of any liquid-liquid transition T_LL above the glass temperature T_g. In addition, evidence is presented which indicates that the viscosity at T_g of high-molecular-weight polystyrenes is proportional to the 3.4 power of the molecular weight. Hence T_g is not an isoviscous temperature.     

Epoxy resins (DGEBA): The curing and physical aging process

Differential scanning calorimetry (DSC) and infrared spectroscopy (IR) were used to monitor the degree of cure of partially cured epoxy resin (Epon 828/MDA) samples. The extent of cure, as determined by residual heat of reaction, concurred with that determined by monitoring the infrared radiation absorbance of the epoxide group near 916 cm^?l. The fictive temperature T_{f, g} was found to increase with the degree of cure, increasing rapidly during cure until reaching a value near the cure temperature T_c of 130°C (approximately 80% cure) where the material vitrified. The greatly reduced reaction rate during the final 20% of cure was not only a consequence of vitrification but, as revealed by infrared spectroscopy, the result of the depletion in the number of reactive epoxide groups. The endothermic peak areas and peak temperatures evident during the DSC scans were used as a measure of the extent of “physical aging” which took place during the cure of this resin, and after, fully cured samples were aged 37°C below their ultimate glass temperature for various periods of time. The rate of physical aging slowed as the temperature increment (T_t,g ? T_c) increased. Although an endothermic peak was evident after only 1 h of cure (T_{f, g} = 138.3°C), such a peak did not appear until fully cured samples were aged for 16 h or more. Enthalpy data revealed that for partially cured material, the fictive temperature T_{f, a}, reflecting physical aging, increased with curing time. In contrast, the T_{f, a}, for fully cured samples decreased with sub-T_g aging time. The characteristic jump in the heat capacity ΔC_p which occurred at the T_{f, g} decreased as curing progressed. This decrease appears to be dependent upon the rotational and vibrational degrees of freedom of the glass. Finally, a graphical method of determining the fictive temperature T_{f, a}, of partially and fully cured epoxy material from measured endothermic peak areas was developed.     

Effects of thermal treatment of biaxially oriented poly(ethylene terephthalate)

Two distinguishable effects of thermal exposure of biaxially oriented poly(ethylene terephthalate) (PET) have been observed in the temperature range from room temperature to 140°C. Upon heating above the glass transition temperature T_g of the film an irreversible shrinkage of a few percent occurred with a concomitant decrease in the rate of creep. Some loss of orientation in the noncrystalline phase with an attendant slight increase in density is believed to be responsible. Since the film was anisotropic in its plane, different amounts and rates of shrinkage were observed along with differing thermal expansion coefficients in various directions relative to the primary optic axis. Upon cooling the 50% crystalline PET from above T_g to lower temperatures, reversible “physical aging” was observed. Creep rates were found to decrease with the residence time below T_g. As with purely amorphous polymers, the effects of the aging are removed by heating the specimen above T_g where the density of the amorphous phase achieves equilibrium values.     

On the use of stretched-exponential functions for both linear viscoelastic creep and stress relaxation

The use of the stretched-exponential function to represent both the relaxation function g(t)=(G(t)-G _∞)/(G ₀-G _∞) and the retardation function r(t) = (J _∞+t/η-J(t))/(J _∞-J ₀) of linear viscoelasticity for a given material is investigated. That is, if g(t) is given by exp (?(t/τ)^β), can r(t) be represented as exp (?(t/λ)^µ) for a linear viscoelastic fluid or solid? Here J(t) is the creep compliance, G(t) is the shear modulus, η is the viscosity (η^?1 is finite for a fluid and zero for a solid), G _∞ is the equilibrium modulus G _e for a solid or zero for a fluid, J _∞ is 1/G _e for a solid or the steady-state recoverable compliance for a fluid, G ₀= 1/J ₀ is the instantaneous modulus, and t is the time. It is concluded that g(t) and r(t) cannot both exactly by stretched-exponential functions for a given material. Nevertheless, it is found that both g(t) and r(t) can be approximately represented by stretched-exponential functions for the special case of a fluid with exponents β=µ in the range 0.5 to 0.6, with the correspondence being very close with β=µ=0.5 and λ=2τ. Otherwise, the functions g(t) and r(t) differ, with the deviation being marked for solids. The possible application of a stretched-exponential to represent r(t) for a critical gel is discussed.