Amorphous stress relaxation

Below Tx, stress relaxes out faster in quenched specimens than in slowly cooled ones for amorphous polymerysuch as poly(methyl methacrylate) (109). Quenched specimens of the same polymer have a creep rate at high... 

The temperature dependence of the compliance and the stress relaxation modulus of crystalline polymers well above Tf is greater than that of cross-linked polymers, but in the glass-to-rubber transition region the temperature dependence is less than for an amorphous polymer. A factor in this large temperature dependence at T >> TK is the decrease in the degree of Crystallinity with temperature. Other factors arc the reciystallization of strained crystallites ipto unstrained ones and the rotation of crystallites to relieve the applied stress (38). All of these effects occur more rapidly as the temperature is raised. 

Figure 23. Stress-relaxation curves of amorphous bisphenol A polycarbonate at the different temperatures shown by the curves. The numbers in brackets are the maximum deformations used in the tests. (From Ref. 217.)...

Fig. 3.14. The data is for a very broad range of times and temperatures. The superposition principle is based on the observation that time (rate of change of strain, or strain rate) is inversely proportional to the temperature effect in most polymers. That is, an equivalent viscoelastic response occurs at a high temperature and normal measurement times and at a lower temperature and longer times. The individual responses can be shifted using the WLF equation to produce a modulus-time master curve at a specified temperature, as shown in Fig. 3.15. The WLF equation is as shown by Eq. 3.31 for shifting the viscosity. The method works for semicrystalline polymers. It works for amorphous polymers at temperatures (T) greater than Tg + 100 °C. Shifting the stress relaxation modulus using the shift factor a, works in a similar manner.

The classic example of a NEAS is a supercooled liquid cooled below its glass transition temperature. The liquid solidifies into an amorphous, slowly relaxing state characterized by huge relaxational times and anomalous low frequency response. Other systems are colloids that can be prepared in a NEAS by the sudden reduction/increase of the volume fraction of the colloidal particles or by putting the system under a strain/stress. 

The time-temperature superposition principle has practical applications. Stress relaxation experiments are practical on a time scale of 10 to 10 seconds (10 to 10 hours), but stress relaxation data over much larger time periods, including fractions of a second for impacts and decades for creep, are necessary. Temperature is easily varied in stress relaxation experiments and, when used to shift experimental data over shorter time intervals, can provide a master curve over relatively large time intervals, as shown in Figure 5.65. The master curves for several crystalline and amorphous polymers are shown in Figure 5.66. 

DSC measurements showed that the crystallization ability of this interphase region was reduced by the silane modification of the glass beads. Despite an increase in the amount of amorphous material with increasing number of silane layers, a decrease in the intensity of the fourth lifetime was observed. This decrease in the free volume is in accordance with the earlier observed reduced mobility in the interphase region measured by dynamic-mechanical spectroscopy in the melt state [9,10] and creep and stress relaxation measurements in the solid state [12]. 

For amorphous thermoplastic polymers the general view of the Young modulus is shown as a function of time in Fig. 13.11. In this figure the various regions are present as they were also shown in Figs. 13.3 and 13.7. In those figures, however, the modulus is presented as a function of temperature. Formally a modulus temperature curve is obtained by measuring stress relaxation as a function of time at many different... 

For amorphous polymers the constant n may vary between 0.5 and 1.0 n, a dimensionless number, is a measure of the relative importance of elastic and viscous contributions to stress relaxation it is closely related to tan 8 ... 

Above Tg the stress relaxation and the creep behaviour of amorphous polymers obey the "time-temperature superposition (or equivalence) principle". 

The difference in softening temperatures for amorphous and semi-crystalline polymers becomes also clear from Fig. 13.3, where the Young moduli of amorphous and of semicrystalline polystyrene are illustrated. For amorphous polystyrene the two HDTs appear to be 92 and 97 °C and for the semi-crystalline polystyrene 99 and 114 °C. It has to be mentioned, however, that the curves in Fig. 13.3 are the so-called 10 s moduli, i.e. measured after 10 s of stress relaxation, every point at a specific temperature. The measurements in the softening experiments are not in agreement with the determination of the standard Young modulus. 

In the preceding sections, we have looked at the various types of relaxation processes that occur in polymers, focusing predominantly on properties like stress relaxation and creep compliance in amorphous polymers. We have also seen that there is an equivalence between time (or frequency) and temperature behavior. In fact this relationship can be expressed formally in terms of a superposition principle. In the next few paragraphs we will consider this in more detail. First, keep in mind that there are a number of relaxation processes in polymers whose temperature dependence we should explore. These include ... 

Further aspects of the viscoelastic behavior of ESIs which have been reported to date include linear stress relaxation behavior of amorphous ESI [40] and the creep behavior of amorphous ESI in the glass transition region [41]. Chen et al. [42]... 

The left-hand panel of Fig. 11-17 contains sketches of typical stress relaxation curves for an amorphous polymer at a fixed initial strain and a series of temperatures. Such data can be obtained much more conveniently than those in the experiment summarized in Fig. 11-8, where the modulus was measured at a given time and a series of temperatures. It is found that the stress relaxation curves can be caused to coincide by shifting them along the time axis. This is shown in the right-hand panel of Fig. 11-17 where all the curves except that for temperature Tg have been shifted horizontally to form a continuous master curve at temperature T%. The glass transition temperature is shown here to be Tj at a time of 10" min. The polymer behaves in a glassy manner at this temperature when a strain is imposed within 10 min or less. 

The comparison of E (10s) vs. temperature curves of the dry state and underwater stress relaxation studies for amorphous and semicrystalline Nafion-Na. Reproduced with permission from Ref. 47. Copyright 1984 John Wiley Sons, Inc. 

The semicrystalline, supermolecular structure of the organic carboxylate and the amorphous structure of the sulfonate resins have been studied with x-ray scattering and mechanical relaxation. This work shows no trace of crystallinity in the sulfonates, but the stress-relaxation data suggests the presence of a common structural feature, ion-clustered structure. with regions of high and low ion content. In "Figure 2 is shown the x-ray diffraction patterns depicting the supermolecular structure of perfluorocarboxylate and the sulfonate. Here is shown the amorphous halos in both... 

Figure 15 illustrates the comparison of ten-second tensile modulus E(10 sec) versus temperature of the amorphous and semicrystalline Nafion-Na as observed by dry state and underwater stress relaxation studies. It is evident that the rate of stress relaxation is faster and the relaxation temperature is lower in amorphous Nafion, relative to those of semicrystalline Nafion. 

---