Relaxation transitions amorphous polymers

The WLF equation can be widely applied, and demonstrates the equivalence of time and temperature, the so-called time-temperature superposition principle, on the mechanical relaxations of an amorphous polymer. The equation holds up to about 100° above the glass transition temperature, but after that begins to break down. 

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. 

The approach developed in this paper, combining on the one side experimental techniques (dynamic mechanical analysis, dielectric relaxation, solid-state 1H, 2H and 13C NMR on nuclei at natural abundance or through specific labelling), and on the other side atomistic modelling, allows one to reach quite a detailed description of the motions involved in the solid-state transitions of amorphous polymers. Bisphenol A polycarbonate, poly(methyl methacrylate) and its maleimide and glutarimide copolymers give perfect illustrations of the level of detail that can be achieved. 

In another paper in this issue [1], the molecular motions involved in secondary transitions of many amorphous polymers of quite different chemical structures have been analysed in detail by using a large set of experimental techniques (dynamic mechanical measurements, dielectric relaxation, H, 2H and 13C solid state NMR), as well as atomistic modelling. 

As a general comment about the dynamic mechanical relaxational behavior of this polymer, the results are consistent with dielectric data [210] and with the fact that no glass transition phenomenon is observed, at least in the range of temperature studied. This is striking in an amorphous polymer. It is likely that the residual part of the molecule mechanically active above the temperature of the ft relaxation is only a small one, and this is the reason for the low loss observed in the a zone. 

The high-temperature relaxation process is typical for amorphous polymers and can be assigned to the a-relaxation that appears in the whole frequency range and in the temperature interval from 50 to 100°C. This process is well observed for all samples. It corresponds to the glass-rubber transition of the amorphous phase. 

In general, most polymers lose their ductile properties below the glass transition temperatures (Tg), the point at which the movements of polymer chain segments become extremely restricted. In amorphous polymers, the characteristics of the low temperature relaxations are directly related to the chemical structure and the dynamics of polymer chains. There are several possible types... 

The first secondary transition below Tg, the so called fj-relaxation, is practically important. This became evident after Struik s (1978) finding that polymers are brittle below Tp and establish creep and ductile fracture between Tp and Tg. The p-relaxation is characteristic for each individual polymer, since it is connected with the start of free movements of special short sections of the polymer chain. In view of more recent data of Tp Boyer s relation, Eq. (6.29), is very approximate and fails completely for amorphous polymers with high Tg s (e.g. aromatic polycarbonates and polysulphones). Some rules of thumb may be given for a closer approximation. 

In conclusion, the deformation behavior of poly(hexamethylene sebacate), HMS, can be altered from ductile to brittle by variation of crystallization conditions without significant variation of percent crystallinity. Banded and nonbanded spherulitic morphology samples crystallized at 52°C and 60°C fail at a strain of 0.01 in./in. whereas ice-water-quenched HMS does not fail at a strain of 1.40 in./in. The change in deformation behavior is attributed primarily to an increased population of tie molecules and/or tie fibrils with decreasing crystallization temperature which is related to variation of lamellar and spherulitic dimensions. This ductile-brittle transformation is not caused by volume or enthalpy relaxation as reported for glassy amorphous polymers. Nor is a series of molecular weights, temperatures, strain rates, etc. required to observe this transition. Also, the quenched HMS is transformed from the normal creamy white opaque appearance of HMS to a translucent appearance after deformation. 

Relaxation processes in amorphous polymers below the glass transition involve local... 

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. 

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