Stress-temperature profiles

A model of lamellae formation In stretched networks is proposed. Approximately one-half of the chains do not fold. Formation of such lamellae Is accompanied by declining stress. Highly folded systems (high crystallinity), however, can cause a stress Increase. In the calculations crosslinks are assigned to their most probable positions through the use of a characteristic vector. A contingent of amorphous chains Is also Included. The calculations suggest that the concept of fibrillar-lamellar transformations may be unnecessary to explain observed stress-temperature profiles In some cases. 

The glass transition temperature, Tg, can also be calculated from the stress-temperature profile. It can be taken as the intersection of two lines drawn from the linear regions of the glassy and rubbery regimes, in a manner similar to Tg determination from TMA. Here, however, the measured Tg corresponds more with those derived from dynamic mechanical methods because of the strong dependence of stress on the modulus transition between the rubbery and glassy states. Other ways to measure Tg would be to take the derivative of the a(T) curve to obtain Ea(T) the Tg could then be determined as either the inflection point or the midway point in the transition between glassy Ea and rubbery Ea. 

Both materials were subjected to the same processing conditions. The cure profile consisted of heating from room temperature to 2 60°C at 5°C/min, holding at 260°C for 2 hours, then cooling to room temperature at 5°C/min. As can be seen in Figure 3, their stress-temperature profiles are quite different. Both films left the spin-coater with approximately zero stress. Upon heating, the polyimide film developed substantial tensile stress due to film contraction from solvent evaporation while the BCB film exhibited only mild tensile stress buildup. The stress in the BCB film relaxed at 260°C while the stress in the polyimide did not. 

Figure 3. Comparison of stress-temperature profiles for BCB and PMDA/ODA.

Upon cooling, after a 2 hour cure, both materials exhibit linear stress-temperature profiles. This indicates that the glass transition temperature is at or above the cure temperature, and that measurements have been made in the glassy elastic regime. The glassy-state Ea can be calculated from the slopes of these curves. For the polyimide it is 0.13 MPa/°C and for the BCB it is 0.16 MPa/°C. Note that the polyimide bears a higher cumulative stress at room temperature because of the stress induced by solvent evaporation, in spite of its lower Ea. 

Fig. 12. Non-equilibrium stress-temperature profiles for an amorphous (42.7% cis) and a crystallizable (98.3% cis) polybutadiene at different elongation ratios, a. Gum vulcanizates were used.

Our general plan of investigation was to measure Tm as a function of a to determine the value of 0 via Eq. (l) for several networks of different crosslinking (N). Amounts of crystallinity might then be calculated with Eq. (2). The stress-temperature profiles, calciilated with Eq. (3), could then be compared with those obtained experimentally. Several questions are of particular interest ... 

Are the theoretical stress-temperature profiles consistent with experimental ones, particularly with regard to shape and valley width ... 

Fig. 1. Experimental stress-temperature profile of sample E. (dotted line is cooling curve, solid line is heating curve)... 

Fig. 3. Experimental stress-temperature profile of Sample C crystallized at 50-UO-25 C...

Stress-temperature profile of sample C at a = 3.31 (sigma =0.75 and 5.5 monomer units/statistical link)... 

Fig. 10. Theoretical stress-temperature profile of sample A. [at constant sigma = 1.6o)...

The stress-temperature profile is intimately tied to a and also to crystallinity 03, which too is controlled by a. This makes it difficult to speculate about stress-temperature profiles in general. As a nucleation parameter for lateral growth, a is expected to be unique for the polymer in question. Consequently we cannot draw conclusions about the expected behavior of other polymers (say polychloroprene) from what we have learned about trans-polyisoprene. To do so requires a detailed understanding of all factors affecting a, which we lack at this time. 

Hie thermal stress component became more pronounced by the elevation of bake temperature. Figure 3 presents the stress-temperature profile of the film... 

In addition, the of the films can be estimated firom the stress-temperature profiles. In general, stress is not built up above 7 because of high polymer chain mobility. However, the chain mobility is restricted in the glassy state below Tg allowing the generation of stress. In the overall stress-temperature profile measured on cooling, the temperature at which the stress started to increase was chosen as Tg. For the films b ed at 400 C, Tg was 235 °C for the Sixef-33,300 C for the Sixef-44, and 400 °C for the Probimide 412. 

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