Non-Isothermal Curing
During many thermoset processing steps (and in this example, lamination of a B-staged (partially cured) prepreg, a non-isothermal temperature ramp is used in the process. The viscosity profile for the B-staged prepreg at a heating rate of 10°C/minute to a cure temperature of 175°C is shown in Figure 1.
Figure 1. Viscosity as a function of time for a non-isothermal heating rate to a cure temperature of 175°C for an epoxy prepreg.
As the temperature ramps in the press, the viscosity is fairly high since the prepreg is below its glass transition temperature. As the prepreg is heated through Tg, the viscosity begins to drop dramatically. This is due to the temperature dependence of the now liquid resin. In this case, the prepreg for circuit board lamination is an ungelled glass and has a Tg around 50-60°C.
The viscosity continues to decrease until the resin polymerization and crosslinking start. When the crosslinking reaction leads to a higher molecular weight and thus higher viscosity, the viscosity increases due to crosslinking now dominating and the viscosity rapidly increases and eventually reaches a plateau (for small amplitude oscillatory measurements, we can monitor the viscosity through the entire cure).
A step-change in dielectric measurements occurred with the introduction of the microdielectrometer in the early 1980’s led by Professor Steve Senturia and his group at MIT [1-3].
When I was at IBM, I developed a method to measure the viscosity and the dielectric response simultaneously [4]. The experiment used a microdielectrometer with an inter-digitated comb electrode configuration as shown in Figure 2.
Figure 2. Schematic of the microdielectrometer and comb electrode configuration.
In Figure 2, the dielectric sensor is shown in the top figure. The sensors come as an integral package with the sensing area consisting of inter-digitated comb electrodes as shown on the left side of Figure 8. In the schematic on the right, a cross-section shows how the sample material covers the electrodes. This feature allows the sensors to be embedded in various types of process tools, since during curing, the materials will soften, flow over and cover the electrodes allowing dielectric measurements.
The microdielectric sensors were small enough to embed into thermoset process tools. Back at IBM I was developing a fundamental understanding of the composite lamination process used to fabricate very expensive multilayer circuit boards. I was looking for a way to measure the viscosity in-situ during the lamination process but was challenged with how to embed a rheometer in a large manufacturing lamination press! Recall that the equations relating to the dielectric response were very similar to those used in dynamic mechanical (i.e. oscillatory rheometry in this case) and the objective was to measure the rheological and dielectric response simultaneously by embedding the microdielectric sensor into the bottom plate of the rheometer. In this case, disposable aluminum plates were used and inserted into the upper and lower fixtures in the rheometer. Figure 3 shows a schematic of the microdielectric sensor embedded in the lower disposable plate in the rheometer.
Figure 3. Schematic of the embedded dielectric sensor in the bottom plate of the rotational parallel plate rheometer.
A rheometer with disposable plates was used for the rheology measurements. The disposable plates allowed a small slot to be machined in the bottom plate to accommodate the dielectric sensor and be mounted flush with the top surface of the bottom plate. To ensure good contact with the disposable parallel plates, a process was developed to mold a compacted resin disk using the prepreg powder.
The molded disk was free of trapped air and was solid (the molding process was done above Tg, but at a low enough temperature that the cure reaction did not occur). To get good contact with the comb electrodes, a small amount of prepreg powder was placed over the comb electrodes prior to inserting the disk between the parallel plates. This ensured good electrode contact allowing a dielectric signal to be obtained as the prepreg went through the Tg. The details of the simultaneous measurements may be found in Gotro and Yandrasits [6].
Dielectric Loss Factor and Viscosity Measured Simultaneously
In Figure 4, the dielectric loss factor (solid line) and the complex viscosity measured simultaneously are plotted as a function of time for a Bis-maleimide Triazine Epoxy resin system. The fully cured Tg for this system is approximately 185ºC. The temperature was ramped in the rheometer at approximately 5ºC/minute to a final temperature of 175ºC.
Figure 4. Dielectric loss factor (solid line) and the complex viscosity (open triangles) measured simultaneously are plotted as a function of time.
The complex viscosity in Figure 4 exhibits the typical behavior for a B-staged thermoset resin. The viscosity decreases rapidly after the resin is heated above the B-staged Tg. Further heating continues to cause the viscosity to decrease until the chain extension and crosslinking reactions result in long growing chains and network formation leading to a minimum in the viscosity and subsequent rapid increase in the viscosity.
The dielectric loss factor (solid line) exhibits several features. The first is the shoulder that is observed in the vicinity of the glass transition region. The second feature is the maximum in the loss factor that occurs near the minimum in the complex viscosity.
The third feature is the shoulder on the dielectric loss factor at longer cure times. Note that the shoulder on the loss factor occurs at approximately the same time as the viscosity increases rapidly and the rheometer shuts down (due to force input overload, a protection feature to prevent transducer damage).
Let’s look at each of these features more closely. In the experiment in the figure above, the dielectric loss factor was measured at multiple frequencies. In Figure 5, the scale was expanded to examine more details of the loss factor response in the vicinity of the glass transition region.
Figure 5. Dielectric loss factor plotted as a function of time. The temperature was ramped in the rheometer at approximately 6ºC/minute to a final temperature of 175ºC
The Bis-maleimide Triazine Epoxy resin in Figure 5 was obtained from a B-staged prepreg sample. Thus, the resin was in the ungelled glassy state at room temperature.
During the initial heating ramp, the ungelled glass went through the glass transition temperature. In Figure 5, in the plot on the left, the loss factor exhibits a shoulder during the initial temperature ramp (indicated in the blue circle). The loss factor was measured at multiple frequencies and shows the classic frequency dependence associated with dipolar relaxations in the glass transition region in the plot on the right in Figure 5. The loss factor equation is highlighted to show the contributions from the ionic conductivity and the dipoles.
Examining the loss factor past the maximum will also provide insights into the curing pathways. In Figure 6, the temperature ramp was varied from 5.8 – 16ºC/minute to a cure temperature of 175ºC for a cyanate ester resin system. The fully cured Tg for the cyanate ester resin system was 275°C and is greater than the cure temperature.
Figure 6. Dielectric loss factor plotted as a function of time. The temperature ramp was varied in the rheometer from approximately 6ºC-16 ºC/minute to a final temperature of 175ºC for a cyanate ester resin system.
In Figure 6, there are a series of peaks in the loss factor past the maximum. Since the fully cured glass transition temperature is greater than the cure temperature, vitrification can occur when Tg =Tcure. In a similar manner as was shown in Figure 6, where dipole relaxation peaks were observed as the temperature reached the glass transition temperature (Tg), when the chemical crosslinking causes the Tg to increase during curing, at a temperature where Tg=Tcure vitrification occurs (the “reverse” of the glass transition). At vitrification, frequency dipolar relaxations are observed.
The next post will explore more results from simultaneous dielectric and viscosity during non-isothermal curing profiles.
References
S. A. Bidstrup, N. F. Sheppard and S. D. Senturia, Polymer Engineering and Science, March 1989, v 29, issue 5
D. Senturia and N. F. Sheppard, Advances in Polymer Science, vol. 80 1986
F Sheppard, Ph.D. Thesis, Massachusetts Institute of Technology, 1986S. D. Senturia and N. F. Sheppard, Adv. Polym. Sci., vol. 80 1986
Gotro and M. Yandrasits, Polymer Engineering and Science, March 1989 vol 29, no. 5
