An Interesting Experiment Using the Time Temperature Transformation Diagram
The previous post discussed the dielectric and rheological changes during non-isothermal curing. In this post we will use the information presented so far in this series and present a very interesting case study on how dielectric measurements in conjunction with complex viscosity measurements can shed light on the physical changes occurring during thermoset curing.
We have seen that dipoles can be used to determine both the glass transition region and if vitrification is occurring during cure. Let’s look at the Time Temperature Transformation (TTT) diagram below [1]:
Figure 1. Time-Temperature-Transformation (TTT) Diagram [1]
The TTT diagram shown in Figure 1 is a pseudo phase diagram for a curing thermoset [1]. Temperature (either the cure temperature or Tg) is plotted on the Y-axis versus log time on the X-axis. The TTT diagram shows the different phases as a function of time at a given temperature. Various glass transition temperatures are noted along with the cure temperature, Tcure.
The term “glass transition” is defined as the transition from a glassy state to the liquid or rubbery phase for thermosets. The glass transition is typically measured during a programmed heating rate, and frequency dependent dipolar relaxations appear during heating through the glass transition temperature. The glass transition temperature Tg can be measured using DSC, DMA, or TMA.
For example, following the green Tcure line in Figure 1, as a function of time, the material begins as a liquid and with chemical reaction undergoes gelation (blue curve), continues to cure in the gelled rubber phase until the Tg=Tcure at vitrification (red curve). After vitrification (the process of transitioning into a glassy material), the rate of reaction slows dramatically.
A simultaneous rheology/dielectric experiment with an epoxy-amine system was designed to follow the green line in the TTT diagram of Figure 1. The Tg of the fully cured system was 170ºC but the temperature in the rheometer was ramped to only 140ºC.
Moving from left to right along the green line in the TTT diagram, the material begins as a liquid with low initial glass transition temperature Tg0. With chemical reaction the epoxy-amine system polymerizes and eventually reaches the blue gelation curve to become a gel—at this time the glass transition temperature has increased to the value identified as gel Tg. The resin continues to cure in the gelled rubber phase and builds a highly crosslinked network with Tg steadily increasing.
In the experiment shown in Figure 1, the red curve of the TTT diagram indicates vitrification occurs when Tg is equal to Tcure (~140ºC). In this case, Tg increases with the ongoing chemical reactions (epoxy-amine reactions) as the network crosslinks. When the increasing Tg is equal to Tcure (~140ºC), vitrification starts. Vitrification is the transition from a rubbery state (high temperature crosslinking network) to the glassy state. It is essentially a “backwards” glass transition driven by the chemical conversion and not temperature. In other words, when the Tg of the growing network nears the curing temperature, the network will transition into the glassy state. In this case, at vitrification dipolar relaxations also appear.
For the epoxy-amine system, Figure 2. the complex viscosity and the dielectric loss factor at multiple frequencies are plotted as a function of time for a non-isothermal ramp to 140ºC. As temperature increases, viscosity initially decreases, goes through a minimum then rapidly increases as the system cures.
In the TTT diagram in Figure 1, one observes that the cure path will pass the blue gelation curve, with additional curing will build the highly crosslinked network, but when Tg is approximately equal to Tcure (~140ºC), the TTT diagram indicates that vitrification will occur (the red curve above). As we showed in the last post, at the glass transition, frequency dependent dipolar relaxations are observed and at vitrification, dipolar relaxations also are observed.
In Figure 2, the complex viscosity and dielectric loss factor at multiple frequencies are plotted as a function of time for a non-isothermal ramp to 140ºC. As the temperature increases the viscosity initially decreases, goes through a minimum, and rapidly increases as the epoxy-amine systems cures.
Figure 2. Dielectric loss factor (solid line) at multiple frequencies and the complex viscosity (open triangles) measured simultaneously are plotted as a function of time.
As the temperature increases for the B-staged resin and goes through the uncured glass transition temperature, frequency dependent dipolar relaxations appear around 8- 12 minutes. These dipolar relaxations correspond to the rapid decrease in viscosity above Tg.
The maximum loss factor occurs at the same time for all frequencies because conductivity is constant and independent of frequency, as shown in the equation for ε”. When dominated by frequency independent conductivity, loss factor is inversely proportional to frequency so the values of the loss factor peaks increase with decreasing frequency.
The most interesting features of Figure 2 are the frequency dependent relaxations when the epoxy vitrifies, that is when Tg is equal to Tcure (~140ºC). During this time, circled in red, the rheometer shut down from input overload protection, which prevented damage to the force transducer.
Work by Day [2] investigated the curing of a blend of EPON 828 (difunctional bisphenol A epoxy) and DDS (diamino diphenyl sulfone). The loss factor was measured as a function of time during curing at 177°C. Recall that the loss factor is a function of both dipole motion and ionic conduction. Dipole movement causes a peak in the loss factor as the material vitrifies during curing [3]. In this case, the Tg is greater than 177°C. Figure 3 shows the loss factor as a function of time for the 828/DDS resin cured at 177°C.
Figure 3. Dielectric loss factor as a function of time during curing at 177°C
Early in the curing process the ion mobility is high, leading to a large contribution from the ionic conductivity. As cure progresses, the crosslinking reaction causes the network to “tighten” and the ionic conductivity decreases dramatically during curing. At vitrification, frequency dependent dipolar relaxations are observed as a series of peaks in Figure 3. For comparison, past the loss factor peak in Figure 2, when the temperature has reached the final cure temperature (i.e. is isothermal), the shapes of the loss factor curves in the right hand oval are very similar to the data in Figure 3. Figure 2 and Figure 3 represent two different epoxy chemistries but, in both cases, when cured at a temperature below Tg∞, vitrification is observed in the dielectric measurements. The input overload in the rheometer of Figure 2 implies that at vitrification the viscosity increased significantly.
In this experiment we have shown that the TTT diagram can be a useful tool to guide the processing of thermosets. Additionally, the dielectric loss factor was shown to be an effective probe for thermoset curing being capable of delineating both the glass transition and vitrification events during non-isothermal cure profiles.
References
B. Enns and J. K. Gilham, J. Appl Polym. Sci., 28,2567 (1983)
Day, D. R., (1986) Polymer Engineering and Science, V26, No.5 p.363
Senturia, S. D. and Sheppard, N. F. (1986), Adv. Polym. Sci. 80, 1
