In the previous posts, the basics of dielectric analysis was presented. Part Three of this series will demonstrate the relationships between dielectric data during isothermal curing. First, let’s examine the isothermal during process. A nice example is the work of Bidstrup, Sheppard and Senturia at MIT in 1989 [1]. They examined the isothermal curing of DGEBA and DDS:
DGEBA (diglycidyl ether of bisphenol-A, a common difunctional epoxy)
DDS (diamino diphenyl sulphone, a common amine hardener for aerospace epoxies)
To establish the curing relationship, they measured the glass transition temperature (Tg) as a function of cure time at various isothermal temperatures. The Tg-time data is plotted in Figure 1.
Figure 1. Tg as a function of time at various isothermal cure temperatures noted in the legend [1].
As shown in Figure 1, the curing rate is strongly dependent on the isothermal cure temperature. The Tg-time relationship establishes the baseline for dielectric measurements.
To investigate how the dielectric response correlates to the changes in Tg, the dielectric loss factor was measured for the DGEBA/DDS resin at the same isothermal temperatures in Figure 1. In Figure 2, the log of the ionic conductivity is plotted as a function of time at various isothermal temperatures:
Figure 2. log of the ionic conductivity is plotted as a function of time at various isothermal temperatures [1]
In Figure 2, the ionic conductivity provides a very useful probe for thermoset curing. Remember the ionic conductivity is a probe of segmental mobility, so as the epoxy system above crosslinks, the segmental mobility steadily decreases (analogously, the Tg increases).
The dielectric data clearly shows how the curing rate increases with temperature (the slope of the ionic conductivity/time plot gets steeper as the temperature increases). We now have a basis for using dielectric methods to probe curing during processing. In the next posts we will discuss dielectric cure monitoring during non-isothermal curing.
The Williams-Landel-Ferry (WLF) relationship [2] was demonstrated to apply to the ionic conductivity by Bidstrup et. al. [1].
Where the shift factor aT is defined as the ratio of the conductivity (σ) at temperature T to the conductivity measured at the glass transition temperature, Tg and C1 and C2 are constants. Details of the WLF modeling and curve fitting for an epoxy-amine system may be found in [1]. In the Bidstrup et.al. paper, the WLF equation was successfully used to model the dependence of the ionic conductivity (σ) to the glass transition temperature as shown in Figure 3.
Figure 3. The solid line represents the fit to the WLF equation, and the solid points are the Tg and ionic conductivity data at the isothermal temperatures noted in the legend [1].
Careful isothermal measurements of an epoxy-amine system demonstrated that the ionic conductivity could be correlated with the glass transition temperature and modeled using the well-established WLF equation.
The next series of posts will cover the dielectric analysis of non-isothermal curing. Most industrial curing processes are non-isothermal so the next posts will provide the underlying concepts to enable in-situ dielectric cure monitoring.
References
A. Bidstrup, N. F. Sheppard and S. D. Senturia, Polymer Engineering and Science, March 1989, v 29, issue 5
L. Williams, R. F. Landel, J. D. Ferry, J. Am. Chem. Soc., 77, 3701 (1955)
