Part two of this series will cover the basics of curing monitoring using dielectric spectroscopy. For cure monitoring, we are going to focus on the dielectric loss factor. The dielectric loss factor is given by:
From the above relationship, one observes the dielectric loss factor is comprised of two components: one from ionic conductivity and one from the contributions from the dipoles. The main difference between the dynamic mechanical measurement is that the dielectric loss factor has a component that arises from the ionic conductivity (i.e. from the movement of the chlorine or sodium impurities) which we will see is a key factor in probing the curing of thermosets.
Let’s take a closer look at the components of the ionic conductivity:
The strength of the ionic conductivity comes from three factors.
- The charge magnitude of the ionic species (that is how “strong” is the chlorine or sodium)
- The amount of the species
- Lastly, but most important, is the ion mobility.
This is the key feature allowing the dielectric measurements to probe curing.
From the ionic conductivity equation above, the ions have a charge and will move in response to the applied voltage. The ionic conductivity provides a nice means to probe the progress of chemical reactions during curing. As the thermoset cures, the first chemical reaction is chain extension (i.e., amine nucleophilic addition to the epoxy group) and then as the degree of polymerization increases, crosslinking occurs. As the molecular weight increases, the mobility of the chain segments decreases. Once the crosslinking reaction kicks in, the segmental mobility will decrease very quickly.
Figure 1 shows the schematic of an uncured thermoset resin and a partially cured resin at gelation.
Figure 1, Schematic of ion mobility during the early stages of curing. In this case, the positive electrode is on the right, and the negative electrode is on the left ([adapted from [1]).
In the case of epoxy resins, there are typically some residual sodium (+) and chlorine (-) ions which are useful probes and are denoted in the uncured resin on the left in Figure 2. The path of the mobile ion is denoted by the length of the arrows. Early in the cure, there is little resistance to the flow of ions, and the arrows are long. As the curing progresses, the resistance to the ion movement becomes more restricted as shown in Figure 2 on the right. The thermoset network has undergone chain extension with some crosslinking and as such, the mobility of the ions decreases. Figure 2 shows a schematic of a fully cured network.
Figure 2. Schematic of ion mobility in a fully cured network ([adapted from [1]).
When the network is fully cured, the segmental mobility is very low (i.e., the short arrows near the ions) so by measuring the ionic mobility during curing provides a convenient way to monitor the extent of cure in real time.
Probing the ionic conductivity in the glassy state would result in very low ion mobility. As temperature increases, segmental mobility increases. It is important to remember that the ionic conductivity is controlled by temperature dependence and cure state dependence. For example, when a thermoset is fully cured, the ionic conductivity will be higher at higher temperature compared with the ionic conductivity at a lower temperature. In this case, only the temperature dependence of segmental mobility will control the ionic conductivity. The next post will detail the relationships between the dielectric data during isothermal curing.
Reference:
- For detailed derivations see https://lambient.com/lambient-university See Class B Application Note 4.05
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