Evaluating Epoxy Curing Using Frequency Chirps

Windowed chirps, or “Optimally Windowed Chirps (OWCh),” have recently seen so much development [1,2] that they can now be used to replace or enhance discrete frequency data for many applications. Epoxy curing reactions in particular benefit from the wealth of data generated by chirps compared to discrete frequency sweeps because the Winter-Chambon gel point [3] can be determined using the frequency spectrum from a short chirp. The following note describes the use of chirps to determine the gel point in an epoxy that lacks a clear G’/G” crossover.

The gel point is an important piece of information when characterizing an epoxy reaction. The storage modulus, G’, can be thought of as the solid-like behavior where the loss modulus, G”, is the liquid or viscous-like. The crossover, therefore, is the transition from mostly liquid-like to mostly solid-like and is used as an effective gel point. The crossover gel point is usually frequency dependent and may not occur anywhere near the true gel point. The gel point determined using the Winter-Chambon criterion [3] is observed when there is an independence of phase angle (or tan[δ]) with respect to frequency and power law relationship between modulus and frequency. There are often materials that do not have a G’/G” crossover near the point of gelation due to filler or other formulation decisions.

The crossover gel point is often used because a single frequency vs. time is all that is needed. The Winter-Chambon gel point requires the frequency dependence of the phase angle vs. time, which necessitates measuring the material at multiple different frequencies as the material cures. Discrete frequency sweeps often take too long when considering that the material itself is changing or providing too few frequencies to make the determination. The alternative would be to run multiple time sweeps at different frequencies and hope there is no variation between repeat samples. Another solution is using the multi-wave functionality, but several experimental design challenges such as an appropriate amplitude for each frequency for an appropriate number and range of frequencies, among other challenges, can make the experiment difficult.

Windowed chirps recently developed [1,2] and popularized for both strain and stress-based inputs provide a much easier experimental design with a single amplitude input and a user-selected frequency range. The Frequency Chirp experiment allows users to utilize these advancements for evolving systems such as epoxy curing and can provide a wealth of data including the true gel point as shown in this note. Frequency chirps provide the same or more data than a frequency sweep in the same time it takes to complete one cycle of the lowest frequency probed. Because the chirp is fast and provides data for many frequencies, the Winter-Chambon gel point criteria can be determined as easily as the crossover modulus gel point. Experimental design is greatly simplified over the multi-wave experiment as only a single amplitude needs to be chosen, and the experiment can utilize auto-strain for this single amplitude.

Two commercial epoxies, here named Epoxy A and Epoxy B, were measured for these experiments. Sets of 25 mm disposable aluminum ETC plates were used, and all measurements were done on a TA Instruments™ Discovery™ HR 30 Rheometer using the frequency chirp procedure.

Epoxy A and B are commercial two-part epoxies with a “set time” specified at 5 minutes. Epoxy A has a stated cure time of 1 hour. Epoxy B has a 30-minute recommended wait before handling (clamp time) and a 24-hour full cure time. Instructions for both called for mixing of equal precursor parts for 20 to 30 seconds. The mixture was applied to the 25 mm plates, trimmed, and the experiment started within 30 seconds of the mixing. Both epoxies were cured under ambient conditions 25-30 °C. A Conditioning Options segment (Figure 1) is used to control axial force and automatically adjust the strain or stress during the measurement.

Axial force can be important since the epoxy shrinks during cure so the stage will move down to keep axial force within 0.1 N of 0. This movement is done between chirps. The auto-strain will increase or decrease the strain or stress (displacement or torque) according to the limits shown in the figure to optimize data collection. Auto-strain works for both torque and strain-controlled frequency chirps.

The data output for the frequency chirp isothermal selection for Epoxy A is shown in Figure 3A. This figure contains all the data for each chirp and at each frequency. The relevant data can be extracted by a simple transformation in TRIOS Software: Right-click the file in the File Manager, select “Transformations,” and then select “Rearrange frequency cycles into temperature sweeps” (Figure 4). This data in Figure 3B shows all frequencies in the chirps converging to a near single point at 710 s then diverging as the material cures. The noise at the start of the experiment is due to inertia being dominant when the material is uncured for the high frequency signals. As the material cures, the inertia becomes minor and smooth data is observed. These data are also noisy because the storage modulus for a near Newtonian liquid is very low and any noise in the phase angle causes an apparent large change in the storage modulus. The loss modulus at this point is the dominant signal and is not noisy.

A few of the frequencies from 3B are shown in Figure 5A for clarity. These 5 frequencies span the entire frequency range of the chirp. Figure 5A has the inertial noise at the highest frequency labelled as well as the Winter-Chambon gel point. The moduli in Figure 5B also show power law dependence with frequency while tan(δ) is independent, which fit the Winter-Chambon criterion [3]. This gel point is somewhat close to the “set time” for this epoxy specified as 300 s by the manufacturer.