# A Guide to Dielectric Cure Monitoring Equipment

Dielectric cure monitors are capable of quantifying the dielectric properties of composite or thermoset. The response of dipole rotation and ion motion is selectively revealed by using a range of frequencies, enabling the analysis of the material state through the entire cure.

## Dielectric/Conductivity Sensors

Dielectric cure monitors can quantify the capacitance (C) and resistance (R) of a material between two electrodes. These electrodes can be modeled as a resistance in parallel with a capacitance, as illustrated in Figure 1.

Figure 1. Dielectric model of a Material Under Test. Image Credit: Lambient Technologies.

Figure 2 shows simple parallel plate electrodes that are generally utilized for this purpose. Here, the ratio of electrode area A as well as the distance D between them — the A/D ratio — is considered a figure of merit.

Figure 2. Comparison of the parallel plate and interdigitated electrodes. Image Credit: Lambient Technologies.

A larger A/D ratio correlates to a greater sensitivity of the sensor. Moreover, the A/D ratio is the scaling factor used for estimating permittivity (ε′) from capacitance and resistivity (ρ) from resistance.

However, pressure can cause a change in the distance D and so do the contraction and expansion of the material, leading to incorrect results.

The interdigitated electrode, illustrated in Figure 2, offers an alternative solution. The electrodes are supported by a rigid substrate, and the resulting planar structure does not vary with pressure, or with the contraction and expansion of the material under test (MUT).

An interdigitated sensor performs a surface measurement, while the parallel plate sensor performs a bulk measurement.

As a rule of thumb, interdigitated electrodes that have the same separation and width measure to a depth that is almost equivalent to the width of the electrode. Also, the A/D ratio parameter applies to interdigitated electrodes as a figure of merit and is considered the scaling factor for estimating permittivity and resistivity.

A Varicon1 disposable dielectric/conductivity sensor with 100 µm wide interdigitated electrodes is shown in Figure 3.

Figure 3. Disposable Varicon1 dielectric/conductivity sensor on the polyimide flex circuit. Image Credit: Lambient Technologies.

The Varicon sensor, which is built as a Kapton® flex circuit, is so thin that it can be inserted between a laminate’s plies and can be discarded after use. The narrow interdigitated electrodes are too small to be seen in the photograph yet result in a large A/D = 160, with proportionately greater sensitivity. The only trade-off is the measurement of dielectric properties within 100 µm of the surface.

A Ceramicomb-1"2 reusable dielectric/conductivity sensor integrated into a platen for a small press is shown in Figure 4. The sensor is built with interdigitated electrodes integrated into ceramic and has A/D = 10.

Figure 4. Reusable Ceramicomb-12 dielectric/conductivity sensor embedded in press platen. Image Credit: Lambient Technologies.

When mounted as illustrated, a sample can be placed in the press and can then be heated and compressed, while concurrently making dielectric measurements to track the cure. Following this, the sample can be removed from the sensor and the process can be performed again.

Reusable sensors are convenient to use in applications like quality control/quality assurance (QC/QA), which involve repetitive testing. The wider electrodes can be seen in Figure 4. This sensor is capable of measuring in-depth into the material, and the only trade-off is reduced sensitivity due to the smaller A/D ratio.

## AC Versus DC Measurements

Fascinatingly, measuring frequency-independent resistivity (ρDC) using DC signals is usually not useful. During early cure, a phenomenon known as electrode polarization can produce a blocking layer across sensor electrodes, specifically when the material is most conductive. This blocking layer serves as a capacitor and inhibits the flow of DC current.

Dielectric data resulting from very low excitation frequencies are distorted in the presence of electrode polarization, as illustrated in Figures 5 and 6 for the cure of a “five-minute” epoxy.

Figure 5. Distortion in ion viscosity from electrode polarization. Image Credit: Lambient Technologies.

Figure 6. Distortion in ion viscosity from electrode polarization (detail). Image Credit: Lambient Technologies.

Plots of resistivity against an axis labeled ion viscosity are shown in Figures 5 and 6. For convenience purposes, these data can be collectively referred to as ion viscosity.

At the start of the cure, measurements made at the higher excitation frequencies — of 1 to 10 kHz — did not show any distortion and precisely identified the ion viscosity minimum.

Electrode polarization induces a slight distortion in the 10 Hz data, as seen in the expanded plot shown in Figure 6. This distortion alters the predicted single minimum in resistivity/ion viscosity to a peak with a couple of local minima.

Data obtained from 1 Hz measurements show relatively more distortion because decreasing frequency leads to an increase in the boundary layer effect. This distortion turns out to be worse at lower frequencies, and with DC signals, a conductive material can also seem to be non-conductive.

Apart from preventing the distorted data from blocking layers, AC signals can also perform measurements via a release film. A release film is a very thin layer of plastic utilized to prevent the material from sticking to a platen or mold.

AC signals have considerable benefits when compared to DC signals. For dielectric cure monitoring, the material and application govern the optimum range of frequencies. Very low frequency data needs long acquisition times and is prone to distortion from electrode polarization.

A reasonable lower limit for a majority of the thermosets is 0.1 to 10 Hz. Dipolar rotation is likely to dominate high-frequency data and conceals ion viscosity at the end of cure as illustrated in Figure 5. For a majority of the thermosets, 10 to 100 kHz is a good upper-frequency limit for ion viscosity measurements.

## Temperature Measurements

Temperature measurement is often made with a thermocouple and is a crucial function for dielectric cure monitoring. This is because ion viscosity relies on the cure state as well as temperature. At a specified cure state, ion viscosity increases as temperature decreases and decreases as temperature increases. If the temperature is known, it can provide a deeper understanding of the nature of the cure and prevent misinterpretation of data.

The isothermal cure of an epoxy is shown in Figure 7, wherein the minimum ion viscosity takes place at time t = 0, and during cure, ion viscosity increases monotonically.

Figure 7. Isothermal epoxy cure at 50 °C. Image Credit: Lambient Technologies.

By contrast, Figure 8 illustrates the cure of a “five-minute” epoxy, which creates an exotherm. In this case, temperature first increases as curing starts, discharging heat and causing a reduction in ion viscosity.

Figure 8. Five-minute epoxy cure with exotherm. Image Credit: Lambient Technologies.

Ultimately, the reaction dominates and ion viscosity undergoes a minimum and then increases. It can be seen how the peak exotherm occurs simultaneously as the maximum slope of ion viscosity — detecting the point of maximum reaction rate. Temperature data is useful to gain an understanding of how a material cures, and is essential when developing a formulation or process.

## A Dielectric Cure Monitoring System

The essential elements of a dielectric cure monitoring system are shown in Figure 9. The dielectric/conductivity sensors make contact with the thermoset under test and include two general configurations — interdigitated electrodes or a parallel plate. The choice of a sensor relies on the preferred type of measurement, either bulk or surface, and the preferred sensitivity as shown by the A/D ratio.

Figure 9. Essential elements of a dielectric cure monitoring system. Image Credit: Lambient Technologies.

Sensors generally link to an instrument. AC signals are used by the most versatile instruments for measurement. A broad range of excitation frequencies helps select an optimal frequency for viewing ion viscosity, and multiple frequencies allow the analysis of the dipolar response. Temperature measurement is significant for understanding cure, specifically under non-isothermal conditions.

Finally, the instrument is controlled by software. This is often done via a computer linked to the dielectric cure monitor. It is not possible to determine the cure state from a single point measurement, but should be extracted from the shape of the curve and the change of ion viscosity over time. Therefore, software, which stores and analyzes data and makes repetitive measurements, is very important for the system performance.

## References

1. Varicon sensor, manufactured by Lambient Technologies, Cambridge, MA USA. https://lambient.com
2. Ceramicomb-1″ sensor, manufactured by Lambient Technologies, Cambridge, MA USA

This information has been sourced, reviewed and adapted from materials provided by Lambient Technologies.

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