AC and DC methods can both be utilized to investigate composite and thermoset cure. Also called Dielectric Analysis (DEA), dielectric cure monitoring is where a sensor is excited with a sinusoidal signal of a selected amplitude and frequency with a DC bias of zero volts.
The measured ion viscosity, which is also called frequency independent resistance, performs as an exemplary electronic component and corresponds to cure state. DC resistance cure monitoring equally probes a material but employs a constant excitation voltage VDC instead.
Figure 1. AC and DC signals. Image Credit: Lambient Technologies
Ideally, DC resistance and AC frequency independent resistance should be the same. During early through to mid-cure, thermoset resins under DC bias do not function as ideal electronic components as DC results can be affected by electrochemical reactions.
On the other hand, AC measurements without a DC bias have an average current of zero and are unaffected by electrochemical reactions. AC measurements are precise throughout the complete cure when frequencies have been correctly selected, while DC measurements deviate from AC results during mid-cure.
At the end of cure, AC and DC measurements align to the same value and can both be employed with equal accuracy at this time. While the nature of resin electrochemistry is not understood, the behavior of DC resistance measurements can be reproduced when a DC electrochemical resistance is added to a curing thermoset model.
Basic Circuit Model of a Dielectric Material
Dielectric cure monitoring quantifies the capacitance and bulk resistance of a Material Under Test. These are utilized to determine the material properties of relative permittivity and resistivity.
Figure 2 depicts a basic model of a dielectric Material Under Test (MUT) in a parallel plate cell which comprises a capacitance CMUT in parallel with a resistance RMUT.
Figure 2. Basic AC model of a dielectric material in a parallel plate cell. Image Credit: Lambient Technologies
The material properties of resistivity (ρMUT) and relative permittivity are calculated from the measurements of capacitance and bulk resistance. Resistivity (ρMUT) has both frequency dependent (ρAC) and frequency independent (ρDC) components.
In an oscillating electric field, ρAC originates from the rotation of stationary dipoles whereas ρDC originates from the flow of mobile ions. While often referred to as ‘DC resistivity’, frequency independent resistivity more precisely describes resistivity that is almost constant throughout a range of frequencies, including 0 Hz.
When a thermoset resin is subjected to a constant DC voltage (DC bias), the subsequent electrochemical reactions can influence resistivity. To avoid confusion, frequency independent resistivity is represented by ρFI and resistivity measured with a DC bias is represented by ρDC.
For cure monitoring, frequency independent resistivity is particularly important. Prior to gelation, the degree of polymerization influences both the movement of ions and mechanical viscosity, which affects ρFI.
Published research on a range of materials has demonstrated that the change in ρFI is in proportion to the change in mechanical viscosity. The term ion viscosity (IV) was created to emphasize this relationship as a synonym for frequency independent resistivity and is defined as:
|IV = ρFI (ohm-cm)
AC Cure Monitoring of PR520 Epoxy Resin
A Mini-Varicon1 dielectric/conductivity sensor is depicted in Figure 3, which was employed for AC and DC measurements when curing a pre-mixed epoxy resin system designed for resin transfer molding (RTM), called the PR5202.
A Kapton substrate is used in the construction of this sensor which has a cell constant or A/D of 80, with supporting electrodes of equal separation and width (0.004”).
A series of tests monitored the isothermal cure of PR520 at 180 °C. The AC dielectric properties were recorded with an LT-451 Dielectric Cure Monitor3 at several excitation frequencies from 1 Hz to 10 kHz.
Figure 3. Mini-Varicon dielectric/conductivity sensor (A/D = 80). Image Credit: Lambient Technologies
From the AC measurements of PR520 epoxy, Figure 4 is a plot of resistivity which has both frequency dependent (ρAC) and frequency independent (ρFI) components. All resistivity data is plotted against an axis labeled ion viscosity for convenience and can be collectively called ion viscosity.
Figure 4. Ion viscosity / resistivity during cure of PR520 epoxy. Image Credit: Lambient Technologies
The plot of Figure 4 demonstrates three key features:
- During early cure which is from 0 to 25 minutes, there is a distortion of 1 Hz and 10 Hz curves as a result of the boundary layer effect and electrode polarization4.
- The ‘Flat top’ of distorted data suggests that the measurements are out of range for the instrument.
- The dominance of frequency independent resistivity (ρFI) is demonstrated by curves that overlap or almost overlap.
- Produced by the flow of mobile ions, known as true ion viscosity.
- The change of ρFI is frequently proportional to the change of viscosity prior to gelation.
- After gelation, the change of ρFI is frequently proportional to the modulus change.
- The dominance of frequency dependent resistivity (ρAC) is demonstrated by curves that diverge.
- Produced by the rotation of dipoles.
- Does not correspond well with cure state.
Electrode polarization distorts the 1 Hz and 10 Hz data during early cure, which should be ignored. At the higher excitation frequencies, measurements exhibit no distortion and accurately determine the minimum ion viscosity.
The remaining frequency independent resistivity is shown in Figure 5 after the data dominated by a dipolar response and the data affected by electrode polarization is algorithmically removed by the software. This data can now be accurately called ion viscosity and correctly corresponds to cure state for the duration of the test.
The ion viscosity curve shown in Figure 5 is a combination of frequencies from 1 Hz to 10 kHz. For convenience, the data from only one or two frequencies is sufficient and can be used to replace a composite of several frequencies.
Figure 5. Ion viscosity following entire cure of PR520 epoxy. Image Credit: Lambient Technologies
DC Cure Monitoring of PR520
A standard circuit for DC cure monitoring is depicted in Figure 6, like the one employed in the LT-440 Dielectric Channel.5 The resistance, RMUT, of the Material Under Test can be determined with the subsequent expression:
|RMUT = RL ( [ VDC / VL ] – 1 )
With the cell constant of the sensor, or the A/D ratio, the ion viscosity is calculated by:
|IV = RMUT ( A/D )
Figure 6. Typical DC resistance measurement circuit for cure monitoring. Image Credit: Lambient Technologies
An ideal resistance corresponds to current and terminal voltage by Ohm’s law. If the resistance does not change with the magnitude of applied voltage, it is linear. If the DC resistance of a thermoset resin performed in an ideal manner, the calculated RMUT would be the same regardless of the VDC or RL value.
A sequence of tests monitored the isothermal cure of PR520 at 180 °C. DC resistance was analyzed with an LT-440 Dielectric Channel with load resistances of 2 Gohm, 200 Mohm, 50 Mohm and 10 Mohm and a VDC of 4.0 V. The data acquired was converted to ion viscosity (resistivity) utilizing Equation 3 and are displayed in Figure 7.
AC cure was monitored by an LT-451 Dielectric Cure Monitor and the subsequent ion viscosity curves for 4.0 V and 1.0 V excitation amplitude have been included for reference.
This data demonstrates that regardless of the excitation voltage amplitude, AC ion viscosity measurements are the same. As it is independent of both amplitude and frequency, AC ion viscosity performs as an ideal resistance and corresponds with material state during the complete cure.
In contrast, DC ion viscosity (DC resistivity) exhibits significant variation among measurements with various load resistances from early through to mid cure. At this time, DC ion viscosity is significantly and consistently higher in comparison to AC ion viscosity. Both AC and DC measurements converge at the end of cure only, after t = 35 minutes.
Figure 7. DC resistivity during cure of PR520 epoxy at 180 °C. Image Credit: Lambient Technologies
In other resin systems, DC resistance measurements demonstrate overall behavior that corresponds to PR520. DC ion viscosity throughout the cure of five-minute epoxy is displayed in Figure 8.
Figure 8. DC resistivity during room temperature cure of five-minute epoxy. Image Credit: Lambient Technologies
Plotted for reference, AC curves are essentially the same for excitation amplitudes of 1 V and 4 V, proving that AC ion viscosity for five-minute epoxy performs as an ideal resistance.
The results for alternative resin systems indicate that the differences between AC and DC measurements could be a widespread phenomenon. The variation is greatest at the beginning of cure and gradually decreases towards the end of cure. It is presumed that this effect is the result of an electrochemical reaction.
While the nature of the electrochemistry is unknown, the variation between the DC and AC ion viscosity can be modeled as an additional resistance in series with the capacitance (CMUT) and existing resistance (RMUT) of the Material Under Test. As displayed in Figure 9, this DC electrochemical resistance decreases over time and emerges solely under DC bias.
Figure 9. Circuit model of a thermoset resin with DC electrochemical resistance. Image Credit: Lambient Technologies
Transient Effects During DC Cure Monitoring
Transient reactions in DC ion viscosity at the start of cure are depicted in Figure 10. The model of Figure 9 would generate this behavior as a result of capacitance CMUT charging through the DC electrochemical resistance.
The standard determination of DC resistance from measured voltage assumes a circuit only of resistance and would generate an inaccurate result. In practice, the transient effect only emerges at the start of cure when material suddenly experiences the fast application of DC bias or contacts the sensor.
Data from this early stage can be ignored, and the loss of data may be sufficient if the user is mainly interested in the latter phases of cure.
Figure 10. Transient response of curing PR520 at 180 °C. Image Credit: Lambient Technologies
Model of DC Cure Behavior
It is evident that the electrochemical resistance describes the temporary along with the total resistance during DC cure monitoring. The following expression can be used to encompass both behaviors for DC and AC ion viscosity:
|IVDC(t) = IVAC(t) • ( [ ( 1 – C1 e-t/T1) • C0 e-t/T0 ] + 1 )
IVDC(t) = DC ion viscosity
IVAC(t) = AC ion viscosity
C0 = Coefficient during steady state cure
C1 = Coefficient during transient response
t = Time
T0 = Time constant during steady state cure
T1 = Time constant during transient response
The model of Equation 4 has been plotted against the actual PR520 DC ion viscosity in Figure 11.
Figure 11. Model fit to DC cure data of PR520, 180 °C isothermal cure. Image Credit: Lambient Technologies
Figure 12. Model fit to DC cure data of five-minute epoxy, room temperature cure. Image Credit: Lambient Technologies
Figure 12 similarly compares the data and model for five-minute epoxy, validating the generality of the DC electrochemical resistance model for various materials.
While AC resistance correctly probes the complete cure of composites and thermosets, DC resistance displays discrepancies when compared to AC in early to mid-cure.
AC and DC results correspond during end of cure which shows how DC methods can also quantify cure state but must be carefully used with an understanding of their constraints.
The amplitude of the sinusoidal drive voltage does not affect the AC resistance of thermoset resins. AC resistance functions as an ideal, linear electronic component when it is also frequency independent.
In line with the standard electrical model of a resin, the variation in this amplitude independent, frequency independent resistivity, corresponds to the change in modulus after gelation and corresponds to the change in viscosity before gelation.
Opposed to AC resistance, the DC resistance of resins do not perform ideally for large portions of cure, varying with the details of the measurement circuit and the magnitude of the applied DC bias.
A current-driven electrochemical reaction is likely to be the cause of the discrepancies in DC measurements. While the nature of the electrochemistry is not understood, a DC electrochemical resistance can be added to the standard model of a resin to reproduce the DC response during cure, as displayed in Figure 13.
This DC electrochemical resistance reduces over time with an exponential rate law and is in proportion to the concentration of unreacted monomers.
An increase in viscosity at the start of cure has incorrectly been attributed to the transient effects in DC measurements. In Figure 9, the DC model demonstrates this transient behavior is the result of the charging of material capacitance through the DC electrochemical resistance.
Agreement between the data and DC model suggests that this electrochemical resistance causes both the temporary and overall behavior of DC measurements during cure.
Figure 13. AC and DC electrical models of thermoset resins. Image Credit: Lambient Technologies
References and Further Reading
- Mini-Varicon sensor, manufactured by Lambient Technologies, Cambridge, MA USA. https://lambient.com.
- Cycom PR520N RTM manufactured by Solvay, Brussels, Belgium.
- LT-451 Dielectric Cure Monitor, manufactured by Lambient Technologies, Cambridge, MA USA.
- Day, D.R.; Lewis, J.; Lee, H.L. and Senturia, S.D., “The Role of Boundary Layer Capacitance at Blocking Electrodes in the Interpretation of Dielectric Cure Data in Adhesives,” Journal of Adhesion, V18, p.73 (1985).
- LT-440 Dielectric Channel, manufactured by Lambient Technologies, Cambridge, MA USA.
This information has been sourced, reviewed and adapted from materials provided by Lambient Technologies.
For more information on this source, please visit Lambient Technologies.