Lambient

Dielectric Analysis Theory

Terms and Definitions

Here are some common terms and definitions used in the study of dielectric analysis.
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Electrical Modeling of Polymers

The dielectric—literally “two-electric”—properties of conductivity s, and permittivity e, arise from ionic current and dipole rotation in bulk material. For polymers, mobile ions are often due to impurities and additives, while dipoles result from the separation of charge on nonpolar bonds or across a molecule. When analyzing dielectric properties, it is possible and convenient to separate the influence of ions from dipoles to consider their individual effects.
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Basics of Thermoset Cure and Dielectric Measurements

Thermosets are an important class of materials used for adhesives, coatings and composites. They include epoxies, (poly)urethanes, acrylics, phenolics, vinyl esters, silicones and many other compounds. Uncured thermosets, or A-stage materials, are composed of small molecules called monomers
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Measuring Degree of Cure with DEA

Data from dielectric cure monitoring (DEA) correlate with glass transition temperatures ( Tg ) obtained from differential scanning calorimetry (DSC). In many cases a linear relationship exists between log(ion viscosity) and Tg. Dielectric measurements can be converted to Cure Index, which is a reproducible indicator of the state of cure. For some materials, Cure Index closely follows the degree of cure, , calculated by the DiBenedetto equation, which uses glass transition temperature information.
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Dielectric Measurement Techniques

Dielectric instrumentation measures the conductance G (or resistance R) and capacitance C between a pair of electrodes at a given frequency. The Material Under Test (MUT) between a pair of electrodes can be modeled as a conductance in parallel with a capacitance.
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Ion Viscosity and Temperature

For the measurement of mechanical viscosity and cure state, ion viscosity (DC resistivity) provides valuable information from a simple electrical measurement. Ion viscosity depends on the mobility of free ions under the influence of an electric field, but also varies with temperature. Therefore, correct interpretation of ion viscosity requires knowledge of temperature at the time of measurement and an understanding of how temperature influences the data. For brevity, ion viscosity will alternatively be called IV.
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Sensor A-D Ratio and Base Capacitance

Measurements of dielectric properties often involve the use of simple parallel plate electrodes. However, their separation can change with pressure, or expansion and contraction of the material between them. The ratio of electrode area A and the distance D between them—the A/D ratio—therefore may not be well known. As the scaling factor between conductance and conductivity, or capacitance and permittivity, uncertainty in A/D causes inaccuracies in determining dielectric material properties.
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Calculating A-D Ratio and Base Capacitance

The cross section of the planar electrodes shown in Figure 15-1 shows that the total capacitance Ctot is the sum of CMUT from the Material Under Test above electrodes and Cbase from the substrate beneath the electrodes. This second component Cbase is called the base capacitance.
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Parallel Plate Measurements

Dielectric instrumentation measures the electrical properties of the Material Under Test (MUT) between a pair of electrodes, which can be modeled as a conductance in parallel with a capacitance.
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Data Processing for the Floating Electrode Configuration

Both the LT-451 and LTF-631 dielectric cure monitors use the floating electrode configuration of Figure AN 5-1 for sensor measurements. Calculating dielectric properties from raw measurements consists of the following steps...
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Dielectric Measurements, Viscosity and Critical Points

Dielectric cure monitoring measures the bulk conductance and capacitance of Material Under Test (MUT), which are used to calculate the material properties of conductivity and permittivity.
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Linear vs. Logarithmic Scales - Seeing all the Data

During cure, the conductance GMUT of a thermoset between the electrodes of a sensor changes by several orders of magnitude. Before processing starts, conductance is normally low because the material is either in a solid state or is at a temperature too low for significant crosslinking. Typically the thermoset is cured by heating to an elevated temperature. As the material becomes warm and softens, the conductance increases. The rate of crosslinking increases with temperature, also, and at some point its influence dominates and the material begins to harden—conductance reaches a maximum at this time then decreases as the material becomes more viscous then rigid. By the end of cure the conductance may have decreased by a factor of 100 or more from its peak value. Plotting conductance on a logarithmic scale is the optimum method for seeing all the information available from dielectric measurements.
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Loss Factor and Ion Viscosity

Calculating loss factor and Ion Viscosity
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Critical Point Detection and Signal Processing

The dielectric cure curve is characterized by four Critical Points:

• CP(1)—A user defined level of ion viscosity that is typically used to identify the onset of material flow at the beginning of cure.

• CP(2)—Ion viscosity minimum, which typically also corresponds to the physical viscosity minimum. This Critical Point indicates the time when the crosslinking reaction and resulting increasing viscosity begin to dominate the decreasing viscosity due to melting.

• CP(3)—Inflection point, which identifies the time when the crosslinking reaction begins to slow. CP(3) is often used as a signpost that can be associated with gelation.

• CP(4)—A user defined slope that can define the end of cure. The decreasing slope corresponds to the decreasing reaction rate. Note that dielectric cure monitoring continues to reveal changes in the evolving material past the point when mechanical measurement of viscosity is not possible.
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Electrode Polarization and Boundary Layer Effects

When the incorrect model is used to determine dielectric properties, low frequency measurements of highly conductive materials may appear to have unusually low conductivity. This phenomenon is caused by electrode polarization, the accumulation of charge against the electrodes, which occurs when the material under test ....
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