Dielectric Analysis Theory
Here are some common terms and definitions used in the study of dielectric analysis.
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
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
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.
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.
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.
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.
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.
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.
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...
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.
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.
Calculating loss factor and Ion Viscosity
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.
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 ....