Various dielectric materials used in capacitor industry can be considered as two-phase systems such as polymer capacitors filled with ceramic particles (3-1 composites). Even pure ceramic capacitors often behave as two-phase systems because of significant differences between the physical properties of the grain and the physical properties of the grain boundaries. Hence, to better understand the electrical properties of the overall system, the contributions of the individual phases should be distinguished. Regarding polymer-particle composites for electronic applications, although the dielectric properties of the polymeric phase can be measured simply using a bulk sample, it remains a challenging task to determine the dielectric properties of ceramic filler particles.
Various approaches have been used to estimate the dielectric constant of ceramic particles. One such approach arises from electrical characterization of sintered dense ceramic materials. This approach allows precise characterization of the sintered material, but cannot be used to estimate the dielectric properties of loose ceramic particles. For example, internal stresses within the polycrystalline sintered ceramics could unpredictably influence the local dielectric properties of the material, whereas loose particles in the form of powders are not mechanically constrained. Furthermore, the dielectric properties of particles in nanometer size scale may be significantly different than those in micrometer size scale. Although the dielectric properties of sintered ceramics as a function of grain size are widely studied, such investigations for particulate materials have been limited mainly due to the lack of reliable characterization methods to determine the permittivity of particulate materials.
Another approach to estimate the dielectric properties of particles is to conduct capacitance measurements on powder compacts or slurries (particles suspended in a liquid) as two-phase systems, followed by application of theoretical models based on mixing rules. In particular, the Lorentz-Lorenz equation allows estimating effective dielectric constant ∈eff of a two component composite composed of uniformly distributed spherical particles with dielectric constant ∈1 and volume fraction χ1 in the host media with dielectric constant ∈2:
                                                        ɛ              eff                        -                          ɛ              2                                                          ɛ              eff                        +                          2              ⁢                              ɛ                2                                                    =                              x            1                    ⁢                                                                      ɛ                  1                                -                                  ɛ                  2                                                                              ɛ                  1                                +                                  2                  ⁢                                      ɛ                    2                                                                        .                                              (        1        )            Unfortunately, powder compacts do not represent an ideal system for which the mathematical models such as Eq. (1) would be applicable. The effective dielectric constant of the compact is highly sensitive to particle-particle interaction, which can lead to errors in estimation of the permittivity of particles based on mixing rules.
Characterization of slurries may be a more suitable approach to evaluate the dielectric constant of particles. In slurries the particles are dispersed in a liquid so that the application of Lorentz-Lorenz equation (1) would be more reasonable. Using liquids with a high dielectric constant ∈2 would result in more accurate estimation of ∈1 for particles with high dielectric constant (>1000) such as ferroelectrics. However, availability of liquids with sufficiently high permittivity is limited (∈2˜70 for propylene carbonate or other highly polarizable liquids) so that calculating the permittivity of particles from the effective dielectric constant of slurry may involve high margin of errors.
In several studies, dielectric measurements using slurries are conducted at high frequency (10-20 MHz range) to ensure low dielectric losses so that the effective medium theory [such as Lorentz-Lorenz equation (1)] would be applicable. However, the dielectric constant of the slurry ∈eff should be measured very precisely with an accuracy of several decimal points in order to be able to calculate the dielectric constant of particles ∈1 with an acceptably small margin of error. Other factors affecting the reliability of measurements using slurries include size, shape, agglomeration, and sedimentation of the particles. Non-ideal slurries with respect to particle dispersion could lead to significant errors in the calculated value of the dielectric constant of particles ∈1. Hence, the theoretical models have been modified by introducing various parameters based on, e.g., particle shape and size factors to minimize deviations of slurries from ideal systems. Lorentz-Lorenz equations or fine element models which are modified by incorporating such parameters are used to calculate the dielectric constant ∈1 of particles. The effects of introducing multiple parameters and correction factors into a measurement technique already requiring high accuracy are to render the calculated dielectric constant values inherently suspect.
Thus, there remains a need for a technique or means for measuring the dielectric constant of insulative particles, such as ceramic, polymer, and/or biological particulate materials. The present invention addresses this need.
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