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Carbon-Loaded Polymer Composites Used as Human Phantoms: Theoretical Modeling for Predicting Low-Frequency Dielectric Behavior.



Richard G. Geyer, James R. Baker-Jarvis, Michael D. Janezic, Raian K. Kaiser


Conductive carbon black-loaded polymers are considered for use as semi-solid biologic phantom materials. Adapted forms of Clausius-Mossoti, Maxwell-Garnett, and Bruggeman predictive dielectric mixing rules are considered that take into account disordered cluster topologies of the conductive particles in a metal-dielectric composite. The disordered cluster suspensions can lead to rapid, nonlinear increases of permittivity and conductivity at volume loading fractions far below the close-packing limit, where the percolation threshold would normally be expected in well-stirred metal-dielectric composites. The measured low-frequency electrical properties of fabricated carbon-black loaded silicone composite exhibit a threshold percolation at carbon loading fractions of one-third the close-packing limit. This conductivity and permittivity behavior is predicted by an adapted form of the classical Bruggeman rule that takes into account the cluster topology of the carbon black particles in the fabricated composites. Conductivity measurements of carbob black-loaded silicone polymer composites from 10-25'C exhibits a temperature behavior similar to that of a extrinsic, partially compensated n-type semiconductor. The measured conductivity temperature dependence can be related to the conduction band density of states, as well as donor and acceptor concentrations in the composite. A large positive temperature coefficient with respect to resistance as observed at temperatures greater than 40'C for the 7% carbon black loaded silicon composite, consistent with non-percolative behavior at these temperatures.
Technical Note (NIST TN) - 1529
Report Number


polymer phanton materials., carbon black, clusters, conductivity, effective medium theory, metal-dielectric composites, percolation, permittivity


Geyer, R. , Baker-Jarvis, J. , Janezic, M. and Kaiser, R. (2003), Carbon-Loaded Polymer Composites Used as Human Phantoms: Theoretical Modeling for Predicting Low-Frequency Dielectric Behavior., Technical Note (NIST TN), National Institute of Standards and Technology, Gaithersburg, MD (Accessed April 19, 2024)
Created May 31, 2003, Updated October 12, 2021