Comparison of different thermal conductivity models with one specific electrical conduction model to elucidate differenc
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Comparison of different thermal conductivity models with one specific electrical conduction model to elucidate differences between thermal and electrical conduction in polymer composites Richard D. Sudduth1,* 1
Materials Research and Processing, LLC, 3718 Dunlin Shore Court, Peachtree Corners, GA 30092, USA
Received: 19 May 2020
ABSTRACT
Accepted: 7 September 2020
The Modified Maxwell model developed to fit thermal conductivity data in this study was found to yield the same end points independent of the value of the single adjustable constant, s, utilized. This model ranges from the thermal conductivity of the base polymer at zero concentration to the thermal conductivity of the filler at 100% filler for all values of s chosen. Surprisingly, the Modified Maxwell model was found to describe a reasonably good fit of different sets of thermal conduction data using only one adjustable constant. The Modified Geometric Mean Model introduced in this study also typically fits thermal conduction data quite well using only one adjustable constant. However, the upper concentration limit for the Modified Geometric Mean Model does not necessarily yield the conductivity of the filler. While a large number of the thermal conduction models were evaluated in this study with the same limits as the Modified Maxwell model, most of these other models did not fit the thermal conduction data very effectively. In general, the Percolation Threshold model developed by this author gave an excellent fit for measurements of both thermal conductivity data and electrical conductivity data. However, major differences were found between the components of the Controlling Conductivity Function, F(u), for this model for each of the two different forms of conductivity measurements. It was also found that a difference in the interfacial surface energy appears to play a major role in the difference between these different forms on conductivity measurements in composites.
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Springer Science+Business
Media, LLC, part of Springer Nature 2020
Address correspondence to E-mail: [email protected]
https://doi.org/10.1007/s10854-020-04457-6
J Mater Sci: Mater Electron
1 Introduction
Some of the models included in Fig. 1 can be described in general form as
Several reviews of thermal conducting models for composites have recently appeared in the literature [1–4]. In addition, several other useful reviews of thermal conducting models for composites have previously appeared in the literature [5, 6]. Some of the more well-known thermal conductivity models have been summarized by Ngo et al. [1] and these models [7–18] are summarized in Table 1. For reference the equation variables for the models indicated in Table 1 would include
r 1 þ sgu ; ¼ rp 1 gu
ke = effective thermal conductivity (ETC) of composite km= thermal conductivity of matrix material kp = thermal conductivity of a filler particulates / = volume fraction of filler particulates /m = maximum volume fraction of filler particulates In general, the models indicated in Table 1 are of
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