L-280 Mixing Rules for Energetic Materials: Transport Properties

April 2022
Paul Schrama (NLDA), Kevin M. Jaansalu (MSIAC)
In great many cases the properties of energetic materials have not been obtained by measurement. Therefore they have to be estimated by mixing rules for the technical literature, which are often not validated and it is often unknown which mixing rule works best. This study provides insight and recommendations of the usage of the mixing rules for a selection of these composite properties, consisting of electric conductivity, dielectric constant and thermal conductivity.
The experimental values of energetic and non-energetic materials have been compared with the predictions by various mixing rules, such as the Maxwell, Dobratz, and Bruggeman equations. Besides, for composites with more than one filler, the equations are interpolated, according to the Toop model. Finally, the predictions are reviewed and the best predicting mixing rules are presented.
For electrical conductivity, none of the reviewed mixing rules takes percolation into account. There is evidence that for a non-conducting matrix, the Agari and Uno equation (or simply a logarithmic sum) provided reasonable estimates. For the prediction of the dielectric constant, the three equations examined gave comparable results.  The Poon and Shin equation may be preferred as it is explicit and provided slightly better estimates than the Dobratz equation.  Finally, the predictions by the Agari and Uno (with C1 and C2 equal to 1) gave the best predictions for thermal conductivity, with an average deviation of 24% for two filler energetic composite materials. 
Therefore, the recommendations are to: first, conduct more research for electrical conductivity, with more sophisticated mixing rules that do take percolation into account; second, use the Poon and Shin equation for the prediction of the dielectric constant; and third; use the Agari and Uno equation for the prediction of the thermal conductivity. 

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