# Recent results

**(1) A novel equation to precisely predict the conductivity of the ternary composites (Composites Science and Technology, 150, 24-31.)**

The binary CPC system with only one carbon filler can be detailed described already, however, to predict the conductivity of the ternary CPC system was always a challenge due to the interaction between two conductive fillers. In our recent work, a parameter was proposed to describe this interaction as a synergy, and the complete equation can be used to the precisely predict the conductivity of the ternary composites PMMA/CB/CF. Fig. 1 (A) presents logarithm value of conductivity of composite filament vs filler volume fraction of CFs and CB in a waterfall plot diagram. Fig. 1 (B) shows experimental data as filled symbols while the simulation curves with predicted data represented by solid lines.

*Fig. 1 (A) Logarithm value of conductivity of composite filament vs. filler volume fraction of CFs and CB in a waterfall plot diagram (B) Logarithm value of conductivity of composite filament vs. filler volume fraction of CB in a 2-D coordinates system. Filled symbols represent experimental data while solid lines represent the simulation curves with predicted data, where line a-c are chosen to present the volume fraction ratio between CB and CFs.*

**(2) A Novel definition on synergistic effect between CB and CNTs in a ternary CPC system (Nanotechnology, 2019, 30)**

In a recent work from LSP, the ternary PMMA/CB/CNTs composites filament was produced (Fig. 2 (A)). A success validation for binary CPC system is presented in Fig. 2 (B). The 4^{th} synergy and the comparison between the experimental data and the predicted curve are presented in Fig. 2 (C). All the available literature on the synergistic effect between CB and CNTs in a ternary CPC system has been carefully discussed, and a quantifiable “synergasm” between CNTs and CB is defined as the novel 5^{th} synergistic effect in this work.

*Fig. 2 (A) Mor**p**hology of the **Nanoparticles (a) CNTs and (b) CB used in this study; Morphology of the anisotropic ternary CPCs filament with 5.44 vol. % CNTs and 6 vol. %** CB u**sing SEM: (c) the cross-section of the specimen; (d) the cross-section of the specimen along the fiber axis. (B) The logarithm of the conductivity vs. filler volume fraction of CNTs and CB, resp**ectively. The solid lines show the best fit with the GEM equation. (C) Logarithm of the composite conductivity versus volume filler fraction of CNTs and CB in a contour plot. The inset shows experimental- and modelled data along the four dotted lines. (D) The logarithm of **the composite conductivity vs volume filler fraction of CNTs and CB in a contour plot diagram, defining a quantifiable “synergasm” between CNTs and CB. The inset synergism map illu**strates the synergistic effect of the different compositions of CNTs and CB from this study.*

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