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. 2019 Dec 6;10:5590. doi: 10.1038/s41467-019-13461-2

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© The Author(s) 2019

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 2 — The electrical conductivity of composite threads was improved under compression. a The electrical conductivity σ of both n-type and p-type threads were improved with increasing applied compression pressures p in a log-linear plot. b, c Log-log plots demonstrate an asymptotic power-law relation between conductivity and pressure at high pressures. For the pure theoretical power-law fit line (central gray dash) the volume fraction is equal to the critical value with power-law exponent s = 0.87 (0.90) for p- (n-) type threads according to modified percolation theory in Eq. 2. The downward trend of experimental data matches the fit lower gray dash curve, implying that the initial concentration is just below the percolation threshold for conduction Φ(0) < Φ_c. Conversely, if the conductivity were to saturate at low pressure (upper gray dash curves), this would imply that the initial concentration exceeded the percolation threshold Φ(0) > Φ_c.