Supporting Information for Multifunctional bi-continuous composite foams with ultralow percolation thresholds Jiabin Xi 1,, Yingjun Liu 1,, Ying Wu 1,4, Jiahan Hu 1, Weiwei Gao 1, Erzhen Zhou 1,3, Honghui Chen 2, Zichen Chen 3, Yongsheng Chen 2 & Chao Gao 1, * 1 MOE Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Zhejiang University, 38 Zheda Road, Hangzhou 310027, China 2 The Centre of Nanoscale Science and Technology and Key Laboratory of Functional Polymer Materials, State Key Laboratory and Institute of Elemento-Organic Chemistry, College of Chemistry, Nankai University, Tianjin, 300071, China. 3 Department of Mechanical Engineering, Zhejiang University, 38 Zheda Road, Hangzhou 310027, China 4 School of Material Science and Engineering, University of Science and Technology Beijing, 30 Xueyuan Road, Beijing 100083, China E-mail: chaogao@zju.edu.cn The authors contributed equally to this paper. S-1
Figure S1. SEM images of (a) the surface of gbccf-3, and (b) interior of the gbccf-3 with a thickness of 10 mm. S-2
Figure S2. Linear contraction ratios, calculated by (1-original volume/volume after annealing) 1/3, of BCCFs after 1000 C treatment. S-3
Figure S3. Structural model of BCCFs for calculation of percolation thresholds In this structural model, the pores inner the BCCFs are deemed as hollow cubic boxes which are surrounded by the graphene sheets. The lateral size of the graphene boxes are denoted as w, which corresponds to the lateral size of graphene sheets in BCCFs. We assume that the percolation network is formed when the graphene sheets can construct such structural model. Therefore, the percolation threshold of graphene in this model is 100 3 vol % 300 vol % Where Φ c is the percolation threshold, l is the thickness of graphene (0.334 nm), w is the lateral size of graphene sheets (50 10 3 nm). Therefore, the theoretical percolation threshold of gbccfs is 0.002 vol%. S-4
Figure S4. Strain-stress curves of (a) MF and BCCFs; and (b) GAs. S-5
Figure S5. RL curves of (a) sbccf-3; (b) sbccf-5; (c) gbccf-1; and (d) gbccf-7. S-6
Figure S6. Real and imaginary permittivity of (a,b) gbccf-1, and (c,d) gbccf-5 with different compression ratios. S-7
Figure S7. RL curves of gbccf-5 with different compression ratio at an original thickness of 6 mm. S-8
Figure S8. (a) Real and (b) imaginary permittivity curves of gbccf-3 at different compression cycles. S-9
Table S1. Filler content, volume fraction and density of BCCF samples Graphene filler content (mg cm -3 ) Graphene volume fraction vol% MFs BCCF-0.1 BCCF-0.2 BCCF-0.5 BCCF-1 BCCF-3 BCCF-5 BCCF-7 0 0.07 0.14 0.34 0.68 2.04 3.40 4.76 0 0.003 0.006 0.015 0.031 0.093 0.155 0.216 Density (mg cm -3 ) 10.00 10.07 10.14 10.34 10.68 12.04 13.40 14.76 S-10
Table S2. Comparison of microwave absorption performance of BCCFs are previous works. Category of functional fillers Carbon Carbon-magnetic composites Thick- Filler fraction Tested frequency range materials ness wt% (GHz) (mm) RL max Absorption bandwidth (db) (GHz) gbccf-5 0.34 4 2-18 -35 9.0 (9.0-18) gbccf-3 0.20 10 2-18 -13 8.1 (4.3-9.1, 14.7-18) Refs This work Carbon nanotube-graphene foam 0.16 10 2-18 -39.5 16 (2-18) 1 Graphene foam 0.14 9-10 2-18 -30.5 13.9 (4.1-18) 2 HCNFs/CF 15 2.5 2-18 -32 9.8 (9.2-18) 3 Carbon coils CFs 10 3.0 2-18 -30 9.6 (8.4-18) 4 Graphene networks 1 3.5 2-18 -44.5 7.5 (9.3-16.8) 5 Cross-stacking aligned CNT films coated with PANI 70 2.0 2-18 -47.7 4.4 (10.8-15.2) 6 SWCNTs 5 2.0 2-18 -21.9 2.6 (7.5-10.1) 7 Graphene/CuS 5 2.5 2-18 -32.8 2.6 (8.8-12.4) 8 Carbon foam composite 20 2.5 2-18 -45.12 2.5 (6.9-9.4) 9 Cl-CF 67 1 2-18 -12 10 (8-18) 10 Graphite-coated FeNi 40 2.5 2-18 -23 8.5 (9.5 18.0) 11 G-Fe 3 O 4 -Fe-ZnO 20 2.5 2-18 -32.5 6.8 (11.2-18.0) 12 (Fe, Ni-C) nanocapsules 40 2.0 2-18 -26.9 5.7 (12.3 18.0) 13 Cr-Graphene 2.0 32.4 2-18 -32.4 5.6 (12.4 18) 14 Graphene-Fe3O4-SiO2-NiO 25 1.8 2-18 -51.5 5.3 (12.3 17.6) 15 Graphene/MnFe2O4 5 3.0 2-18 -29.0 4.9 (8.0 12.9) 16 Fe3O4-Carbon nanorods 55 2.0 2-18 -27.9 4.7 (13.1-17.8) 17 SiO 2 -Fe 3 O 4 core/shell nanorod array/graphene 20 3.5 2-18 -23.5 4.7 (8.0-12.7) 18 rgo/fe 3 O 4 50 1.7 2-18 -65.1 4.6 (13.4-18) 19 S-11
Graphene/Fe 20 2.5 2-18 -31.5 4.5 (12-16.5) 20 Graphene/carbonyl iron 60 3 2-18 -52.46 4.2 (7.8-12.0) 21 FeCo/C/BaTiO3 40 2 2-18 -41.7 4.2 (9.8-14.0) 22 GN pfe3o4-zno 30 3.0 2-18 -33.8 4.0 (3.7-5.2, 13.3-15.8) 23 Fe3O4-Al2O3-CNCs 25 2.0 2-18 -28.3 3.5 (10.5-14.0) 24 Fe 3 O 4 -graphene 10 3 2-18 ~-21 3.5 (7-10.5) 25 PEDOT-graphene-Co3O4 50 2 2-18 -51.1 3.1 (9.4-12.5) 26 Fe 3 O 4 /graphene 15 1.48 2-18 -30.1 3 (15-18) 27 graphene/poly (3,4-ethylenedioxythiophene) 50 2.9 2-18 -56.5 3 (7.6-10.6) 28 Conductive polymer Conductive polymer-magnetic composites Inorganic dielectric or magnetic materials /Fe 3 O 4 Laminated graphene/ Fe 3 O 4 40 2 2-18 -15.38 2.8 (10.4-13.2) 29 -Fe2O3/MWNTs/PBO 12 2.7 2-18 -32.7 2.7 (11.2-13.9) 30 polypyrrole aerogel 7 2.5 2-18 ~-24 6.20 (10.72-16.92) 31 PEDOT Nanofiber-Graphene 25 2 2-18 -48.1 3.1 (9.2-12.3) 32 Fe 3 O 4 -PEDOT 50 vol% 2.5 1-18 -29 7.2 (10.3-17.5) 33 PANI-BaFe11Ti0.5Co0.5O19 50 2 2-18 -32.5 5.4 (12.1 17.5) 34 PS-P(Py-PyCOOH)-Ni 50 2 1-18 -20.1 4.59 (9.16 13.75) 35 M-BaFe12O19 50 vol% 2 2-18 -28.5 8.7 (9.3-18) 36 Co-CoO 50 1.3 2-18 -90.2 7.2 (10.8-18) 37 Hollow CdSe 70 4 2-18 -31 3.6 (4.0-6.6, 17.0-18) 38 3.1 (3.6-5.4, Fe3O4@SnO2 nanorods 80 4.0 2-18 -27.4 16.2-17.5) 39 BaTiO3 nano-torus 16.7 2.8 2-18 -28.4 3.0 (10.1-13.1) 40 (Mn0.5Co0.5)3O4 16.7 2.5 2-18 -20.7 3.0 (7.4-10.4) 41 BaTiO3 nanowire 16.7 3.0 2-18 -24.6 2.4 (8.0-10.4) 42 TiN 45 3 2-18 -27 1.4 (6.1-7.5) 43 S-12
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