Electronic Supplementary Material

Multiaxial electrospun generation of hollow graphene aerogelspheres for broadband high-performance microwave absorption Tian Li1, Dandan Zhi1, Yao Chen1, Bing Li2, Zuowan Zhou1, and Fanbin Meng1 ()

1 Key Laboratory of Advanced Technologies of Materials (Ministry of Education), School of Materials Science and Engineering, Southwest

Jiaotong University, Chengdu 610031, China 2 Shandong Qiangjunwei Intelligent Equipment Co. LTD., Yantai 264000, China Supporting information to https://doi.org/10.1007/s12274-020-2632-0

 Figure S1 Optical microscope view of HGAS2

Table S1 Specific surface area, total pore volume, and the most probable pore size of the graphene aerogel in recent literatures

Sample Specific surface

area (m2/g) Pore volume (cm3/g) Ref.

Graphene aerogel fibers 884 5.85 [S1] SnS2-ND@G-aerogel

GAF 132 584

- 2.27

[S2] [S3]

GA 358 0.44 [ S4] Ni–MnO/rGO aerogels CoOx/Graphene aerogel

carbon sphere-graphene polylithic aerogels N-doped graphene aerogel

Ordered Mesoporous Carbon/Graphene aerogel GAS

109 1359

609.3

420

1030

1634.7

- 7.2

1.41

0.399

1.30 1.64

[ S5] [S6]

[S7]

[S8]

[S9]

This work HGAS2 2367.6 2.69 This work

[S1] Xu, Z.; Zhang, Y.; Li, P. G.; Gao, C. Strong, conductive, lightweight, neat graphene aerogel fibers with aligned pores. ACS Nano 2012, 6, 8

7,103–7113. [S2] Luo, L.; Chung, S. H.; Manthiram, A. A three-dimensional self-assembled SnS2-nano-dots@graphene hybrid aerogel as an efficient polysulfide

reservoir for high-performance lithium–sulfur batteries J. Mater. Chem. A 2018, 6, 7659–7667. [S3] Li, G. Y.; Hong. G.; Dong, D. P.; Song, W. H.; Zhang, X. T. Multiresponsive graphene–aerogel–directed phase–change smart fibers. Adv. Mater.

2018, 30, 1801754. [S4] Hu, S.; Han, T.; Lin, C.; Xiang, W. K.; Zhao, Y. H.; Gao, P.; Du, F. P.; Li, X. P.; Sun, Y. H.. Enhanced electrocatalysis via 3D graphene aerogel

engineered with a silver nanowire network for ultrahigh–rate Zinc–Air Batteries. Adv. Funct. Mater. 2017, 27, 1700041.

Address correspondence to mengfanbin_wing@126.com

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[S5] Fu, G. T.; Yan, X. X.; Chen, Y. F.; Xu, L.; Sun, D. M.; Lee, J. M.; Tang, Y. W. Boosting bifunctional oxygen electrocatalysis with 3D graphene aerogel-supported Ni/MnO particles. Adv. Mater. 2018, 30, 1704609.

[S6] Xia, W.; Qu, C.; Liang, Z. B.; Zhao, B. T; Dai, S, G,; Qiu, B.; Jiao, Y.; Zhang, Q. B.; Huang, X. Y.; Guo, W. H.; Dang, D.; Zou, R. Q.; Xia, D. G.; Xu, Q.; Liu, M. L. High-performance energy storage and conversion materials derived from a single metal–organic framework/graphene aerogel composite. Nano Lett. 2017, 17, 2788–2795.

[S7] Dong. D. P.; Guo, H. T.; Li, G. Y.; Yan, L. F.; Zhang, X. T.; Song, W. H. Assembling hollow carbon sphere-graphene polylithic aerogels for thermoelectric cells. Nano Energy 2017, 39, 470–477.

[S8] Wang, J.; Duan, X. G.; Dong, Q.; Meng. F. P.; Tan, X. Y.; Liu, X. M.; Wang, S. B. Facile synthesis of N-doped 3D graphene aerogel and its excellent performance in catalytic degradation of antibiotic contaminants in water. Carbon 2019, 144, 781–790.

[S9] Liu, R. L.; Wan, l.; Liu, S. Q.; Pan, L. X.; Wu, D. Q.; Zhao, D. Y. An interface-induced Co-assembly approach towards ordered mesoporous carbon/ graphene aerogel for high-performance supercapacitors. Adv. Funct. Mater. 2015, 25, 526–533.

 Figure S2 TEM image of HGAS2

 Figure S3 Optical microscope view of HGAS1 with a diameter of about 1.5 mm (a), HGAS3 with a diameter of about 2.5 mm (b) and HGAS4 with a diameter of about 3.0 mm

 Figure S4 Optical microscope view of BGAS1 with a diameter of about 2.0 mm (a), BGAS3 with a diameter of about 3.0 mm (b) and HGAS4 with a diameter of about 3.5 mm

 Figure S5 3D representation of RL values at different thickness (a-e), effective bandwidth at 2.1, 2.3, 2.6, 2.8, 3.0 and 3.4 mm respectively (f), 3D plots of minimum reflection loss evaluation of HGAS1, HGAS3, HGAS4, BGAS1 and BGAS3 respectively (g), effective bandwidth of BGAS3 at 2.7 mm and reflection loss at 2.1 mm.

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 Figure S6 Plots of εc″ and εp″ vs frequency of graphene aerogel spheres

Appendix: For competition of both relaxation and conductance losses, Non-linear least squares fitting method is applied to fit a curve. According to this theory, the model function in this work is ε=ε∞+(εs-ε∞)/(1+ω2τ2)- i ( (εs-ε∞) ωτ/(1+ω2τ2)+σ/(ωε0)), where ε∞ is optical dielectric constant, εs is static dielectric constant, ε0 is free space dielectric constant, τ is the relaxation time and σ is the conductivity.

To obtain εc" and εp", the εs, ε∞, σ and τ should be fitted firstly, which are signed as a group β. The sum of squares is 2

1

mii

S r=

=å , where ri presents εfit-ε. Our goal is minimizing the S by adjusting β. In order to fit these data as precise as possible, the original data are divided into twenty parts and fitted separately. The average value is used as the final result. As well, we use a Python package Scipy* to simplify our code.

import numpy as np from scipy.optimize import least_squares import xlrd def realimag(array): return np.array([(x.real, -x.imag) for x in array]) def func(x,p):

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s,u,sigma,t=p #s:static dielectric constant;u:optical dielectric constant;sigma:conductivity;t:relaxation time d=complex(0,1) o=8.854187817*10**(-12) return realimag( u+(s-u)/(1+x*x**t*t) -np.dot(d,np.dot(np.dot(x,t),np.divide((s-u),(1+np.dot(np.dot(np.dot(x,x),t),t)))))

-np.dot(d,np.divide(sigma,np.dot(x,o))) ) def condut_loss_result(x,p): s,u,sigma,t=p o=8.854187817*10**(-12) return np.divide(sigma,np.dot(x,o)) def residuals(p,y,x): return (realimag(np.array(y)) - func(x, p)).flatten() p0 = [20,10,1,10**-12] data=xlrd.open_workbook('original_data.xlsx') data_number=200 groups=20 table=data.sheets()[3] fcost=0 fsig=0 #fitting conductivity ft=0 #fitting relaxation time fplsq=[] fs=0 #fitting static dielectric constant fu=0 #fitting optical dielectric constant fconduct_loss=0 #fitting conducting loss frelaxation_loss=0 #fitting polarization loss for i in range(1,int(groups)+1): end=i*(int(data_number/groups)) start=end-int(data_number/groups) #print("Reading data group",i,": from ",start," to ",end) xdata=table.col_values(0)[start:end] ydata_1=table.col_values(2)[start:end] #imaginary permitivity ydata_2=table.col_values(1)[start:end] #real permitivity ydata=[] for m in range(int(data_number/groups)): xdata[m]=xdata[m]*10**9 # GHz ydata.append(complex(ydata_2[m],-ydata_1[m])) plsq = least_squares(residuals, p0, bounds=([0,0,0,0],[200,200,200,10**-1]),args=(ydata, xdata),max_nfev=100000) fplsq.append(plsq) print(plsq.x[0]," ",plsq.x[1]," ",plsq.x[2]," ",plsq.x[3]," ") conduct_loss=np.mean(condut_loss_result(xdata,plsq.x)) #print("Conduct_loss ",i,":",conduct_loss) fconduct_loss += conduct_loss relaxation_loss=np.mean(ydata_1)-conduct_loss #print("Relaxation_loss",i,":",relaxation_loss) #print("Imaginary:",np.mean(ydata_1),", Conduct Loss:",conduct_loss,", Relaxation Loss:",relaxation_loss) #print(np.mean(xdata)/10**9," ",np.mean(ydata_1)," ",conduct_loss," ",relaxation_loss)

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frelaxation_loss += relaxation_loss fsig=fsig+plsq.x[2] fs=fs+plsq.x[0] fu=fu+plsq.x[1] ft=ft+plsq.x[3] fcost=plsq.cost+fcost 

 Figure S7 the calculated delta value maps of HGAS1 (a), HGAS3 (b), HGAS4 (c), BGAS1 (d), and BGAS3 (e), respectively.