Supporting information

Through-plane assembly of carbon fibers into 3D skeleton achieving

enhanced thermal conductivity of a thermal interface material

Jiake Ma a,b, Tianyu Shang a,b，Linlin Ren a, Yimin Yao a, Tao Zhang a, Jinqi Xie a, Baotan Zhang a

Xiaoliang Zeng a*， Rong Sun a, Jian-Bin Xu c, and Ching-Ping Wong d

a Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055,

China

b Department of Nano Science and Technology Institute, University of Science and Technology of

China, Suzhou 215123, China

c Department of Electronics Engineering, The Chinese University of Hong Kong, Hong Kong

999077, China

d School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia

30332, United States

* Corresponding author. Tel: 0755-86392103. E-mail: xl.zeng@siat.ac.cn (Xiaoliang Zeng)

Contents： Figure S1. Length distribution of CFs.

Figure S2. XRD image of carbon fiber before and after surface functionalization.

Figure S3. Optical images of a) epoxy b) epoxy/random CFs composites c) epoxy/oriented CFs

composites.

Figure S4. SEM images of (a) RD-CFs skeleton and (b) fracture morphology of RD-CFs

composites.

Figure S5. SEM fracture micrographs images of epoxy/oriented 3D-CFs network composites

as a function of CF loading.

Figure S6. (a) SEM sectional micrographs images of isotropic 3D-CFs skeleton at CFs loading

of 13.0 vol %. (b) The through-plane thermal conductivity of isotropic 3D-CFs/epoxy resin

composites as a function CFs loadings.

Figure S7. In-plane and through-plane thermal conductivity of 3D CFs/epoxy resin composites

as a function CFs loadings.

Theoretical approach used in the data analysis for composites with CF random dispertion.

Figure S8. Schematic illustration of a composite unit cell of a carbon fiber. The transverse and

longitudinal equivalent thermal conductivities, K11cand K33

c.

Theoretical approach used in the data analysis for composites with oriented CFs

dispertion.

Figure S9.EMT model fitting of epoxy/oriented 3D-CFs composites with the nonlinear fitting

method. The a of fitting table is K0∼11.66 W m−1 K−1 and the b is β∼0.70.

Figure S10. Raw thermomechanical analysis curves of different CFs loading epoxy/ random

CFs composites and epoxy/oriented CFs network composites.

Figure S11. Storage modulus vs. temperature for the cured pure epoxy and its 3D-CFs

composites at different filler loadings.

Figure S1. Length distribution of CFs.

Figure S2. XRD patterns of carbon fiber before and after surface functionalization.

Figure S3. Optical images of a) epoxy b) epoxy/random CFs composites c) epoxy/oriented CFs

composites.

Figure S4. SEM images of (a) RD-CFs skeleton and (b) fracture morphology of RD-CFs

composites.

Figure S5 SEM fracture micrographs images of epoxy/oriented 3D-CFs network composites as a

function of CF loading.

Figure S6. (a) SEM sectional micrographs images of isotropic 3D-CFs skeleton at CFs loading of 13.0 vol %. (b) The through-plane thermal conductivity of isotropic 3D-CFs/epoxy resin composites as a function CFs loadings.

Figure S7. In-plane and through-plane thermal conductivity of 3D CFs/epoxy resin composites

as a function CFs loadings.

Theoretical approach used in the data analysis for composites with random CFs dispertion

Figure S8. Schematic illustration of a composite unit cell of a carbon fiber. The transverse and

longitudinal equivalent thermal conductivities, K11cand K33

c.

For the random CF/epoxy composites with small loading of CF, the effective medium theory

(EMT) is valid. In the CF composites, the thermal conductivity K c of the CF is much larger than

that K m of the matrix , and the aspect ratio p of the CF is high. According to the EMT, the resultant

effective thermal conductivity K e of the CF composite with CF randomly dispersed in a matrix can

be derived as

K e

Km=

3+V f (βx +βz )3-f βx

(1)

With

βx=2(K11

C −Km)K11

C +Km

, βz=K33

C

Km−1(2)

Where Vf is the volume fraction of the CF, K 11c and K 33c are, respectively, the equivalent

thermal conductivities along transverse and longitudinal axes of a composite unit cell and can be

expressed as

K11C =

K c

1+2 aK K c

d Km

, K 33C =

K c

1+2 aK K c

L Km

(3)

where d and L (p=L/d) are the diameter and length of the CF, respectively; and a K is a so-called

Kapitza radius defined by

ak =Rk ×Km (4)

Equation (1) is a desired EMT formulation for the thermal conductivity enhancement of the CF

composites, which contains the effects of the diameter, aspect ratio, and volume fraction of the CF,

interface thermal resistance, and thermal conductivity ratio K c /K m , on the effective thermal

conductivity of the CF composites. Eq. (1) for the thermal conductivity enhancement is simplified

as

K e

Km=1+

Vf ×p3

×Kc /Km

p+2ak

d×

Kc

Km

(5)

Theoretical approach used in the data analysis for composites with oriented CFs dispertion

The average aspect ratio p=32.5 (L/D). Using Foygel’ results and Monte Carlo simulations, for

large α≫1, the Vc is inversely proportional to α.

Vc (α≫1)≈ 0.60α

(6)

Then Vc=0.018.

Figure S9. EMT model fitting of epoxy/oriented 3D-CFs composites with the nonlinear fitting

method. The a of fitting table is K0∼11.66 W m−1 K−1 and the b is β∼0.70

Figure S10. Raw thermomechanical analysis curves of different CFs loading epoxy/ random CFs

composites and epoxy/oriented CFs network composites.

Figure S11. Storage modulus vs. temperature for the cured pure epoxy and its 3D-CFs composites

at different filler loadings