SUPPORTING INFORMATION
Ultrahigh-Aspect-Ratio Boron Nitride Nanosheets Leading to Superhigh In-Plane Thermal Conductivity of Foldable Heat Spreader
Qingwei Yan,a,b Wen Dai,b,c Jingyao Gao,b,c Xue Tan,b,c Le Lv,b,c Junfeng Ying,b,c Xiaoxin Lu,d Jibao Lu*,d,e
Yagang Yao,f Qiuping Wei,g Rong Sun,e Jinhong Yu,b,c Nan Jiang,b,c Ding Chen*,a,h Ching-Ping Wong,i Rong
Xiang,j Shigeo Maruyama,j and Cheng-Te Lin*b,c
a
College of Materials Science and Engineering, Hunan University, Changsha, 410082, P. R. China b
Key Laboratory of Marine Materials and Related Technologies, Zhejiang Key Laboratory of Marine Materials and Protective Technologies, Ningbo Institute of Materials Technology and Engineering (NIMTE), Chinese Academy of Sciences, Ningbo 315201, P.R. China
c Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, P.R. China
d Shenzhen Institute of Advanced Electronic Materials, Shenzhen 518103, China
e Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China
f National Laboratory of Solid State Microstructures, College of Engineering and Applied Sciences, Jiangsu Key laboratory of Artificial Functional Materials, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China.
g
School of Materials Science and Engineering, Central South University, Changsha 410083, P. R. China h
State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha, 410082, P. R. China
i School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, United States
Figure S1. Photographs of BNNS dispersion (a) as-prepared by microfluidization exfoliation and (b)
after standing for 90 days, showing excellent dispersibility of the as-prepared BNNS in ethanol/water mixture.
Figure S2. (a) UV–Vis absorbance at 550 nm of BNNS dispersions with different concentrations in
various solvents. The evolution of (b) absorbance and (c) concentration of BNNS supernatant in
various solvents as a function of storage days (initial concentration: 0.2 mg mL-1). The corresponding
photos: (d) as-prepared and (e) after 20 days. (f) Rapid settlement of h-BN in ethanol/water mixture.
In order to identify the influence of surface tension of the dispersion solvent on the storage stability
mixture (mass ratio = 1:1, 28 mJ m-2), respectively, for comparison.S1, S2 The absorbance at 550 nm in
the UV–Vis spectra was used as indicator to monitor the concentration of BNNS supernatant based on
Lambert–Beer law.S3 In Figure S2a, the as-prepared BNNS dispersions with the same concentration in
different solvents have similar absorbance. The evolution of absorbance (concentration) of BNNS supernatant in different solvents as a function of storage days was monitored, as the results presented in Figure S2b and c. Obviously, the decrease of absorbance (concentration) of BNNS supernatant in ethanol/water mixture (≈ 28%) is much smaller than that in ethanol (≈ 50%) and water (≈ 86%), demonstrating the critical role of the matching of surface tension between BNNS and dispersion solvent, as the images shown in Figure S2d and e. A control experiment was also performed by dispersing h-BN flakes in ethanol/water mixture, and we found that h-BN precipitates rapidly over ten hours, indicating that the sample thickness is also a significant factor to maintain the storage stability, as shown in Figure S2f.
Figure S3. (a) A typical AFM image of a single BNNS prepared under an applied pressure of 125
MPa and (b) the corresponding height profile.
Figure S4. SEM image of h-BN powders with a lateral size of 5 – 15 µm and thicknesses of several
Figure S5. Typical AFM images of a single sheet prepared at different applied pressures of (a) 125,
(b) 100, (c) 75, and (d) 50 MPa, and the (e–h) corresponding height trace curves.
Figure S6. Thickness and lateral size distribution of BNNS prepared under an applied pressure of (a)
Table S1. Comparison of the aspect ratio of the obtained BNNS and the processing time (efficiency)
based on state-of-the-art exfoliation methods.
Method The details
Thickness (nm) Lateral size (nm) Aspect ratio Efficiency (min) Ref. Chemical exfoliation
With molten hydroxides ≈ 4 ≈ 500 125 120 S4
With potassium intercalation
0.9 ≈ 10 ≈ 11 > 600 S5
With molten hydroxides and sonication
≈ 2.9 ≈ 1800 ≈ 621 180 S6
Ball milling
With hydroxide assistance ≈ 2.2 ≈ 1500 ≈ 682 1440 S3
With urea assistance ≈ 2.5 ≈ 100 40 1200 S7
With sugar assistance ≈ 4.4 ≈ 98 ≈ 22 720 S8
Liquid-phase sonication In ionic liquids ≈ 1.5 ≈ 1200 800 480 S9 In chlorosulfonic acid ≈ 2 ≈ 200 100 480 S10 In isopropanol aqueous solution ≈ 2.5 ≈ 1300 520 240 S11 In dimethylformamide ≈ 3 ≈ 300 100 600 S12 Other methods Thermal exfoliation ≈ 0.69 < 200 < 290 ≈ 120 S13 Thermal expansion-assisted sonication ≈ 1.4 ≈ 1600 ≈ 1143 > 4320 S14 Our method Microfluidization 3.1 4650 1500 30 This work
Table S2. The parameters for the calculation of in-plane thermal conductivities of pure PVA and
BNNS/PVA composite films.
Sample Thermal diffusivity (mm2 s-1) Specific heat capacity (J g-1 K-1) Density (g cm-3) Thermal conductivity (W m-1 K-1) BNNS content (wt%) Pure PVA 0.10 ± 0.01 1.43 1.30 0.19 ± 0.02 0 BNNS-1500/PVA 18.37 ± 0.80 1.08 1.66 32.93 ± 1.43 56 20.80 ± 0.90 1.02 1.76 37.34 ± 1.62 65 29.40 ± 1.00 0.96 1.86 52.50 ± 1.79 74 38.10 ± 1.25 0.91 1.95 67.61 ± 2.22 83 BNNS-1000/PVA 15.36 ± 0.75 1.08 1.66 27.54 ± 1.34 56 16.70 ± 0.90 1.02 1.76 29.98 ± 1.62 65 22.90 ± 0.95 0.96 1.86 40.89 ± 1.70 74 28.70 ± 1.10 0.91 1.95 50.93 ± 1.61 83
Figure S7. (a) Through-plane thermal diffusivity (TD) and (b) conductivity (TC) of the composite
films as a function of aspect ratios and contents of BNNS.
Table S3. The parameters for the calculation of through-plane thermal conductivity of the composite
films using BNNS with aspect ratios of 1000 and 1500, respectively.
Sample Thermal diffusivity (mm2 s-1) Specific heat capacity (J g-1 K-1) Density (g cm-3) Thermal conductivity (W m-1 K-1) BNNS content (wt%) BNNS-1500/PVA 0.97 ± 0.05 1.08 1.66 1.74 ± 0.09 56 1.09 ± 0.06 1.02 1.76 1.96 ± 0.11 65 1.55 ± 0.08 0.96 1.86 2.77 ± 0.14 74 2.01 ± 0.11 0.91 1.95 3.57 ± 0.20 83 BNNS-1000/PVA 0.87 ± 0.04 1.08 1.66 1.56 ± 0.07 56 0.95 ± 0.05 1.02 1.76 1.71 ± 0.09 65 1.30 ± 0.06 0.96 1.86 2.32 ± 0.10 74 1.64 ± 0.08 0.91 1.95 2.91 ± 0.14 83
Table S4. Comparison of specific TCE (TCE per 1 wt% of filler) between our sample with h-BN or
BNNS/polymer composites films reported in literatures.
Composite TC of matrix (W m-1 K-1) TC of composite (W m-1 K-1) Content (wt%) TCE (%) Ref. BNNS/PVA 0.2 21.4 33.1 353 S15 BNNS/PVA 0.2 6.9 94 35.6 S16 BNNS/PVDF 0.2 16.3 33 244 S17 BNNS/PVDF 0.2 11.88 60 97 S18 BNNS/CNF 1.6 30.25 70 25.6 S19 BNNS/CNF 1.6 24.27 60 23.6 S12 h-BN/ANF 7.33 122.5 70 22.4 S20 BNNS/ANF 8.53 46.7 30 14.9 S21 BNNS/PMMA 0.22 14.7 80 82.3 S10 BNNS/PI 0.25 2.95 7 154 S22
BNNS-1500/PVA 0.19 67.6 83 427 This work
PVA: poly(vinyl alcohol); PVDF: polyvinylidene fluoride; CNF: cellulose nanofiber; ANF: aramid nanofiber;
Table S5. The estimated aspect ratios of h-BN or BNNS used in the composites listed in table S4. Composite Lateral size (nm) Thickness (nm) Aspect ratio
Exfoliation method Ref.
BNNS/PVA ≈ 2.5 ≈ 1300 ≈ 520 Sonication S15
BNNS/PVA 200 3 67
Ball milling followed by sonication S16 BNNS/PVDF ≈ 2.5 ≈ 1300 ≈ 520 Sonication S17 BNNS/PVDF 494 1.9 260 Ball milling S18 BNNS/CNF 260 3 87 Probe sonication S19 BNNS/CNF 300 3 100 Probe sonication S12
h-BN/ANF 2000 - 10000 50 ≈ 120 Without treatment S20
BNNS/ANF 1000 3 333 Urea-assisted ball milling S21 BNNS/PMMA 200 2 100 Chlorosulfonic acid-assisted sonication S10 BNNS/PI 1800 2.9 621 Exfoliation with molten hydroxides and sonication S22
BNNS-1500/PVA 4650 3.1 1500 Microfludiziation This work
PVA: poly(vinyl alcohol); PVDF: polyvinylidene fluoride; CNF: cellulose nanofiber; ANF: aramid nanofiber;
Figure S8. (a) Modeling structure of BNNS composed of regular points. The distribution of (b) high-
and (c) low-aspect-ratio BNNS in single layer (top view) and in RVE of the composites (perspective). In this computation, we assumed that the BNNS are composed of regular points as shown in Figure S8a, and the distance between the neighboring points (L) is set as the thickness of BNNS. According to the aspect ratio of BNNS determined in the experiment, the lateral dimensions are set as 465 × 465 μm2 and 220 × 220 μm2 for the systems of high- and low-aspect-ratio BNNS, with a
thickness of 0.30 μm and 0.22 μm, respectively. The size of RVE is 1800 × 1800 × 1.8 μm3, where 1.8
μm is the thickness along the Z axis. Considering that the volume fraction of BNNS in the system is 73.7%, there are 66 sheets randomly distributed in the RVE with high-aspect-ratio BNNS (BNNS-1500), which are separated in 6 layers with 11 sheets per layer (see Figure S8b). Similarly, 400 sheets are dispersed in the RVE of low-aspect-ratio BNNS (BNNS-1000), which are separately are separated in 8 layers with 50 sheets per layer, as presented in Figure S8c.
In Figure S8b and c, the different microstructures of BNNS in each layer are generated by a
configuration is that the BNNS are regularly located in the plane without overlapping. Next, one randomly chosen BNNS is moved for each step based on the Metropolis algorithm. The position and
the orientation of the chosen BNNS are defined by three random parameters: (Δx, Δy) ∈ [−𝛿𝑥, 𝛿𝑥]
denoting the displacement of X and Y coordinates, respectively, and Δα ∈ [0, 𝜋] denoting the rotation angle in the Cartesian coordinate system. Note that (Δx, Δy) are generated with a uniform distribution over their definition domain. The acceptance step of the Metropolis algorithm is to guarantee that the displacement does not cause an overlapping area which is larger than 6.25% of the area of either BNNS. In order to generate a series of independent distribution of BNNS in every layer, their position and orientation are saved during a Markov chain samples with regular interval. The representative results in Figure S8b and c present the distribution of BNNS-1500 and BNNS-1000 in a single layer and RVE, respectively. The overlapping area of BNNS in the generated configuration includes two parts: the overlap in the same layer and between two neighboring layers. Our calculation results indicate that the total overlap area of 1500 in the system is ≈ 62% that of 1000 and the number of 1500 is ≈ 6 times that of 1000, thus leading to a higher average overlapping area of BNNS-1500 (3.75 times) than that of BNNS-1000 in the composite films.
Figure S9. The models and corresponding grid divisions of the (a) high- and (b) low-aspect-ratio
BNNS used in the ANSYS simulation. (c)(d) Temperature distributions at the top part of two models.
The finite element simulation software (ANSYS) was employed to investigate the effect of aspect ratio on the heat transfer capabilities of the composites. In the typical process of simulation, a linear heat source (100 °C) was set at the bottom of model, and the convection coefficient of the exposed
surface of the system was set to 10 W m-2 K-1 with a fixed ambient temperature of 25 °C. The thermal
conductivities of the BNNS and PVA matrix are set to 280 W m-1 K-1 and 0.19 W m-1 K-1, respectively,
according to the previous literature.S26 The aspect ratio of BNNS used in high-aspect-ratio model (Figure S9a) is 1.5 times larger than that in low-aspect-ratio case (Figure S9b), and the simulated temperature distribution at the top of two models is shown in Figure S9c and d, respectively. As a result, the average temperature at the top surface of the model embedded with high-aspect-ratio BNNS is 6.3 °C higher than that of the model with low-aspect-ratio one. Note that the temperature fluctuation in Figure S9c and d is originated from the large difference of thermal conductivity between BNNS and PVA matrix, suggesting that the heat transfer through the model is mainly dominated by interconnected BNNS networks.
Figure S10. The typical stress-strain curves of (a) BNNS-1500/PVA composite films with different
filler contents and the corresponding (b) tensile strength as well as (c) modulus of the samples. (d) The mechanical properties of pure PVA films.
Figure S11. (a) The photograph of the linear motion slide driven by a stepper motor. (b) The PET
substrate with a crease in its middle used in the bending test. (c) Front and (d) top view during one cycle of bending process. The insert of (c) is the SEM image at the crease after bending.
This experiment is based on a linear motion slide, which can do cyclically reciprocating motion drove by a stepper motor, as shown in Figure S11a. To maximize the bending degree of the composites, the polyethylene terephthalate (PET) films, used as the supporting substrates, were folded in half, resulting a crease in the middle, as shown in Figure S11b. Figure S11c and d are the front and top view of the bending process in one cycle, where the thin film was nearly fold in half, with a radius of curvature of 0.5 mm at the crease (see the SEM inserted in Figure S11c).
Figure S12. (a) The configuration of flexible copper clad laminate (FCCL) and (b) photograph of
high-power LED modules (10 W) used in this study.
The flexible copper clad laminate (FCCL) is a mature commercial product for use as flexible and electrically insulating substrates for thermal management applications in electronic devices. The main body of FCCL is a copper foil with a thickness of ≈ 25 μm and high thermal conductivity (≈ 400 W
m-1 K-1), covering with a PI layer with a thickness of ≈ 45 μm and low thermal conductivity (≈ 0.25 W
m-1 K-1). In real applications, the electrical circuits and devices are mounted on the electrically
insulating PI layer. In this work, a LED lamp (10 W) with a light-emitting area of 11 mm × 11 mm was used to investigate the heat dissipation performance of our samples and FCCL, as shown in Figure S12b.
Supplementary method S1. Theoretical analysis of the effect of the aspect ratio of BNNS on the heat transfer capability of the composites based on Foygel's nonlinear model.
When phonons propagate through interconnected BNNS networks in the composites, the contact resistance between partially overlapped BNNS dominates heat transfer efficiency of the composites. Such behavior of phonon transport between adjoining BNNS can be theoretically explained by
Foygel's theory, which is defined as the following equations:S27
𝜅 = 𝜅0(𝑉𝐵𝑁𝑁𝑆− 𝑉𝑐)τ (1)
where κ is the thermal conductivity of the composite films; κ0 is a pre-exponential factor ratio
contributed by interconnected BNNS network; 𝑉𝐵𝑁𝑁𝑆 is the measured volume fraction of BNNS in
the composites; τ is the conductivity exponent determined by the aspect ratio of BNNS; 𝑉𝑐 is the
critical volume fraction of BNNS, which is the intercept of the tangent with the X-axis in the figure of
thermal conductivity of the composites as a function of filler content.S28, S29 In our case, 𝑉𝑐 for the
case of BNNS-1500/PVA and BNNS-1000/PVA is 4.4 vol% and 4.6 vol%, respectively. In order to
obtain the values of κ0 and τ, the equation 1 needs to be transformed into a linear form:
𝑙𝑔𝜅 = 𝑙𝑔𝜅0+ 𝜏 𝑙𝑔(𝑉𝐵𝑁𝑁𝑆− 𝑉𝑐) (2)
where 𝑙𝑔𝜅 is a linear function with the independent variable of BNNS content (𝑉𝐵𝑁𝑁𝑆) in the
composites, and, both 𝑙𝑔𝜅0 and τ are the constant terms, which are equal to a and b in the linear
equation of 𝑦 = 𝑎𝑥 + 𝑏, respectively. Accordingly, the values of 𝜅0 and τ can be calculated by linear
Figure S13. Linear fitting results based on Foygel's model for (a) 1500/PVA and (b)
BNNS-1000/PVA.
Based on the calculated values of 𝜅0 and τ, we can obtain the contact resistance (𝑅𝑐) between
the adjacent BNNS by the following equation: 𝑅𝑐 =
1 𝜅0𝐿𝑉𝑐τ
(3)
L is the lateral size of BNNS, which of the BNNS-1500 and BNNS-1000 are 4.65 and 2.20 µm,
respectively. As a result, the calculated 𝑅𝑐 of BNNS-1000/PVA is 2.2 × 105 K W-1, which is 2 times
Supplementary method S2. The mechanism of the exfoliation during microfluidization and the shear rate calculation in the process
During the microfluidization process, the mechanism of exfoliation of h-BN into BNNS is fundamentally based on the effect of ultrahigh shear rate caused by a highly turbulent flow in the
microchannel. The shear rate in the microfluidization process is calculated to be ≈ 8.77 × 107 s-1, which
is 3 orders of magnitude higher than that required to overcome the interlayer interactions of h-BN (the calculation details can be found below). The shear stress induced by ultrahigh shear rate would be applied to the edge of h-BN to promote the exfoliation when the dispersion was passed through the microchannel, and then peel it off, as shown in Figure S14. Compared to other mechanical exfoliation methods, the key advantage of the proposed process is that the h-BN flakes were primarily exposed to high unidirectional shear forces in microfluidic systems, leading to a significant effect on delamination of h-BN rather than fragmentation of the starting material. In addition, the short processing time (≈ 30 min) avoids further reduction of the lateral size of as-obtained BNNS, as compared to that in other preparation methods (over several hours or up to tens of hours),S3, S7, S8, S10 thus resulting in the successful preparation of high-aspect-ratio BNNS in our study.
Figure S14. (a) Partial delamination and (b) peeling off of h-BN flakes through microfluidization. (c)
Shear rate calculation in the microfluidization process
In order to explain the mechanism of h-BN exfoliation during the microfluidization process, the shear rate of microfluidics was calculated based on fluid dynamics equations as follows. In the
beginning, the mean velocity of microfluidics (U, m s-1) can be obtained by:S30, S31
𝑈 = 𝑄 𝐴 (4) 𝑄 = 𝐶𝑉 𝑡 (5) 𝐴 = 𝜋(𝐷 2) 2 (6)
Where 𝑄 (m3 s-1) is the volumetric flow rate, 𝐶 is the cycle numbers (50 cycles); 𝑉 (m3) is the
volume of BNNS dispersion (3.34 × 10-4 m3); and 𝑡 (s) is the processing time (1800 s). According to
equations 4 and 5, the volumetric flow rat (𝑄) is calculated to 9.28 × 10-6 m3 s-1. And, the
cross-sectional area of the microchannel (A, m2) can be estimated to be 1.77 × 10-8 m2 by equation 6, where
D is the hydraulic diameter (150 µm). As a result, we obtained that the mean velocity of microfluidics (U) is 524 m s-1.
Reynolds number (Re) was then calculated to determine the type of microfluidics, as given by: S30
𝑅𝑒 = 𝜌𝑈𝐷
𝜇 (7)
where ρ is the liquid density (≈ 900 kg m-3), and µ is the dynamic viscosity of dispersion (2.8 ×
10-3 Pa s, measured by a rotational rheometer). The calculated Reynolds number (Re) is 2.5 × 104
(much higher than 4000),S32 indicating a fully developed, highly turbulent flow in the microchannel
during the microfluidization process. The pressure drop (∆𝑝 , Pa) can be estimated by the Darcy– Weisbach equation:S30
∆𝑝 = 𝑓𝐿𝜌𝑈
2
2𝐷 (8)
can be obtained when Re is 2.5 × 104 based on the Moody chart.S33 Accordingly, the energy dissipation
rate per unit mass (ε, m2 s-3) in the microchannel can be written as the following equation:
𝜀 = 𝑄∆𝑝
𝜌𝑉𝑐 (9)
where Vc is the volume of microfluidics (m3), which is equal to the product of the cross-sectional
area (A) and the length (L) of the microchannel. Thus, the energy dissipation rate per unit mass (ε) can
be evaluated to be 2.4 × 1010 m2 s-3 by combining the equations 8 and 9, as shown in equation 10:
𝜀 = 𝑄 𝜌𝑉𝑐 × 𝑓𝐿𝜌𝑈2 2𝐷 = 𝑈𝐴 𝜌𝑉𝑐 × 𝑓𝐿𝜌𝑈2 2𝐷 = 𝑓𝑈3 2𝐷 (10) 𝛾 = √𝜀 𝜈 (11) 𝜈 = 𝜇 𝜌 (12)
Finally, the shear rate of microfluidics (γ) can be calculated by equations 11 and 12,S34 where the
Kinematic viscosity (ν, m2 s-1) is 3.11 × 10-6 m2 s-1, and we can obtain that the shear rate of
microfluidics (γ) is ≈ 8.77 × 107 s-1.
According to the previous literature,S35 the minimum shear rate (𝛾
𝑚𝑖𝑛) required to overcome the
interlayer interactions of h-BN in liquid phase exfoliation can be predicted by the following equation:
𝛾𝑚𝑖𝑛 =
(√𝐸𝐵𝑁− √𝐸𝑆)2
𝜇𝐿 (13)
Where the EBN and ES are the surface tensions of h-BN powders (35 mJ m-2) and the mixture of
ethanol/water with a mass ratio of 1:1 (28 mJ m-2),S1, S36 and L is the h-BN flake length (most lateral
sizes of the raw materials are ranging in 5 – 15 µm). As a result, the minimum shear rate (𝛾𝑚𝑖𝑛) is
calculated to be ≈ 2.78 × 104 s-1, which is 3 orders of magnitude lower than the shear rate (≈ 8.77 ×
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