For a classical composite material, the modulus change should follow the rule of mixtures:

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1 Eletroni Supplementary Material (ESI for Journal of Materials Chemistry C. This journal is The Royal Soiety of Chemistry 2017 Eletroni Supplementary Information (ESI Super ompatible funtional BN nanosheets/polymer films with exellent mehanial property and ultra-high thermal ondutivity for thermal management Jiemin Wang, a Yuanpeng Wu, a,b Ye Xue, Dan Liu, *a Xuebin Wang, d,e Xiao Hu, Yoshio Bando, d,f Weiwei Lei *a a Institute for Frontier Materials, Deakin University, Waurn Ponds Campus, Loked Bag 20000, Vitoria 3220, Australia. b Shool of Materials Siene and Engineering, Southwest Petroleum University, Chengdu , PR China. Department of Physis and Astronomy and Department of Biomedial Engineering, Rowan University, 201 Mullia Hill Road, Glassboro, New Jersey 08028, United States. d International Center for Materials Nanoarhitetonis (WPI-MANA, National Institute for Materials Siene (NIMS, Namiki 1-1, Tsukuba, Ibaraki , Japan. e College of Engineering and Applied Sienes, Nanjing University, Nanjing , China. f Australian Institute for Innovative Materials University of Wollongong North Wollongong, NSW 2500, Australia. J. Wang and Y. Wu have ontributed equally. *Corresponding authors should be addressed at: dan.liu@deakin.edu.au (D. Liu and weiwei.lei@deakin.edu.au (W.W. Lei. 1. Supplementary Methods: The temperature distribution test of FBN/PVA films, Cu and Al foils: In the experimental setup, an iron head was used as hot spot and insulated with a quartz tube to onentrate the heat. In addition, the top end of quartz tube was higher than iron head by 6 mm to protet the samples. Heat transfer experiments were onduted on opper foil, Al foil, and FBN/PVA film with same thiknesses (20 μm. Temperature of the iron dead was set to be 95 C to avoid the oxidizing of the samples. All the samples were oated by graphite paint in order to get a same emissivity. The tested samples were put on a hot iron head, and an infrared thermal amera was used to reord the temperature distribution under a steady-state. The test of thermal ondutivity (through-plane diretion The thermal ondutivity (through-plane diretion of the FBN/PVA films was analyzed by the devie of ai- Phase Mobile 1u using a temperature-wave-analysis method aording to ISO The samples were sandwihed between the heater and sensor plates. By sanning the frequeny of heat soure, the delay in the phase of the temperature wave was reorded within the range from -180 o to -230 o based on an empirial riterion. The linear fitting of phase lag versus square root of frequeny, sqrt(f, was onduted to alulate thermal diffusivity a following = d sqrt( f/a where d is the thikness of samples. The thermal ondutivity was further alulated based on the thermal diffusivity as well as theoretial density and speifi heat apaity of omposites. 1

2 The thermal ondutivity was further alulated based on the thermal diffusivity as well as theoretial density and speifi heat apaity of omposites aording to the rule of mixtures, f f 1 f ( f f 1 f ( m, m, where is the density, is the speifi heat apaity, is the volumetri filling fration, and subsripts of, f, and m indiate the omposites, fillers and polymer matries respetively. The Calulation of Young's modulus of FBN/PVA films E For a lassial omposite material, the modulus hange should follow the rule of mixtures: f Ef 1 f ( E m, where E is Young's modulus, f is the volumetri filling fration, and subsripts of, f, and m mean the omposite, filler and polymer matrix, respetively. Yet the monotoni variation assumes that the filler, whih usually has a muh higher modulus than polymer, would beome a rystal when f beomes 1. However, the fillers are atually often powders, whih have no strong bonding between partiles, unless subjeted to sintering Sine pure FBN films are weak, as disussed above, the equation for the Young s modulus should be modified as E 1 SVoid / Sf f Ef (1 f ( E, m where S Void represents the surfae of BN untouhed by polymers, and S f is the total surfae area of BN. If there is enough polymer, most of BN partiles are surrounded by polymer moleules. When BN filling fration is lose to 1, a part of BN surfae does not interat with polymer. Beause there is atually little mehanial interation between two BN filler sheets, these surfaes (S void atually do not ontribute to the modulus, so S Void /S f will approah 1 when the filling fration of BN approahes 1. The S Void /S f ratio is kept onstant and is lose to 0 for small filling fration of BN. As a result, the modulus inreases with inreasing BN filling fration at first. When the BN filling fration approahes 1, the modulus does not reah that of single-rystal BN instead, it approahes the modulus of BN powder. When BN fration inreases heavily, the polymer matrix annot provide enough glue to onnet the flakes. 2

3 2. Supplementary Figures: Fig. S1 Sheme for the thermal ondutivity in-plane diretion measurement setup. The in-plane thermal ondutivity of the FBN/polymer films was measured by a Physial Property Measurement System (PPMS, Quantum Design, USA using the steady-state method. A film sample with a radiation shield is plaed in a vauum hamber ( Torr to minimize the radiation, onvetion, and ondution heat loss. The radiation heat loss is also alulated by the measurement system. Usually, the speimen is 4 mm 18 mm with a retangular shape. A heater shoe is onneted to one end of the sample, and the other end is fixed to a old sink. The hot thermometer shoe and old thermometer shoe are both onneted to the measured sample at a distane L. At steady state, the thermal ondutivity (K of the sample is determined by equation K=(Q L/(A ΔT where Q is the net heat flowing through a known ross setion A of the measured sample, ΔT is the temperature differene between the hot thermometer and old thermometer, and L is the distane between the two thermometer shoes. Fig. S2 (a SEM images of FBN nanosheets and (b the FBN water dispersion (30 mg/ml. 3

4 Fig. S3 Photos of FBN/PVA films. Photos of free-standing FBN/PVA10 wt%, 20 wt%, 40 wt%, 50 wt% and 60 wt% films plaed over paper with a printed logo. Fig. S4 Optial transmittane of the freestanding FBN/PVA 30 wt% films. Fig. S5 XRD patterns of FBN/PVA films (PVA 10 wt%, 20 wt%, 30 wt%, 40 wt% and 60 wt%. 4

5 Fig. S6 FTIR spetrum of PVA and FBN/PVA films (PVA 10 wt%, 20 wt%, 30 wt%, 40 wt%, and 60 wt%. Fig. S7 The failure strain as a funtion of the PVA ontent. 5

Fig. S8 (a Fire-retardant properties of FBN/PVA 30 wt% and (btga urves of FBN, PVA and FBN/PVA films. Although the FBN/PVA 30 wt% is urved due to the surfae tension when PVA setion is under heating.

6 Fig. S8 (a Fire-retardant properties of FBN/PVA 30 wt% and (btga urves of FBN, PVA and FBN/PVA films. Although the FBN/PVA 30 wt% is urved due to the surfae tension when PVA setion is under heating. However, it ould be learly observed that the omposite membrane still remains un-ignited and keeps intat, demonstrating the fire resistane ability. 3. Supplementary Tables: Table S1. The summary of mehanial properties of FBN/PVA films. Samples Young s modulus Tensile strength (MPa Strain to failure (MPa (% FBN 28.3 ± ± ± 1.8 FBN/PVA 10 wt% ± ± ± 0.6 FBN/PVA 20 wt% ± ± ± 1.2 FBN/PVA 30 wt% ± ± ± 1.5 FBN/PVA 40 wt% ± ± ± 1.2 FBN/PVA 50 wt% ± ± ± 1.4 FBN/PVA 60 wt% ± ± ± 2.1 PVA 68.5 ± ± ±

7 Table S2. Theoretial density and speifi heat apaity of FBN/PVA films. FBN/PVA films Density g/m 3 Thermal Capaity (J/Kg Pure FBN FBN/PVA 10 wt% FBN/PVA 20 wt% FBN/PVA 30 wt% FBN/PVA 40 wt% FBN/PVA 50 wt% FBN/PVA 60 wt% PVA

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