Bispyrene Functionalization Drives Self-Assembly of Graphite Nanoplates into Highly Efficient Heat Spreader Foils

Thermally conductive nanopapers fabricated from graphene and related materials are currently showing great potential in thermal management applications. However, thermal contacts between conductive plates represent the bottleneck for thermal conductivity of nanopapers prepared in the absence of a high temperature step for graphitization. In this work, the problem of ineffective thermal contacts is addressed by the use of bifunctional polyaromatic molecules designed to drive self-assembly of graphite nanoplates (GnP) and establish thermal bridges between them. To preserve the high conductivity associated to a defect-free sp2 structure, non-covalent functionalization with bispyrene compounds, synthesized on purpose with variable tethering chain length, was exploited. Pyrene terminal groups granted for a strong π–π interaction with graphene surface, as demonstrated by UV–Vis, fluorescence, and Raman spectroscopies. Bispyrene molecular junctions between GnP were found to control GnP organization and orientation within the nanopaper, delivering significant enhancement in both in-plane and cross-plane thermal diffusivities. Finally, nanopapers were validated as heat spreader devices for electronic components, evidencing comparable or better thermal dissipation performance than conventional Cu foil, while delivering over 90% weight reduction.


S1.6. Comments on UV-Vis spectra
The UV absorbance spectra ( Figure S16a) of bispyrene molecules 2a -2e, exhibit the distinctive absorption bands assigned to pyrene units at 314 nm, 328 nm and 345 nm. Position and relative intensities of these bands are insensitive to the linker chain length between pyrene ends, which is expected because these depend exclusively on π-π* electronic transition of conjugation system of pyrene. On the other hand, there is a wide bathochromic shift of BP spectra, in comparison to pyrene ( Figure S16b), related to the higher molecular weight, which changes the dipole moment of chromophore group.    Nanopapers cross sections were also routinely observed by FESEM ( Figure S24), showing qualitatively similar alignments of the GnP flakes and porosity. Moreover, cross section examinations were used to measure thickness, used to calculate density of each sample ( Figure S24).

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Densities of nanopapers were found to be significantly different form the reference GnP nanopaper and in particular, lower densities were obtained for all of the GnP-bispyrene nanopapers, ranging between 0.61 g/cm 3 (GnP 2a) and 0.94 g/cm 3 (GnP 2e). Interestingly, density values continuously increase with increasing the length of the alkyl chain in BP in GnP-bispyrene nanopaper.  Nanopapers were also compared with copper foil (30 μm), which is the most widely used metal for thermal management applications. However, a fair comparison between the different heat spreader materials cannot be done without taking into account the porosity of GnP nanopapers, directly affecting density and thus reducing thermal conductivity.

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To discuss the effect of nanopapers density on their thermal conductivity value, a series of pristine GnP nanopapers having different densities (Table S3) were prepared, by varying the uniaxial compressive load and time.
Nanopaper porosity (φ) was calculated as: (eq. 1) = 1where ρ nanopaper is the density (calculated as the mass/volume of a die cut disk), ρ GnP is the density of an individual graphite nanoplatelet, assumed equal to bulk graphite, i.e. 2.2 gcm -3 .  The problem of heat conduction in heterogeneous materials consisting of a solid continuous phase and a filler dispersed phase, dates back to the early works by Maxwell and Rayleigh, in which different models were proposed to predict the effective thermal conductivity of various types of composite materials. Such models may be applied also to porous media, in which the dispersed phase is air. Different mathematical models were previously proposed for the correlation of thermal conductivity and porosity, including Maxwell-Eucken model, the linear model and effective medium S-26 theories (EMT) 12 . Such models were applied to the experimental data to identify the best fitting, aiming at calculating thermal conductivity of the continuous phase, made of the GnP network, this parameter being independent on the nanopaper porosity. In Figure S26, Copper benchmark is shown in Figure S29. Thermal images acquired in time were systematically analysed to extract temperature profiles vs. time and vs. radial coordinate. Hotspot temperature profiles were recorded on heating (up to 300 s) and on cooling (additional 300s).

Heat spreader
Temperature plots are reported in Figure S30. Thermal maps for the different heat spreaders, compared with the heater without heat spreader foil, as a function of time on heating (0, 30, 60s) and on cooling (300, 330 and 360s) are reported in Figure   S31 and Figure S32, respectively. Temperature profiles for each nanopaper were automatically extracted from such thermal maps, along three different directions (x, y axes and bisector) in order to obtain a representative average. Then, the average temperature vs. radius profile was fitted with an exponential decay function, for all the different heat spreader ( Figure S33). It is worth noting that decay rates for GnP nanopapers are S-32 significantly higher than for copper foil, reflecting the steepest temperature gradients vs. radius, coherently with the lower thermal conductivity of the nanopapers compared to copper.

Radius (mm)
GnP 2b R 0 = 0.151 Figure S33: Fitting of temperature vs radius profiles. In black are temperature plots on the different directions (marked on the thermal maps), in blue is the average plot and in red is the exponential fit. Decay rates for fitting plots are also reported