Highly Thermally Conductive and Structurally Ultra-Stable Graphitic Films with Seamless Heterointerfaces for Extreme Thermal Management

Highlights Presenting the first investigation into the structurally bubbling-failure mechanism of graphitic film during cyclic liquid nitrogen shocks. Proposing an innovative design about seamless heterointerface constructing a Cu-modified structure. Inventing a new ultra-stable species of highly thermally conductive films to inspire new techniques for efficient and extreme thermal management. Supplementary Information The online version contains supplementary material available at 10.1007/s40820-023-01277-1.


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for 1 ns with a time step of 1 fs by using canonical ensemble (NPT) simulations.Under environment at 77 K and 1 bar pressure.Then, another 100 ps of simulation was performed for MSD analysis, and another 1 ns of simulation was performed for carbon position analysis.The coordinates were recorded every 0.1 ps.
Step three: Following step two, the case was allowed to equilibrate for 1 ns with a time step of 1 fs by using NPT simulations.Under environment at 300 K and 1 bar pressure.And another 1 ns of simulation was performed for graphene position analysis.The coordinates were recorded every 0.1 ps.
Step four: Following step three, the N2 were deleted, and the case was allowed to equilibrate for 1 ns with a time step of 1 fs by using NPT simulations.Under environment at 300 K and 1 bar pressure.Another 1 ns of simulation was performed for graphene position analysis.The coordinates were recorded every 0.1 ps.
The case was allowed to equilibrate for 1 ns with a time step of 1 fs by using NPT simulations, the pressure was applied in x direction.Under environment at 77 K and 1 bar pressure.The graphene sheets were set as rigid to ensure that the atoms of the substrates were fixed during this step simulation.The number of N2 molecules between the graphene slits region with time was analyzed under 77 K and 300 K.The region between slits is (-1.6~1.6,-1.6~1.6,-0.35~0.35)nm in x, y, z.
The airebo model [S1] was used for graphene.N2 model was taken from Vekeman et al [S2].The van der Waals (vdW) interaction parameters of N2 and graphene was taken from Zhang et al [S3].All the cases were placed in periodic orthogonal boxes.And all the molecular dynamic simulations were performed by using LAMMPS software package [S4].
Furthermore, two confined cases (system 1-2) were built for Molecular Dynamic simulations to verify the enhancement mechanism of the seamless heterogeneous interface (Cu layer).
The initial configuration systems were constructed through the software of PACKMOL 1 , all the N2 molecules were randomly inserted in a cubic simulation box.
The airebo mode [S1] was used for graphene.N2 model was taken from Vekeman et al [S2].The van der Waals (vdW) interaction parameters of N2 and graphene were taken from Zhang et al [S3].The FCC model [S5] was used for Cu.The arithmetic mix rule was applied for Cu and graphene, Cu and N2 .
The system 1 was allowed to equilibrate for 400 ps with a time step of 1 fs by using canonical ensemble (NPT) simulations, under an environment at 77 K and 101.325 kPa pressure.The slit in system 2 was set as freeze to ensure that the atoms of the substrates were fixed during Nano-Micro Letters S3/S18 the simulation.Then, another 1000 ps of NPT simulation was performed for system 2, under an environment at 300 K and 101.325 kPa pressure.The slits in system 2 were set as unfreeze to ensure that the atoms of the substrates were flexible during the simulation.
The temperature and pressure are kept via the Nose-Hoover thermostat and Parrinello-Rahman barostat, respectively.
All the cases were placed in periodic orthogonal boxes.And all the Molecular Dynamic simulations were performed by using LAMMPS software package [S4].

S1.2 Calculation of Diffusion Coefficients from Molecular Dynamics Simulations
The diffusion coefficient can be obtained from the well-known Einstein relation, by determining the slope of the mean square displacement (MSD) over time.The MSD is given by the following equation: Where <r 2 > is the MSD, r(t) is the position vector of the penetrant molecule at time t.If the simulation time is long enough, the diffusion coefficient is described by the following equation: Here, D is the self-diffusion coefficient, t is the time, r(t) is the position vector of the penetrant molecule at time t and the angle brackets give the ensemble average.

S1.3 Supporting Simulation Method of First-principles
The first-principles calculations are carried out using the density functional theory (DFT) approach implemented in the Vienna Ab Initio Package (VASP) within the generalized gradient approximation (GGA) using the Perdew-Burke-Ernzerhof (PBE) formulation [S5-S7].We have chosen the projected augmented wave (PAW) potentials [S8,S9] to describe the ionic cores and take valence electrons into account using a plane wave basis set with a kinetic energy cutoff of 520 eV.Partial occupancies of the Kohn−Sham orbitals were allowed using the Gaussian smearing method and a width of 0.2 eV.The electronic energy was considered self-consistent when the energy change was smaller than 10 −5 eV.A geometry optimization was considered convergent when the energy change was smaller than 0.02 eV Å −1 .The vacuum spacing in a direction perpendicular to the plane of the structure is 18 Å.The weak interaction was described by DFT+D3 method using empirical correction in Grimme's scheme [S10, S11].Supplementary References

Fig. S5
Fig.S5LNS impacts for two GFs in different contact states with liquid nitrogen.Among them, LNS impacts without direct contacting with liquid nitrogen use plastic sealing to isolate N2

Fig. S13
Fig. S13 (a) Schematic diagram of the bubbling process of original GF.(b) Schematic diagram of Cu@GF with seamless heterointerface, which could prevent the bubbling phenomenon

Fig. S19 (
Fig. S19 (a-c)Schematic diagrams of composite parallel model and (d) calculation method of in-plane thermal conductivity by composite parallel model

Fig. S24
Fig. S24 Schematic of the EMI shielding mechanism of (a) GF and (b) Cu@GF

Table S1
Nanoindentation information of GF and GF@Cu

Table S2
Overall performances of some reported graphitic films with this work