Effects of Structure Defects on Thermal Transport at the Graphene–Water Interface

The graphene microchannel heat sinks have attracted extensive attention due to its high cooling efficiency in microelectric devices. The interfacial thermal resistance (ITR) between graphene as the bottom layer of microchannel and water is one of the key factors of its good working performance. In this paper, the impacts of structure defects in graphene surfaces on ITR of the graphene–water interface are investigated using molecular dynamic simulations. The results indicate that graphene layer with different types of structure defects shows different variation trends of ITR as the defect concentration or temperature increases. A peak ITR reduction of nearly 30% is generated with the Stone‐Wales defect of 2%. Finally, the density of phonon states and interfacial binding energy analysis are performed to verify the correctness of the simulation results. The present work expands the understanding of structure defects effect on thermal transport in graphene microchannel.


Effects of Structure Defects on Thermal Transport at the Graphene-Water Interface
Xingli Zhang,* Hao Chen, Degao Qiao, and Ming Yang* DOI: 10.1002/admi.202202518 associated with the interfacial thermal transport between graphene layers and water. [6][7][8][9] Generally, the interfacial thermal resistance (ITR) measurements of the solid-liquid interface can be conducted by experimental, theoretical, and computational methods. Although experimental measurements usually face many difficulties, many methods have been developed to detect the ITRs, such as the time-domain thermoreflectance (TDTR) method, the transient hot wire method, the electron-beam (e-beam), and the e-beam method. [10][11][12][13][14][15][16] In the theoretical methods area, the acoustic mismatch model (AMM) and the diffuse mismatch model (DMM) are successfully used to measure the ITR at low temperatures. However, the two methods which based on the continuum theories neglect the actual atomic structures of the interface. [17,18] In this regard, computational methods have been extensively used to calculate the ITR and explore the underlying physical mechanisms for heat transfer. For the graphene-water interface, various realistic factors are investigated to tune the ITR by molecular dynamics (MD) simulation, which is the most popular computational method to study interfacial thermal transport. [19,20] For example, Ma et al. [21] investigated the impact of interfacial charge decoration on the ITR between graphene and water using MD. Their simulation results demonstrated the ITR was substantially reduced by up to 97% compared with the case without charge decoration. Alexeev et al. [22] found that the ITR between few-layer graphene (FLG) and water depended on the number of layers in the FLG, not on the water block thickness. The distinct size dependence was attributed to the large difference in the phonon mean free path between the FLG and water. Cao et al. [23] found that the ITR of the graphene-water interface after interlayer functionalization by oxygen atoms reduced nearly 50%. Pham et al. [24] showed that the Kapitza length between graphene and water gradually increased as the number of graphene layers on the Cu surface increased. These results indicated that the interfacial structure and heterostructures significantly affected the ITR, and it might be an effective strategy to allow for improving the thermal transport across the graphene-water interface.
The graphene layers on microchannel substrate are often atomically fabricated by chemical methods. However, limited by the synthesis technology, the processing of graphene layers could cause various structural defects, such as vacancies, impurities, and Stone-Wales (SW) defects. [25][26][27][28] Some MD investigations have been performed to understand the different defect The graphene microchannel heat sinks have attracted extensive attention due to its high cooling efficiency in microelectric devices. The interfacial thermal resistance (ITR) between graphene as the bottom layer of microchannel and water is one of the key factors of its good working performance. In this paper, the impacts of structure defects in graphene surfaces on ITR of the graphene-water interface are investigated using molecular dynamic simulations. The results indicate that graphene layer with different types of structure defects shows different variation trends of ITR as the defect concentration or temperature increases. A peak ITR reduction of nearly 30% is generated with the Stone-Wales defect of 2%. Finally, the density of phonon states and interfacial binding energy analysis are performed to verify the correctness of the simulation results. The present work expands the understanding of structure defects effect on thermal transport in graphene microchannel.

Introduction
As the size of electrical and mechanical devices reaches the microscale, the issue of their thermal management has become serious. The graphene microchannel heat sink as a novel liquid cooling device, has significantly promoted heat dissipation due to its unique material and structural property. [1][2][3][4][5] The substrates of those devices have many graphene layers on them, so the utilization efficiency of the graphene microchannel is www.advmatinterfaces.de effect on heat conduction in graphene. [29][30][31] These results have indicated that the structural defects have adverse effect on heat conduction of graphene, for the defects will lead to extra phonon scattering in the model and become obstacles to the thermal transport. Related investigation also have pointed out that the thermal conductivity of defective graphene depends on the defect concentration, topological configuration, and temperature. Although thermal transport properties in defective graphene are extensive reported, few efforts have been devoted to the research of thermal transport between defective graphene and water interface. It is no surprising that surface imperfection of graphene layer will affect the thermal transport at the graphene-water interface inevitably.
In the current work, nonequilibrium molecular dynamics (NEMD) simulations are performed to study the effect of structural defects on the ITR of graphene-water interface. We demonstrate that the ITR of graphene-water interface is influenced significantly by the defects types, defect concentrations, and temperature. Based on the calculations of the density of phonon states and interfacial binding energy, the underlying mechanisms of interfacial heat transfer are proposed.

Model and Methodology
All simulations are performed using the Lammps (Largescale Atomic/Molecular Massively Parallel Simulator) program package with setting time step as 0.5 fs throughout. [32] The BNC-Tersoff potential is used to model the intralayer carbon interactions of graphene layers. [33] The interlayer carbon interactions and the graphene-water interactions are described by the pairwise Lennard−Jones (LJ) potential function with parameters taken from ref. [26,34] and [35] , respectively. The extended simple point charge (SPC/E) model modified by the original parameterization [36] is used to represent the interactions between water molecules. A computational domain with a cross-sectional area of 42 Å × 42 Å in the surface parallel directions is found. Periodic boundary conditions are employed for all directions. There are three types of structure defect arrangements as schematically indicated in Figure 1. The monovacancy defects are introduced by randomly removing a carbon atom in graphene layers, making sure two vacancies are not connected with each other as adjacent atoms. The SW defects are randomly introduced by a 90° rotation of two adjacent carbon atoms. In the graphene-containing impurities, nitrogen atoms are added by randomly substituting carbon atoms. The random distributions of nitrogen atom substitutions are also not accepted for two adjacent atoms.
NEMD simulation modal of water confined between graphene layers is shown in Figure 2. NEMD simulation can directly probe the interfacial temperature jump, and compute the value of ITR for complex material systems with realistic atomic level interfacial structures. As shown in Figure 2, the model is divided into slices along the heat flux direction. The outmost two slices are adiabatic zones to prevent direct heat exchange between the cold and hot reservoir. The graphene in the adiabatic region is involved in the relaxation process, and the velocity and force on the graphene in the adiabatic region are set to zero in the heat transfer process. The hot and cold reservoirs are used to create a temperature gradient by exchanging their energy every few steps. To obtain the model with stable structure, it takes 100 ps to achieve zero stresses under one standard atmospheric pressure in the NPT ensemble (constant mass, pressure, and temperature) at the temperature of 300 K. After that, the system is subjected to a second relaxation of 100 ps in the NVT (constant volume and temperature) ensemble for 100 ps. At last, another 100 ps is used to relax the system with NVE (constant mass, volume, and energy). Record heat flow and temperature gradients after system energy stabilization. As shown in Figure 2b, owing to the presence of the graphene-water interface, there exists a temperature jump ΔT at the interface. The thermal resistance of the graphene-water interface can be calculated from Equation (1) as: where Jis the heat flux across the graphene-water interface.
The final results of ITR are averaged over six independent simulations with different initial defect distributions.

Results and Discussion
The relationship between defect concentration and ITR of graphene-water at 300 K is shown in Figure 3. First, the ITR values between pristine graphene and water is 2.87 × 10 −8 m 2 K W −1 , which is of the same order of magnitude as the previous experimental and theoretical results. [21][22][23]37,38] Furthermore, it can be noted that the ITR between defective graphene and water have a large nonmonotonic decreasing trend with the

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increase of defect concentration. When a peak ITR reduction is generated, the defect concentration of monovacancy, Stone-Wales defect and nitrogen doping are about 3.5%, 2%, and 4%, respectively. The results indicate that the defect concentration of the graphene layer is critical in determining the ITR, and the Stone-Wales defect has the greatest influence. Generally, structural defects might destroy the structural integrity of graphene, leading to the increase of the Kapitza resistance of the graphene layer. The structural defects in the graphene-water interface might also cause the localization aggregation of charges. This is because of the increase in density of the water clusters near the hot and cold reservoirs. [39] As a result, the interactions between graphene layer and water cluster are not only the van der Waals' force but also the coulombian force. The enhancement of interaction strength will improves the interfacial thermal transport at interfaces of defective graphene and water.
To elucidate the physical mechanisms for ITR reduction, first, we investigated the phonon density of states (PDOS). PDOS is calculated from the Fourier transform on the velocity autocorrelation function (VACF), which can be obtained by where v(0) is the velocity of the particle at the initial time, and v(t) is the velocity of the particle at the moment t, fis the vibrational frequency. The PDOS spectra of atoms at the graphene-water with different structural defects are compared in Figure 4. It can be clearly observed that the PDOS of the water cluster in all simulation systems are all below 40 THz. The PDOS of pristine graphene poorly overlaps with that of the water cluster (only with frequency <18 THz) due to many phonon mismatches at the interface. However, the PDOS of graphene with structural  www.advmatinterfaces.de defects provides better overlap with those in water cluster. For example, larger overlap areas (20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30) between the PDOS of the water and the graphene layer containing Stone-Wales defects and nitrogen doping are observed, indicating that the heat flux across their interface has a less thermal resistance. The graphene layer with monovacancy defect has more lowfrequency vibrations compared with the other defect structures, suggesting it is more able to couple vibrationally with the water cluster. For the graphene layer with nitrogen doping, highfrequency vibrations (>40 THz) still exist. The main source of these simulation results could be attributed to the close atomic masses of carbon and nitrogen atoms, which allows the interlayer coupling not to be suppressed too much. The conversion efficiency of high-frequency phonons in graphene to lowfrequency phonons in the water cluster is a key factor in determining the ITR. In addition, the change in ITR is related to the strength of the interaction at the graphene-water interface, and the interfacial binding energy is used to quantify this interaction. In this study, the interfacial binding energy between graphene and water clusters could be calculated by [40] b t otal graphene water where E b is the interfacial binding energy, E total is the energy of the whole system, E graphene is the energy of the graphene, and E water is the energy of the water cluster. The interfacial binding energy between defective graphene and water is presented in Figure 5. It can be seen that there is a lowest value in the interfacial binding energy is 0.0084 eV Å −2 when the graphene layer is perfect. As the concentration of three structural defect increases, the interfacial binding energy increases. The maximum point of the interfacial binding energy is consistent with the previous investigations on the lowest point of ITR. These results can be safely deducted that the existence of structural defect in graphene layer may provide better behaviour of energy transport efficiency between graphene-water interface. The structural defects may generate missing mass, linkages breaking, and variation of the force of bonds. [41,42] For example, the water molecules tend to form more hydrogen bonds and fluid adsorption near the defective layer due to the increase in the density of water clusters. The mechanism of decreasing ITR is associated with the stronger interaction at the interface. [43]

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Our previous studies have shown that temperature is a key factor affecting the heat dissipation efficiency of microchannels, therefore the trend of ITR with temperature at a defect concentration of 3% are investigated. As shown in Figure 6, the ITRs between graphene and water show a nonmonotonic decreasing trend as the temperature increases. The ITRs of all three structural defects reach to minimum values about the temperature of 340 K. The temperature effect could also be explained by the change of interfacial binding energy between defective graphene and water. As presented in Figure 7, the interfacial binding energy of the three models have a large increasing trend with the increase of temperature. Temperature of 340 K leads to the peak value of the interfacial binding energy. This may be because the kinetic energy of the water molecules near the graphene layer becomes larger with the increasing temperature, which helps the energy to cross the interface easily and enhance the decreases of ITR. In addition, temperature-sensitive of ITR when the graphene layer contains monovacancy and S-W defects is more obvious than that of nitrogen doping. The reason for this phenomenon is that the nitrogendoping graphene layer is closer to the pristine graphene layer and has better thermal stability.

Conclusion
In summary, the NEMD method is performed to investigate the effect of structural defect on the thermal resistance of graphene-water interface. It is found that the ITR of graphene layer with monovacancy defects decreases with increasing defect concentration, and the ITR achieves the minimum value at a defect concentration of 3.5%. The ITR of graphene layer with Stone-Wales defects tends to decrease and then increase with increasing defect concentration. When graphene layers are doped with nitrogen atoms, the ITR tends to decrease with increasing doping concentration, and then remain constant. Combined with the analysis of the phonon density of states and interfacial binding energy, we noticed that the higher ITR of the nitrogen-doped graphene-water structure is mainly due to the high-frequency vibrations and weak binding energies. In addition, the ITR of all three structural defects exhibits obvious nonmonotonic decreasing trend as the temperature increases and reaches to minimum values the temperature of 340 K. Our findings provide a guideline to enhance the thermal transport properties across solid-liquid interface.