Method for predicting anisotropic thermal conductivity of two-dimensional material nanobelt
By establishing a molecular dynamics model, simulating the heat transfer process of graphene and black phosphorus nanoribbons, and analyzing the effects of different torsion angles, temperatures, and system lengths on thermal conductivity, the insufficient research on the thermal conductivity of two-dimensional materials under multi-directional, multi-temperature, and multi-size conditions was addressed, and high-precision thermal management optimization was achieved.
Patent Information
- Application Number
- CN202510712030.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-29
- Publication Date
- 2025-09-05
AI Technical Summary
The existing technology lacks systematic research on the thermal conductivity of two-dimensional materials under multi-direction, multi-temperature and multi-size conditions, making it difficult to effectively regulate the thermal management of nanodevices.
A molecular dynamics heat transport model was established. By setting different torsion angles and temperature conditions, the heat transfer process of graphene and black phosphorus nanoribbons was simulated, the anisotropy of in-plane thermal conductivity was analyzed, and the effects of different system lengths and temperatures on thermal conductivity were studied in combination with the phonon scattering mechanism.
A high-precision prediction method for the in-plane thermal conductivity of two-dimensional material nanoribbons is provided, which reveals the physical mechanism of thermal conductivity and provides a theoretical basis for the thermal management optimization of nanodevices.
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Figure CN120600187A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of nanomaterial thermal management, and in particular to a method for predicting the anisotropic thermal conductivity of two-dimensional material (such as graphene and black phosphorus) nanoribbons. Background Art
[0002] With the rapid development of nanotechnology, the thermal management problem of nanodevices has become increasingly prominent. Two-dimensional materials, such as graphene and black phosphorus, have become ideal materials for thermal management of nanodevices due to their excellent thermal conductivity and anisotropic heat transfer properties. However, the research on the in-plane thermal conductivity (IPTC) of two-dimensional materials in the existing technology mainly focuses on a single direction or limited conditions, and lacks a systematic study of thermal conductivity under multi-directional, multi-temperature, and multi-size conditions. Therefore, how to use the in-plane anisotropic thermal conductivity of two-dimensional materials to optimize the thermal management of nanodevices has become an important topic in the current technology field.
[0003] In the field of thermal management technology, regulating in-plane thermal conductivity is key to improving the thermal transfer performance of materials. In-plane thermal conductivity is primarily influenced by the scattering mechanisms of hot carriers (such as phonons and electrons). Therefore, how to effectively control these scattering processes has become a core research issue. In recent years, with the continuous development of computational methods, advanced techniques such as equilibrium molecular dynamics (EMD), non-equilibrium molecular dynamics (NEMD), and atomic Green's function (AGF) have been widely used to study in-plane heat transfer processes, providing important theoretical support for the regulation of material thermal conductivity. Graphene, as a two-dimensional material with excellent thermal conductivity, shows great application potential in the field of thermal management. To meet the needs of different application scenarios, researchers have explored various approaches to regulating graphene thermal conductivity by introducing defects, applying stress, and doping with impurities. For example, point defects, grain boundaries, and different types of doping can significantly affect the thermal conductivity of graphene by introducing additional phonon scattering centers. Hao et al. systematically studied the effects of axial tensile strain and vacancy defects on the thermal conductivity of graphene through molecular dynamics simulations. The study found that tensile strain enhances thermal transport, while vacancy defects significantly reduce thermal conductivity, particularly at high defect concentrations. Panneerselvam et al. further confirmed through equilibrium molecular dynamics simulations that vacancy defects in graphene significantly reduce its thermal conductivity. This reduction is not only closely related to the defect concentration but also influenced by the spatial distribution of the defects, indicating that the spatial distribution of defects plays a significant role in determining thermal conductivity.
[0004] Furthermore, the composites of graphene with other materials offer new avenues for regulating thermal conductivity. For example, Fang et al. investigated the effects of graphene coatings on the thermal dissipation properties of macroscopic metals. They found that the presence of graphene effectively excites phonons in the metal substrate, significantly enhancing the phonon contribution to the metal's overall thermal conductivity. This finding provides theoretical support for the application of graphene in metal-matrix composites and opens new avenues for the development of efficient thermal management materials. In addition to defects and composite material manipulation, the influence of inherent geometric properties (especially size effects) on heat transfer cannot be ignored. For two-dimensional materials such as graphene and black phosphorus (BP) nanoribbons, boundary scattering effects become more pronounced as the nanoribbon width decreases, leading to a decrease in thermal conductivity. However, recent studies have found that coherent phonon transport at rough boundaries can induce nonmonotonic variations in thermal conductivity, even leading to anomalous enhancement, through selective interference mechanisms. This suggests that conventional boundary scattering theory needs to be further modified to incorporate the wave-particle duality of phonons. Furthermore, temperature also affects thermal conductivity by altering phonon distribution and propagation properties. Narayan et al. studied the temperature dependence of black phosphorus lattice thermal conductivity in the zigzag and armchair directions based on Boltzmann transport theory. Their study showed that as temperature decreases, the mean free path of phonons in the zigzag and armchair directions increases, thereby increasing thermal conductivity. The orthogonal structure of two-dimensional materials imparts high in-plane thermal conductivity and low interlayer thermal conductivity, enabling anisotropic thermal management and effectively protecting devices from high-temperature damage.
[0005] As representative two-dimensional materials, graphene and black phosphorus exhibit significant anisotropic IPTC due to their unique structural and phonon properties. Studies have shown that by rotating atomic-scale van der Waals materials with moiré fringes, efficient transmission of low-frequency acoustic phonons can be achieved. This phenomenon is attributed to the change in the coupled phase space, especially the main contribution of the bending phonon mode. The research of Arabha et al. shows that rotational deformation reduces the thermal conductivity of nanostructures, which is mainly due to the change in the wrinkle amplitude caused by the deformation, which inhibits the effective transmission path of phonons. The research of Meng et al. further reveals that the rotation angle can affect the overlap of the phonon density of states between two-dimensional van der Waals heterojunctions, thereby regulating the atomic vibration caused by the potential energy surface and adjusting the phonon transport properties, thereby achieving precise regulation of thermal conductivity.
[0006] Although a large number of studies have revealed the influence of various factors on thermal conductivity, under the combined influence of size scaling, temperature changes and phonon scattering mechanisms, comparative studies on the thermal conductivity of two-dimensional nanoribbons with different structural symmetries in different heat propagation directions are still relatively limited, making it difficult to guide the thermal management optimization of nanodevices. Summary of the Invention
[0007] The technical problem to be solved by the present invention is to provide a method for predicting the anisotropic thermal conductivity of two-dimensional material nanoribbons.
[0008] To solve the above problems, the present invention provides a method for predicting the anisotropic thermal conductivity of two-dimensional material nanoribbons, comprising the following steps:
[0009] ⑴ Establish molecular dynamics heat transport models for graphene nanoribbons and black phosphorus nanoribbons composed of hot and cold regions respectively;
[0010] The hot area is composed of a heat source and a fixed wall A, and the cold area is composed of a fixed wall B and a cold source; heat conduction is carried out between the heat source and the cold source through the heat transfer zone;
[0011] Aperiodic boundary conditions were set in the x, y, and z directions of the model, and Berendsen thermostats (a temperature control method based on velocity scaling) were set at both ends of the model to control the temperature of the system.
[0012] ⑵Perform molecular dynamics simulation and data processing:
[0013] ① The graphene nanoribbons were twisted at angles ranging from 0 to 120°, and the black phosphorus nanoribbons were twisted at angles ranging from 0 to 360°. The heat source and cold source temperatures were set at 320K and 280K, respectively. By comparing the in-plane thermal conductivity data at different twist angles, the in-plane thermal conductivity anisotropy of the two-dimensional material was determined.
[0014] ② The graphene nanoribbons were twisted at angles ranging from 0 to 120°, and the black phosphorus nanoribbons were twisted at angles ranging from 0 to 360°. The heat source and cold source temperatures were set to 320K and 280K, respectively. The phonon dispersion curves were analyzed to reveal the dependence of the in-plane thermal conductivity on the transport direction.
[0015] ③ The torsion angle range of graphene nanoribbons is 0-120°, and the torsion angle range of black phosphorus nanoribbons is 0-360°. The heat source and cold source temperatures are set to 320K and 280K, respectively. When the length of graphene nanoribbons is 40-90nm and the length of black phosphorus nanoribbons is 70-130nm, the effect of different system lengths on the in-plane thermal conductivity is studied.
[0016] ④ The temperature range of the graphene system is 100K~500K, and the temperature range of the black phosphorus system is 100K~500K. The temperature difference between the heat source and the cold source is always maintained at 40K. The changes in the in-plane thermal conductivity, heat flux and phonon number at different system temperatures are calculated respectively. By comparing the changes in heat flux and in-plane thermal conductivity at different system temperatures, combined with the phonon scattering mechanism, the influence of temperature on the in-plane thermal conductivity and its internal mechanism are analyzed.
[0017] The molecular dynamics simulation and data processing performed in step (2) also include: taking the graphene nanoribbons torsional angle range of 0 to 120° and the black phosphorus nanoribbons torsional angle range of 0 to 360°, comparing the effects of different heat transfer directions on the phonon group velocity, and determining the physical mechanism of the anisotropic in-plane thermal conductivity.
[0018] The molecular dynamics simulation and data processing performed in step (2) further includes: taking the temperature range of the graphene system to be 100K~500K and the temperature range of the black phosphorus system to be 100K~500K, comparing the number of phonons at different system temperatures, and determining the intrinsic mechanism of the influence of different system temperatures on the in-plane thermal conductivity.
[0019] Compared with the prior art, the present invention has the following advantages:
[0020] 1. This study uses graphene and black phosphorus as research objects. A molecular dynamics heat transfer model is first established and run under different torsion angles and temperatures. By calculating and analyzing the in-plane thermal conductivity at different torsion angles and temperatures, the dependence of the in-plane thermal conductivity of graphene and black phosphorus on the heat transfer direction and temperature is systematically investigated.
[0021] 2. The present invention determines the dependence of the in-plane thermal conductivity on different heat transfer directions by calculating the in-plane thermal conductivity at different torsion angles.
[0022] 3. This invention reveals the physical mechanism of the anisotropy of in-plane thermal conductivity of two-dimensional materials by statistically analyzing the phonon dispersion curves and phonon group velocities at different torsion angles.
[0023] 4. The present invention characterizes the temperature gradient, heat flow and in-plane thermal conductivity at different torsion angles and system temperatures to display the changing relationship curve between in-plane thermal conductivity and system temperature at different torsion angles.
[0024] 5. The present invention simulates graphene nanoribbons (GNRs) and black phosphorus nanoribbons (BPNRs) of different sizes, analyzes the influence of size effect on in-plane thermal conductivity, and predicts the in-plane thermal conductivity at infinite size.
[0025] 6. The present invention reveals the intrinsic mechanism by which system temperature affects in-plane thermal conductivity by extracting the number of phonons at different system temperatures.
[0026] 7. This invention provides an important theoretical basis for a deeper understanding of the heat transfer mechanism of two-dimensional materials with different heat transfer directions and for exploring methods to effectively control in-plane thermal conductivity. BRIEF DESCRIPTION OF THE DRAWINGS
[0027] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.
[0028] Figure 1Figure 1 shows simulation models of graphene and black phosphorus nanoribbons and schematic diagrams of different heat propagation directions in an embodiment of the present invention. Figure a shows the graphene nanoribbon model and heat transport diagram; b shows the graphene lattice structure after a 30° rotation, transitioning from armchair to zigzag; c shows the black phosphorus nanoribbon model and heat transport diagram; and d shows the graphene lattice structure after a 90° rotation, transitioning from armchair to zigzag.
[0029] Figure 2 2 : The temperature distribution (a) and heat flux (b) change with time in the thermal equilibrium state in an embodiment of the present invention.
[0030] Figure 3 Figure 1 shows the variation of the in-plane thermal conductivity of graphene and black phosphorus at different temperatures as a function of heat propagation direction. (a) Graphene's in-plane thermal conductivity as a function of rotation angle at 300K and 400K, respectively; (b) black phosphorus' in-plane thermal conductivity as a function of rotation angle at 300K and 400K, respectively.
[0031] Figure 4 Figure 1 shows the thermal conductivity variations and inverse fitting results of graphene and black phosphorus at different sizes in the present invention. (a) shows the thermal conductivity variation trends of graphene in the zigzag and armchair directions at different sizes; (b) shows the thermal conductivity variation trends of black phosphorus in the zigzag and armchair directions at different sizes; (c) shows the thermal conductivity of an infinite system predicted by the inverse fitting method for a finite-length sample in graphene; and (d) shows the thermal conductivity of an infinite system predicted by the inverse fitting method for a finite-length sample in black phosphorus.
[0032] Figure 5 2. The Brillouin zone of graphene (a) and the phonon dispersion curve of graphene (b) in an embodiment of the present invention; the Brillouin zone of black phosphorus (c) and the phonon dispersion curve of black phosphorus (d).
[0033] Figure 6 2 is the variation trend of the in-plane thermal conductivity of graphene (a) and black phosphorus (b) at different temperatures in the embodiment of the present invention.
[0034] Figure 7 The phonon numbers of graphene (a) and black phosphorus (b) at different temperatures in the embodiments of the present invention; the average phonon free paths of graphene (c) and black phosphorus (d) at different temperatures. DETAILED DESCRIPTION
[0035] A method for predicting the anisotropic thermal conductivity of two-dimensional material nanoribbons comprises the following steps:
[0036] ⑴ Establish molecular dynamics heat transport models of graphene nanoribbons and black phosphorus nanoribbons composed of hot areas and cold areas respectively.
[0037] The hot area is composed of a heat source and a fixed wall A, and the cold area is composed of a fixed wall B and a cold source; heat conduction is carried out between the hot source and the cold source through the heat transfer zone.
[0038] Non-periodic boundary conditions are set in the x, y, and z directions of the model, and Berendsen thermostats (a temperature control method based on velocity scaling) are set at both ends of the model to regulate the temperature of the system.
[0039] ⑵Perform molecular dynamics simulation and data processing:
[0040] ① The graphene nanoribbons were twisted at angles ranging from 0 to 120°, and the black phosphorus nanoribbons were twisted at angles ranging from 0 to 360°. The heat source and cold source temperatures were set at 320K and 280K, respectively. By comparing the in-plane thermal conductivity data at different twist angles, the in-plane thermal conductivity anisotropy of the two-dimensional material was determined.
[0041] ② The graphene nanoribbons were twisted at angles ranging from 0 to 120°, and the black phosphorus nanoribbons were twisted at angles ranging from 0 to 360°. The heat source and cold source temperatures were set to 320K and 280K, respectively. The phonon dispersion curves were analyzed to reveal the dependence of the in-plane thermal conductivity on the transport direction.
[0042] ③ The torsion angle range of graphene nanoribbons is 0-120°, and the torsion angle range of black phosphorus nanoribbons is 0-360°. The heat source and cold source temperatures are set to 320K and 280K, respectively. When the length of graphene nanoribbons is 40-90nm and the length of black phosphorus nanoribbons is 70-130nm, the effect of different system lengths on the in-plane thermal conductivity is studied.
[0043] ④ The temperature range of the graphene system is 100K~500K, and the temperature range of the black phosphorus system is 100K~500K. The temperature difference between the heat source and the cold source is always maintained at 40K. The changes in the in-plane thermal conductivity, heat flux and phonon number at different system temperatures are calculated respectively. By comparing the changes in heat flux and in-plane thermal conductivity at different system temperatures, combined with the phonon scattering mechanism, the influence of temperature on the in-plane thermal conductivity and its internal mechanism are analyzed.
[0044] The present invention also includes performing molecular dynamics simulation and data processing:
[0045] The graphene nanoribbons are twisted in the range of 0 to 120°, and the black phosphorus nanoribbons are twisted in the range of 0 to 360°. The effects of different heat transfer directions on the phonon group velocity are compared to determine the physical mechanism of anisotropic in-plane thermal conductivity.
[0046] The temperature range of the graphene system is 100K~500K, and the temperature range of the black phosphorus system is 100K~500K. The number of phonons at different system temperatures is compared to determine the intrinsic mechanism of the influence of different system temperatures on the in-plane thermal conductivity.
[0047] Example
[0048] This paper uses graphene and black phosphorus systems as research objects, constructs a molecular dynamics heat transport model, and simulates and analyzes the in-plane thermal conductivity of graphene and black phosphorus nanoribbons at different torsion angles, temperatures, and system sizes. This reveals the anisotropic characteristics of the thermal conductivity of two-dimensional materials and provides an optimization strategy for heat transport in nanodevices. The specific process is as follows:
[0049] (1) Establishing a molecular dynamics model
[0050] like Figure 1 As shown, an in-plane heat transport system consisting of hot areas and cold areas is established to explore the intrinsic mechanism of the in-plane heat transport anisotropy of graphene and black phosphorus.
[0051] The present invention constructs a graphene and black phosphorus nanoribbon structure consisting of a heat source and a cold source. Initially, heat conduction occurs along the armchair direction. To ensure that the models with different propagation directions have a uniform heat transfer area, a larger fixed single-layer structure is placed under the nanoribbon during the modeling process. After rotation, the nanoribbon is trimmed so that its size is consistent with the fixed single-layer structure. The heat flow deflection angle is defined as the deviation of the heat flow direction in the hot zone relative to the heat flow direction in the cold zone. The dimensions of the single-layer graphene and black phosphorus nanoribbon along the x, y, and z directions are 120×30×1 regular unit cell (UC). The system transfers heat along the x-axis. In order to prevent the overall structure from rotating, two UCs are set at both ends of the graphene nanoribbon and the black phosphorus nanoribbon as fixed areas. The three UCs adjacent to the fixed area are designated as temperature control areas, respectively called heat source and heat sink. middle The motion zone is subdivided into 20 plates, each containing five unit cells (UCs). Non-periodic boundary conditions are applied to the system along the x, y, and z directions.
[0052] The system was initially run in the canonical ensemble (NVT) to ensure temperature equilibrium, with a relaxation time of 150 ps at 300 K and a time step of 0.5 fs. The simulation then shifted to the microcanonical ensemble (NVE), where the temperatures of the heat source and heat sink were adjusted using a Brensen thermostat. The temperature regulation regions for the graphene / black phosphorus nanoribbons were set to 320 K and 280 K, respectively. After reaching equilibrium, the system simulation was run for 1500 ps to collect stable temperature distribution and heat flux data, which were subsequently used to calculate the IPTC.
[0053] The Stillinger-Weber (SW) potential proposed by Stillinger and Weber is used to describe the covalent interactions between phosphorus atoms. In addition, the Tersoff potential proposed by Tersoff is used to describe the interactions between carbon atoms because it can more accurately describe the covalent bonds between carbon atoms.
[0054] All simulations were performed using the LAMMPS software package.
[0055] (2) Determine the effect of different twist angles on the anisotropic thermal conductivity of graphene and black phosphorus
[0056] Graphene and black phosphorus heat transfer models were used to investigate the in-plane heat transfer behavior at different twist angles. The twist angles were selected within the ranges of 0-120° and 0-360°, respectively. The heat source and heat sink temperatures for the graphene and black phosphorus heat conduction models were set to 320K and 280K, respectively. By comparing the in-plane thermal conductivity data at different twist angles, the dependence of in-plane thermal conductivity on different heat transfer directions was determined.
[0057] The temperature change of the moving plate is represented by the symbol ΔT and is determined by the temperature position curve, such as Figure 2 Figure a shows the system divided along the x-axis into hot and cold zones, each containing ten plates. The local temperature of each plate is calculated based on the atomic velocity, and the plate temperatures within each zone are averaged. A linear fit is then used to determine the temperature gradient (ΔT / ΔL), where ΔT represents the temperature change and ΔL represents the effective length of the heat flux from the hot source to the cold source.
[0058] The Berendsen thermostat is designed to adjust the heat source and heat sink area to achieve the desired temperature, so that the system can produce a heat flux in the x-direction. After the system relaxes and equilibrates (e.g. Figure 2 b), the heat flux can be obtained by plotting the change of the heat energy absorbed by the Berendsen thermostat over time. The least squares method is used to linearly fit the curve, where the slope represents the heat flux. Therefore, the heat flux J can be expressed as Where: Q is the heat absorbed or removed by the thermostat, unit: eV; S is the area of the contact interface, unit: m 2 ; t represents simulation time, unit: s.
[0059] The in-plane thermal conductivity of GNR and BPNR is expressed by Fourier's law of heat conduction. Where κ represents the in-plane thermal conductivity, unit: W / mK; ΔT represents the temperature change of the moving plate, unit: K.
[0060] Figure 3Figures 3a and 3b show the effect of twist angle on the IPTC of graphene and black phosphorus nanoribbons at different temperatures. The results show that at 300K, as θ increases from 0° (armchair orientation) to 30° (zigzag orientation), graphene's IPTC initially rises gently and then increases significantly, reaching a peak of 2024 W / mK at θ = 30°, compared to 1247.5 W / mK at θ = 0°. Black phosphorus's IPTC exhibits a nonmonotonic trend within a single period (θ from 0° to 180°), reaching a maximum of 375.3 W / mK at θ = 90°, compared to a mere 102 W / mK at θ = 0°.
[0061] That is to say, the thermal conductivity peaks of graphene and black phosphorus in the zigzag direction (θ = 30°) below 300K are significantly higher than those in the armchair direction (θ = 0°).
[0062] It is worth noting that compared with GNR, the IPTC of BPNR reaches 375.3W / mK at θ = 90°, which is 268% higher than that at θ = 0° (102W / mK), confirming the high sensitivity of its thermal conductivity to direction. The research results show that the IPTC of both GNR and BPNR exhibits significant anisotropy, with the maximum value in the zigzag direction and the minimum value in the armchair direction.
[0063] (3) Compare the in-plane thermal conductivity at different system lengths to determine the dependence of the in-plane thermal conductivity of the two-dimensional material on the system size
[0064] In atomic-scale simulations, system size has a significant impact on the IPTC of two nanoribbons, often a non-negligible effect. To further investigate the size-dependent effect of the thermal conductivity of monolayer graphene and black phosphorus nanoribbons in the armchair and zigzag directions, two models with different lengths but identical widths (approximately 20 nm) were simulated at 300 K. The lengths of the monolayer graphene were set to 40, 50, 60, 70, 80, and 90 nm, and the lengths of the black phosphorus were set to 70, 80, 90, 100, 120, and 130 nm. To improve computational accuracy, five independent MD simulations were performed for each length group, and the average value was taken.
[0065] like Figure 4As shown in Figures a–4d, the thermal conductivity of both graphene and black phosphorus increases monotonically with increasing system length. In the armchair direction, graphene's thermal conductivity increases from 1247.50 W / m·K to 2616.32 W / m·K; in the zigzag direction, it increases from 2024.08 W / m·K to 3765.32 W / m·K. Black phosphorus exhibits a similar trend: in the armchair direction, its thermal conductivity increases from 102.52 W / m·K to 237.53 W / m·K, while in the zigzag direction, it increases from 324.61 W / m·K to 508.92 W / m·K. This trend can be attributed to the fact that the system size allows more long-wavelength phonons to participate in the heat transport process, driving the increase in thermal conductivity.
[0066] In order to verify the reliability of the simulation results and ensure that the size effect has approached the limit convergence value, this study uses the inverse fitting method to process the calculation results of finite length samples. The formula is as follows:
[0067]
[0068] Where: κ ∞ is the thermal conductivity of an infinitely long system, L is the system length, and λ is the effective phonon mean free path. The formula shows that there is a linear relationship between the inverse of thermal conductivity and the inverse of length.
[0069] (4) Determine the effect of temperature on the in-plane heat transport of graphene and black phosphorus
[0070] Temperature is also important for heat transport. To gain a deeper understanding of the impact of temperature-related phonon effects on thermal conductivity in different directions, the present invention performed additional calculations, such as Figure 6 a and 6b. A Berendsen thermostat was still used to adjust the temperature to achieve different target temperatures. After reaching a steady state, the changing trends of the in-plane thermal conductivity of graphene and black phosphorus were calculated at average temperatures between 100K and 500K. The results show that as the temperature increases from 100K to 500K, the IPTC of graphene in the armchair and zigzag directions decreases by 6% and 12.4%, respectively. In contrast, the downward trend of black phosphorus is more significant, with its thermal conductivity in the armchair direction decreasing by 26.4% and in the zigzag direction decreasing by 32.6%.
[0071] Particularly noteworthy is that at the same temperature, the rate of thermal conductivity decrease in the zigzag direction is significantly higher than that in the amchair direction, highlighting the anisotropic nature of the temperature response of graphene and black phosphorus thermal conductivity. As temperature increases, the high density of phonons leads to an increase in the frequency of phonon-phonon scattering, particularly the non-momentum-conserving Umklapp scattering process (U scattering). This scattering mechanism disrupts the directional transport of phonons, significantly shortening the mean free path (MFP) of phonons, thereby suppressing thermal conductivity.
[0072] In order to quantify this effect, the present invention calculates the variation of the phonon mean free path of GNR (graphene nanoribbon) and BPNR (black phosphorus nanoribbon) with temperature, such as Figure 7 c and 7d. The results show that in the zigzag direction, the MFP of the GNR decreases from 155.55 nm at 100 K to 27.31 nm at 500 K, while the MFP of the BPNR decreases from 66.72 nm to 9.28 nm. Since thermal conductivity is proportional to the phonon mean free path, and the MFP is inversely proportional to the scattering rate, the enhanced Umklapp scattering caused by the temperature increase is the main reason for the decrease in thermal conductivity.
[0073] (5) Determine the effect of temperature on the phonon number
[0074] The trend of thermal conductivity decreasing with increasing temperature indicates that temperature significantly affects the phonon transport properties within 2D materials. To further explore the physical mechanism of this phenomenon, the present invention combines the changes in phonon spectra at different temperatures. Figure 5 The graphene Brillouin zone shown in a and Figure 5 c) shows how the enhanced phonon scattering in the Brillouin zone of black phosphorus leads to a decrease in IPTC. In the present invention, based on the conservation of total energy and combined with the spectral characteristics of the velocity autocorrelation function, an expression for the phonon number applicable to the classical MD system is derived.
[0075] The number of excited phonons in the plane can be calculated as:
[0076]
[0077] Where: N v Indicates the number of atoms per unit volume; m indicates atomic mass, unit: amu; ω indicates vibration frequency, unit: Thz; is the reduced Planck constant; S v (ω) is the energy spectral density, unit: J / Thz.
[0078] This formula is based on the equipartition theorem and the conservation of total energy. It can effectively reflect the contribution of vibration modes of different frequencies to the total energy of the system, thereby reasonably describing the excitation behavior of phonons in classical systems.
[0079] Figure 7 Figures 7a and 7b show the changes in the number of phonons within the surface of a single-layer graphene and a single-layer black phosphorus at different temperatures. As temperature increases, the number of phonons in both nanoribbons increases significantly at the same frequency. This phenomenon can be explained by lattice dynamics theory. Temperature reflects the intensity of atomic vibrations in the crystal structure. As temperature rises, the amplitude of atomic thermal vibrations increases, thereby exciting more phonons. However, although the number of phonons per unit volume increases with temperature, this does not necessarily mean that the efficiency of phonons in heat conduction will increase accordingly. In fact, a higher number of phonons per unit volume may lead to more frequent collisions between phonons. Especially at high temperatures, phonon-phonon scattering becomes the primary scattering mechanism, which significantly affects the mean free path of phonons. According to the three-phonon scattering process, the phonon-phonon scattering rate increases with temperature, which shortens the path for phonon propagation and reduces the efficiency of phonon heat transfer. Therefore, the results of the present invention indirectly reflect that although increasing temperature increases the number of phonons per unit volume, it also increases the frequency of collisions between phonons, reducing the efficiency of phonon energy transfer, ultimately leading to a decrease in thermal conductivity.
[0080] In summary, as the twist angle increases, the phonon dispersion relation changes from a small angle to a large angle, and the lattice vibration mode changes accordingly, resulting in a gradual decrease in the phonon group velocity (e.g. Figure 5 b and 5d), and at the same time, the degree of coupling between phonons decreases. Some phonons are localized inside the lattice, which hinders the effective transmission of phonons. In addition, as the degree of lattice mismatch increases, the mean free path of phonons decreases, which significantly reduces the in-plane thermal conductivity. The effect of temperature on in-plane thermal conductivity also shows significant characteristics. Under high temperature conditions, the frequency of collisions between phonons increases, resulting in an enhanced phonon-phonon scattering effect. At the same time, the thermal expansion effect of the lattice causes the phonon state density to reconstruct, further affecting the transmission characteristics of phonons. As the temperature increases, phonon-phonon scattering gradually becomes the dominant scattering mechanism, significantly reducing the mean free path of phonons, resulting in a decrease in in-plane thermal conductivity.
[0081] This paper systematically studies the thermal conductivity characteristics of graphene and black phosphorus in different directions, temperatures and sizes. By integrating multi-parameter control models such as torsion angle, size, and temperature, and combining phonon dynamics and scattering mechanism analysis, it provides a high-precision prediction tool for thermal management of nanodevices. It is particularly suitable for the directional optimization design of anisotropic heat transfer channels.
[0082] The above embodiments are only intended to help understand the method and core concept of the present invention. It should be noted that, without departing from the principles of the present invention, a number of improvements and modifications may be made to the present invention by those skilled in the art, and such improvements and modifications also fall within the scope of protection of the claims of the present invention.
Claims
1. A method for predicting the anisotropic thermal conductivity of two-dimensional material nanoribbons, comprising the following steps: ⑴ Establish molecular dynamics heat transport models for graphene nanoribbons and black phosphorus nanoribbons composed of hot and cold regions respectively; The hot area is composed of a heat source and a fixed wall A, and the cold area is composed of a fixed wall B and a cold source; heat conduction is carried out between the heat source and the cold source through the heat transfer zone; In the model x 、 y 、 z Aperiodic boundary conditions are set in the direction, and Berendsen thermostats are set at both ends of the model to control the temperature of the system; ⑵Perform molecular dynamics simulation and data processing: ① The graphene nanoribbons were twisted at angles ranging from 0 to 120°, and the black phosphorus nanoribbons were twisted at angles ranging from 0 to 360°. The heat source and cold source temperatures were set at 320 K and 280 K, respectively. By comparing the in-plane thermal conductivity data at different twist angles, the in-plane thermal conductivity anisotropy of the two-dimensional material was determined. ② The graphene nanoribbons were twisted at angles ranging from 0 to 120°, and the black phosphorus nanoribbons were twisted at angles ranging from 0 to 360°. The heat source and cold source temperatures were set to 320 K and 280 K, respectively. Phonon dispersion curves were analyzed to reveal the dependence of in-plane thermal conductivity on the transport direction. ③ The torsion angle range of graphene nanoribbons was 0-120°, and the torsion angle range of black phosphorus nanoribbons was 0-360°. The heat source and cold source temperatures were set to 320 K and 280 K, respectively. When the length of graphene nanoribbons was 40-90 nm and the length of black phosphorus nanoribbons was 70-130 nm, the effect of different system lengths on the in-plane thermal conductivity was studied. ④ The temperature range of the graphene system is 100 K~500 K, and the temperature range of the black phosphorus system is 100 K~500 K. The temperature difference between the heat source and the cold source is always maintained at 40 K. The changes in the in-plane thermal conductivity, heat flux and phonon number at different system temperatures are calculated respectively. By comparing the changes in heat flux and in-plane thermal conductivity at different system temperatures, combined with the phonon scattering mechanism, the influence of temperature on the in-plane thermal conductivity and its internal mechanism are analyzed.
2. The method for predicting anisotropic thermal conductivity of two-dimensional material nanoribbons according to claim 1, wherein: The molecular dynamics simulation and data processing performed in step (2) also include: taking the graphene nanoribbons torsional angle range of 0~120° and the black phosphorus nanoribbons torsional angle range of 0~360°, comparing the effects of different heat transfer directions on the phonon group velocity, and determining the physical mechanism of anisotropic in-plane thermal conductivity.
3. The method for predicting anisotropic thermal conductivity of two-dimensional material nanoribbons according to claim 1, wherein: The molecular dynamics simulation and data processing in step (2) further includes: taking the temperature range of the graphene system to be 100 K~500 K and the temperature range of the black phosphorus system to be 100 K~500 K, comparing the number of phonons at different system temperatures, and determining the intrinsic mechanism of the influence of different system temperatures on the in-plane thermal conductivity.