Orientation of graphene nanosheets in suspension under an electric field: theoretical model and molecular dynamic simulations.

Orientation regulation of nanoparticles in a suspension by an electric field is a powerful tool to tune its mechanical, thermal, optical, electrical properties etc. However, how molecular modification can affect the orientation of two-dimensional nanoparticles is still unclear. In this paper, the influence of molecular modification on the orientation of graphene nanosheets (GNS) in water was investigated through theoretical analyses and molecular dynamics (MD) simulations. Firstly, a new orientation angle model was proposed, which considers hydration effects, dipole moments and resistance torque. Then, MD simulations were conducted to investigate the effects of position, direction, type, and number of functional groups on the orientation of GNS. The trend observed in MD simulations is consistent with the proposed theoretical model. The results reveal that, under the combined influence of the dipole moment and hydration effects, the modification with hydrophilic functional groups can reduce the orientation angle from 21.31° to 8.34°, while the modification with hydrophobic functional groups increases it to 26.43°. Among the hydrophilic functional groups, orientation of hydroxylated GNS is the best. With an increase in the number of hydroxyl groups, orientation angle is decreased from 12.61° to 8.34°. This work can provide valuable guidance for the design of high-performance suspensions and composites, such as thermal smart materials with adjustable thermal conductivity and intelligent devices with tailored capabilities.

Pulsed thermoreflectance imaging for thermophysical properties measurement of GaN epitaxial heterostructures.

Multilayer heterostructures composed of a substrate and an epitaxial film are widely utilized in advanced electronic devices. However, thermal bottlenecks constrain their performance and reliability, and efficient approaches to comprehensively measure the thermophysical properties of heterostructures are urgently needed. In this work, a pulsed thermoreflectance imaging (PTI) method is proposed, which combines the transient temperature mapping of thermoreflectance thermal imaging with transient pulsed excitation. By executing merely three transient tests, six thermophysical properties, including the film thermal conductivity and specific heat capacity, the substrate thermal conductivity and specific heat capacity, the film-substrate thermal boundary resistance, and the equivalent thermal conductivity of the insulating layer, can be simultaneously measured in a heterostructure sample. The proposed method applies a pulsed current excitation to a metal heater line on the sample surface and utilizes the thermoreflectance thermal imaging system to measure the temperature of different spatial regions on the sample surface at different time windows. The temporal and spatial variation information of the temperature field is then extracted and combined with finite element method inversion calculation to obtain the thermophysical properties of heterostructures. To validate the accuracy and reliability of this method, we conducted measurements on a GaN-on-SiC heterostructure sample and obtained thermophysical properties consistent with the representative literature data that have previously been reported. The proposed PTI method, characterized by its high sensitivity, demonstrates good efficiency and reliability in conducting comprehensive thermophysical property characterization of GaN epitaxial heterostructures.

Topology optimization for near-junction thermal spreading of electronics in ballistic-diffusive regime.

Hotspots in electronic devices can cause overheating and reduce performance. Enhancing the thermal spreading ability is critical for reducing device temperature to improve the reliability. However, as devices shrink, phonon ballistic effects can increase thermal resistance, making conventional optimization methods less effective. This paper presents a topology optimization method that combines the phonon Boltzmann transport equation with solid isotropic material with penalization method to optimize high thermal conductivity (HTC) material distributions for thermal spreading problems. Results show that the contraction-expansion structure can effectively reduce thermal resistance. Optimal distributions differ from that based on Fourier's heat conduction law, and only the trunk structure appears in optimized layouts due to the size effect. Additionally, HTC material with longer mean free paths tends to be filled around the heat source with a gap in a ballistic-diffusive regime. This work deepens understanding of thermal spreading and aids in thermal optimization of microelectronic chips.

Thermal Interface Materials with High Thermal Conductivity and Low Young's Modulus Using a Solid-Liquid Metal Codoping Strategy.

Thermal interface materials (TIMs), as typical thermal functional materials, are highly required to possess both high thermal conductivity and low Young's modulus. However, the naturally synchronized change in the thermal and mechanical properties seriously hinders the development of high-performance TIMs. To tackle such a dilemma, a strategy of codoping solid fillers and liquid metal fillers into polymer substrates is proposed in this study. This strategy includes a large amount of liquid metals that play the role of thermal paths and a small amount of uniformly dispersed solid fillers that further enhance heat conduction. Through the synergistic effect of the liquid metal and solid fillers, the thermal conductivity can be improved, and Young's modulus can be kept small simultaneously. A typical TIM with a volume of 55% gallium-based liquid metal and 15% copper particles as fillers has a thermal conductivity of 3.94 W/(m·K) and a Young's modulus of 699 kPa, which had the maximum thermomechanical performance coefficient compared with liquid metal TIMs and solid filler-doped TIMs. In addition, the thermal conductivity of the solid-liquid metal codoped TIM increased sharply with an increase of liquid metal content, and Young's modulus increased rapidly with an increase of the volume ratio of copper and polymer. The high-low-temperature cycling test and large-size light-emitting diode (LED) application demonstrated that this TIM had stable physical performance. The synergistic effect of the solid fillers and liquid metal fillers provides a broad space to solve the classic tradeoff issue of the mechanical and thermal properties of composites.

Thermomass Theory in the Framework of GENERIC.

Thermomass theory was developed to deal with the non-Fourier heat conduction phenomena involving the influence of heat inertia. However, its structure, derived from an analogy to fluid mechanics, requires further mathematical verification. In this paper, General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) framework, which is a geometrical and mathematical structure in nonequilibrium thermodynamics, was employed to verify the thermomass theory. At first, the thermomass theory was introduced briefly; then, the GENERIC framework was applied in the thermomass gas system with state variables, thermomass gas density ρh and thermomass momentum mh, and the time evolution equations obtained from GENERIC framework were compared with those in thermomass theory. It was demonstrated that the equations generated by GENERIC theory were the same as the continuity and momentum equations in thermomass theory with proper potentials and eta-function. Thermomass theory gives a physical interpretation to the GENERIC theory in non-Fourier heat conduction phenomena. By combining these two theories, it was found that the Hamiltonian energy in reversible process and the dissipation potential in irreversible process could be unified into one formulation, i.e., the thermomass energy. Furthermore, via the framework of GENERIC, thermomass theory could be extended to involve more state variables, such as internal source term and distortion matrix term. Numerical simulations investigated the influences of the convective term and distortion matrix term in the equations. It was found that the convective term changed the shape of thermal energy distribution and enhanced the spreading behaviors of thermal energy. The distortion matrix implies the elasticity and viscosity of the thermomass gas.

Machine learning interatomic potential developed for molecular simulations on thermal properties of ß-Ga2O3.

The thermal properties of ß-Ga2O3 can significantly affect the performance and reliability of high-power electronic devices. To date, due to the absence of a reliable interatomic potential, first-principles calculations based on density functional theory (DFT) have been routinely used to probe the thermal properties of ß-Ga2O3. DFT calculations can only tackle small-scale systems due to the huge computational cost, while the thermal transport processes are usually associated with large time and length scales. In this work, we develop a machine learning based Gaussian approximation potential (GAP) for accurately describing the lattice dynamics of perfect crystalline ß-Ga2O3 and accelerating atomic-scale simulations. The GAP model shows excellent convergence, which can faithfully reproduce the DFT potential energy surface at a training data size of 32 000 local atomic environments. The GAP model is then used to predict ground-state lattice parameters, coefficients of thermal expansion, heat capacity, phonon dispersions at 0 K, and anisotropic thermal conductivity of ß-Ga2O3, which are all in excellent agreement with either the DFT results or experiments. The accurate predictions of phonon dispersions and thermal conductivities demonstrate that the GAP model can well describe the harmonic and anharmonic interactions of phonons. Additionally, the successful application of our GAP model to the phonon density of states of a 2500-atom ß-Ga2O3 structure at elevated temperature indicates the strength of machine learning potentials to tackle large-scale atomic systems in long molecular simulations, which would be almost impossible to generate with DFT-based molecular simulations at present.

Tuning the thermal conductivity of nanoparticle suspensions by electric field.

Active thermal management is essential for the operation of modern technologies like electronic circuits and spacecraft systems to deal with the complex control and conversion of thermal energy. One basic requirement for the materials is its tunable and reversible thermal properties. Here, we try to provide a systematic investigation of the thermal smart materials composed of low-dimensional solid particles suspended in liquid media, whose structures and properties can be tuned by external field. A two-step theoretical model, which takes into account the effects from particle aggregation and orientational variation, was proposed and obtained reasonable agreement with both literature and our own experimental results. Graphene nanosheets/Mg-Al layered double hydroxides (GNS/LDH) were fabricated and their silicone oil suspension shows reversible thermal conductivity switching under DC electric field due to the formation/break-up of chain-like structures with a maximum switching ratio around 1.35×. This study reveals the underlying mechanism of thermal conductivity enhancement in nanoparticle suspensions, and provides a preliminary example to design and fabricate responsive thermal materials for the next generation technologies.

Fractional-order heat conduction models from generalized Boltzmann transport equation.

The relationship between fractional-order heat conduction models and Boltzmann transport equations (BTEs) lacks a detailed investigation. In this paper, the continuity, constitutive and governing equations of heat conduction are derived based on fractional-order phonon BTEs. The underlying microscopic regimes of the generalized Cattaneo equation are thereafter presented. The effective thermal conductivity κeff converges in the subdiffusive regime and diverges in the superdiffusive regime. A connection between the divergence and mean-square displacement 〈|Δx|2〉 ∼ tγ is established, namely, κeff ∼ tγ-1, which coincides with the linear response theory. Entropic concepts, including the entropy density, entropy flux and entropy production rate, are studied likewise. Two non-trivial behaviours are observed, including the fractional-order expression of entropy flux and initial effects on the entropy production rate. In contrast with the continuous time random walk model, the results involve the non-classical continuity equations and entropic concepts. This article is part of the theme issue 'Advanced materials modelling via fractional calculus: challenges and perspectives'.

Molecular dynamic simulation of thermal transport in monolayer C3B x N1-x alloy.

Recently, two-dimensional (2D) monolayers C3B and C3N attract growing research interest due to the excellent physical properties. In this work, the thermal conductivities (k) of the monolayer C3B x N1-x alloy and the special C3B0.5N0.5 superlattice (C3B0.5N0.5-SL) alloy are systematically evaluated by using molecular dynamic simulation. First, the k of monolayer C3B x N1-x alloy presents a U-shaped profile with the increasing random doping ratio (x), in which the lowest k exists in x = 0.5. Second, we further calculate the thermal conductivity of C3B0.5N0.5-SL. The result shows an initial decreasing and then rising trend, and the coherent length is 5.11 nm which occupies the minimum thermal conductivity. Furthermore, to uncover the phonon thermal transport mechanism, we calculate the spatiotemporal thermal transport, phonon density of states, phonon group velocity, participation ratio and the phonon wave packet simulations in monolayer alloy system. We note that on account of the random doping atoms, the enhancive phonon-impurity scattering and phonon localization reduce the thermal conductivity in monolayer C3B x N1-x alloy. In C3B0.5N0.5-SL, when the period length is smaller than the coherent length, coherent phonon modes emerge because of the phonon interference, in which the superlattice can be regarded as a 'newly generated material'. However, when the period length is larger than the coherent length, the decreasing number of the interface in superlattice lessens phonon-interface scattering and cause the increasing thermal conductivity. This work contributes the fundamental knowledge for thermal management in 2D monolayer C3B x N1-x alloy based nanoelectronics.

Diffusion Tensors of Arbitrary-Shaped Nanoparticles in Fluid by Molecular Dynamics Simulation.

The anisotropic diffusive behavior of nanoparticles with complex shapes attracts great interest due to its potential applications in many fields ranging from bionics to aeronautic industry. Although molecular dynamics (MD) simulations are used widely to investigate nanoparticle diffusion properties, universal methods to describe the diffusion process comprehensively are still lacking. Here, we address this problem by introducing diffusion tensor as it can describe translational and rotational diffusion in three dimensions both individually and their coupling. We take carbon triple sphere suspended in argon fluid as our model system. The consistency of our results and velocity autocorrelation function(VAF) method validates our simulations. The coupling between translational and rotational diffusion is observed directly from analyzing diffusion tensor, and quantified by coupling diffusion coefficient. Our simulation reveals non-trivial effect of some factors in diffusion at nanoscale, which was not considered in previous theories. In addition to introducing an effective method to calculate the diffusion tensor in MD simulations, our work also provides insights for understanding the diffusion process of arbitrary-shaped particles in nanoengineering.

On Entropic Framework Based on Standard and Fractional Phonon Boltzmann Transport Equations.

Generalized expressions of the entropy and related concepts in non-Fourier heat conduction have attracted increasing attention in recent years. Based on standard and fractional phonon Boltzmann transport equations (BTEs), we study entropic functionals including entropy density, entropy flux and entropy production rate. Using the relaxation time approximation and power series expansion, macroscopic approximations are derived for these entropic concepts. For the standard BTE, our results can recover the entropic frameworks of classical irreversible thermodynamics (CIT) and extended irreversible thermodynamics (EIT) as if there exists a well-defined effective thermal conductivity. For the fractional BTEs corresponding to the generalized Cattaneo equation (GCE) class, the entropy flux and entropy production rate will deviate from the forms in CIT and EIT. In these cases, the entropy flux and entropy production rate will contain fractional-order operators, which reflect memory effects.

Thermal rectification at the bimaterial nanocontact interface.

Thermal rectification can help develop modern thermal manipulation devices but has been rarely engineered. Here, we validated the nanoscale bimaterial interface-induced thermal rectification experimentally for the first time and investigated its underlying mechanism via molecular dynamics simulations. The thermal diode consists of polyamide (PA) and silicon (Si) nanowires in contact with each other. The thermal rectification ratio measured by a high-precision nanoscale experiment reached 4% with an uncertainty of <1%. The temperature has little influence on the ratio, while the decrease in contact length or increase in temperature differences can increase the ratio. The molecular dynamics simulations further confirmed the thermal rectification in the PA/Si nanowires. We found that the localized modes generally gather on the edge, and the higher extent of phonon localization is responsible for the lower thermal conductance in the thermal rectification. Our findings not only have guiding significance, but can also promote the development of interface-based solid-state thermal diodes.

Mathematical and information-geometrical entropy for phenomenological Fourier and non-Fourier heat conduction.

The second law of thermodynamics governs the direction of heat transport, which provides the foundational definition of thermodynamic Clausius entropy. The definitions of entropy are further generalized for the phenomenological heat transport models in the frameworks of classical irreversible thermodynamics and extended irreversible thermodynamics (EIT). In this work, entropic functions from mathematics are combined with phenomenological heat conduction models and connected to several information-geometrical conceptions. The long-time behaviors of these mathematical entropies exhibit a wide diversity and physical pictures in phenomenological heat conductions, including the tendency to thermal equilibrium, and exponential decay of nonequilibrium and asymptotics, which build a bridge between the macroscopic and microscopic modelings. In contrast with the EIT entropies, the mathematical entropies expressed in terms of the internal energy function can avoid singularity paired with nonpositive local absolute temperature caused by non-Fourier heat conduction models.

Nanoscale thermal cloaking in graphene via chemical functionalization.

Macro-thermal cloaking is typically produced by coordinate transformations, but this method is unsuitable for nanostructures. We designed a graphene-based nanoscale thermal cloak using a novel mechanism of phonon localization. The nanocloak in graphene was produced via the chemical functionalization of hydrogen, methyl and hydroxyl using molecular dynamics simulations. The cloaking performance was quantified by the ratio of thermal cloaking (RTC). We found that the RTC correlated with the functionalization fraction and it has a local maximum at a certain width, since the heat flux reduction in the exterior and the protected region reversed if the width was excessive. The atomic mass of the functional group also correlated with the RTC. Our simulations determined that phonon localization occurred due to sp2-to-sp3 bonding transitions, which caused the heat flux to avoid the transition region. Finally, the extent of phonon localization was related to the cloaking performance.

Phonon thermal properties of graphene from molecular dynamics using different potentials.

Phonon thermal transport in graphene has attracted significant interest in recent years. Phonon thermal properties of graphene are investigated by molecular dynamics simulations using the Tersoff, Tersoff-2010, REBO, and AIREBO potentials. By calculating the phonon properties and thermal conductivity of graphene, the performance of the potentials is evaluated based on comparisons with experimental data. It shows that the Tersoff-2010 and REBO display better dispersion curves for graphene than the original Tersoff and AIREBO. The Tersoff-2010 correctly provides the Γ point phonon velocities of the LA and TA branches as well as the G peak frequency with a value of 46 THz. In addition, the acoustic phonon relaxation time derived from the Tersoff-2010 satisfies the ideal relation "τ-1 ∝ ν2." It is also found that the Tersoff-2010 provides the highest graphene thermal conductivity among the used potentials, and estimates about 30.0% contribution for flexural phonons to the total thermal conductivity. By comparison, the Tersoff-2010 potential is demonstrated to be the most suitable one to describe the phonon thermal properties of graphene.

Transient in-plane thermal transport in nanofilms with internal heating.

Wide applications of nanofilms in electronics necessitate an in-depth understanding of nanoscale thermal transport, which significantly deviates from Fourier's law. Great efforts have focused on the effective thermal conductivity under temperature difference, while it is still ambiguous whether the diffusion equation with an effective thermal conductivity can accurately characterize the nanoscale thermal transport with internal heating. In this work, transient in-plane thermal transport in nanofilms with internal heating is studied via Monte Carlo (MC) simulations in comparison to the heat diffusion model and mechanism analyses using Fourier transform. Phonon-boundary scattering leads to larger temperature rise and slower thermal response rate when compared with the heat diffusion model based on Fourier's law. The MC simulations are also compared with the diffusion model with effective thermal conductivity. In the first case of continuous internal heating, the diffusion model with effective thermal conductivity under-predicts the temperature rise by the MC simulations at the initial heating stage, while the deviation between them gradually decreases and vanishes with time. By contrast, for the one-pulse internal heating case, the diffusion model with effective thermal conductivity under-predicts both the peak temperature rise and the cooling rate, so the deviation can always exist.

Experimental study on thermophoresis of colloids in aqueous surfactant solutions.

Thermophoresis refers to the motion of particles under a temperature gradient and it is one of the particle manipulation techniques. Regarding the thermophoresis of particles in liquid media, however, many open questions still remain, especially the role of the interfacial effect. This work reports on a systematic experimental investigation of surfactant effects, especially the induced interfacial effect, on the thermophoresis of colloids in aqueous solutions via a microfluidic approach. Two kinds of commonly used surfactants, sodium dodecyl sulfate (SDS) and cetyltrimethylammonium bromide (CTAB), are selected and the results show that from relatively large concentrations, the two surfactants can greatly enhance the thermophilic mobilities. Specifically, it is found that the colloid-water interfaces modified with more polar end groups can potentially lead to a stronger thermophilic tendency. Due to the complex effects of surfactants, further theoretical model development is needed to quantitatively describe the dependence of thermophoresis on the interface characteristics.

Investigation of Rotational Diffusion of a Carbon Nanotube by Molecular Dynamics.

The rotational diffusion coefficient of a single carbon nanotube in fluid is calculated by equilibrium and nonequilibrium molecular dynamics (MD). The validity and accuracy of the MD simulations are checked on plenty of data points by varying the length and diameter of the nanotube. The three-dimensional (3D) coefficients are larger than the two-dimensional (2D) ones, both having non- negligible deviations from the theoretical predictions [J. Chem. Phys. 1984, 81, 2047-2052]. By changing the parameter εC-Ar of Lennard-Jones potential, the interaction strength between carbon and argon atoms is also taken into account. A monotonic decrease of the coefficients for both 2D and 3D cases with the increase of εC-Ar can be observed. Our present work suggests that we must be cautious when using the literature theory in practical situations.

Molecular Dynamics Studies on Thermal Transport Through Multiwalled Carbon Nanotubes.

The influence of the temperature and strength of the inter-wall interaction on the thermal conductivities of the (5,5) and (10, 10) double-walled carbon nanotubes (DWNTs) is studied by using molecular dynamics (MD) simulations with two different temperature control methods. One method is imposing heat baths (HBs) only on the outer wall, while the other is imposing HBs on both the two walls. The results show that the thermal conductivities of the DWNTs with the first method are about two-third of those with the second method. The relationship is the same even if the temperature and strength of the inter-wall interaction vary. Besides, the thermal conductivities of the DWNTs with the two different temperature control methods both slightly increase with the increasing energy parameters of Lennard-Jones (LJ) potential describing the inter-wall interaction and decrease with increasing temperature. Based on the analyses of the temperature profiles and phonon density of states (PDOS) spectra of the DWNTs with the two different temperature control methods, the results are well explained and the thermal transport mechanisms of multiwalled carbon nanotubes (MWNTs) under different conditions are explored.

Effects of nanosized constriction on thermal transport properties of graphene.

Thermal transport properties of graphene with nanosized constrictions are investigated using nonequilibrium molecular dynamics simulations. The results show that the nanosized constrictions have a significant influence on the thermal transport properties of graphene. The thermal resistance of the nanosized constrictions is on the order of 10(7) to 10(9) K/W at 150 K, which reduces the thermal conductivity by 7.7% to 90.4%. It is also found that the constriction resistance is inversely proportional to the width of the constriction and independent of the heat current. Moreover, we developed an analytical model for the ballistic thermal resistance of the nanosized constrictions in two-dimensional nanosystems. The theoretical prediction agrees well with the simulation results in this paper, which suggests that the thermal transport across the nanosized constrictions in two-dimensional nanosystems is ballistic in nature. PACS: 65.80.CK; 61.48.Gh; 63.20.kp; 31.15.xv.