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.

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.

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'.

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.

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.

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.

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.

Molecular dynamics calculation of rotational diffusion coefficient of a carbon nanotube in fluid.

Rotational diffusion processes are correlated with nanoparticle visualization and manipulation techniques, widely used in nanocomposites, nanofluids, bioscience, and so on. However, a systematical methodology of deriving this diffusivity is still lacking. In the current work, three molecular dynamics (MD) schemes, including equilibrium (Green-Kubo formula and Einstein relation) and nonequilibrium (Einstein-Smoluchowski relation) methods, are developed to calculate the rotational diffusion coefficient, taking a single rigid carbon nanotube in fluid argon as a case. We can conclude that the three methods produce same results on the basis of plenty of data with variation of the calculation parameters (tube length, diameter, fluid temperature, density, and viscosity), indicative of the validity and accuracy of the MD simulations. However, these results have a non-negligible deviation from the theoretical predictions of Tirado et al. [J. Chem. Phys. 81, 2047 (1984)], which may come from several unrevealed factors of the theory. The three MD methods proposed in this paper can also be applied to other situations of calculating rotational diffusion coefficient.

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.

Molecular dynamics study on evaporation and condensation of n-dodecane at liquid-vapor phase equilibria.

Molecular dynamics simulations are performed to study the evaporation and condensation of n-dodecane (C(12)H(26)) at temperatures in the range 400-600 K. A modified optimized potential for liquid simulation model is applied to take into account the Lennard-Jones, bond bending and torsion potentials with the bond length constrained. The equilibrium liquid-vapor n-dodecane interface thickness is predicted to be ~1.2-2.0 nm. It is shown that the molecular chains lie preferentially parallel to the interface in the liquid-vapor transition region. The predicted evaporation/condensation coefficient decreased from 0.9 to 0.3 when temperature increased from 400 to 600 K. These values can be used for the formulation of boundary conditions in the kinetic modeling of droplet heating and evaporation processes; they are noticeably different from those predicted by the transition state theory. We also present the typical molecular behaviors in the evaporation and condensation processes. The molecular exchange in condensation, typical for simple molecules, has never been observed for n-dodecane molecular chains.

A uniform source-and-sink scheme for calculating thermal conductivity by nonequilibrium molecular dynamics.

A uniform source-and-sink (USS) scheme, which combines features of the reverse [F. Müller-Plathe, J. Chem. Phys. 106, 6082 (1997)] and improved relaxation [B. Y. Cao, J. Chem. Phys. 129, 074106 (2008)] methods, is developed to calculate the thermal conductivity by nonequilibrium molecular dynamics (NEMD). The uniform internal heat source and sink are realized by exchanging the velocity vectors of individual atoms in the right half and left half systems, and produce a periodically quadratic temperature profile throughout the system. The thermal conductivity can be easily extracted from the mean temperatures of the right and left half systems rather than by fitting the temperature profiles. In particular, this scheme greatly increases the relaxation of the exited localized phonon modes which often worsen the calculation accuracy and efficiency in most other NEMD methods. The calculation of the thermal conductivities of solid argon shows that the simple USS scheme gives accurate results with fast convergence.

Thermal gradient induced actuation in double-walled carbon nanotubes.

Molecular dynamics simulations are applied to investigate the thermal gradient induced actuation in double-walled carbon nanotubes, where a temperature difference can actuate the relative motion of double-walled carbon nanotubes. The thermal driving force calculated through a stationary scheme is on the order of pico Newtons for a 1 K nm(-1) temperature gradient. The driving force is approximately proportional to the temperature gradient, but not sensitive to the system temperature. For the outer tube longer than 5 nm, the thermal driving force is nearly constant. For the outer tube shorter than 5 nm, however, the driving force decreases with decreasing tube length. The motion trace is found to depend on both the chirality pair and system temperature. A critical temperature can be defined by the potential barrier perpendicular to the minimum energy track of potential patterns. When the system temperature is higher than the critical temperature, the motion shows random behavior. When the system temperature is lower than the critical temperature, the motion, translational and/or rotational, is confined within the minimum energy track, which is indicative of the feasibility of directional control.

Molecular momentum transport at fluid-solid interfaces in MEMS/NEMS: a review.

This review is focused on molecular momentum transport at fluid-solid interfaces mainly related to microfluidics and nanofluidics in micro-/nano-electro-mechanical systems (MEMS/NEMS). This broad subject covers molecular dynamics behaviors, boundary conditions, molecular momentum accommodations, theoretical and phenomenological models in terms of gas-solid and liquid-solid interfaces affected by various physical factors, such as fluid and solid species, surface roughness, surface patterns, wettability, temperature, pressure, fluid viscosity and polarity. This review offers an overview of the major achievements, including experiments, theories and molecular dynamics simulations, in the field with particular emphasis on the effects on microfluidics and nanofluidics in nanoscience and nanotechnology. In Section 1 we present a brief introduction on the backgrounds, history and concepts. Sections 2 and 3 are focused on molecular momentum transport at gas-solid and liquid-solid interfaces, respectively. Summary and conclusions are finally presented in Section 4.

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.

Nonequilibrium molecular dynamics calculation of the thermal conductivity based on an improved relaxation scheme.

A nonequilibrium molecular dynamics (NEMD) method using stochastic energy injection and removal as uniform heat sources and sinks is developed to calculate the thermal conductivity. The stochastic energy is generated by a Maxwell function generator and is imposed on only a few individual molecules each time step. The relaxation of the thermal perturbation is improved compared to other NEMD algorithms because there are no localized heat source and sink slab regions in the system. The heat sources are uniformly distributed in the right half of the system while the sinks are in the left half, which leads to a periodically quadratic temperature distribution that is almost sinusoidal. The thermal conductivity is then easily calculated from the mean temperatures of the right and left half systems rather than by fitting the temperature profiles. This improved relaxation NEMD scheme is used to calculate the thermal conductivities of liquid and solid argons. It shows that the present algorithm gives accurate results with fast convergence and small size effects. Other stochastic energy perturbation, e.g., thermal noise, can be used to replace the Maxwell-type perturbation used in this paper to make the improved relaxation scheme more effective.

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.