Thermal transport of small systems

2017 ◽  
Author(s):  
Takahiro Yamamoto ◽  
Kazuyuki Watanabe ◽  
Satoshi Watanabe
Keyword(s):  
Thermal Transport ◽  
Thermal Conductance ◽  
Transmission Function ◽  
Mean Free Path ◽  
Phonon Transport ◽  
Fourier Law ◽  
Small Systems ◽  
One Dimensional ◽  
Sample Dimension ◽  
The Mean

This article focuses on the phonon transport or thermal transport of small systems, including quasi-one-dimensional systems such as carbon nanotubes. The Fourier law well describes the thermal transport phenomena in normal bulk materials. However, it is no longer valid when the sample dimension reduces down to below the mean-free path of phonons. In such a small system, the phonons propagate coherently without interference with other phonons. The article first considers the Boltzmann–Peierls formula of diffusive phonon transport before discussing coherent phonon transport, with emphasis on the Landauer formulation of phonon transport, ballistic phonon transport and quantized thermal conductance, numerical calculation of the phonon-transmission function, and length dependence of the thermal conductance.

scholarly journals Nanoscale Quantum Thermal Conductance at Water Interface: Green’s Function Approach Based on One-Dimensional Phonon Model

Molecules ◽  
2020 ◽  
Vol 25 (5) ◽  
pp. 1185
Author(s):  
Toshihito Umegaki ◽  
Shigenori Tanaka
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Thermal Conductance ◽  
Transmission Function ◽  
Transmission Probability ◽  
Phonon Transport ◽  
Tunnel Effect ◽  
Water Molecules ◽  
One Dimensional ◽  
Phonon Model

We have derived the fundamental formula of phonon transport in water for the evaluation of quantum thermal conductance by using a one-dimensional phonon model based on the nonequilibrium Green’s function method. In our model, phonons are excited as quantum waves from the left or right reservoir and propagate from left to right of H 2 O layer or vice versa. We have assumed these reservoirs as being of periodic structures, whereas we can also model the H 2 O sandwiched between these reservoirs as having aperiodic structures of liquid containing N water molecules. We have extracted the dispersion curves from the experimental absorption spectra of the OH stretching and intermolecular modes of water molecules, and calculated phonon transmission function and quantum thermal conductance. In addition, we have simplified the formulation of the transmission function by employing a case of one water molecule (N=1). From this calculation, we have obtained the characteristic that the transmission probability is almost unity at the frequency bands of acoustic and optical modes, and the transmission probability vanishes by the phonon attenuation reflecting the quantum tunnel effect outside the bands of these two modes. The classical limit of the thermal conductance calculated by our formula agreed with the literature value (order of 10 − 10 W/K) in high temperature regime (>300 K). The present approach is powerful enough to be applicable to molecular systems containing proteins as well, and to evaluate their thermal conductive characteristics.

Heat Conduction in Nanostructured Materials Predicted by Phonon Bulk Mean Free Path Distribution

2015 ◽  
Vol 137 (7) ◽  
Author(s):  
Giuseppe Romano ◽  
Jeffrey C. Grossman
Keyword(s):  
Free Path ◽  
Nanostructured Materials ◽  
Thermal Transport ◽  
High Efficiency ◽  
Theoretical Models ◽  
Mean Free Path ◽  
Phonon Transport ◽  
Computational Effort ◽  
Boltzmann Transport ◽  
Computational Framework

We develop a computational framework, based on the Boltzmann transport equation (BTE), with the ability to compute thermal transport in nanostructured materials of any geometry using, as the only input, the bulk cumulative thermal conductivity. The main advantage of our method is twofold. First, while the scattering times and dispersion curves are unknown for most materials, the phonon mean free path (MFP) distribution can be directly obtained by experiments. As a consequence, a wider range of materials can be simulated than with the frequency-dependent (FD) approach. Second, when the MFP distribution is available from theoretical models, our approach allows one to include easily the material dispersion in the calculations without discretizing the phonon frequencies for all polarizations thereby reducing considerably computational effort. Furthermore, after deriving the ballistic and diffusive limits of our model, we develop a multiscale method that couples phonon transport across different scales, enabling efficient simulations of materials with wide phonon MFP distributions length. After validating our model against the FD approach, we apply the method to porous silicon membranes and find good agreement with experiments on mesoscale pores. By enabling the investigation of thermal transport in unexplored nanostructured materials, our method has the potential to advance high-efficiency thermoelectric devices.

scholarly journals Tuning the Anisotropic Thermal Transport in {110}-Silicon Membranes with Surface Resonances

Nanomaterials ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 123
Author(s):  
Keqiang Li ◽  
Yajuan Cheng ◽  
Maofeng Dou ◽  
Wang Zeng ◽  
Sebastian Volz ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Thermal Transport ◽  
Heat Dissipation ◽  
Mean Free Path ◽  
Dynamic Simulations ◽  
Resonant Structures ◽  
Thermoelectric Energy ◽  
Thin Membranes ◽  
The Mean ◽  
Equilibrium Molecular Dynamic

Understanding the thermal transport in nanostructures has important applications in fields such as thermoelectric energy conversion, novel computing and heat dissipation. Using non-homogeneous equilibrium molecular dynamic simulations, we studied the thermal transport in pristine and resonant Si membranes bounded with {110} facets. The break of symmetry by surfaces led to the anisotropic thermal transport with the thermal conductivity along the [110]-direction to be 1.78 times larger than that along the [100]-direction in the pristine structure. In the pristine membranes, the mean free path of phonons along both the [100]- and [110]-directions could reach up to ∼100 µm. Such modes with ultra-long MFP could be effectively hindered by surface resonant pillars. As a result, the thermal conductivity was significantly reduced in resonant structures, with 87.0% and 80.8% reductions along the [110]- and [100]-directions, respectively. The thermal transport anisotropy was also reduced, with the ratio κ110/κ100 decreasing to 1.23. For both the pristine and resonant membranes, the thermal transport was mainly conducted by the in-plane modes. The current work could provide further insights in understanding the thermal transport in thin membranes and resonant structures.

scholarly journals Thermal Transport in One-Dimensional Van Der Waals Heterostructures: Effects of Coating Layers on the Thermal Conductivity of Carbon Nanotubes

2020 ◽  
Author(s):  
Penghua Ying ◽  
Jin Zhang ◽  
Yao Du ◽  
Zheng Zhong
Keyword(s):  
Heat Flux ◽  
Thermal Transport ◽  
Van Der Waals ◽  
Thermal Conductance ◽  
One Dimensional ◽  
Interfacial Thermal Conductance ◽  
Quantitative Understanding ◽  
Non Equilibrium Molecular Dynamics ◽  
Dynamics Simulations ◽  
The Individual

In this paper, we conduct a comprehensive investigation on the thermal transport in one-dimensional (1D) van der Waals (vdW) heterostructures by using non-equilibrium molecular dynamics simulations. It is found that the boron nitride nanotube (BNNT) coating can increase the thermal conductance of inner carbon nanotube (CNT) base by 36%, while the molybdenum disulfide nanotube (<a>MSNT</a>) coating can reduce the thermal conductance by 47%. The different effects of BNNT and MSNT coatings on the thermal transport behaviors of 1D vdW heterostructures are explained by the competition mechanism between improved heat flux and increased temperature gradient in 1D vdW heterostructures. By taking CNT@BNNT@MSNT as an example, thermal transport in 1D vdW heterostructures containing three layers is also investigated. It is found that the coaxial BNNT-MSNT coating can significantly reduce the thermal conductance of inner CNT base by 61%, which is even larger than that of an individual MSNT coating. This unexpected reduction in thermal conductance of CNT@BNNT@MSNT can be explained by the suppression of heat flux arising from the possible compression effect, since BNNT-MSNT coating in CNT@BNNT@MSNT can more significantly suppress the vibration of inner CNT when compared to the individual MSNT coating in CNT@MSNT. In addition to the in-plane thermal transport, the interfacial thermal conductance between inner and outer nanotubes in 1D vdW heterostructures is also examined to provide a quantitative understanding of the thermal transport behaviors of1D vdW heterostructures. This work is expected to provide molecular insights into tailoring the heat transport in carbon base 1D vdW heterostructures and thus facilitate their broader applications as thermal interface materials.

scholarly journals Non-local effects in radial heat transport in silicon thin layers and graphene sheets

2011 ◽  
Vol 468 (2141) ◽  
pp. 1217-1229 ◽  
Author(s):  
A. Sellitto ◽  
D. Jou ◽  
J. Bafaluy
Keyword(s):  
Heat Transport ◽  
Local Equilibrium ◽  
Mean Free Path ◽  
Thin Layers ◽  
Graphene Sheets ◽  
Fourier Law ◽  
Local Effects ◽  
Radial Heat ◽  
Non Local ◽  
The Mean

We explore non-local effects in radially symmetric heat transport in silicon thin layers and in graphene sheets. In contrast to one-dimensional perturbations, which may be well described by means of the Fourier law with a suitable effective thermal conductivity, two-dimensional radial situations may exhibit a more complicated behaviour, not reducible to an effective Fourier law. In particular, a hump in the temperature profile is predicted for radial distances shorter than the mean-free path of heat carriers. This hump is forbidden by the local-equilibrium theory, but it is allowed in more general thermodynamic theories, and therefore it may have a special interest regarding the formulation of the second law in ballistic heat transport.

Ballistic Heat Transfer Modelling in Semiconductor Electronic Devices: A Modified Fourier-Based Approach

2010 ◽  
Author(s):  
Aydin Nabovati ◽  
Daniel P. Sellan ◽  
Cristina H. Amon
Keyword(s):  
Electronic Devices ◽  
Mean Free Path ◽  
Characteristic Size ◽  
Fourier Law ◽  
Transport Models ◽  
Size Dependent ◽  
Semiconductor Electronic ◽  
Ballistic Heat Transfer ◽  
The Mean ◽  
Boltzmann Method

It is well known that continuum-based thermal transport models, such as the Fourier law, fail when the characteristic size of a system becomes comparable to the mean free path of carriers that transport thermal energy. The current work uses the lattice Boltzmann method to develop two modifications to the Fourier heat equation so that it can capture sub-continuum effects. The two modifications are: (i) a size-dependent thermal conductivity and (ii) a size-dependent temperature jump at the system boundaries.

THERMAL TRANSPORT BY BALLISTIC PHONON IN A SEMICONDUCTOR RECTANGULAR QUANTUM WIRE MODULATED WITH QUANTUM DOT

2009 ◽  
Vol 23 (30) ◽  
pp. 3597-3607 ◽  
Author(s):  
XIAO-YAN YU ◽  
XIAO-FANG PENG ◽  
KE-QIU CHEN
Keyword(s):  
Quantum Dot ◽  
Thermal Transport ◽  
Low Temperatures ◽  
Quantum Wire ◽  
Thermal Conductance ◽  
Phonon Transport ◽  
Total Transmission ◽  
Coefficient Versus ◽  
Increasing Temperature ◽  
Scattering Matrix Method

Thermal transport by ballistic phonon in a semiconductor rectangular quantum wire modulated with quantum dot at low temperatures is investigated with the use of the scattering matrix method. The calculated results show that the total transmission coefficient versus the reduced phonon frequency exhibits interesting characteristics such as inhomogeneous quantum transport steps. Quantized thermal conductance plateau can be observed at low temperatures, and the thermal conductance is not increased monotonically with increasing temperature. The results also show that the phonon transport probability and thermal conductance can be controlled to a certain degree by adjusting the parameters of the proposed quantum structure.

scholarly journals Thermal Transport in One-Dimensional Van Der Waals Heterostructures: Effects of Coating Layers on the Thermal Conductivity of Carbon Nanotubes

2020 ◽  
Author(s):  
Penghua Ying ◽  
Jin Zhang ◽  
Yao Du ◽  
Zheng Zhong
Keyword(s):  
Heat Flux ◽  
Thermal Transport ◽  
Van Der Waals ◽  
Thermal Conductance ◽  
One Dimensional ◽  
Interfacial Thermal Conductance ◽  
Quantitative Understanding ◽  
Non Equilibrium Molecular Dynamics ◽  
Dynamics Simulations ◽  
The Individual

In this paper, we conduct a comprehensive investigation on the thermal transport in one-dimensional (1D) van der Waals (vdW) heterostructures by using non-equilibrium molecular dynamics simulations. It is found that the boron nitride nanotube (BNNT) coating can increase the thermal conductance of inner carbon nanotube (CNT) base by 36%, while the molybdenum disulfide nanotube (<a>MSNT</a>) coating can reduce the thermal conductance by 47%. The different effects of BNNT and MSNT coatings on the thermal transport behaviors of 1D vdW heterostructures are explained by the competition mechanism between improved heat flux and increased temperature gradient in 1D vdW heterostructures. By taking CNT@BNNT@MSNT as an example, thermal transport in 1D vdW heterostructures containing three layers is also investigated. It is found that the coaxial BNNT-MSNT coating can significantly reduce the thermal conductance of inner CNT base by 61%, which is even larger than that of an individual MSNT coating. This unexpected reduction in thermal conductance of CNT@BNNT@MSNT can be explained by the suppression of heat flux arising from the possible compression effect, since BNNT-MSNT coating in CNT@BNNT@MSNT can more significantly suppress the vibration of inner CNT when compared to the individual MSNT coating in CNT@MSNT. In addition to the in-plane thermal transport, the interfacial thermal conductance between inner and outer nanotubes in 1D vdW heterostructures is also examined to provide a quantitative understanding of the thermal transport behaviors of1D vdW heterostructures. This work is expected to provide molecular insights into tailoring the heat transport in carbon base 1D vdW heterostructures and thus facilitate their broader applications as thermal interface materials.

scholarly journals The Random Walks between Pseudo-Specific DNA Sites as Model of the Facilitated Diffusion of DNA-Binding Proteins

2015 ◽  
Vol 10 (2) ◽  
pp. 473-481
Author(s):  
Р.Т. Сибатов ◽  
R.T. Sibatov
Keyword(s):  
Random Walks ◽  
First Passage Time ◽  
Regulatory Protein ◽  
Free Path Length ◽  
Mean Free Path ◽  
Passage Time ◽  
Facilitated Diffusion ◽  
One Dimensional ◽  
Ballistic Motion ◽  
The Mean

The facilitated diffusion of a regulatory protein in the process of searching for a specific target site on the DNA molecule is considered. On the basis of the hypothesis of ballistic motion of the protein between scatterings of pseudo-specific sites, we proposed a phenomenological model of one-dimensional translocation of the protein along DNA. Combining this approach with the model of discrete random walks we were able to get the relationships between the mean first passage time and such characteristics as the binding energy, the mean free path length between pseudo-specific sites, the speed of protein movement and the temperature. These dependencies allow revealing the thermal and energetic optima, at which minimum values of searching time are achieved.

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