- Nano Express
- Open Access
Influence of Nanopore Shapes on Thermal Conductivity of Two-Dimensional Nanoporous Material
© The Author(s). 2016
- Received: 25 May 2016
- Accepted: 20 September 2016
- Published: 26 September 2016
The influence of nanopore shapes on the electronic thermal conductivity (ETC) was studied in this paper. It turns out that with same porosity, the ETC will be quite different for different nanopore shapes, caused by the different channel width for different nanopore shapes. With same channel width, the influence of different nanopore shapes can be approximately omitted if the nanopore is small enough (smaller than 0.5 times EMFP in this paper). The ETC anisotropy was discovered for triangle nanopores at a large porosity with a large nanopore size, while there is a similar ETC for small pore size. It confirmed that the structure difference for small pore size may not be seen by electrons in their moving.
- Thermal conductivity
- Nanoporous material
- Two-dimensional material
- Electron mean free path
While the specific heat contributed by electrons in an MNM is equal to that in the bulk material , following kinetic theory, the reduced ETC will equal to the reduced electron mean free path (EMFP) , i.e., k e* = l e*, where k e is the ETC, l e is the EMFP, the superscript “*” in this paper indicates a dimensionless quantity scaled by that of the corresponding bulk quantity. While a linear relationship (k e* = l e*) exists between the ETC and the EMFP, only the EMFP should be obtained. A simulation method based on the kinetic theory has already been set up to predict the EMFP in our previous work [9–12]. This simulation method was also applied in this work to predict the EMFP. For consistency, the hypotheses applied in the simulation method were summarized here: (a) The free-electron-gas model (also denoted as the Drude model)  was applied. (b) Each electron moves along a straight line at the Fermi velocity until terminated at a boundary surface or after a sufficiently long path has been traveled [16, 17]. (c) Only the Z component of free path contributes to the EMFP. Based on the similar hypotheses, an EMFP calculation model was also set up for a hollow nanowire in Ref. .
In this paper, the influence of nanopore shapes on the ETC of two-dimensional MNMs was studied with a method setup in our previous work. Three typical shapes were selected to probe their influence. While the ETC can be also affected by the nanopore distributions, a similar nanopore distribution was applied to get rid of their influence. The result shows that different nanopore shape will lead to different ETC at same porosity. This can be easily understood by that different nanopore shape with same porosity will lead to a different electron transfer channel width. The different channel width should be responsible for the difference. So a further study was carried out with a same channel width. Results tell that the nanopore shape has little effect on ETC at small pore size, because the scattering caused by a small size nanopore may like a defect-scattering while the structure difference between different nanopore shapes with small pore size is difficult to be seen by electrons in their moving. For large pore size, the ETC for different nanopore shapes will be quite different at a large porosity. This can be easily understood by that the nanopore shape becomes large to be seen by electrons in their moving. It can be concluded that the nanopore shapes can be approximately omitted if the nanopore is small enough (smaller than 0.5 times EMFP in this paper). The ETC anisotropy was discovered for triangle nanopores at a large porosity with a large nanopore size, while there is a similar ETC for small pore size. It confirmed that the structure difference for small pore size (d* ≤ 0.5) is too small to be seen by electrons in their moving.
a, Distance between two adjacent pores; d, Side length of a square nanopore; EMFP, Electron mean free path; ETC, Electronic thermal conductivity; k e, ETC; l 0, Bulk EMFP; l e, EMFP of MNM; LTC, Lattice thermal conductivity; MNM, Metallic nanoporous materials
*, Dimensionless quantity scaled by that of the corresponding bulk
This work has been supported by the Fundamental Research Funds for the Central Universities (2015XKMS062).
We admit that no other funding should be declared except the Fundamental Research Funds for the Central Universities (2015XKMS062), which was added in the Acknowledgements, for the funding interpretation of data and writing the manuscript.
CLH contributed to the method setup, simulation, and manuscript preparation. ZH and ZZL carried out the simulation of the study. YHF carried out the simulation and manuscript preparation. XXZ contributed to the method setup and simulation of the study. GW participated in the method setup and simulation of the study. All authors read and approved the final manuscript.
The authors declare that they have no competing interests.
Ethics Approval and Consent to Participate
We admit that ethical identity is not involved.
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