Elsevier

Physics Letters A

Volume 380, Issue 38, 7 September 2016, Pages 3103-3106
Physics Letters A

Electronic thermal conductivity of 2-dimensional circular-pore metallic nanoporous materials

https://doi.org/10.1016/j.physleta.2016.07.045Get rights and content

Highlights

  • For metallic nanoporous materials, there is an appropriate pore size for thermal conductivity tuning.

  • ETC increases with increasing pore size until pore size reaches about four times EMFP.

  • The ETC difference between different directions will be less than 10%.

  • The ETC can be decreased by 30% with tuning specular coefficient.

Abstract

The electronic thermal conductivity (ETC) of 2-dimensional circular-pore metallic nanoporous material (MNM) was studied here for its possible applications in thermal cloaks. A simulation method based on the free-electron-gas model was applied here without considering the quantum effects. For the MNM with circular nanopores, there is an appropriate nanopore size for thermal conductivity tuning, while a linear relationship exists for this size between the ETC and the porosity. The appropriate nanopore diameter size will be about one times that of the electron mean free path. The ETC difference along different directions would be less than 10%, which is valuable when estimating possible errors, because the nanoscale-material direction could not be controlled during its application. Like nanoparticles, the ETC increases with increasing pore size (diameter for nanoparticles) while the porosity was fixed, until the pore size reaches about four times that of electron mean free path, at which point the ETC plateaus. The specular coefficient on the surface will significantly impact the ETC, especially for a high-porosity MNM. The ETC can be decreased by 30% with a tuning specular coefficient.

Introduction

In 2006, Leonhardt [1] and Pendry et al. [2] separately proposed a theory to develop an optical cloak. It has gained wide attention since then, and some cloaks have already been obtained [3], [4], [5]. The principle of optical cloaking has extended from light transfers to thermal transfers; although thermal conduction follows diffusion equations similar to those of a light transfer equation, thermal conduction has different physical mechanisms. Some principles [6], [7], [8] have already been raised to develop the thermal cloak; however, there are still some difficulties in creating a thermal cloak. One such difficulty is the development of proper thermal metamaterials. Considering the small size for potential applications and tunable thermal conductivity (varying with porosity or pore size) of nanoporous materials, a type of metallic nanoporous material (MNM) has been considered here.

The lattice thermal conductivity (LTC) and the electronic thermal conductivity (ETC) both contribute to the thermal conductivity of an MNM. A number of studies have already been carried out to probe the LTC of nanoporous materials [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22]; the ETC of nanoporous materials has not been discussed yet. The ETC of nanoporous materials will be discussed in our other works; here we expect to find a way to develop a suitable nanoporous materials for application in thermal cloak. While the ETC dominates thermal conductivity and the LTC has already been thoroughly discussed [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], this work focuses on the ETC. We have already developed a simulation method, which we applied in our previous works [23], [24], [25] in the study of the ETC of nanomaterials. Our method will be summarized and introduced in the next section. The ETC under the influence of the nanopore-surface scattering has been studied and will be discussed in the third section.

Section snippets

Theoretical basis and simulation method

Following kinetic theory, the reduced ETC is equal to the reduced electron mean free path (EMFP) [19], [24], [25], [26], i.e., ke=le, where ke is the ETC, and le is the EMFP. While a linear relationship (ke=le) exists between the ETC and the EMFP, only the EMFP should be obtained. A statistic simulation method [23], [24], [25] was applied here to obtain the EMFP. This method was based on the free-electron-gas model (also denoted as the Drude model [27]). In the Drude model, it was supposed

Results and discussion

A 2-dimensional circular-pore MNM was studied. The cross sectional view of the MNM is shown in Fig. 1. Circular nanopores are distributed in a square arrangement. The ETCs along two different directions is shown in Fig. 1: along X direction, as shown in Fig. 1(a), and at a 45° angle, as shown in Fig. 1(b). Nanopores with radius r=0.141, 0.282, 0.564, 1.128, and 2.256 were considered. r signifies the value of r scaled by the bulk EMFP, and an equivalent length d was defined to compare results

Conclusions

A simulation method based on the free-electron-gas model was applied here to study 2-dimensional circular-pore MNMs. We first confirmed the hypothesis included in the method that electrons distribute randomly in the MNM. Next, the ETCs of MNMs with circular nanopores were studied. The cross sectional shape of the nanopore significantly influences the ETC's magnitude as well as its tendency (versus porosity). No linear relationship exists between the ETC and the porosity for the MNM. While an

Acknowledgement

This work has been supported by the Fundamental Research Funds for the Central Universities (2015XKMS062).

References (28)

  • T. Kunugi et al.

    Superlattices Microstruct.

    (2004)
  • L.-C. Liu et al.

    Int. J. Therm. Sci.

    (2010)
  • R.H. Tarkhanyan et al.

    Int. J. Therm. Sci.

    (2013)
  • C.L. Huang et al.

    Physica B

    (2014)
  • C.L. Huang et al.

    Int. J. Therm. Sci.

    (2015)
  • C.L. Huang et al.

    Physica E

    (2014)
  • A.E. Yarimbiyik et al.

    Microelectron. Reliab.

    (2006)
  • U. Leonhardt

    Science

    (2006)
  • J.B. Pendry et al.

    Science

    (2006)
  • D. Schurig et al.

    Science

    (2006)
  • M. Yan et al.

    Phys. Rev. Lett.

    (2007)
  • U. Leonhardt et al.

    Science

    (2009)
  • C.Z. Fan et al.

    Appl. Phys. Lett.

    (2008)
  • J.Y. Li et al.

    J. Appl. Phys.

    (2010)
  • Cited by (5)

    • Effect of nano-copper-structure on thermal energy storage performance of phase change materials-copper composite

      2020, Journal of Energy Storage
      Citation Excerpt :

      As shown in Fig. 2(a), in the terms of sensitive heat storage capacity, the nanostructure is a better choice than the corresponding bulk one (more details can be referred to Appendix A) [26,27]. The thermal conductivities of Cu matrix at nanoscale were shown in Fig. 2(b), which is obtained by methods given in Refs. [28-30]. It is clearly seen that the thermal conductivity of Cu matrix in nanoscale becomes lower and lower as the feature size decreases.

    • Thermal conductivity prediction of 2- dimensional square-pore metallic nanoporous materials with kinetic method approach

      2017, International Journal of Thermal Sciences
      Citation Excerpt :

      It seems that the presence of the tri-stage decrease tendency may depend on not only the pore size but also the nanopore shapes and nanopore distributions. And further researches are required to reveal the hidden mechanism, while the tri-stage tendency should be avoided for tuning thermal conductivity to design a thermal cloak [54]. At a value for φ less than 20–40% (depending on d*), ETCs along different directions are generally equivalent in Fig. 2(b).

    • Theoretical Thermotics: Transformation Thermotics and Extended Theories for Thermal Metamaterials

      2019, Theoretical Thermotics: Transformation Thermotics and Extended Theories for Thermal Metamaterials
    View full text