Electronic thermal conductivity of 2-dimensional circular-pore metallic nanoporous materials
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., , where is the ETC, and is the EMFP. While a linear relationship () 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 , 0.282, 0.564, 1.128, and 2.256 were considered. signifies the value of r scaled by the bulk EMFP, and an equivalent length 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).
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