Applied Physics
Vol.07 No.11(2017), Article ID:22725,7 pages
10.12677/APP.2017.711039

Thermodynamic Properties of RbxC60 (x = 3,4,6) at Wide Temperature and Pressure

Wei Yang*, Hong Liu, Songhui Dai

School of Information Science and Engineering, Chengdu University, Chengdu Sichuan

*通讯作者。

Received: Oct. 29th, 2017; accepted: Nov. 10th, 2017; published: Nov. 20th, 2017

ABSTRACT

Based on the free volume theory (FVT), the thermodynamic properties of RbxC60 (x = 3,4,6) are studied by means of analytic mean field approximation. According to the double exponential potential model and the compression experimental data in the literature, three sets of potential parameters are obtained, and the corresponding potential function curves are compared and analyzed. The thermodynamic properties of three alkali metal doped fullerene RbxC60 (x = 3,4,6), including thermal expansion, bulk modulus, constant volume heat capacity and Helmholtz free energy, were calculated and analyzed under wide temperature and pressure. Our method is not only simple in calculation, but also in good agreement with the experimental data in the literature.

Keywords:Free Volume Theory, RbxC60 (x = 3,4,6), Exponential Potential, Thermodynamic Properties

1. 引言

2. 自由体积模型

$F=F\left(V,T\right)=-NkT\left[\frac{3}{2}\mathrm{ln}\left(2\pi \mu kT/{h}^{2}\right)+\mathrm{ln}{v}_{f}\right]$ (1)

${v}_{f}={v}_{f}\left(V,T\right)=4\pi {\int }_{\text{}0}^{\text{}{r}_{m}}\mathrm{exp}\left[-g\left(r,V\right)/kT\right]\text{}{r}^{2}dr$ (2)

$g\left(r,V\right)$ 表示某一分子漂移距中心分子为 $r$ 时的势能。基于物理意义上的考虑，用这种近似方法将平均势能用冷能来表示，可以很方便地建立RbxC60 (x = 3,4,6)的解析状态方程并对其热力学性质研究。

3. 势函数的选取

$\epsilon \left(s\right)={\epsilon }_{0}\cdot \left[{C}_{1}{e}^{{\lambda }_{1}\left(1-s\right)}+{C}_{2}{e}^{{\lambda }_{2}\left(1-s\right)}\right],s=r/{r}_{0}$ (3)

$\left\{\begin{array}{l}{C}_{1}={\lambda }_{2}/\left({\lambda }_{1}-{\lambda }_{2}\right)\hfill \\ {C}_{2}=-{\lambda }_{1}/\left({\lambda }_{1}-{\lambda }_{2}\right)\hfill \end{array}$ (4)

4. 计算结果分析

Figure 1. Compression curves at 296 K and 2800 K, experimental data [10] (small circle)

Figure 2. Potential function curves of RbxC60 (x = 3,4,6)

Figure 3. Variations of bulk modulus versus pressure

Figure 4. Variations of free energy versus density

Table 1. The nearest-neighbor distance a in nm, linear thermal expansion coefficient α in 10−5 K−1, the bulk modulus BT in GPa, the heat capacity CV in kJ∙mol−1∙K−1

5. 结论

Thermodynamic Properties of RbxC60 (x = 3,4,6) at Wide Temperature and Pressure[J]. 应用物理, 2017, 07(11): 313-319. http://dx.doi.org/10.12677/APP.2017.711039

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