Minimum-Modified Debye-Hückel Theory for Size-Asymmetric Electrolyte Solutions with Moderate Concentrations

Tiejun Xiao^,,
Yun Zhou

Guizhou Provincial Key Laboratory of Computational Nano-Material Science, Guizhou Synergetic Innovation Center of Scientific Big Data for Advanced Manufacturing Technology, Guizhou Education University, Guiyang 550018, China

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Corresponding author: E-mail: tjxiao3@mail.ustc.edu.cn

摘要

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Abstract: A minimum-modified Debye-Hückel (DH) theory for electrolytes with size asymmetry is developed. Compared with the conventional DH theory, the minimum-modified DH theory only introduces an extra surface charge density to capture the electrostatic effect of the size asymmetry of the electrolytes and hence facilitates a boundary element method for electrostatic potential calculation. This theory can distinguish the electrostatic energies and excess chemical potentials of ions with the same sizes but opposite charges, and is applied to a binary primitive electrolyte solution with moderate electrostatic coupling. Compared with the hyper-netted chain theory, the validity of this modified DH theory demonstrates significant improvement over the conventional DH theory.
- Electrolyte solution /
- Size-asymmetry /
- Debye-Hückel theory /
- Electrostatic energy /
- Chemical potential

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Figure 1. A schematic plot for the MMDH model of a spherical ion with point charge Q and radius b, where σ_eis a surface charge density due to size asymmetry of the electrolyte solution, k_D is the inverse Debye length, $\Phi(r) $ is the electric potential. The response equation for $\Phi(r) $ is valid in the region r>b.

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Figure 2. (a) Reduced electrostatic energy βu^e, (b) reduced excess chemical potential βμ^ex for ions with size $\sigma_{2}$=0.7 and tunable $k_{\rm{D}}$, from the HNC theory (filled square and circle), the MMDH theory (hollow star and diamond) and the DH theory (hollow triangle). The lines are guides to the eye.

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Figure 3. (a) Reduced electrostatic energy βu^e, (b) reduced excess chemical potential βμ^exfor ions with size $\sigma_{2}$= 0.5 and tunable $k_{\rm{D}}$, from the HNC theory (filled square and circle), the MMDH theory (hollow star and diamond) and the DH theory (hollow triangle). The lines are guides to the eye.

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Figure 4. Thermodynamic properties (a) Reduced electrostatic energy βu^e, (b) Reduced excess chemical potential βμ^ex for ions with size $\sigma_{2}$=0.25 and tunable $k_{\rm{D}}$, from the HNC theory (filled square and circle), the MMDH theory (hollow star and diamond) and the DH theory (hollow triangle). The lines are guides to the eye.

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Figure 5. Thermodynamic properties (a) Reduced electrostatic energy βu^e, (b) Reduced excess chemical potential βμ^ex for ions with size $\sigma_{2}$=1, 0.15 and tunable $k_{\rm{D}}$, from the HNC theory (filled square and circle), the MMDH theory (hollow star and diamond) and the DH theory (hollow triangle). The lines are guides to the eye.

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