离子溶液的介电常数：相关性和排除体积的联合效应
Dielectric Constant of Ionic Solutions: Combined Effects of Correlations and Excluded Volume
摘要：
已知离子溶液的介电常数随着离子浓度的增加而降低。然而，这种效应的起源还没有被彻底探索。在本文中，我们研究了两个可能的来源：长程库仑相关和溶剂排除体积。相关性起源于波动的静电势超出平均场泊松-玻尔兹曼理论，评价采用场理论循环扩展的自由能。另一方面，溶剂排除体积源于通过晶格气体模型占的有限离子尺寸。我们表明，这两个相关性和排除的体积是必需的，以捕捉的介电行为的重要特征。对于高极性溶剂，例如水，介电常数由溶剂体积分数和每体积分数的浓度依赖性磁化率的乘积给出。由于离子的体积分数增加，可用溶剂体积作为离子强度的函数而减小。由于离子和溶剂之间的相关性，磁化率也会发生类似的降低，从而进一步降低介电响应。我们的预测的介电常数拟合很好的实验范围广泛的浓度，不同的盐在不同的温度下，使用一个单一的拟合参数相关的离子大小。
英文摘要：
The dielectric constant of ionic solutions is known to reduce with increasing ionic concentrations. However, the origin of this effect has not been thoroughly explored. In this paper we study two such possible sources: long-range Coulombic correlations and solvent excluded volume. Correlations originate from fluctuations of the electrostatic potential beyond the mean-field Poisson-Boltzmann theory, evaluated by employing a field-theoretical loop expansion of the free energy. The solvent excluded-volume, on the other hand, stems from the finite ion size, accounted for via a lattice-gas model. We show that both correlations and excluded volume are required in order to capture the important features of the dielectric behavior. For highly polar solvents, such as water, the dielectric constant is given by the product of the solvent volume fraction and a concentration-dependent susceptibility per volume fraction. The available solvent volume decreases as function of ionic strength due the increasing volume fraction of ions. A similar decrease occurs for the susceptibility due to correlations between the ions and solvent, reducing the dielectric response even further. Our predictions for the dielectric constant fit well with experiments for a wide range of concentrations for different salts in different temperatures, using a single fit parameter related to the ion size.
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