本体电解质的 Debye-Hückel（DH）形式体系等价于静电 Schwinger-Dyson 恒等式在不含离子间硬核（HC）耦合时的高斯层级闭合；本文通过对这些增补了 HC 相互作用的方程进行累积量处理，对该形式体系加以扩展。通过将我们的累积量修正 DH（CCDH）理论对一价离子活度和压强的预测，与文献中的超网链结果及 Monte-Carlo 模拟进行对照，我们表明这种修正把 DH 形式体系的准确性从亚摩尔浓度扩展到了摩尔级盐浓度。对于主要由电荷关联支配的内能情形或二价电解质的一般情形，CCDH 理论改善后的准确性仅限于亚摩尔离子浓度。与文献实验数据的比较表明，通过调节水合离子半径，CCDH 形式体系同样能够再现直至摩尔浓度下盐浓度增加对离子活度系数的非均匀影响。这些 HC 尺寸所满足的不等式与 Hofmeister 序列的阳离子分支一致。
英文摘要：
The Debye-Huckel (DH) formalism of bulk electrolytes equivalent to the gaussian-level closure of the electrostatic Schwinger-Dyson identities without the interionic hard-core (HC) coupling is extended via the cumulant treatment of these equations augmented by HC interactions. By confronting the monovalent ion activity and pressure predictions of our cumulant-corrected DH (CCDH) theory with hypernetted-chain results and Monte-Carlo simulations from the literature, we show that this rectification extends the accuracy of the DH formalism from submolar into molar salt concentrations. In the case of internal energies or the general case of divalent electrolytes mainly governed by charge correlations, the improved accuracy of the CCDH theory is limited to submolar ion concentrations. Comparison with experimental data from the literature shows that via the adjustment of the hydrated ion radii, the CCDH formalism can equally reproduce the non-uniform effect of salt increment on the ionic activity coefficients up to molar concentrations. The inequality satisfied by these HC sizes coincides with the cationic branch of the Hofmeister series.
Generalizing the Debye-Huckel equation in terms of density functional integral
讨论了Fisher { \itshape et al.}提出的广义Debye-Hückel（GDH）方程的有效性。从功能积分的角度来看。GDH理论考虑了正电荷和负电荷的规定密度周围的波动。因此，我们首先建立了库仑气体正则系统的密度泛函积分表达式，并证明了这是Sine-Gordon理论的对偶形式。我们的形式揭示了以下几点：（i）在假定密度附近的感应电荷分布不仅有利于象原始DH理论那样的附加静电势的抵消，而且有利于抵消施加值和平衡值之间的化学电势差。(ii)因此，在我们的广义方程中出现了GDH方程中没有的表观电荷。(iii)也就是说，GDH方程仅在特殊情况下成立。
On the analogy between the restricted primitive model and capacitor circuits. Part II: A generalized Gibbs-Duhem consistent extension of the Pitzer-Debye-Hückel term with corrections for low and variable relative permittivity
Interaction between like-charged polyelectrolyte-colloid complexes in electrolyte solutions: a Monte Carlo simulation study in the Debye-Hückel approximation
