Paoletti S, Benegas J, Cesàro A, Manzini G, Fogolari F, Crescenzi V
Dipartimento di Biochimica, Biofisica e Chimica delle Macromolecole, Università di Trieste, via A. Valerio 22, I-34127 Trieste Italy.
Biophys Chem. 1991 Oct;41(1):73-80. doi: 10.1016/0301-4622(91)87211-m.
An extension of the counterion-condensation (CC) theory of linear polyelectrolytes has been developed for the case of a system containing a mixture of counterions of different valency, i and j. The main assumption in the derivation of the model is that the relative amount of the condensed counterions of the type i and j is strongly correlated and it is determined by the overall physical bounds of the system. The results predicted by the model are consistent, in the limiting cases of single species component, with those of the original CC theory. The most striking results are obtained for the cases of low charge density and excess of counterion species: in particular, an apparent positive "binding" cooperativity of divalent ions is revealed for small, increasing additions of M2+ ions to a solution containing a swamping amount of monovalent salt and a polyelectrolyte of low charge density. Apparent "competitive binding" of mono- and divalent ions derives as a bare consequence of the electrostatic interactions. Theoretical calculations of experimentally accessible quantities, namely single-(counter) ion activity coefficients, confirm the surprising predictions at low charge density, which qualitatively agree with the measured quantities.
针对含有不同价态（i和j）抗衡离子混合物的体系，已对线性聚电解质的反离子凝聚（CC）理论进行了扩展。该模型推导过程中的主要假设是，i型和j型凝聚抗衡离子的相对量高度相关，且由体系的整体物理边界决定。在单一组分的极限情况下，该模型预测的结果与原始CC理论的结果一致。在低电荷密度和抗衡离子种类过量的情况下，可得到最显著的结果：特别是，当向含有大量单价盐和低电荷密度聚电解质的溶液中少量增加M2+离子时，会显示出二价离子明显的正“结合”协同性。一价和二价离子的明显“竞争性结合”仅仅是静电相互作用的结果。对实验可获取量（即单（抗衡）离子活度系数）的理论计算证实了低电荷密度下的惊人预测，这些预测与测量量在性质上相符。
