Transformed Poisson-Boltzmann relations and ionic distributions
Transformed Poisson-Boltzmann relations and ionic distributions
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DOI：
10.1021/jp994168m
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发表时间：
2000-12-07
影响因子：
3.3
通讯作者：
Schellman, JA
中科院分区：
文献类型：
--
作者：
Qian, H;Schellman, JA
在许多应用中，水溶液中大分子周围的电荷分布比电势更有意义。我们证明了用泊松-玻尔兹曼（PB）关系来建立离子分布的微分方程是可能的。这些方程的解是积分分布函数，其导数给出了反离子和冒号的电荷密度函数。在这种形式下，圆柱形聚电解质的无盐气氛很容易被反离子溶解。“缩合半径”（Le Bret， M.; Zimm， B. Il.《生物聚合物》1984年第23期，287-312页）和“Bjerrum缔合半径”（Bjerrum， N.，离子缔合的研究，I. In Niels Bjerrum Selected Papers; Munksgaard: Copenhagen, 1926； pp 108-19页）等量自然地作为反离子分布函数曲线的拐点出现。此外，在变换后的PB方程的标度极限中还出现了一些缩合理论的性质。在加入盐的情况下，可以推导出反离子和冒号的多余电荷分布方程。在这种情况下，总过量的反离子phi （ct）和结肠phi （co）只是与实验有关。这两个量的不同组合导致公式(1)总电荷，(2)Donnan排除，(3)反离子释放(Record， M. T.; Lohman， T. M.; de Haseth， P. J. Mel。生物学报，1976,107,145-158)，以及(4)“缩合”离子的分数。本文在变换后的泊松-玻尔兹曼理论的背景下讨论了Bjerrum的离子结合理论和Manning的反离子凝聚理论。
For many applications, charge distributions around macromolecules in aqueous solution are of greater interest than the electrical potential. We show that it is possible to use the Poisson-Boltzmann (PB) relation to develop differential equations for the ionic distributions. The solutions to these equations are the integral distribution functions whose derivatives give the charge density functions for counterions and colons. In this formalism the salt-free atmosphere of a cylindrical polyelectrolyte is very easily solvable for the counterion. Quantities such as the "condensation radius" (Le Bret, M.; Zimm, B. Il. Biopolymers 1984, 23, 287-312) and the "Bjerrum association radius" (Bjerrum, N. Investigations on Association of Ions, I. In Niels Bjerrum Selected Papers; Munksgaard: Copenhagen, 1926; pp 108-19) appear naturally as inflection points in curves of the counterion distribution functions. Moreover, a number of the properties of condensation theory arise as scaling limits of the transformed PB equation. In the presence of added salt separate equations can be derived for the excess charge distributions of counterions and colons. In this case the total excesses of counterion phi (ct) and of colon phi (co) are simply related to experiment. Various combinations of these two quantities lead to formulas for (1) the total charge, (2) Donnan exclusion, (3) counterion release (Record, M. T.; Lohman, T. M.; de Haseth, P. J. Mel. Biol. 1976, 107, 145-158), and (4) fraction of "condensed" ions. Bjerrum's theory of ion assocition and Manning's theory of counterion condensation are discussed in the context of the transformed Poisson-Boltzmann theory.