Stigter D
Department of Pharmaceutical Chemistry, University of California, San Francisco 94143, USA.
Biophys J. 1995 Aug;69(2):380-8. doi: 10.1016/S0006-3495(95)79910-6.
We compare free energies of counterion distributions in polyelectrolyte solutions predicted from the cylindrical Poisson-Boltzmann (PB) model and from the counterion condensation theories of Manning: CC1 (Manning, 1969a, b), which assumes an infinitely thin region of condensed counterions, and CC2 (Manning, 1977), which assumes a region of finite thickness. We consider rods of finite radius with the linear charge density of B-DNA in 1-1 valent and 2-2 valent salt solutions. We find that under all conditions considered here the free energy of the CC1 and the CC2 models is higher than that of the PB model. We argue that counterion condensation theory imposes nonphysical constraints and is, therefore, a poorer approximation to the underlying physics based on continuum dielectrics, point-charge small ions, Poisson electrostatics, and Boltzmann distributions. The errors in counterion condensation theory diminish with increasing distance from, or radius of, the polyion.
我们比较了从圆柱形泊松-玻尔兹曼（PB）模型以及曼宁的反离子凝聚理论预测得到的聚电解质溶液中反离子分布的自由能：CC1（曼宁，1969a，b），其假设反离子凝聚区域无限薄；以及CC2（曼宁，1977），其假设凝聚区域具有有限厚度。我们考虑了在1-1价和2-2价盐溶液中具有B-DNA线性电荷密度的有限半径的棒状聚电解质。我们发现，在此处考虑的所有条件下，CC1和CC2模型的自由能均高于PB模型。我们认为，反离子凝聚理论施加了非物理约束，因此，基于连续介质电介质、点电荷小离子、泊松静电学和玻尔兹曼分布，它对基础物理的近似较差。反离子凝聚理论中的误差随着与聚离子的距离增加或聚离子半径的增加而减小。
