Biesheuvel P M, van Soestbergen M
The Netherlands Institute for Metals Research, Mekelweg 2, 2628 CD Delft, The Netherlands.
J Colloid Interface Sci. 2007 Dec 15;316(2):490-9. doi: 10.1016/j.jcis.2007.08.006. Epub 2007 Sep 14.
When a monolayer of negatively charged surfactant molecules is brought in contact with an aqueous solution containing mixtures of counterions of different size and valency, very large deviations from Poisson-Boltzmann theory (PBT) develop at a high surface charge, with the smaller counterion outcompeting the larger one (even if divalent) near the interface, leading to counterion segregation [V.L. Shapovalov, G. Brezesinski, J. Phys. Chem. B 110 (2006) 10032]. We use a modified PBT that empirically includes an extended Carnahan-Starling equation-of-state to describe hard-sphere interactions in electrical double layers containing ions of different size and charge. Model calculations are made for ion concentration profiles, free energies, surface pressures, and differential capacities. At high surface charge, volume interactions become important, leading to significant deviations from PBT. In contrast to PBT, at high surface charge, contributions to energy and pressure are no longer mainly entropic, but instead volume and electrostatic field effects now dominate. When the hydrated size of the divalent ion is used as an adjustable parameter, the theory is in good agreement with the experimental data.
当一层带负电荷的表面活性剂分子与含有不同大小和价态抗衡离子混合物的水溶液接触时，在高表面电荷下会出现与泊松 - 玻尔兹曼理论（PBT）的极大偏差，较小的抗衡离子在界面附近会胜过较大的抗衡离子（即使是二价离子），导致抗衡离子分离[V.L. 沙波瓦洛夫，G. 布雷泽辛斯基，《物理化学杂志B》110 (2006) 10032]。我们使用一种改进的PBT，它凭经验包含一个扩展的卡纳汉 - 斯塔林状态方程，以描述包含不同大小和电荷离子的双电层中的硬球相互作用。对离子浓度分布、自由能、表面压力和微分电容进行了模型计算。在高表面电荷下，体积相互作用变得重要，导致与PBT有显著偏差。与PBT不同的是，在高表面电荷下，对能量和压力的贡献不再主要是熵性的，而是体积和静电场效应现在占主导。当将二价离子的水合尺寸用作可调参数时，该理论与实验数据吻合良好。
