Chan D Y, Halle B
Biophys J. 1984 Sep;46(3):387-407. doi: 10.1016/S0006-3495(84)84035-7.
A theoretical description of ion diffusion in the electric field set up by the double layer in the neighborhood of a charged interface is presented. Such a description is needed for the understanding of diffusion-controlled chemical kinetics and transport of ionic species in a variety of systems of interest in biophysics, electrochemistry, and colloid science. The ion dynamics are taken to be governed by the Smoluchowski diffusion equation and the average electrostatic field is obtained from the nonlinear Poisson-Boltzmann equation. Diffusion in finite regions with partially absorbing boundaries of planar, cylindrical, or spherical geometry is considered. The complete analytical solution of the Smoluchowski-Poisson-Boltzmann equation for counterions between two planar charged interfaces is given. Simple expressions are derived for certain useful integral quantities, viz., mean absorption times and absorption probabilities, in all geometries considered. Finally, lateral counterion diffusion and its consequences for surface re-encounter-enhanced chemoreception is considered.
本文给出了在带电界面附近由双层建立的电场中离子扩散的理论描述。对于理解生物物理学、电化学和胶体科学中各种感兴趣系统中的扩散控制化学动力学和离子物种传输，这样的描述是必要的。离子动力学被认为由斯莫卢霍夫斯基扩散方程控制，平均静电场由非线性泊松 - 玻尔兹曼方程获得。考虑了在具有平面、圆柱或球形几何形状的部分吸收边界的有限区域中的扩散。给出了两个平面带电界面之间抗衡离子的斯莫卢霍夫斯基 - 泊松 - 玻尔兹曼方程的完整解析解。针对所考虑的所有几何形状，推导了某些有用积分量的简单表达式，即平均吸收时间和吸收概率。最后，考虑了横向抗衡离子扩散及其对表面再相遇增强化学感受的影响。
