Poisson Boltzmann方程和硅-水界面的电荷分离现象：整体方法
The Poisson Boltzmann equation and the charge separation phenomenon at the silica-water interface: A holistic approach
摘要：
泊松-玻尔兹曼方程以其成功地描述了由二氧化硅/水界面处的电荷分离现象引起的德拜层而闻名。然而，通过仅处理液体中的移动离子电荷，泊松玻尔兹曼方程仅占双电层的一半，另一半，表面电荷层，超出其计算域。在这项工作中，我们采取一个整体的方法来处理，在一个单一的计算域，双电层，包括在液体中的移动离子和表面电荷密度的电荷分离现象在二氧化硅/水界面。泊松能斯特普朗克方程被用作我们的方法的严格基础。整体方法的优点是能够预测表面电荷的变化，所产生的盐和酸添加到液体中，或从液体通道宽度的减少到低于两倍的德拜长度。由于双电层必须是整体中性的，我们使用这个约束来导出泊松能斯特普朗克方程的静态极限的形式，以及一个全局化学势，它取代了经典的zeta电位作为PB方程的边界值，这可以从我们的形式主义重新推导出来。我们提出了我们的理论的几个预测，这些预测超出了PB方程的框架，例如，表面电容和所谓的pK和pL值，表面电荷层被中和的等电子点，以及由在连接到本体储库的纳米通道的入口区域处形成双电层引起的唐南电势的出现。所有的理论预测都与实验结果吻合得很好。
英文摘要：
The Poisson Boltzmann equation is known for its success in describing the Debye layer that arises from the charge separation phenomenon at the silica/water interface. However, by treating only the mobile ionic charges in the liquid, the Poisson Boltzmann equation accounts for only half of the electrical double layer, with the other half, the surface charge layer, being beyond its computational domain. In this work, we take a holistic approach to the charge separation phenomenon at the silica/water interface by treating, within a single computational domain, the electrical double layer that comprises both the mobile ions in the liquid and the surface charge density. The Poisson Nernst Planck equations are used as the rigorous basis for our methodology. The holistic approach has the advantage of being able to predict surface charge variations that arise either from the addition of salt and acid to the liquid, or from the decrease of the liquid channel width to below twice the Debye length. As the electrical double layer must be overall neutral, we use this constraint to derive both the form of the static limit of the Poisson Nernst Planck equations, as well as a global chemical potential that replaces the classical zeta potential as the boundary value for the PB equation, which can be re-derived from our formalism. We present several predictions of our theory that are beyond the framework of the PB equation alone, e.g., the surface capacitance and the so-called pK and pL values, the isoelectronic point at which the surface charge layer is neutralized, and the appearance of a Donnan potential that arises from the formation of an electrical double layer at the inlet regions of a nano-channel connected to the bulk reservoir. All theory predictions are shown to be in good agreement with the experimental observations.
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