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Repulsion Between Finite Charged Plates with Strongly Overlapped Electric Double Layers
Langmuir ( IF 3.7 ) Pub Date : 2016-09-08 00:00:00 , DOI: 10.1021/acs.langmuir.6b02171 Sandip Ghosal 1 , John D. Sherwood 2
Langmuir ( IF 3.7 ) Pub Date : 2016-09-08 00:00:00 , DOI: 10.1021/acs.langmuir.6b02171 Sandip Ghosal 1 , John D. Sherwood 2
Affiliation
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Screened Coulomb interactions between uniformly charged flat plates are considered at very small plate separations for which the Debye layers are strongly overlapped, in the limit of small electrical potentials. If the plates are of infinite length, the disjoining pressure between the plates decays as an inverse power of the plate separation. If the plates are of finite length, we show that screening Debye layer charges close to the edge of the plates are no longer constrained to stay between the plates, but instead spill out into the surrounding electrolyte. The resulting change in the disjoining pressure is calculated analytically: the force between the plates is reduced by this edge correction when the charge density is uniform over the surface of the plates, and is increased when the surface is at constant potential. A similar change in disjoining pressure due to loss of lateral confinement of the Debye layer charges should occur whenever the sizes of the interacting charged objects become small enough to approach the Debye scale. We investigate the effect here in the context of a two-dimensional model problem that is sufficiently simple to yield analytical results.
中文翻译：
具有强重叠双电层的有限电荷板之间的排斥
在极小的电势极限内，在德比层强烈重叠的极小板间距下，可以考虑均匀充电的平板之间的屏蔽库仑相互作用。如果板的长度是无限的，则板之间的分离压力会随着板间距的倒数而减小。如果极板的长度有限，我们将证明屏蔽极板边缘附近的德拜层电荷不再受约束留在极板之间，而是溢出到周围的电解液中。通过分析计算得出解体压力的最终变化：当电荷密度在板的整个表面上均匀时，通过边缘校正可以减小板之间的力，而在表面处于恒定电势时，板之间的力会增大。每当相互作用的带电物体的尺寸变得小到足以接近德拜规模时，由于德拜层装药的侧向限制损失而引起的分离压力的类似变化应该发生。我们在二维模型问题的背景下研究此效应，该问题足够简单以产生分析结果。
更新日期：2016-09-08
中文翻译：
具有强重叠双电层的有限电荷板之间的排斥
在极小的电势极限内，在德比层强烈重叠的极小板间距下，可以考虑均匀充电的平板之间的屏蔽库仑相互作用。如果板的长度是无限的，则板之间的分离压力会随着板间距的倒数而减小。如果极板的长度有限，我们将证明屏蔽极板边缘附近的德拜层电荷不再受约束留在极板之间，而是溢出到周围的电解液中。通过分析计算得出解体压力的最终变化：当电荷密度在板的整个表面上均匀时，通过边缘校正可以减小板之间的力，而在表面处于恒定电势时，板之间的力会增大。每当相互作用的带电物体的尺寸变得小到足以接近德拜规模时，由于德拜层装药的侧向限制损失而引起的分离压力的类似变化应该发生。我们在二维模型问题的背景下研究此效应，该问题足够简单以产生分析结果。
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