恒电荷等同平板颗粒之间的相互作用能

The Interaction Energy Between Two Identical Parallel Plates With Constant Surface Charge Density

按照Langmuir的方法 ,在高电位时 ,将PB方程中的双曲正弦函数简化 ,sinhy≈ey/2。由此 ,按照Langmuir的方法 ,在高电位或高电荷密度时 ,将PB方程中的双曲正弦简化为sinhy≈ey/2。导出计算高电位时平行平板颗粒之间相互作用能的近似方法。按照同样的方法 ,在颗粒具有高的恒定的表面电荷密度的条件下 ,虽然无法导出相互作用能的表达式 ,却可以用联立方程组的形式求出相互作用能。无绕动电位在 5～ 10的范畴内 ,将近似方法同精确的数值解作了详细的比较 ,近似方法可以在无量纲距离κh≤ 4的范围内 ,满意的应用。和恒电位情况相比 ,同样是无绕动电位越高 ,精确度越好 ,同时 ,近似方法的应用上限有所提高 ,这是因为随颗粒之间的距离减少 ,yh将大大的超过y∞ 的大小 。

According to Langmuir's suggestion that is sinh y ≈ e y /2 in the nonlinear Poisson-Boltzmann equation for the particles with high surface potential, we derive approximate expressions for the repulsive energy between two similar plates with constant high surface potential. According same method the approximate expressions for interaction energy between two similar plates with constant high surface charge density cannot be derived. However, the interaction energy between two similar plates with constant high surface charge density may be calculated by banding with equations. A detailed comparison of the approximate expressions of interaction energy between two parallel plates due to electrical double layer repulsion with the exact numerical solution have presented. From these comparisons, we quantified the accuracy of present approximations for reduced unperturbed surface potentials from 5 up to 10 and explain the approximate equations may be used safely for similar plates at κh ≤ 4. However, applicable upper limit of the approximate equations for similar plates becomes smaller at constant surface charge density than at constant surface potential. The reason is that the differences between y ∞ and y h become large on the decrease of plate separation h .