Burak Yoram, Andelman David, Orland Henri
School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2004;70(1 Pt 2):016102. doi: 10.1103/PhysRevE.70.016102. Epub 2004 Jul 1.
We present a model for the ion distribution near a charged surface, based on the response of the ions to the presence of a single test particle. Near an infinite planar surface this model produces the exact density profile in the limits of weak and strong coupling, which correspond to zero and infinite values of the dimensionless coupling parameter. At intermediate values of the coupling parameter our approach leads to approximate density profiles that agree qualitatively with Monte Carlo simulation. For large values of the coupling parameter our model predicts a crossover from exponential to algebraic decay at large distance from the charged plate. Based on the test-charge approach we argue that the exact density profile is described, in this regime, by a modified mean-field equation, which takes into account the interaction of an ion with the ions close to the charged plate.
我们基于离子对单个测试粒子存在的响应，提出了一个带电表面附近离子分布的模型。在无限平面表面附近，该模型在弱耦合和强耦合极限下产生精确的密度分布，这分别对应于无量纲耦合参数的零值和无穷大值。在耦合参数的中间值时，我们的方法得出的近似密度分布与蒙特卡罗模拟在定性上是一致的。对于耦合参数的大值，我们的模型预测在远离带电板的大距离处从指数衰减到代数衰减的转变。基于测试电荷方法，我们认为在这种情况下，精确的密度分布由一个修正的平均场方程描述，该方程考虑了一个离子与靠近带电板的离子之间的相互作用。
