电荷多分散反离子的平面屏蔽
Planar screening by charge polydisperse counterions
摘要：
我们研究如何中和云的抗衡离子屏幕电场的均匀带电的平面膜板，当抗衡离子的特点是由分布的电荷（或价），$n(q)$。在非线性Poisson-Boltzmann理论的水平上，我们分析了单板和双板的情况。的（基本上是渐近的）预测成功地进行了比较，充分泊松-玻尔兹曼理论的数值解，但也蒙特卡罗模拟。具有最小价的反离子控制相互作用的长距离特征，并且可能定性地改变与经典的单分散情况有关的结果，其中所有反离子具有相同的电荷。重点放在连续分布$n(q)$，新的幂律可以证明，无论是离子密度或压力，在一个和两个板的情况下分别。我们表明，对于离散分布，更相关的实验，这些标度律坚持在一个中间，但可观察到的范围。此外，从实践的角度来看，连续$n(q)$行为的特征已经表现为具有相对少量组分的离散混合物。
英文摘要：
We study how a neutralising cloud of counterions screens the electric field of a uniformly charged planar membrane plate, when the counterions are characterised by a distribution of charges (or valence), $n(q)$. We work out analytically the one-plate and two-plate cases, at the level of non-linear Poisson-Boltzmann theory. The (essentially asymptotic) predictions are successfully compared to numerical solutions of the full Poisson-Boltzmann theory, but also to Monte Carlo simulations. The counterions with smallest valence control the long-distance features of interactions, and may qualitatively change the results pertaining to the classic monodisperse case where all counterions have the same charge. Emphasis is put on continuous distributions $n(q)$, for which new power-laws can be evidenced, be it for the ionic density or the pressure, in the one- and two-plates situations respectively. We show that for discrete distributions, more relevant for experiments, these scaling laws persist in an intermediate but yet observable range. Furthermore, it appears that from a practical point of view, hallmarks of the continuous $n(q)$ behaviour is already featured by discrete mixtures with a relatively small number of constituents.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
