Guest Charges in an Electrolyte: Renormalized Charge, Long- and Short-Distance Behavior of the Electric Potential and Density Profiles
Guest Charges in an Electrolyte: Renormalized Charge, Long- and Short-Distance Behavior of the Electric Potential and Density Profiles
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DOI：
10.1007/s10955-005-8069-8
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发表时间：
2005-04
影响因子：
1.6
通讯作者：
G. Téllez
中科院分区：
文献类型：
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作者：
G. Téllez
我们补充了L. Šamaj最近对沉浸在电荷为+1/−1的二维电解质中的来宾电荷q的性质的精确研究。我们特别感兴趣的是由电荷和电解质产生的密度分布和电势的行为，以及从电势的远距离渐近得到的重整化电荷的确定。在Šamaj之前的工作中，对于一个所有电荷都是点的系统，提供β q < 2和β < 2，获得了任意库仑耦合β的精确结果。在这里，我们首先关注平均场情况，我们认为它正确地描述了极限β→0，但β qlarge。在这个极限下，我们可以研究当来宾电荷是一个硬盘，并且它的电荷大于坍缩值βQ >2的情况。我们将重整化电荷的结果与精确的预测进行了比较，并在坚实的基础上验证了前人研究的一些猜想。我们的研究表明，Šamaj得到的重整化电荷的精确公式对βQ >2是无效的，这与Šamaj提出的假设相反。对于任意库仑耦合，我们还确定了客人电荷附近正离子和反离子密度分布的近距离渐近性。我们发现，当客体电荷足够大（β q≥2−β）时，离子密度曲线表现出行为变化。这被解释为反离子凝聚的第一步（对于大库仑耦合），第二步发生在通常的曼宁-乌泽阈值βQ= 2。
We complement a recent exact study by L. Šamaj on the properties of a guest chargeQimmersed in a two-dimensional electrolyte with charges +1/−1. In particular, we are interested in the behavior of the density profiles and electric potential created by the charge and the electrolyte, and in the determination of the renormalized charge which is obtained from the long-distance asymptotics of the electric potential. In Šamaj’s previous work, exact results for arbitrary coulombic coupling β were obtained for a system where all the charges are points, provided βQ< 2 and β < 2. Here, we first focus on the mean field situation which we believe describes correctly the limit β→ 0 but βQlarge. In this limit we can study the case when the guest charge is a hard disk and its charge is above the collapse value βQ> 2. We compare our results for the renormalized charge with the exact predictions and we test on a solid ground some conjectures of the previous study. Our study shows that the exact formulas obtained by Šamaj for the renormalized charge are not valid for βQ> 2, contrary to a hypothesis put forward by Šamaj. We also determine the short-distance asymptotics of the density profiles of the coions and counterions near the guest charge, for arbitrary coulombic coupling. We show that the coion density profile exhibit a change of behavior if the guest charge becomes large enough (βQ≥ 2−β). This is interpreted as a first step of the counterion condensation (for large coulombic coupling), the second step taking place at the usual Manning–Oosawa threshold βQ= 2.