Naji Ali, Podgornik Rudolf
Physics Department, Technical University of Munich, James Franck St., D-85748 Garching, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Oct;72(4 Pt 1):041402. doi: 10.1103/PhysRevE.72.041402. Epub 2005 Oct 18.
We develop a general formalism to investigate the effect of quenched fixed charge disorder on effective electrostatic interactions between charged surfaces in a one-component (counterion-only) Coulomb fluid. Analytical results are explicitly derived for two asymptotic and complementary cases: (i) mean-field or Poisson-Boltzmann limit (including Gaussian-fluctuations correction), which is valid for small electrostatic coupling, and (ii) strong-coupling limit, where electrostatic correlations mediated by counterions become significantly large as, for instance, realized in systems with high-valency counterions. In the particular case of two apposed and ideally polarizable planar surfaces with equal mean surface charge, we find that the effect of the disorder is nil on the mean-field level and thus the plates repel. In the strong-coupling limit, however, the effect of charge disorder turns out to be additive in the free energy and leads to an enhanced long-range attraction between the two surfaces. We show that the equilibrium interplate distance between the surfaces decreases for elevated disorder strength (i.e., for increasing mean-square deviation around the mean surface charge), and eventually tends to zero, suggesting a disorder-driven collapse transition.
我们开发了一种通用形式体系，以研究淬灭固定电荷无序对单组分（仅抗衡离子）库仑流体中带电表面间有效静电相互作用的影响。针对两种渐近且互补的情况明确推导了分析结果：（i）平均场或泊松 - 玻尔兹曼极限（包括高斯涨落修正），适用于小静电耦合；（ii）强耦合极限，其中由抗衡离子介导的静电关联变得显著大，例如在具有高价抗衡离子的系统中实现的情况。在两个具有相等平均表面电荷的并置且理想可极化平面表面的特定情况下，我们发现无序在平均场水平上的影响为零，因此平板相互排斥。然而，在强耦合极限下，电荷无序的影响在自由能中是累加的，并导致两个表面之间增强的长程吸引力。我们表明，对于增加的无序强度（即围绕平均表面电荷的均方偏差增加），表面之间的平衡板间距减小，最终趋于零，这表明存在无序驱动的塌缩转变。
