Pergamenshchik V M
Display&Semiconductor Physics, Korea University, Jochiwon-eup, Yeongi-gun, Chungnam 339-700, South Korea.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Jan;79(1 Pt 1):011407. doi: 10.1103/PhysRevE.79.011407. Epub 2009 Jan 28.
It is shown that in a cluster of many colloids, trapped at a liquid-air interface, the well-known vertical-force-induced pairwise logarithmic attraction changes to a strongly enhanced power-law attraction. In large two-dimensional clusters, the attraction energy scales as the inverse square of the distance between colloids. The enhancement is given by the ratio eta = (square of the capillary length) / (interface surface area per colloid) and can be as large as 10;{5} . This explains why a very small vertical force on colloids, which is too weak to bring two of them together, can stabilize many-body structures on a liquid-air interface. The profile of a cluster is shown to consist of a large slow collective envelope modulated by a fast low-amplitude perturbation due to individual colloids. A closed equation for the slow envelope, which incorporates an arbitrary power-law repulsion between colloids, is derived. For example, this equation is solved for a large circular cluster with the hard-core colloid repulsion. It is suggested that the predicted effect is responsible for mysterious stabilization of colloidal structures observed in experiments on a surface of isotropic liquid and nematic liquid crystal.
结果表明，在许多被困于液-气界面的胶体簇中，众所周知的垂直力诱导的成对对数吸引力转变为强烈增强的幂律吸引力。在大型二维簇中，吸引力能量与胶体之间距离的平方成反比。增强因子由η =（毛细管长度的平方）/（每个胶体的界面表面积）给出，其值可高达10⁵。这解释了为什么作用在胶体上非常小的垂直力，虽弱到无法使两个胶体聚集在一起，却能稳定液-气界面上的多体结构。簇的轮廓显示为由一个大的缓慢集体包络组成，该包络由单个胶体引起的快速低振幅扰动调制。推导了包含胶体间任意幂律排斥力的缓慢包络的封闭方程。例如，针对具有硬核胶体排斥力的大型圆形簇求解了该方程。有人认为，所预测的效应是导致在各向同性液体和向列型液晶表面实验中观察到的胶体结构神秘稳定性的原因。
