Institute for Theoretical Physics, University of Münster, Wilhelm-Klemm-Str. 9, D-48149 Münster, Germany.
Langmuir. 2010 Jul 6;26(13):10444-7. doi: 10.1021/la101900z.
The formation of regular stripe patterns during transfer of surfactant monolayers onto solid substrates is investigated. Two coupled differential equations describing the surfactant density and the height profile of the water subphase are derived within the lubrication approximation. If the transfer is carried out in the vicinity of a first order phase transition of the surfactant, the interaction with the substrate plays a key role. This effect is included in the surfactant free-energy functional via a height-dependent external field. Using transfer velocity as a control parameter, a bifurcation from a homogeneous transfer to regular stripe patterns arranged parallel to the contact line is investigated in one and two dimensions. Moreover, in the two-dimensional case, a secondary bifurcation to perpendicular stripes is observed in a certain control parameter range.
我们研究了在固体基底上转移表面活性剂单层时规则条纹图案的形成。在润滑近似条件下，推导出了描述表面活性剂密度和水亚相高度轮廓的两个耦合微分方程。如果转移是在表面活性剂的一级相变附近进行的，则与基底的相互作用起着关键作用。这种效应通过一个依赖于高度的外部场包含在表面活性剂自由能函数中。通过使用转移速度作为控制参数，在一维和二维中研究了从均匀转移到平行于接触线排列的规则条纹的分岔。此外，在二维情况下，在一定的控制参数范围内观察到了到垂直条纹的二次分岔。
