Parisen Toldin Francesco, Tröndle Matthias, Dietrich S
Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany and Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, D-01187 Dresden, Germany.
Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, D-70569 Stuttgart, Germany and IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Nov;88(5):052110. doi: 10.1103/PhysRevE.88.052110. Epub 2013 Nov 8.
Recent experiments have measured the critical Casimir force acting on a colloid immersed in a binary liquid mixture near its continuous demixing phase transition and exposed to a chemically structured substrate. Motivated by these experiments, we study the critical behavior of a system, which belongs to the Ising universality class, for the film geometry with one planar wall chemically striped, such that there is a laterally alternating adsorption preference for the two species of the binary liquid mixture, which is implemented by surface fields. For the opposite wall we employ alternatively a homogeneous adsorption preference or homogeneous Dirichlet boundary conditions, which within a lattice model are realized by open boundary conditions. By means of mean-field theory, Monte Carlo simulations, and finite-size scaling analysis we determine the critical Casimir force acting on the two parallel walls and its corresponding universal scaling function. We show that in the limit of stripe widths small compared with the film thickness, on the striped surface the system effectively realizes Dirichlet boundary conditions, which generically do not hold for actual fluids. Moreover, the critical Casimir force is found to be attractive or repulsive, depending on the width of the stripes of the chemically patterned surface and on the boundary condition applied to the opposing surface.
近期的实验测量了作用于浸没在二元液体混合物中、处于连续 demixing 相变附近且暴露于化学结构化基底的胶体上的临界卡西米尔力。受这些实验的启发，我们研究了一个属于伊辛普适类的系统在薄膜几何结构下的临界行为，其中一个平面壁具有化学条纹，使得二元液体混合物的两种组分存在横向交替的吸附偏好，这是通过表面场实现的。对于相对的壁，我们交替采用均匀吸附偏好或均匀狄利克雷边界条件，在晶格模型中这是通过开放边界条件实现的。通过平均场理论、蒙特卡罗模拟和有限尺寸标度分析，我们确定了作用在两个平行壁上的临界卡西米尔力及其相应的普适标度函数。我们表明，在条纹宽度与薄膜厚度相比很小的极限情况下，在有条纹的表面上系统有效地实现了狄利克雷边界条件，而这对于实际流体通常并不成立。此外，发现临界卡西米尔力是吸引性的还是排斥性的，取决于化学图案化表面的条纹宽度以及应用于相对表面的边界条件。
