Critical Casimir force between spheres and planes: Monte Carlo simulations of spin models

1978年，Fisher和de Gennes意识到临界或接近临界系统的空间限制会引起作用在系统壁上的力。由于这种效应与卡西米尔效应相似，所以称为临界或热力学卡西米尔效应。在过去的十年中，可以通过实验确定在λ跃迁附近的4He薄膜和临界二元混合物的临界卡西米力。从理论上确定薄膜的临界卡西米尔力可以通过自旋模型的蒙特卡罗模拟来实现。该计划的目的是确定作用于球体或球体与平面之间的临界卡西米尔力。在实验中，这种球体可以通过将胶体粒子浸入混合-脱混过渡附近的二元流体混合物中来实现。在这种情况下，平面由基底的表面给出。临界卡西米尔力由通用标度函数控制。这些普适性标度函数取决于系统的几何形状、整体系统的普适性和曲面的普适性。混合-脱混过渡具有三维Ising模型的通用性。我打算通过使用自旋模型的蒙特卡罗模拟来计算这种缩放函数。在球平面几何的情况下，我在我最近的工作中第一次实现了这一点，在那里我研究了均匀的，强吸附的表面。有必要更好地理解用于优化算法参数的算法。以后的研究应扩展到其他类型的表面，如弱吸附或图案表面。请注意，这种类型的表面已经过实验研究。此外，我打算研究球-球几何。此外，还可以研究许多球体系统中的聚集现象。

In 1978 Fisher and de Gennes realized that a spatial confinement of a critical or near criticalsystem induces a force that acts on the walls of the system. Since this effect is similar to the Casimir effect it is called critical or thermodynamic Casimir effect. In the last decade the critical Casimirforce could be determined experimentally for films of 4He near the lambda-transition and of critical binary mixtures. A theoretical determination of the critical Casimir force in the case of films could be achieved by Monte Carlo simulations of spin models.The aim of the proposed project is to determine the critical Casimir force that acts between spheres or a sphere and a plane. Experimentally such a sphere could be realized by a colloidalparticle that is submersed in a binary mixture of fluids near the mixing-demixing transition. In such a case the plane is given by the surface of the substrate. The critical Casimir force is goverend by universal scaling functions. These universal scaling functions depend on the geometry of the system, the universality class of the bulk system and the universality classes of the surfaces. The mixing-demixing transition shares the universality class of the three-dimensional Ising model. I intend to compute such scaling functions by using Monte Carlo simulations of spin models. In the case of the sphere-plane geometry I have achieved this for the first time in my recent work, where I studied homogeneous, strongly adsorbing surfaces. It is necessaryto obtained a better understanding of the algorithm that is used to optimise the parameters ofthe algorithm. Later the study should be extended to other types of surfaces such as weakly adsorbing or patterend surfaces. Note that such types of surfaces have been studied experimentally. Furthermore, I intend to study the sphere-sphere geometry. Also aggregation in many sphere systems might be studied.