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

1978年，Fisher和de Gennes意识到，临界或近临界系统的空间限制会导致作用在系统壁上的力。由于这种效应类似于卡西米尔效应，因此被称为临界或热力学卡西米尔效应。在过去的十年中，临界Casimirforce可以通过实验确定的薄膜附近的4 He和临界的二元混合物。薄膜临界Casimir力的理论确定可以通过自旋模型的Monte Carlo模拟来实现。拟议项目的目的是确定作用在球体之间或球体与平面之间的临界Casimir力。 在实验上，这种球体可以通过浸没在混合-分层过渡附近的二元流体混合物中的胶体颗粒来实现。在这种情况下，平面由衬底的表面给出。临界Casimir力由普适标度函数控制。 这些普适标度函数依赖于系统的几何形状、体系统的普适类和表面的普适类。混合-去混合转变具有三维伊辛模型的普适性。我打算用自旋模型的蒙特卡罗模拟来计算这种标度函数。在球-平面几何的情况下，我在最近的工作中首次实现了这一点，在那里我研究了均匀的强吸附表面。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patterend表面。请注意，这种类型的表面已被实验研究。此外，我打算研究球-球几何。 也可以研究许多球系统中的聚集。

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.