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

球体和平面之间的临界卡西米尔力：自旋模型的蒙特卡罗模拟

• 批准号: 238391646
• 负责人: Dr. Martin Herbert Hasenbusch
• 金额: --
• 依托单位: Institut für Theoretische Physik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2013
• 资助国家: 德国
• 起止时间: 2012-12-31 至 2015-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/238391646?language=en
• 关键词: Critical; Casimir; force; between; spheres

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.

1978 年，Fisher 和 de Gennes 意识到，临界或接近临界系统的空间限制会产生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，可以通过实验确定 4He 接近 lambda 跃迁的薄膜和临界二元混合物的临界卡西米尔力。薄膜情况下临界卡西米尔力的理论确定可以通过自旋模型的蒙特卡罗模拟来实现。该项目的目的是确定作用在球体或球体与平面之间的临界卡西米尔力。 实验上，这样的球体可以通过在混合-分层过渡附近浸没在流体的二元混合物中的胶体颗粒来实现。在这种情况下，该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。 这些通用缩放函数取决于系统的几何形状、本体系统的通用性类别和表面的通用性类别。混合-解混合转变共享三维伊辛模型的普适性类别。我打算通过使用自旋模型的蒙特卡罗模拟来计算此类缩放函数。在球面几何形状的情况下，我在最近的工作中首次实现了这一点，我研究了均匀的强吸附表面。有必要更好地理解算法来优化算法的参数。 稍后，该研究应扩展到其他类型的表面，例如弱吸附或图案化表面。请注意，此类表面已经经过实验研究。此外，我打算研究球-球几何。 还可以研究许多球体系统中的聚集。