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

• Applicant: Dr. Martin Herbert Hasenbusch
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: from 2013 to 2016
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 238391646

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.

• DFG Programme: Research Grants