Fluctuation-induced interactions in colloidal suspensions

• Applicant: Professor Dr. Alfred Hucht
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: from 2015 to 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 269422592

• Final Report Year: 2019

Final Report Abstract

In this research, we could successfully implement an efficient cluster Monte-Carlo algorithm, that enabled us to calculate three-body Casimir interactions between particles immersed in a critical binary liquid mixture. These three-body interactions turned out to be much stronger than expected. An analytical treatment at criticality using conformal field theory verified the obtained results. In the second half of the project, the universal finite-size scaling functions required for the description of off-critical temperatures were calculated analytically for a large number of boundary conditions within the framework of the two-dimensional Ising model. While the final goal of this task was an extension of the CFT results to near-critical temperatures, we were not able to deform the conformal symmetry at Tc to off-critical temperatures. However, the obtained exact results are important on their own, as they show an unexpected modularity of the Casimir contributions. Furthermore, they can serve as a benchmark for numerical calculations and approximations.

Publications

• Direct simulation of critical Casimir forces. EPL, 106(5):56005, Jun 2014
  Hendrik Hobrecht and Alfred Hucht
  
• Many-body critical Casimir interactions in colloidal suspensions. Phys. Rev. E, 92:042315, Oct 2015
  Hendrik Hobrecht and Alfred Hucht
  
• Critical Casimir force scaling functions of the two-dimensional Ising model at finite aspect ratios. J. Stat. Mech.: Theory Exp., 2017:024002, Feb 2017
  Hendrik Hobrecht and Alfred Hucht
  
• The square lattice Ising model on the rectangle I: finite systems. J. Phys. A: Math. Theor., 50(6):065201 [Erratum: J. Phys. A: Math. Theor., 51(31):319601, Jun 2018]
  Alfred Hucht
  
• The square lattice Ising model on the rectangle II: finite-size scaling limit. J. Phys. A: Math. Theor., 50(26):265205
  Alfred Hucht
  
• Anisotropic scaling of the two-dimensional Ising model I: the torus. 2018
  Hendrik Hobrecht and Alfred Hucht
  
• Anisotropic scaling of the two-dimensional Ising model II: surfaces and boundary fields. 2018
  Hendrik Hobrecht and Alfred Hucht