Many-body critical Casimir interactions in colloidal suspensions

Abstract

We study the fluctuation-induced Casimir interactions in colloidal suspensions, especially between colloids immersed in a binary liquid close to its critical demixing point. To simulate these systems, we present a highly efficient cluster Monte Carlo algorithm based on geometric symmetries of the Hamiltonian. Utilizing the principle of universality, the medium is represented by an Ising system while the colloids are areas of spins with fixed orientation. Our results for the Casimir interaction potential between two particles at the critical point in two dimensions perfectly agree with the exact predictions. However, we find that in finite systems the behavior strongly depends on whether the $Z_2$ symmetry of the system is broken by the particles. Eventually we present Monte Carlo results for the three-body Casimir interaction potential and take a close look onto the case of one particle in the vicinity of two adjacent particles, which can be calculated from the two-particle interaction by a conformal mapping. These results emphasize the failure of the common decomposition approach for many-particle critical Casimir interactions.

13 pages, 9 figures, accepted

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Cited by in corpus (17)

• Collective behavior of colloids due to critical Casimir interactions
• Nonadditivity of Critical Casimir Forces
• Critical Casimir Effect: Exact Results
• Critical adsorption and critical Casimir forces in the canonical ensemble
• The square lattice Ising model on the rectangle I: Finite systems
• The square lattice Ising model on the rectangle II: Finite-size scaling limit
• Tracer particle in a confined correlated medium: an adiabatic elimination method
• Critical Casimir force scaling functions of the two-dimensional Ising model at finite aspect ratios
• Dynamics and steady states of a tracer particle in a confined critical fluid
• Anisotropic scaling of the two-dimensional Ising model I: the torus
• Critical Casimir forces between defects in the 2D Ising model
• Effective Pair Interaction of Patchy Particles in Critical Fluids
• Casimir interaction of rod-like particles in a two-dimensional critical system
• Casimir effect between pinned particles in two-dimensional jammed systems
• The square lattice Ising model on the rectangle III: Hankel and Toeplitz determinants
• Discontinuous change from thermally- to geometrically- dominated effective interactions in colloidal solutions
• Critical Casimir Interactions and Percolation: the quantitative description of critical fluctuations