2019/08/12 by A Squarcini, Alessio Squarcini, Anna Maciołek +5 · 1 citation
Engineering · Materials Science · Physics and Astronomy · #Binary number #Boundary value problem #Casimir effect #Cauchy stress tensor #Conformal symmetry #Critical point (mathematics) #Ising model #Isotropy #Particle (ecology) #Phase Equilibria and Thermodynamics #Pickering emulsions and particle stabilization #Quantum Electrodynamics and Casimir Effect #Tensor (intrinsic definition) #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1088/1742-5468/ab7658
81 pages, 25 figures
arxiv created 2019/08/12 · openalex created_date 2019/08/22 · openalex publication_date 2020/04/01 · arxiv updated 2020/06/24 · openalex updated_date 2026/08/05
Abstract We study colloidal particles with chemically inhomogeneous surfaces suspended in a critical binary liquid mixture. The inhomogeneous particle surface is composed of patches with alternating adsorption preferences for the two components of the binary solvent. By describing the binary liquid mixture at its consolute point in terms of the critical Ising model we exploit its conformal invariance in two spatial dimension. This allows us to determine exactly the universal profiles of the order parameter, the energy density, and the stress tensor as well as some of their correlation functions around a single particle for various shapes and configurations of the surface patches. The formalism encompasses several interesting configurations, including Janus particles of circular and needle shapes with dipolar symmetry and a circular particle with quadrupolar symmetry. From these single-particle properties we construct the so-called small particle operator expansion (SPOE), which enables us to obtain asymptotically exact expressions for the position- and orientation-dependent critical Casimir interactions of the particles with distant objects, such as another particle or the confining walls of a half plane, strip, or wedge, with various boundary conditions for the order parameter. In several cases we compare the interactions at large distances with the ones at close distance (but still large on the molecular scale). We also compare our analytical results for two Janus particles with recent simulation data.