Diagrammatic method for tunable interactions in colloidal suspensions in rotating electric or magnetic fields

Tunable interactions in colloids, induced by rotating electric or magnetic fields, provide a flexible and promising tool for self-assembly of soft materials, as well as for fundamental particle-resolved studies of phase transitions and other generic phenomena in condensed matter. In the case of two-dimensional systems and the in-plane rotating fields, the interactions are known to have a long-range (dipolar) attraction and an expressed three-body part at short distances, but still remain poorly understood. Here, we show that the interactions and polarization mechanisms governing the tunable interactions can be described, calculated, and analyzed in detail with the diagrammatic method we proposed. The diagrams yield a clear illustration of different polarization processes contributing to the Keesom, Debye, London, self, and external energies, classified in colloids similarly to intermolecular interactions. The real tunable interactions, obtained with the boundary element method, can be simply and accurately interpolated with the set of basis of the diagrams attributed to different physically clear polarization processes. Calculation of large-distance behavior and interpolation of the many-body interactions (and analysis of the leading mechanisms contributing to them) excellently illustrate that the diagrammatic method provides deep insights into the nature of tunable interactions. The method can be generalized for multicomponent systems, suspensions of particles with a composite structure and a complicated shape. The results provide significant advance in theoretical methods for detailed analysis of tunable interactions in colloids and, therefore, the method is of broad interest in condensed matter, chemical physics, physical chemistry, materials science, and soft matter.