Chain structures and clusters of particles with the mixed dipole-quadrupole interaction in smectic freely suspended nanofilms

The formation of unusual chain structures and clusters of particles with the mixed dipole-quadrupole interaction has been found in smectic nanofilms. Unlike topological dipoles and quadrupoles, the interaction between which leads to the formation of structures with finite interparticle distances, the particles with the mixed interaction touch each other and form stable chains and two-dimensional clusters. The orientation of particles in chains is intermediate between dipole and quadrupole chains. The variation of the interparticle distance and orientation of chains is explained qualitatively on the basis of the calculation of the $c$-director (field lines) near particles and the mutual arrangement of particles providing the minimum distortion of field lines.