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The theoretical description of the elastic interaction between colloidal particles in NLC with incorporation of higher-order elastic terms beyond the limit of dipole and qudrupole interactions was proposed. The expression for the elastic interaction potential between axially symmetric colloidal particles, taking into account the high-order elastic terms, was obtained. The general paradigm of elastic interaction between colloidal particles in NLC was proposed so that every particle with strong anchoring and radius a has three zones surrounding itself. The first zone for a < r ⪅ 1.3a is the zone of topological defects; the second zone at the approximate distance range 1.3a ⪅ r ⪅ 4a is the zone where crossover from topological defects to the main multipole moment takes place. The higher-order elastic terms are essential here (from 10% to 60% of the total deformation). The third zone is the zone of the main multipole moment, where higher-order terms make a contribution of less than 10%. This zone extends to distances where r ⪆ 4a = 2D . The case of spherical particles with planar anchoring conditions and boojums at the poles was considered as an example. It was found that boojums can be described analitically via multipole expansion with accuracy up to 1/r(7) and the whole spherical particle can be effectively considered as the multipole of the order 6 where multipolarity equal 2(6) = 64. The corresponding elastic interaction with higher-order elastic terms gives the angle θ(min) = 34.5° of minimum energy between two contact beads which is close to the experimental value of θ(min) = 30° . In addition, high-order elastic terms make the effective power of the repulsive potential to be non-integer at the range 4.5 < γ(eff) < 5 for different distances. The incorporation of the high-order elastic terms in the confined NLC also produce results that agree with experimental data.

High-order elastic terms, boojums and general paradigm of the elastic interaction between colloidal particles in the nematic liquid crystals