Electric field shielding in dielectric nanosolutions

To gain some insight into electrochemical activity of dielectric colloids of technical and biomedical interest we investigate a model of dielectric nanosolution whose micro-constitution is dominated by dipolarions -- positively and negatively charged spherically symmetric nano-structures composed of ionic charge surrounded by cloud of radially polarized dipoles of electrically neutral molecules of solvent. Combing the standard constitutive equations of an isotropic dielectric liquid with Maxwell equation of electrostatics and presuming the Boltzmann shape of the particle density of bound-charge we derive equation for the in-medium electrostatic field. Particular attention is given to numerical analysis of obtained analytic solutions of this equation describing the exterior fields of dipolarions with dipolar atmospheres of solvent molecules endowed with either permanent or field-induced dipole moments radially polarized by central symmetric field of counterions. The presented computations show that the electric field shielding of dipolarions in dielectric nanosolutions is quite different from that of counterionic nano-complexes of Debye-H\"uckel theory of electrolytes.