  We present a nonlocal statistical field theory of a dilute electrolyte
solution with small additive of dipolar particles. We postulate that every
dipolar particle is associated with an arbitrary probability distribution
function (PDF) of distance between its charge centers. Using the standard
Hubbard-Stratonovich transformation, we represent the configuration integral of
the system in the functional integral form. We show that in the limit of a
small permanent dipole moment, the functional in integrand exponent takes the
well known form of the Poisson-Boltzmann-Langevin (PBL) functional. In the
mean-field approximation we obtain a non-linear integro-differential equation
with respect to the mean-field electrostatic potential, generalizing the PBL
equation for the point-like dipoles obtained first by Abrashkin et al. We apply
the obtained equation in its linearized form to derivation of the expressions
for the mean-field electrostatic potential of the point-like test ion and its
solvation free energy in salt-free solution, as well as in solution with salt
ions. For the 'Yukawa'-type PDF we obtain analytic relations for both the
electrostatic potential and the solvation free energy of the point-like test
ion. We obtain a general expression for the bulk electrostatic free energy of
the solution within the random phase approximation (RPA). For the salt-free
solution of the dipolar particles for the Yukawa-type PDF we obtain an analytic
relation for the electrostatic free energy.
