  The path to understanding star formation processes begins with the study of
the formation of molecular clouds. The outskirts of these clouds are
characterized by low column densities that allow the penetration of ultraviolet
radiation, resulting in a non-negligible ionization fraction and the charging
of the small dust grains that are mixed with the gas; this diffuse phase is
then coupled to the ambient magnetic field. Despite the general assumption that
dust and gas are tightly correlated, several observational and theoretical
studies have reported variations in the dust-to-gas ratio toward diffuse and
cold clouds. In this work, we present the implementation of a new charged
particles module for analyzing the dust dynamics in molecular cloud envelopes.
We study the evolution of a single population of small charged grains (0.05
$\mu$m) in the turbulent, magnetized molecular cloud envelope using this
module. We show that variations in the dust-to-gas ratio arise due to the
coupling of the grains with the magnetic field, forming elongated dust
structures decoupled from the gas. This emphasizes the importance of
considering the dynamics of charged dust when simulating the different phases
of the interstellar medium, especially for star formation studies.
