  Considering a grand canonical ensemble, we study the phase structures and
transitions of RN black holes surrounded by quintessence dark energy on two
different boundary conditions, namely AdS space and a Dirichlet wall. For AdS
space, under the condition of fixed temperature and potential, as the
temperature increases for lower potential, the black hole undergoes a
first-order phase transition, while for higher potential, no phase transition
occurs. There are two different regions in the parameter space. For the
Dirichlet wall, on which the temperature and potential are fixed and the state
parameter of quintessence $\omega=-2/3$ is analyzed in detail. Then, three
different physically allowed regions in the parameter space of the black hole
are well studied. As the temperature rises, a first-order phase transition and
a second-order phase transition may occur. In this case, there are nine regions
in the parameter space, which is obviously distinct from the case of AdS space.
