More insight into microscopic properties of RN-AdS black hole surrounded by quintessence via an alternative extended phase space

In this work, we study the phase transition of the charged-AdS black hole surrounded by quintessence via an alternative extended phase space defined by the charge square Q(2) and her conjugate Psi, a quantity proportional to the inverse of horizon radius, while the cosmological constant is kept fixed. The equation of state is derived under the form Q(2) = Q(2) (T, Psi) and the critical behavior of such black hole analyzed. In addition, we examine the role of the quintessence parameter and its effects on phase transitions. Besides that, we explore the connection between the microscopic structure and Ruppeiner geothermodynamics. We also find that, at certain points of the phase space, the Ruppeiner curvature is characterised by the presence of singularities that are interpreted as a signal of the occurrence of the phase transitions.