Phase structure and critical behaviour of charged-AdS black holes with perfect fluid dark matter

We get an exact nonlinear electrodynamics (NED) charged black holes endowed with the perfect fluid dark matter (PFDM) in the AdS background-charged PFDM AdS black holes with additional parameter charge parameter q and PFDM parameter β apart from mass M. We investigate the extended phase space thermodynamics wherein we identify the black hole mass with the chemical enthalpy rather than internal energy. We analysed it in a canonical ensemble to probe the effects of the parameter β on the thermodynamic quantities. The behaviour of heat capacity reveals the existence of two second-order phase transitions for decreasing β, the former occurring at increasing horizon radii xc1 and the latter at reduced values of xc2, where x is ratio of radial coordinate r and AdS length l (x=r/l). Whereas an analysis of Gibbs’ free energy confirms our black hole exhibits first order (small to large black hole) phase transition. The behaviour of the solution is consistent with Van der Waals fluid, which can also result from the P−V criticality describing the liquid/gas phase transition observed by the isotherms for temperatures less than the critical temperature. Thus, we show black holes can be understood from the viewpoint of chemistry, in terms of concepts such as Van der Waals fluids and can undergo phase transitions.