Peng-Robinson equation of state: 40 years through cubics

These modifications to the PR EoS have been grouped in four main categories according to the nature of the modification: (a) by changing the dependence structure of α with temperature or the expressions for parameter a and b, (b) by introducing deviation functions (like volume translation), (c) by incorporating new parameters or terms in the equation of state, and finally (d) by modifying the mixing rules for mixture applications. Although great efforts have been made to improve accuracy and performance of the PR EoS, as demonstrated by the wide range of modifications, the necessity for further development of a universal, simple and accurate model is a rich source for research and discussion, considering the success of most of modifications is restricted to the studied properties and compounds, and therefore, they are limited to be just applied to the studied field. However, after 40 years, PR is still an invaluable and prominent tool, which will be under continuous development and research for next decades.