Vol.:(0123456789) International Journal of Thermophysics (2021) 42:67 https://doi.org/10.1007/s10765-021-02815-y 1 3 Modeling of Phase Equilibria and Surface Tension for N,N‑Dimethylcyclohexylamine + Alcohol Mixtures at Diferent Temperatures Ariel Hernández 1  · Reza Tahery 2 Received: 30 January 2021 / Accepted: 10 February 2021 / Published online: 11 March 2021 © The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021 Abstract Surface tension and phase equilibria of N,N-dimethylcyclohexylamine (DMCA) mixtures with alcohol (propanol, iso-propanol, butanol, and iso-butanol) were mod- eled over the whole range of composition and diferent temperature ranging from (288.15 to 308.15) K. The predictive results of the Peng–Robinson equation of state with quadratic mixing rule indicated that the DMCA + alcohol mixtures are not aze- otropic and that the bubble curve is linear, except for the DMCA + ethanol mixture. The surface tension of the binary mixtures was modeled with linear gradient theory, parachor method, Shereshefsky method, and Lamperski method. The linear gradient theory used as adjustment approach improved the results of surface tension predic- tion and correctly modeled this thermodynamic property for all mixtures, the fex- ibility of parachor method as an adjustment approach improved the predictive results for some mixtures, Shereshefsky method was able to successfully model the surface tension of the DMCA + ethanol, DMCA + propanol, and DMCA + butanol mix- tures, and Lamperski method was able to successfully model the surface tension of the DMCA + propanol and DMCA + butanol mixtures, while the DMCA + ethanol and DMCA + isobutanol mixtures had an acceptable statistical deviation. Further- more, Lamperski method was the best predicted model to model surface tension of the binary mixtures. Based on Shereshefsky model, the standard Gibbs energy of adsorption and the free energy change in the surface region were calculated. The free energy change was used to obtain the number of molecular layers in the surface region. Also, with Shereshefsky method it was obtained that alcohol is not absorbed at the surface which was also confrmed with Lamperski method. Finally, it is impor- tant to note that phase equilibria and surface tension of the DMCA + alcohol mix- tures is modeled with theoretical approaches for the frst time. On the other hand, for future experimental measurements of phase equilibria, our results could serve as an initial approximation of equilibrium, and the correlations obtained for the binary parameters of the linear gradient theory and parachor method can be used to predict surface tension at other temperatures outside the range 288.15 to 308.15 K. Extended author information available on the last page of the article