An extended critical-scaling equation with a nonlinear order parameter and its use for the fits to vapor/liquid equilibria

A method to extend the region of validity of the critical-scaling equations is presented and is tested by fits to the vapor/liquid equilibria (VLE) of ethane, propane, and n-butane.In this method there are two elements. One of them is to find an appropriate order parameter (OP) and the other one is how to fit the equations to equilibrium data. As for the OP, the nonlinear OP Smith and Ferer proposed [7] has been used. For the critical scaling equations, terms different from those they used have been employed. This leads to better results and physically sounder value of exclusion-volume-like fitting parameter b. As for the fitting method, first the critical parameters, Tc and Vc are determined and then linear regressions for the fits to VLE data have been adopted. Otherwise, nonlinear regressions have to be essentially employed.Pre-determination of Tc and Vc and the different terms for critical scaling equations provide relatively significant advantages; (i) it makes fits to VLE binodals linear, (ii) the exclusion-volume-like fitting parameter b is approximately equal to the van der Waals parameter bvdW, and (iii) the fits are in excellent agreement with the VLE data. In fact, the calculated values trace the VLE data almost exactly.