A Geometric Approach for the Calculation of the Nonrandomness Factor Using Computational Chemistry

The nonrandomness factor (α) is a parameter related to the polarity (and consequent randomness of spatial orientation) of the molecules and is generally fixed between 0.20 and 0.47 since no technique has been developed so far for its accurate estimation. However, the consideration of a constant nonrandomness factor for mixtures is known to harden azeotrope description and to cause convergence issues in both the Nonrandom Two-Liquid (NRTL) and Universal Quasi-chemical (UNIQUAC) models, which have been widely applied in the correlation of phase equilibria. In this work, a novel geometric methodology, named Porto's approach, was applied in the calculation of the nonrandomness factors for 50 pure components (mainly alkanes, alcohols, and ketones) at 298.15 K and 0.1 MPa. This methodology relied on computational chemistry (Density Functional Theory, DFT) to minimize the energy of molecules in a cavity within a solvent composed of molecules of their own (applying the Polarizable Continuum Model, PCM), and thereafter define the most stable chemical configuration in the pure liquid state. Then, the nonrandomness factor of each component was determined based on its molecular dipole moment, which was calculated after a population analysis of the optimized partial electrical charges with the Natural Bond Orbital (NBO) function. This innovative approach was applied in the correlation of liquid-liquid equilibria (LLE) data for 15 ternary systems comprising only neutral molecules with NRTL and UNIQUAC. The classical methods (α = 0.2 or 0.3 for NRTL and α = 0.2 for UNIQUAC) were compared against the usage of a component-specific nonrandomness factor, and similar standard deviations were obtained. Hence, this work is considered a strong advance in the application of these excess free Gibbs energy models to phase equilibria estimation and opens the door to more accurate thermodynamic modeling of nonideal mixtures (such as the ones containing electrolytes) by providing enhanced physical meaning to the nonrandomness factors.