On the determination of partial molar polarizations and dipole moments of solutes from multicomponent solutions alone: experimental and model development using deutero-labeled organic compounds

A general inverse problem methodology is introduced to determine the partial molar polarizations and the dipole moments of individual solutes from multicomponent solutions alone. A model quaternary system consisting of three deuterated solutes, for example, acetone-d6, acetonitrile-d3, and dimethylformamide-d7 in cyclohexane at 298.15 K and 0.1013 MPa, was studied. Following an experimental design protocol, multicomponent solutions in the range of concentration 0.0006 < x(solute i) < 0.0085 were prepared using a semi-batch procedure by injecting one solute at a time. In situ FTIR spectroscopic measurements of these quaternary solutions were performed together with simultaneous condensed-phase bulk measurements of density, refractive index, and relative permittivity. Three different numerical approaches were used to determine the individual limiting solute molar polarizations from the multicomponent solutions. These limiting molar polarizations were then used to calculate the individual solute dipole moments using the Debye formula. In addition, direct dipole moment calculations were performed using the Guggenheim-Smith formula where individual solute parameters were obtained from multivariate analysis of the multicomponent solution data. Response surface models played a central role in many of the inverse problems. The results of the various methods are compared. In general, the dipole moments of all solutes from multicomponent solutions were in good agreement with those determined from independent binary experiments. Additionally, numerical sensitivity analysis was performed in order to identify the significant contributions to dipole moment uncertainty. The general approach introduced in the present contribution can be applied to a wide range of systems.