Dynamics in regular solutions: Concentration and viscosity dependence of orientational correlation time of a benzene molecule

Abstract

The conformal solution theory by Longuet-Higgins was extended to the dynamic problem through the first-order perturbation theory for the interpretation of the concentration dependence of dynamic solution properties; molecular similarity and dissimilarity are reflected by the linear ideal terms and the quadratic regular terms, respectively. To test the theory, the orientational correlation times τ2R were determined for benzene-d6 in the three regular solutions of benzene (B) with toluene (T), carbon tetrachloride (C), and cyclohexane (H) as a function of the concentration (mole fraction x, 0≤x≤1) at 25 °C by measuring the spin-lattice relaxation time of the quadrupole nucleus 2H. The temperature effect was also studied in the BC solution. The τ2R–x curve is linear in BT and BC whose excess enthalpies HE are small, but it is quadratic in BH with a larger HE. The quadratic concentration dependence indicates the important effect of liquid structure on the orientation dynamics as well as the viscosity. The validity of the Stokes–Einstein–Debye (SED) law was tested with respect to the linear relation between τ2R and η/T (T the temperature, η the solution viscosity). The SED law holds when η is varied only by T or x under some limited conditions. The conditions for this simple relation have been clarified using the extended conformal solution theory.