A new thermodynamic function for binary mixtures: The co-molar volume

We have developed a new theory relating partial molar volumes of binary mixtures to the intrinsic (Voronoi) volumes. The theory gives detailed insights into the physical meaning of partial molar volumes in terms of the actual volumes occupied by the molecules. The partial molar quantities are defined through the use of the Euler theorem for homogeneous functions. These properties have been in use for a long time, despite the fact that they do not give an intuitive picture of the properties they are to represent. For instance, the partial molar volume of a given component in a mixture is the change in the total volume with a change in composition; hence, it represents the derivative of a volume. The molar volume is a measurable property in the laboratory, and as such, a body of thermodynamics but the derived partial molar volume is not a direct measure of the physical volume occupied by the added component. On the other hand, the physical volume can be computed using, e.g., molecular dynamics simulations by Voronoi tessellation. To bridge the partial molar volume and the intrinsic volume so determined, we define a single new thermodynamic variable-the co-molar volume-thus bringing the latter into thermodynamics. We demonstrate this bridge through molecular dynamics simulations. The co-molar volume is closely related to the co-moving velocity defined in immiscible two-phase flow in porous media.