Simple thermodynamic modeling of liquids
Theoretical thermodynamic models that accurately capture liquid behavior do so at the cost of ease of use, and do not explicitly reduce to simple relationships observed among liquid properties. Of these relationships, the linear response of liquid density to changes in temperature is one of the simplest and most nearly universal. At low pressures, plots of saturated liquid density vs. temperature are linear over a substantial temperature range. This behavior has been observed for liquids as diverse as monoatomic elements, small organics, molten salts and metals, and polymers. Water and liquid helium are the only known exceptions to this low pressure linearity. This observation is extended to liquid isobars at elevated pressure and to liquid mixtures. To capture fluid relationships through easily implemented, analytical equations, a model using a Scaled Particle Theory (SPT) for mixtures of hard spheres in a mean-field approximation is developed. Thermodynamic properties are derived from the random insertion of a hard sphere (HS) chain into an HS mixture and invoking random mixing to calculate energetics. The SPT model completely characterizes pure fluids with three independent parameters that can be calculated from pure component properties. Binary mixtures require only one additional interaction parameter, which can be approximated using a geometric mean combining rule or treated as an adjustable parameter. This SPT chain model is comparable to other thermodynamic models with mean-field configurational energies for mixtures of small, similarly-sized molecules, but yields unsatisfactory results when applied to polymer/solvent systems. The approximations the SPT model makes for the HS chain are investigated as a potential source of error. To improve on the SPT configurational energy approximation, a Quasi-Chemical Square Well (QCSW) model is developed that limits both the attractive range of a given molecular segment and the number of other segments with which it can interact. Though the SPT and QCSW models do not explicitly reduce to a simple isobaric density/temperature relationship, the QCSW model predicts a linear-like regime for saturated liquids at low pressure over an extended temperature range, and introduces promising concepts for modeling liquids.