Oligomer Compatibility by Continuous Thermodynamics

To describe the details of the liquid-liquid equilibrium of oligomer mixtures, it is essential to use Gibbs free energy functions generalizing the classical Flory Huggins relation by replacing Huggins' X-term by a function depending on the averages of the molecular weight distributions. In this paper the concept of continuous thermodynamics is applied to establish a simple calculation procedure for the number-average segment number. Instead of the well-known sums with respect to the species, integrals occur which, in the case of Schulz-Flory distributions, may be calculated analytically, leading to simple formulas for the cloud-point curve and the shadow curve. The method is applied to model calculations showing that the chosen Gibbs free energy function may account for the details of the liquid-liquid equilibrium of oligomer mixtures and to a real oligomer system taken from the literature.