CONTINUOUS THERMODYNAMICS FOR POLYDISPERSE POLYMER-SOLUTIONS

Continuous thermodynamics is a framework which combines continuum modeling for the compositions of complex and multicomponent mixtures with molecular thermodynamic models and efficient numerical methods. In this work, a generalized molecular-thermodynamic model for polydisperse polymer solutions is developed; it is formally similar to the classical Flory-Huggins theory but with a polymer-size dependent and polymer-concentration dependent Flory parameter. Most existing lattice models and equation-of-state models such as the Guggenheim, Orifino-Flory, Koningsveld-Kleintjens, Sanchez-Lacombe and Revised Freed models can be cast into this generalized model but with different polymer-size and polymer-concentration dependence for the Flory parameter. A generalized continuous-thermodynamics framework based on this generalized model is also presented; expressions for chemical potentials, spinodals and critical points are derived using both the discrete multicomponent method and the continuous functional procedure. Internally consistent results are obtained. Criteria for multiple critical points are also derived. Computer programs are established for polydisperse-polymer solutions with either a standard or an arbitrary distribution for the polymer's molecular weight; in the latter case, the derivative method is applied, based on a previously developed spline fit. To illustrate the framework developed here, calculated liquid-liquid-equilibrium phase diagrams are shown, including UCST, LCST and hour-glass-shaped cloud-point curves, shadow curves, spinodals, critical points and their dependence on molecular parameters, on pressure and on molecular-weight distribution properties.