Application of Continuous Thermodynamics to the Stability of Polymer Systems

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Abstract
Continuous thermodynamics is a version of thermodynamics describing the composition of a mixture by a continuous distribution function instead of the mole fractions or weight fractions, etc. of individual components. In this way, continuous thermodynamics permits a simple treatment of phase equilibria in complex multicomponent systems containing a large number of similar species such as heavy petroleum fractions or polymer systems. In this paper, continuous thermodynamics is applied to the thermodynamic stability and the critical state of solutions and mixtures of polydisperse polymers. The traditional form of thermodynamic stability theory leading to the well-known determinant criteria is not applicable within the framework of continuous thermodynamics. The most convenient starting point proves to be determination of the sign of the second-order differential of the Gibbs free energy. The key quantity is the lowest value of this differential, which is obtainable by using Lagrangian multipliers. In this way, the spinodal and the critical point for the liquid-liquid equilibrium of solutions and mixtures of polydisperse polymers can be calculated. For polymer mixtures, these questions are important in studying polymer compatibility.