Costas P. Bokis

An extension of cubic equations of state to vapor-liquid equilibria in polymer-solvent mixtures

Abstract Cubic equations of state (EOS) are extended to describe polymer-solvent vapor-liquid equilibria (VLE). The solvents are described the conventional way using critical parameters. To describe the pure polymers, only the weight-average molecular weight is necessary, though number-average molecular weight, polydispersity and melt density can be incorporated if desired. To extend the model to mixtures, a mixing rule that combines EOS with excess energy models is used. In this formulation, the excess Gibbs energy term is considered in two parts: the classical Flory term for the entropic contributions and a residual term that takes care of specific interactions between the solvent and the polymer. For athermal mixtures that exhibit no such interactions, the residual term drops out and the model becomes completely predictive. Otherwise, for residual contributions, depending upon the complexity of specific molecular interactions anticipated in the mixture, either a single parameter Flory expression or a two-parameter NRTL equation can be used. We conclude that the simple cubic EOS approach presented here is easy to use, yet competes successfully with more sophisticated EOS models developed particularly for polymer solutions. Moreover, it offers more flexibility if one or more parameters are to be tuned to the process data.

A segment contribution method for the vapor pressure of tall-oil chemicals

A segment-contribution method for the estimation of vapor pressure of large, oligomeric molecules encountered in oleochemical industry is described. The method makes use of segment composition, number of segments, and four parameters per segment to estimate vapor pressure as a function of temperature. For major components that occur in crude tall-oil (CTO) distillation, the optimum parameters are reported and the method is shown to be accurate. The open architecture of this segment contribution approach permits the use of new segments, or the treatment of whole molecules as segments if necessary.

Thermodynamic properties of hard‐chain molecules

The density and molecular size dependence of the equation of state for molecules that consist of freely jointed, tangent hard spheres is investigated. It is shown that the properties of hard‐chain molecules can be accurately described using the properties of spherical molecules and a function c which varies approximately linearly with the reduced density. Monte Carlo and molecular dynamics simulation data for hard chains were used to develop the expression for c. The new equation of state is simple in form and more accurate for the calculation of compressibility factors for hard‐chain molecules than either Wertheim’s first‐order thermodynamic perturbation theory or the generalized Flory dimer theory (GFD). Further, this new equation reduces to the correct second virial coefficient limit as the density approaches zero.