M. T. Rätzsch’s research while affiliated with Hochschule Merseburg and other places

Continuous thermodynamics provides a simple way for the thermodynamic treatment of polydisperse systems. Such systems consist of a very large number of similar species whose composition is described not by the mole fractions of the individual components but by continuous distribution functions. For copolymers, multivariate distribution functions have to be used for describing the dependence of thermodynamic behavior on molar mass, chemical composition, sequence length, branching, etc. In this paper, we review continuous thermodynamics as applied to copolymer systems. Special attention is focused on liquid-liquid equilibria and thermodynamic stability. Equilibria in solutions of random copolymers, blends of random copolymers with homo- or copolymers, and also the high pressure phase equilibrium in the mixture of copoly(ethene vinylacetate) with its monomers are also discussed. A special examination of polydispersity effects in solutions with block copolymers is made. Thus, the paper reviews in a comprehensive way how to build up continuous thermodynamics with multivariate distribution functions and how to derive relations necessary for solving special problems. Some short remarks on possible future prospects will round up the paper.

Die Chain-of-Rotators-Zustandsgleichung wird zur Berechnung von Gaslöslichkeiten, Henry-Konstanten, Grenzaktivitätskoeffizienten und dem Hochdruckphasengleichgewicht im System Ethylen + Polyethylenwachs eingesetzt. Durch neu eingeführte geeignete Modifizierungen der Modellparameter und Mischungsregeln kann auf eine Parameteranpassung in Systemen ohne ausgeprägte Wechselwirkungen weitgehend verzichtet werden. Die prediktiven Möglichkeiten und Grenzen werden am Beispiel von Systemen mit Polyisobutylen, Polystyren und Polyethylen dargestellt. The chain-of-rotators equation-of-state is applied to the calculation of gas solubilities, HENRY-constants, limiting activity coefficients and the high-pressure phase equilibrium in the ethylene + polyethylene system. By introducing suitable new modifications regarding the model parameters and the mixing rules it is possible to neglect adjustable parameters in systems without strong interaction. The predictive capabilities and their limits are demonstrated by application to systems with polyisobutylene, polystyrene, and polyethylene.

The method of continuous thermodynamics is applied to describe the experimentally examined demixing equilibrium in the mixture of (ethylene vinylacetate) copolymer with its monomers in the high pressure region. Divariate distribution functions are used to account for a more precise description of copolymer nature in the calculation. Die Methode der kontinuierlichen Thermodynamik wird zur Beschreibung des experimentell untersuchten Entmischungsgleichgewichtes in Mischungen des (Ethylen-Vinylacetat)-Copolymers mit seinen Monomers in der Hochdruckregion eingesetzt. Dabei wird der Copolymernatur in den Berechnungen mit Hilfe von zweidimensionalen Verteilungsfunktionen Rechnung getragen.

Vapour pressures in concentrated solutions of poly(ethylene glycol)s (M̄n = 300, 400, 600, 1000, 1500, 2000, 4000 and 6000 g/mol) in ethylbenzene have been measured in the temperature range of 303.15 K to 403.15 K and segment-molar excess Gibbs energies have been calculated. Results are discussed on the basis of free volume concepts and the UNIFAC-model. Für konzentrierte Lösungen von Polyethylenglycolen (M̄n = 300, 400, 600, 1000, 1500, 2000, 4000 und 6000 g/mol) in Ethylbenzen werden die aus Dampfdruckmessungen im Temperaturbereich von 303,15 bis 403,15 K erhaltenen segmentmolaren freien Exzeßenthalpien mitgeteilt. Die Resultate werden auf der Basis von freien-Volumen-Konzepten sowie des UNIFAC-Modells diskutiert.

For the first time, a quantitative theoretical analysis (liquid/liquid phase equilibria treated by means of the continuous thermodynamics) of the operating characteristics of continuous polymer fractionation (CPF) was performed. The results of these calculations were compared with data published for CPF of polyethylene. It turned out that the efficiency of the conventional CPF corresponds to approximately two theoretical plates only. For this reason, several improvements, suggested by theoretical considerations, were realized experimentally, for which purpose the system dichloromethane/diethylene glycol/bisphenol-A polycarbonate was chosen. The pulsating sieve-bottom column was replaced by a nonpulsating column filled with glass beads. In this manner, the number of theoretical plates could be raised considerably. A further improvement of the fractionation efficiency results from the reflux of part of the polymer contained in the sol phase. In praxi, this situation was realized by putting a condensor on top of the column and introducing the feed somewhere near its upper third. After predictive calculations and orienting experiments, 125 g of a polycarbonate with Mw = 29 kg/mol and a nonuniformity U = 1.3 were fractionated in four consecutive CPF runs (where the gels were directly used as feed for the next step) into five fractions of approximately equal weight. Except for the lowest-molecular-weight fraction, one obtains nonuniformities on the order of 0.1.

A method for establishing in the framework of continuous thermodynamics the stability criteria for multiple critical states of increasing order is presented. The method applies to a relatively general class of Gibbs free energy relations for polymer solutions: The function replacing the χ-term in the classic Flory-Huggins theory is permitted to depend on a finite number of moments of the polymer distribution so as to embrace most Gibbs free energy relations used in practice. In this way, determinant criteria for multiple critical states are formulated that are analogous in structure to those in traditional (discrete) thermodynamics. However, the dimension of the determinants is reduced from N (number of polymer species) to n (number of moments taken into account).

In an earlier paper, continuous thermodynamics was applied to calculate polymer fractionation procedures leading to lucid equations favorable for computer simulations. The present paper refines that treatment by applying more sophisticated Gibbs free energy relations. The simulation results agree closely with the experimental data, assuming the Flory-Huggins interaction parameter to be a function of the concentration.

Spinoidal and critical points of the liquid-liquid equilibrium in random copolymer blends are calculated by application of continuous thermodynamics. Blends are composed of two copolymers, each consisting of two different monomer units. Both copolymers are characterized by divariate distribution functions with respect to molecular weight and to chemical composition. Based on a model for the excess Gibbs free energy of mixing, the necessary relations are derived for the calculation of spinoidal and critical points. The influences of the polydispersities of molecular weight and/or chemical composition on the instability limit are discussed. Miscibility maps are calculated on the basis of the critical point. Cloud-point curves are shown to be most sensitive to polydispersities if the excess Gibbs free energy of mixing exceeds only slightly the lowest value necessary for demixing.

Based on continuous thermodynamics and its application to the theory of successive polymer fractionation procedures, a theory of column fractionation is developed. In continuous thermodynamics the polydispersity of polymers is accounted for by the direct use of the continuous distribution function in the thermodynamic equations. In this way equations which are favorable for computer simulations are obtained. As an example, Baker-Williams fractionation is chosen for presenting theory and computer simulation. The generalization to other column fractionations based on solubility differences is easily possible.

Die Mischungslücken in ternären Systemen aus einem Lösungsmittel und zwei steifkettigen Polymeren oder je einem steifkettigen und einem flexiblen Polymer werden auf der Basis des Flory-Modells starrer Stäbchen berechnet. Das athermische Flory-Modell wird durch einen isotropen Wechselwirkungsbeitrag (χ-Funktion) erweitert, und der Einfluß abstoßender und anziehender Wechselwirkungskräfte auf das Phasenverhalten wird demonstriert. Die Eigenschaften der ternären Systeme werden im wesentlichen durch den entropischen Effekt der stäbchenförmigen Moleküle geprägt. Miscibility gaps are calculated for ternary systems composed of one solvent and two rigid-chain polymers or one rigid-chain and one flexible polymer applying the Flory model of rigid rods. The athermal Flory model is extended by an isotropic interaction contribution (χ-function), and it is demonstrated how repulsive and attractive interaction energies influence on the phase behaviour. Nevertheless, the properties of the ternary systems are mainly formed by the entropic effect of the rod-like molecules.