M. T. Rätzsch

Continuous thermodynamics of polymer systems

Ceci permet le traitement thermodynamique de systemes contenant des polymeres disperses par emploi direct de la fonction de distribution continue

Continuous Thermodynamics of Polymer Solutions: The Effect of Polydispersity on the Liquid-Liquid Equilibrium

Abstract Owing to their very large number, the composition of polymers is usually described by continuous distribution functions. A version of thermodynamics–called continuous thermodynamics–is established which is based directly on a continuous distribution function instead of the mole fractions, weight fractions, etc. of individual components or pseudocomponents. This continuous thermodynamics is applicable to all complex multicomponent systems such as petroleum, coal-derived liquids, tars, and polymers. Continuous thermodynamics is used in this paper for treating the influence of polymer polydispersity on the liquid-liquid equilibrium of polymer solutions. From a practical point of view, the main advantages of continuous thermodynamics in comparison with the pseudocomponent method are fewer convergence problems and a drastic reduction of computer time.

Complex multicomponent distillation calculations by continuous thermodynamics

Abstract Complex multicomponent mixtures such as petroleum fractions, shale oils, coal-derived liquids etc. are usually characterized by continuous distribution functions which, for example, may be obtained from true boiling point distillations. Current methods for separation calculations, however, are based on the flows of discrete components. Hence, to apply these methods the continuous distributions traditionally are split into a number of pseudo-components. This is a crude and arbitrary procedure. Based on earlier work, the present paper shows how to perform distillation calculations for complex multicomponent mixtures by using the continuous distributions directly without splitting into pseudo-components.

FLASH CALCULATIONS FOR A CRUDE OIL BY CONTINUOUS THERMODYNAMICS

Continuous thermodynamics is a suitable concept for performing phase equilibrium calculations of complex multi-component mixtures. In contrast to the traditional pseudo-component method, the continuous distribution density function obtained by the characterization experiment is used directly for the thermodynamic calculations. This paper describes the application of continuous thermodynamics to flash calculations for a crude oil. In the simple version the coexisting phases are assumed to behave ideally. In the refined version the real behavior is accounted for describing non-aromatics and aromatics as two different continuous ensembles. It proves possible to separate in the calculations the problem of the compositions in the coexisting vapor and liquid phases from the problem of the equilibrium temperatures. For the compositions exact explicit equations are provided. To obtain the equilibrium temperatures the numerical solution of only one equation (in the simple version) or of a system of only three equa...

Liquid-Liquid Equilibrium of Polydisperse Copolymer Solutions. Multivariate Distribution Functions in Continuous Thermodynamics

Abstract In addition to the usual polydispersity with respect to molar mass, copolymers show chemical polydispersity. Thus, the species present may not be adequately characterized by a single variable, and a divariate distribution function has to be applied for describing the composition of the copolymer. In continuous thermodynamics, such continuous distribution functions are used directly (without splitting into pseudocomponents) for describing the composition of complex multicomponent systems. Whereas until now usually only one distribution variable has been used in continuous thermodynamics, consideration of copolymers requires an extension to divariate distribution functions. Continuous thermodynamics is generalized to divariate distribution functions in this paper. The liquid-liquid equilibrium of copolymer solutions is considered as a specific example.

Cloud-Point Curve for the System Copoly(Ethylene-Vinyl Acetate) Plus Methyl Acetate. Measurement and Prediction by Continuous Thermodynamics

Abstract The cloud-point curve for the system copoly(ethylene-vinyl acetate) plus methyl acetate has been measured by a simple visual method. The critical point was determined by using the phase volume ratio method. The method of continuous thermodynamics was applied for thermodynamic treatment. The composition of the copolymer is described by a divariate distribution function assumed as a generalized Stockmayer distribution. The activity coefficients were obtained with the aid of the Huggins Chi -parameter concept assuming Chi to be a quadratic polynomial with respect to the weight-average chemical composition of the copolymer. The three model parameters were calculated from the critical point and the slope of the cloud-point curve at the critical point. The cloud-point curve and the shadow curve were predicted from these parameters. The cloud-point curve shows qualitative agreement with experimental data.

Refined Continuous Thermodynamic Treatment for the Liquid-Liquid Equilibrium of Copolymer Solutions

Abstract Based on an improved calculation of activity coefficients, continuous thermodynamics using a generalized divariate Stockmayer distribution is applied to the liquid-liquid equilibrium of random copolymer solutions. The effects of the chemical polydispersity on the cloud-point curve, the shadow curve, the spinodal, and the critical point are discussed. The theory can account for the occurrence of three-phase equilibria as well as for the phase separation in pure copolymers.

Vapour—liquid equilibrium in binary mixtures formed by benzene or cyclohexane with 1-chloropropane or 1-chlorobutane

Abstract The vapour—liquid equilibria (VLE) for the binary systems formed by 1-chloropropane with benzene and cyclohexane at 308.15 K and 318.15 K, and for systems formed by 1-chlorobutane with the same hydrocarbons at 308.22 K, 328.27 K and 348.31 K have been determined by a total pressure ebulliometric method. The accuracy of these results was proved by comparing the heat of mixing data calculated from these VLE results with those obtained by direct measurements (Amaya, 1961; Grolier et al., 1973). The experimental data and the results of correlation by means of the Redlich—Kister equation are given. The systems with benzene were found to be nearly ideal, while those with cyclohexane exhibit positive deviations (GE = 220–260 J mole−1 for an equimolar mixture). New vapour pressure versus temperature data for 1-chlorobutane are reported.

Continuous thermodynamics of copolymer systems

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.

Polymer Compatibility by Continuous Thermodynamics

Abstract By applying a continuous distribution function instead of the mole fractions, mass fractions, etc. of individual components, continuous thermodynamics permits a drastic reduction of the computational expense for calculating phase equilibria in complex multi-component systems such as petroleum fractions, shale oils, polymer solutions, and polymer mixtures. In this paper, continuous thermodynamics is applied to compatibility in mixtures of two polymers. If, e.g., the cloud-point curve is known, the shadow curve, the spinodal, the critical mixing point, and other interesting quantities may easily be calculated. Some examples are given to illustrate the method.