Ronald P. Danner

Diffusion of toluene and n-heptane in polyethylenes of different crystallinity

Abstract Diffusivity and solubility data for toluene and n-heptane in semi-crystalline polyethylene were obtained by gravimetric sorption experiments conducted in two different laboratories. The effects of temperature, concentration and degree of crystallinity on the diffusion and solubility behaviour were investigated at 70°C. The diffusivity data were correlated using a modification of the Vrentas–Duda free-volume theory. All the parameters in the free-volume model were estimated from pure component data except the size of the jumping units, the tortuosity, and the free-volume characteristics of the polymers. These results indicate that both the diffusivity and penetrant solubility in the polymer amorphous phase decrease with increasing crystallinity. Further, the tortuosity or the length of the diffusion path around the crystals increases with the degree of crystallinity.

A group contribution equation of state for polymer solutions

Abstract A new group contribution lattice-fluid (GCLF) equation of state has been developed for polymers and polymer solutions. The lattice fluid theory of Panayiotou and Vera has been revised to include group contributions for solvent and polymer molecules. A lattice model containing holes is a convenient means of representing a polymer solution. The holes in the lattice serve as a means of varying the density of the fluid and are analogous to the free volume in generalized van der Waals models. An external degree of freedom parameter, the “C” parameter is not required. The GCLF equation of state reduces to forms similar to well established models for polymer solutions such as the Flory-Huggins equation. The group contributions for the model were calculated from the saturated liquid density and vapor pressures of small molecules. These group contributions are able to predict liquid densities, vapor pressures and VLE of small molecular systems with reasonable accuracy. The extension of the GCLF model to polymer solutions requires no pure component data and only one binary parameter.

Prediction of solvent activities in polymer solutions

Abstract The Holten-Andersen equation of state and the UNIFAC-FV (Free Volume) activity coefficient models are compared using a polymer solution data base. Both the Holten-Andersen equation of state and the UNIFAC-FV models have a foundation in the equation of state developed by Flory for polymer solutions. The Holten-Andersen equation of state is presented here with some corrections from the original publication. The UNIFAC-FV model is an extension of the UNFAC model for polymer solutions and includes the free volume expression from the Flory equation of state. The Holten-Andersen group contribution equation of state and the UNIFAC-FV activity coefficient model are the only predictive models available that were developed specifically for polymer solutions. Unlike the older correlative methods, these two models have not been previously tested and compared using an experimental data base.

A data base standard for the evaluation of vapor-liquid-equilibrium models

Abstract In order to evaluate vapor-liquid-equilibria models it is necessary to have a reliable data set. While there are many compendiums of VLE data, in many cases they are too large to manage efficiently, too limited in scope, of unknown reliability, or do not allow a classification of the systems so that one can predict how other systems may behave. A standard low pressure VLE data base which avoids these problems has been developed. A total of 104 binary systems has been selected and divided into groups according to the polarity of the components and whether they form ideal or nonideal systems. Each data set has been tested carefully for thermodynamic consistency. As far as possible the data are evenly distributed among the systems and over the entire concentration ranges. This data set is recommended as a standard for testing new VLE models.

Finite concentration inverse gas chromatography: Diffusion and partition measurements

Inverse gas chromatography (IGC) is a very fast, accurate, and reliable technique to measure diffusion coefficients. This technique however, has been limited to measurements in the infinite dilution region, i.e., in the region of negligible amount of solvent in the polymer. We have extended the scope of inverse gas chromatography to measure diffusion coefficients at finite concentrations of the solvent. This involves doping the carrier gas with a solvent of interest to achieve finite concentrations of solvent in the carrier gas and hence in the polymer. The carrier gas is passed through a saturator maintained at constant temperature to achieve this purpose. Diffusion coefficients for polyvinyl acetate–toluene, and polystyrene–toluene systems were determined at finite concentrations. The results were compared with the traditional gravimetric sorption and piezoelectric sorption measurements reported in the literature. The data are in excellent agreement with the values reported, correlate well with the Vrentas–Duda free volume theory, and can also be predicted from infinitely dilute data using the free volume theory.

Evaluation of inverse gas chromatography for prediction and measurement of diffusion coefficients

The inverse gas chromatography (IGC) method has been evaluated as a method to determine diffusion coefficients in polymer–solvent systems near the glass transition temperature. The poly(vinyl acetate)–toluene system was used for this purpose. Diffusion and partition coefficients were measured over a wide range of temperature. At temperatures significantly above the glass transition of the polymer, the capillary column model developed by Pawlisch and co-workers1,2 was used. At temperatures near the glass transition temperature, the modification of the capillary column model, proposed by Vrentas et al.3 was used. A sensitivity analysis of the capillary column model was made to delineate the range of applicability of the model. The diffusion coefficients obtained from IGC were compared with those extrapolated from the gravimetric sorption technique. The values agree within the expected range of error. Finally, free-volume theory was evaluated for its ability to predict the temperature and concentration dependencies of diffusion coefficients at temperatures near the glass transition from high temperature IGC data.

New technique to measure high-pressure and high-temperature polymer-solvent vapor-liquid equilibrium

A new technique, based on absolute vapor pressure measurement, has been used to measure high-pressure polymer-solvent vapor-liquid equilibria (VLE). VLE data are presented for binary mixtures of low density polyethylene (LDce:simple-paraE) with n-pentane, 1-pentene, cyclopentane, 3-pentanol, 3-pentanone, propyl acetate, and isopropyl amine at temperatures of 150°C and 200°C, and solvent concentrations up to 50% by weight. The experimental data obtained are compared with the predictions from the UNIFAC-FV model and the modified GCLF-EOS model. Modifications are also considered to extend the applicability of UNIFAC-FV model to temperatures above the critical point of the solvent. The model predictions are in good agreement with the experimental data at high pressures and temperatures, even above the critical temperature of the solvents.

Inverse gas chromatography applications in polymer–solvent systems

Inverse gas chromatography (IGC) has been shown by previous efforts to be an efficient and reliable method of obtaining the solubility and diffusion coefficients of solvents in polymers when the solvents are infinitely dilute. We have extended the IGC method to finite concentrations and to multicomponent systems. The experimental procedures have been improved to provide data more efficiently without loss of accuracy.

Application of the group-contribution lattice-fluid equation of state to random copolymer-solvent systems

A group-contribution lattice-fluid equation of state (GCLF-EOS), which is capable of predicting the equilibrium properties of polymer-solvent solutions, has been developed. Group contributions for the interaction energy and reference volume have been developed, based only on the saturated vapor pressures and liquid densities of low molecular weight compounds. For a mixture, group contributions of the binary parameter have been developed from the binary vapor-liquid equilibria of low molecular weight compounds. The model can be applied to the prediction of activity coefficients of solvents in random copolymers. The only input required for the model is the structure of the molecules in terms of their functional groups. No other pure component or mixture properties of the polymer or solvent are needed.

Adsorption and diffusion of hydrocarbons in silicalite at very low concentration: effect of defect sites

Abstract Adsorption and diffusion of benzene, p-xylene, ethylbenzene, toluene, isobutene, cis-but-2-ene, trans-but-2-ene, isobutane and n-butane has been studied in large silicalite crystals, at very low sorbate concentration, by non-isobaric concentration pulse chromatography. At these low concentrations the heats of adsorption and Henry constants for the aromatic and olefinic hydrocarbons are substantially greater than previously reported values, which were derived from measurements at higher loading levels, while the intracrystalline diffusivities of these species are substantially smaller with higher activation energies. In contrast, the results for saturated hydrocarbons are similar to the values obtained at higher loadings. This behaviour parallels the previously reported results of detailed calorimetric measurements which, for olefins and aromatics, show a rapid increase in heat of adsorption at very low loadings, suggesting the presence of a small fraction of highly favourable adsorption sites. Such sites are probably associated with defects in the crystal structure and, although the precise nature of these sites is not established, it seems plausible to suggest that they may be associated with the presence of silanol groups.