L. A. Kleintjens

Mean-field lattice gas description of vapour-liquid and supercritical equilibria

Abstract Recently we improved the mean-field two-component lattice-gas model introducing interacting surface areas and an empirical entropy of mixing parameter. The treatment in its present form has proven to be well capable of describing almost quantitatively fluid-phase behaviour of non-polar and polar substances of low- and high molar mass and mixtures thereof in large temperature and pressure ranges. The model works particularly well in the critical fluid region which allows adjustment of the parameters to scarce experimental data with expressions for spinodal, critical condition and equation of state.

The influence of nitrogen on the liquid—liquid phase behaviour of the system n-hexane—polyethylene: experimental results and predictions with the mean-field lattice-gas model

Abstract The phase diagram of the system n-hexane+linear high density polyethylene shows a region of limted miscibility in the liquid phase, which is of the lower critical solutions temperature type (LCST behaviour). The influence of nitrogen on the location of this region of limited miscibility is investigated experimentally at pressures up to 7.5 MPa in the temperature range 393–453 K for weight fractions of nitrogen in the liquid phase between 0 and 0.013. Nitrogen induces a shift of the region of limited miscibility to lower temperatures and higher pressures of about 22 K at constant pressure or 2m.Pa at constant temperature per weight percent nitrogen. Model calculations have been performed for the ternary system nitrogen + n-hexane + polyethylene using the mean-field lattice-gas model of Kleintjens and Koningsveld. Parameters used in these calculations were obtained from pure component and binary data only. The results prove that this model is able to predict the observed peculiar behaviour in the ternay system.

Thermodynamics of mixed polymer melts

Abstract The compatibility of polymer mixtures is discussed from a thermodynamic standpoint. Deviations from the simple lattice theory (Flory-Huggins) show up sensitively in phase diagrams. Possible molecular origins for such deviations are discussed. Experimental techniques that have recently been developed to deal with highly viscous mixtures are described.

Determination of the interaction parameter g by inverse gas chromatography: an additional experimental test of the classic lattice model

Abstract Inverse gas chromatography measurements on narrow polystyrene samples of different molecular weights have been interpreted in terms of the classic lattice model. The analysis includes a rather complex temperature dependence of the interaction parameter, g, different from the usual Flory-Huggins prediction, which only allows a linear dependence on 1 T . The extension of the simple model supplies an adequate description of the data, giving the enthalpic and entropic contributions of the interaction parameter at infinite dilution, g∞. The different coefficients of the new temperature dependence have been determined from experimental data obtained by using chromatographic columns packed with polystyrene samples of different molecular weights, where different molecular probes have been injected. The influence of the molecular weight on these coefficients has also been studied.

Isotope effect in polymer compatibility

SummaryThe deuterium isotope effect on liquid-liquid phase behaviour in polymer blends was investigated with Gordons Pulse Induced Critical Scattering Method. Spinodals in mixtures of polystyrene and polybutadiene were found to be sensitive to replacement of H by D in the polybutadiene. The results indicate a difference in heat of mixing between PS/PBH and PS/PBD-6 as well as an influence on the entropy of mixing.

Solubility of solids in supercritical solvents III mean-field lattice-gas description of G-L and S-L equilibria in the system ethylene-naphtalene

Abstract The present lattice-gas model is a method to correlate and predict the thermodynamic behaviour of pure compounds and mixtures. Calculations were carried out for ethylene and for naphtalene with the aid of a computerprogram that simultaneously opsimises several relations between the parameters in the model to relevant sets of experimental data. For the system ethylene-naphtalene the two binary parameters were adjusted to some G=L critical data for this system. The predicting power of the model was tested by comparing predicted spinodals, G-L equilibria, S-L equilibria and molar volumes with experimental literature data (ref. 12).

Experimental determination of the spinodal P-T-x surface for the system 2-butoxyethanolwater using the ‘PPICS’ apparatus

Abstract The PPICS (Pressure Pulsed Induced Critical Scattering) apparatus has been used in conjunction with the light scattering theory of Debye and Scholte to investigate the spinodal and binodal characteristics of the 2-butoxyethanol + water system in pressure-temperature-composition space. Data have been obtained at 2-butoxyethanol concentrations ranging from 17 to 40 wt%, and pressures up to 200 bar. Corrections were made to counter the effects of solution turbidity and background scatter. The trends observed were consistent with previous studies and the known phase envelope geometry. It was observed however that the system was particularly sensitive to the purity of the 2-butoxyethanol. Trends in the spinodal data obtained at 1 bar were observed to differ significantly from that published by Wenzel et al. (1980). Possible reasons for this discrepancy are discussed.

Developments in the thermodynamics of polymer systems

Abstract In the integration of polymer production, processing and material development the thermodynamics of polymer systems plays a key role. The more advanced the performance of the final polymer material is, the more complex its phase behaviour turns out to be. In this review we give some insight into the thermodynamic phenomena that occur in the production of these High-TECH materials. The high viscosity of polymer solutions and blends hampers the experimental study of these systems. Yet, recently a small-scale mixer became available that allows us to extrude small homogeneous samples that can be used for equilibrium studies with the Pulse Induced Critical Scattering Technique (PICS) or with indirect methods like DSC, Tg-measurements and microscopic evaluation (TEM, SEM). In polymeric systems containing many constituents, like those used in the paint industry, solubility parameter approaches permit a best guess of the phase behaviour. For binary or ternary polymer systems, improved Flory-Huggins-Staverman theories proved to be able to quantitatively describe the experimental phase behaviour, at the cost of a small number of adjustable parameters. Important factors that should be included in the improvement are: the disparity of size and shape between the repeat units of the constituents, changes in polymer chain flexibility and dilute solution effects. The interaction function for statistical copolymers is more involved, but first attempts lead to satisfying descriptions of experimental phase behaviour. For block copolymer systems the thermodynamic modelling is still in a premature state. The influence of pressure can be incorporated in lattice models and reasonable descriptions of the P-T-x space of polymer systems can be achieved.

Solubility of solids in supercritical solvents. IV. Mean-field lattice gas description for the p-T-x space diagram of the system ethylene—naphthalene

The mean-field lattice gas (MFLG) model is a simple molecular model for the description of thermodynamic behaviour of small-molecule mixtures and polymer systems. The model contains several empirical parameters for the pure substance and for the mixture. The adjustment of parameters for the mixture in a binary system is discussed here, based on liquid/vapour (L/V) equilibrium data and L ≡ V critical data. The latter option turns out as favourite, provided relevant expressions for the critical conditions in the MFLG model are used. The predictive power of the model is then tested by calculating the p-T-x space diagram, including spinodals, L/V equilibria, solid/liquid (S/L) equilibria and the S/L/V equilibrium. Comparison with extensive experimental data on p-T-x phase behaviour of ethylene-naphthalene has been made. A final stringent test on the model is the prediction of excess molar volumes, which compared not unfavourably with literature data.

Thermodynamics of organic materials, a challenge for the coming decades

Chemists and polymer scientists are making major advances in the design of complex organic materials. Long lists of papers and patents are evidence of their successes in copying nature with engineering plastics, functional polymers, smart organic materials and supramolecular architectures. This paper explores how the science of thermodynamics might support such developments in organic materials. Quite a lot of progress is being made in the area of polymer thermodynamics. The state of the art in this field, reported here, is a good basis for taking up the challenge of commercially producing complex organic molecules. One may hope that thermodynamics scientists will also make major advances in the field of nanomolecules and smart functional materials and will thus be able to contribute to the optimization of the production processes for these complex materials. This will require a move from process thermodynamics to a more product/material-oriented approach.