Group-contribution Lattice-fluid Equation Of State Research Articles

Group contribution lattice fluid equation of state (GCLF EOS) for ionic liquids

This work focuses on the extension of group parameters and application of the group-contribution lattice-fluid equation of state (GCLF EOS) for the systems with ionic liquids (ILs). The new group parameters ekk and Rkk for ILs in GCLF EOS were obtained by means of correlating the liquid density of pure ILs at different temperatures, while the group binary interaction parameters αmn were obtained by means of correlating the activity coefficients of solutes at infinite dilution in ILs at different temperatures, which were exhaustively collected from references. New IL groups were added into the current parameter matrix. It was verified that GCLF EOS for ILs can be used for predicting liquid densities of pure ILs or the mixture of IL and solute, vapor–liquid equilibria (VLE) and liquid–liquid equilibria (LLE) at finite concentration, as well as identifying the structure–property relation in separation science. This is the first work for us to extend the predictive GCLF EOS to the systems with ILs.

Solubility and diffusivity of cyclohexane in high density polyethylene

AbstractThe diffusivity and solubility of cyclohexane in a high density polyethylene, HDPE, were studied using a gravimetric, quartz‐spring, sorption balance. Solvent concentrations up to a weight fraction of 0.15 over a temperature range of 90 to 160°C were measured. Diffusion coefficients in the range of 10−6 to 10−7 were determined. Two types of polymer samples were used: a commercial bead form and flat sheets prepared by melting the polymer. Within the experimental error no differences were observed between the two forms indicating that there were no significant effects caused by the melting and compression. The solubility of cyclohexane in the HDPE as a function of the activity of the cyclohexane was linear. Above the melt temperature the solubility data were predicted better by the group‐contribution, lattice‐fluid equation of state (GCLF‐EoS) than by the van der Waals free‐volume (UNIFAC‐vdw‐FV) model. Below the melt temperature a correction factor for the elasticity significantly improved the predictions for both models. Although the HDPE has a crystallinity of 77.6%, the experimental data and the Vrentas‐Duda free‐volume theory indicated no significant tortuosity effects. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012

Development of a mathematical model for studying bioethanol–water separation using hydrophilic polyetherimide membrane

AbstractAn essentially predictive mathematical model was developed to simulate pervaporation process. The group contribution method UNIFAC was used for calculating the upstream activity coefficients. The diffusion coefficient in the membrane was predicted using free‐volume theory. Free‐volume parameters were determined with viscosity and temperature data, and the binary interaction solvent–polymer parameter was calculated by a group‐contribution lattice‐fluid equation of state (GCLF‐EOS). A simulator named PERVAP was developed applying the mathematical model. Pervaporation process was simulated for separating bioethanol–water through polyetherimide membrane. The simulated results were validated using experimental data of bioethanol/water separation through polyetherimide membrane. The model presented a satisfactory performance compared to experimental data. Related to the simulation of the studied separation, a 99% molar enriched bioethanol stream was obtained with a recovery of 94%. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2008

A simplified approach to vapor–liquid equilibria calculations with the group-contribution lattice-fluid equation of state

Equations of state that are based on the lattice-statistics approach use Guggenheim's quasi-chemical approximation to describe the non-randomness in the mixture due to the energetic interactions between the molecules. For ternary and higher-component systems the non-randomness expression is complex and requires an iterative calculation procedure. We have shown that the non-randomness parameters play a negligible role in the application of the GCLF-EoS model (based on the Panayiotou–Vera EoS) for predicting vapor–liquid equilibria. Omission of the non-randomness parameters from such calculations can significantly improve the computation efficiency. Binary, ternary, and quaternary vapor–liquid equilibria predictions were made including polystyrene, polyvinyl acetate, polyethylene, and polypropylene in polar and non-polar solvents to test the theory.

Extension of the group-contribution lattice-fluid equation of state

This work focuses on the extension of the numbers of group parameters and application of the group-contribution lattice-fluid equation of state (GCLF EOS). The new group parameters of the GCLF EOS were evaluated by means of the volume translated Peng–Robinson equation of state (VTPR EOS) and the UNIFAC model. Values for 20 main groups and 33 subgroups are added into the current parameter matrix. The procedure used in this work can also be used to evaluate group parameters for the groups not present in the current matrix. Some examples are given to show the reliability of the new group parameters. Two new applications of the GCLF EOS are present: the effect of polymeric additive to solvents in extractive distillation and prediction of the crystallinity of polymers in the presence of gas.

Solubility, swelling degree and crystallinity of carbon dioxide–polypropylene system

Solubilities are reported for carbon dioxide (CO 2) in polypropylene (PP) at temperatures from 313.2 to 483.7 K and at pressures up to 25 MPa. Buoyancy corrections required in the data reduction were estimated with the Sanchez and Lacombe equation of state (S-L EOS). Solubilities of CO 2 in molten state PP could be correlated to within 5% for both the S-L EOS and the group-contribution lattice-fluid equation of state (GCLF EOS). The change in crystallinity of rubbery state PP with CO 2 dissolution into the polymer was predicted with the GCLF EOS and the solubility data under the assumption that CO 2 could dissolve only in the amorphous regions. The trend of the estimated crystallinity with CO 2 dissolution into the polymer was consistent with results in the literature.

Solubility and Diffusivity of Propylene and Ethylene in Atactic Polypropylene by the Static Sorption Technique

In this work, the static sorption technique has been extended to measure the diffusivity as well as the solubility of gases in polymers at elevated pressures. This has been accomplished by operating several static sorption capsules in parallel in order to measure the fractional mass uptake of a gas by a polymer with time. Equilibrium and diffusion data of propylene and ethylene in atactic polypropylene have been measured in the temperature range of 25−70 °C. The group-contribution, lattice-fluid equation of state (GCLF-EoS) was used to correlate the equilibria data with a single value of the binary interaction parameter for each of the systems. The Vrentas−Duda free-volume theory was employed to describe the propylene and ethylene diffusivity data. The chemical potential gradient used in the free-volume correlation of the diffusivity data was obtained from the GCLF-EoS.

Prediction of carbon dioxide solubility in polymers based on a group-contribution equation of state

The group-contribution, lattice-fluid equation of state (GCLF-EoS), has been previously shown to predict accurately vapor solubilities in polymers. The method has been extended to the predictions of carbon dioxide–polymer binary systems. Applying the GCLF-EoS to binary systems requires the characterization of all the groups in the system and estimating the molecular binary interaction parameter from the group interaction parameters. The group parameters for pure carbon dioxide and the group interaction parameters of carbon dioxide with other organic groups commonly found in polymers were estimated. A new mixing rule for the calculation of the molecular interaction parameter is proposed and compared with the one developed originally by Lee and Danner. Results show that the new mixing rule as applied to the sorption of carbon dioxide in polymers and copolymers gives good predictions in large ranges of pressure and temperature.

Thermodynamic Behavior of Ethylene−Styrene Interpolymers

The Dow Chemical Company has recently introduced a new family of copolymers of ethylene and styrene identified as ethylene−styrene interpolymers (ESIs). The ability of the group-contribution lattice-fluid equation of state (GCLF EoS) to predict the volumetric properties of a series of ESIs of different compositions, the solubility parameter of a given copolymer, and the solubility of toluene was tested. The two latter experiments were conducted in the temperature range 50−150 °C. On average, the error in density was less than 1.1% in the temperature and pressure ranges of 100−250 °C and 6.9−690 bar, respectively. The solubility parameter of the polymer was measured using inverse gas chromatography. The solubility parameter was found to have a strong temperature dependency that the model could not reproduce accurately. At 25 °C, however, the model predictions were found to be in the range of the literature data. The GCLF EoS gave good predictions for the solubilities of the vapors at low styrene contents. Discrepancies at high styrene contents were attributed to a less accurate description of the sorption of solvents in pure polystyrene. The investigation shows that crystallinity has an influence on the solvent solubilities even if they are treated on a crystal-free basis.

Prediction of solvent solubility, diffusivity and permeability in glassy polymeric membranes

The filling-type membrane is composed of grafted polymer and solvent resistant substrate; calculation of solubility, diffusivity and the swelling-suppression effect of a substrate enabled us to predict solvent permeability. This approach, noted as membrane design, has previously been used in estimating permeability of aromatic compounds through rubbery polymeric membranes. In this study, the influence of plasticization on solubility and diffusivity is investigated theoretically and experimentally with poly(methyl methacrylate) (PMMA). Solubilities predicted by a group-contribution lattice-fluid equation of state (GCLF-EOS) model are consistent with the results of vapor sorption. A modified free volume model is proposed for calculating solvent diffusion in glassy polymers by taking into account the compositional dependence of depression on the glass transition temperature. The solvent diffusion coefficient has a clear transformation at an isothermal glass transition concentration, and predictions are consistent with those measured by vapor permeation. Fluxes of benzene and toluene through filling-type PMMA membrane are measured by vapor permeation experiments, and it was found that the predictions agreed with the experiments.

Predicting liquid–liquid transitions in polymer solutions using the GCLF equation of state

Group contribution lattice fluid equation of state (GCLF-EOS) have been extended and used to calculate phase equilibria in polymer solutions. Group parameters for three group contributions and nine new group contributions have been calculated. Saturation vapor pressure for pure solvent and weight fraction activity coefficients in polymer solutions have been calculated and the agreement obtained with experimental data indicated the accuracy of the parameters. A combining rule consisting a pair interaction parameter with temperature dependency was proposed. The area method was used with GCLF-EOS to obtain phase diagram for liquid equilibrium (LLE) of polymer solutions. The method was able to predict both lower critical solution temperature (LCST) and upper critical solution temperature (UCST).

Prediction of PVT behavior of polymer melts by the group-contribution lattice-fluid equation of state

The group-contribution lattice-fluid equation of state (GCLF-EOS), which is capable of predicting equilibrium behavior in polymer systems, was developed by establishing group contributions of the lattice-fluid EOS using the PVT properties of low molecular weight compounds only. This model was used to predict the PVT behavior of common polymers over a wide temperature range in the melt region and over a wide range of pressures up to about 2,000 bar. The GCLF-EOS predicted accurately the effect of pressure and temperature on the specific volumes of the polymer melts. Prediction results by the GCLF-EOS were compared with those by the group-contribution volume (GCVOL) method. The GCLF-EOS requires only the structure of the polymer repeat unit in terms of their functional groups as input information. No other polymer properties are needed. The GCLF-EOS is the only model that is capable of predicting the specific volumes of polymer melts as a function of temperature and pressure.

Prediction of infinite dilution solvent activity coefficients in polymer solutions: comparison of prediction models

The modified group-contribution lattice-fluid equation of state (GCLF-EOS), which is capable of predicting accurately vapor-liquid equilibria in polymer-solvent solutions, was developed by calculating group contributions for the adjustable parameters from the equilibrium properties of low molecular weight compounds only. The modified GCLF-EOS has been used to predict the solvent activity coefficients at infinite dilution of solvents, and its prediction results have been compared with those of the original GCLF-EOS, the UNIFAC-free volume (FV), the entropic-FV, and the revised GC-Flory EOS. Extensive statistical analyses were performed using all the currently available experimental data. The modified GCLF-EOS provided the best performance in the prediction of infinite dilution activity coefficients. The modified GCLF-EOS requires only the structures of the solvent and polymer in terms of their functional groups as input information.

Prediction of polymer‐solvent phase equilibria by a modified group‐contribution EOS

AbstractA new group‐contribution lattice–fluid equation of state (GCLF‐EOS), which is capable of predicting the equilibrium properties of polymer–solvent solutions, was developed by modifying the original GCLF‐EOS of High and Danner. The GCLF‐EOS is a group‐contribution form of the Panayiotou–Vera equation of state based on the lattice‐hole theory. Group contributions for the interaction energy and reference volume were developed based only on the saturated vapor pressure and liquid densities of low molecular weight compounds. For a mixture, a binary interaction parameter was introduced into the mixing rules. Group contributions for the binary interaction parameter were developed from the binary vapor–liquid equilibria of low molecular weight compounds. This modified GCLF‐EOS model gives excellent predictions of solvent activity coefficients both at infinite dilution and at finite concentrations. It is significantly better than the original GCLF‐EOS model in its prediction capability. 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.

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.

Prediction of polymer PVT behavior using the group contribution lattice‐fluid EOS

AbstractA scheme has been developed using the group contribution lattice‐fluid equation of state (GCLF‐EOS) to predict the pressure‐volume‐temperature (PVT) behavior of polymers in the amorphous state. The model requires only the structure of the molecule as input information. Prediction results with an average error of 2% have been obtained for a wide variety of polymers. A table of 23 different group contributions is presented. With this set of group parameters, the GCLF‐EOS can be applied in the prediction of equation of state properties of a wide variety of homopolymers, random copolymers, and polymer blends. © 1995 John Wiley & Sons, Inc.

Application of the group contribution lattice‐fluid EOS to polymer solutions

AbstractA new group contribution lattice‐fluid equation of state (GCLF‐EOS) is described that can accurately predict the activities of solvents in polymer solutions. This equation of state is a modification of the equation of state derived by Panayioutou and Vera (1982), which is based on the lattice statistics developments of Guggenheim (1952). The group contribution modification permits the prediction of solvent activity, given only the structure of the polymer and solvent involved. The GCLF‐EOS can accurately predict solvent activities in polystyrene, polyethylene, poly(ethylene oxide), poly(ethylene glycol), poly(propylene oxide), and poly(vinyl chloride). The model does not perform as well for solvent activities in polyisobutylene due to the inaccurate group contribution values for the quaternary carbon group.