Modeling the phase behavior in binary mixtures involving blowing agents and thermoplastic resins

The thermophysical properties of mixtures of thermoplastic resins and blowing agents, together with the knowledge of the solubilities of these components, are the basis for the manufacturing of plastic foams. In this work, the solubilities of blowing agents trichlorofluoromethane, dichlorodifluoromethane, chlorodifluoromehane, and 1,2‐dichloro‐1,1,2,2‐tetrafluoroethane in thermoplastic resins poly(styrene), high density poly(ethylene), low density poly(ethylene), poly(propylene), poly(vinyl chloride), poly(carbonate) and poly(propylene oxide) were modeled by using the Perturbed Chain‐Statistical Associating Fluid Theory (PC‐SAFT) and the Sánchez‐Lacombe equations of state (EoS), fitting a single temperature‐dependent binary interaction parameter. PC‐SAFT is a theoretically based equation of state with three pure component parameters that describe efficiently the thermodynamics of complex systems. Earlier works with this EoS have already predicted the phase coexistence properties of various refrigerants and higher order alkane series compounds, along with their mixtures. The pure component parameters for the blowing agents were obtained by regression of vapor pressure and liquid density data, while the pure component parameters for the thermoplastic resins were obtained by regression of pure liquid PVT data. The parameter estimation was performed by using a modified maximum likelihood method. The solubility results obtained with both EoS have been compared; the results from PC‐SAFT showed a higher accuracy in terms of solubility pressure deviations. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers     

Study of solubility and swelling ratio in polymer‐CO2 systems using the PC‐SAFT equation of state

We use the PC‐SAFT equation of state to model the solubility of CO₂ in various homopolymers. We also model the swelling ratio of the PP (polypropylene)‐CO₂ mixture using PC‐SAFT and then compare the results with Sanchez‐Lacombe (S‐L) and Simha‐Somcynsky (S‐S) equations. The results show that PC‐SAFT can describe the solubility of CO₂ in polymers very well. We compare two sets of parameters in the PC‐SAFT equation, Gross et al.'s and Chen et al.'s. As for the swelling ratio, PC‐SAFT using Chen et al. parameters is better than S‐L equation, which is commonly used by early researchers in studying the solubility of CO₂ in polymers. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 44804.     

Solubility Calculation of Oil‐Conta‐minated Drill Cuttings in Supercritical Carbon Dioxide Using Statistical Associating Fluid Theory (PC‐SAFT)

Supercritical fluid extraction is a new technology that could be effectively used to treat oil‐contaminated drill cuttings generated during drilling for oil and gas. In this work, the solubility of oil‐contaminated drill cuttings in supercritical carbon dioxide is obtained by an experimental flow type apparatus. The solubility was measured at 200 bar pressure, over a temperature range of 55–79.5 °C. The measured solubility and experimental data for oil in drill cuttings were correlated using the PC‐SAFT, PR and SRK EOS models, without any adjustable parameters. Average absolute derivations of less than 15.1 %, 98.7 %, and 99.3 % are achieved between predicted and experimental values for the PC‐SAFT, PR and SRK EOS models, respectively, over a wide range of temperatures.     

Experimental study and thermodynamic model for respective solubilities of CO2 and ethanol for CO2‐ethanol‐polystyrene ternary system at elevated pressure and temperature

Foamed non‐Fickian diffusion (FNFD) model for a ternary system was proposed for the first time to regress the desorption data obtained by the gravimetric method. Results showed that FNFD model could accurately describe the diffusion behavior of CO₂ and ethanol out of foamed polystyrene (PS) and well predict total solubilities of CO₂ and ethanol in foamed PS. Meanwhile, Sanchez–Lacombe equation of state (S–L EoS) was adopted to calculate the respective solubilities (solubility of CO₂ in PS or solubility of ethanol in PS) and total solubilities of CO₂ and ethanol in PS for CO₂‐ethanol‐PS ternary system. Results showed that the total solubility of CO₂ and ethanol obtained from S–L EoS agreed well with values obtained by FNFD model. Furthermore, the respective and total solubilities of CO₂ and ethanol at 313.15, 338.15, and 343.15 K were calculated by S–L EoS. Results indicated that in the dissolving process, ethanol would be accelerated by CO₂ to dissolve into PS, and ethanol would compete with CO₂ to dissolve into PS, simultaneously. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018 , 135, 46281.     

Thermodynamic modeling of solubilities of various solid compounds in supercritical carbon dioxide: Effects of equations of state and mixing rules

No one can ever deny the significance of calculations of solubilities of industrial solid compounds in supercritical CO₂ in separation processes. In this work, the Peng-Robinson (PR) and the Esmaeilzadeh-Roshanfekr (ER) equations of state (EoS) along with several mixing rules including the Wong-Sandler (WS), the covolume dependent (CVD) and the van der Waals one (VDW1) and two (VDW2) fluid mixing rules are applied to evaluate the solubilities of 52 mostly used solid compounds in supercritical carbon dioxide. Besides, the Van-Laar excess Gibbs energy (G^ex) model is applied in phase behavior calculations by the WS mixing rule. The optimal values of the proposed thermodynamic model parameters are evaluated using the DE (differential evolution) optimization strategy. The absolute average deviations of the model results from 1776 experimental data points and the optimal values of the adjustable parameters of the model are reported to investigate the capabilities of combinations of each equation of state with different mixing rules in calculations of the solubilities. The results indicate that the combination of the ER EoS with the WS mixing rule leads to more accurate results (AAD = 9.0%) compared with other ones.     

GAS CHROMATOGRAPHIC DETERMINATION AND CORRELATION OF WEIGHT-FRACTION HENRY'S CONSTANTS FOR HYDROCARBON GASES AND VAPORS IN MOLTEN POLYMERS

In the polymer industry, separation equipment is required to separate unreacted monomers and solvents from polymers. In order to design such equipments, solubilities of gases and vapors in molten polymers are needed as fundamental data. It is very helpful if the weight-fraction Henry's constant, which gives solubilities of a solute at concentrated regions of a polymer, can be estimated by a predictive method.

In the present study, a new expression for the free volume term has been derived and is coupled with the UNIFAC model. The present UNIFAC-FV model was applied to common polymer systems. The weight-fraction Henry's constants were calculated for several volatile hydrocarbons and the calculated results were compared with the experimental data determined by a gas chromatographic technique.

The present UNIFAC-FV model with a new free volume expression was found to be helpful in predicting the weight-fraction Henry's constants of hydrocarbon solutes in molten polystyrene, in polypropylene, and in low-density polyethylene. It is advantageous that our model is applicable both supercritical gases and subcritical vapors with no adjustable parameters.     

Formation of microcapsules of medicines by the rapid expansion of a supercritical solution with a nonsolvent

The rapid expansion from a supercritical solution with a nonsolvent (RESS‐N) was applied to the formation of polymeric microcapsules containing medicines such as p‐acetamidophenol, acetylsalicylic acid, 1,3‐dimethylxanthine, flavone, and 3‐hydroxyflavone. A suspension of medicine in carbon dioxide (CO₂) containing a cosolvent and dissolved polymer was sprayed through a nozzle to atmospheric pressure. The pre‐expansion pressure was 10–25 MPa, and the temperature was 308–333 K. The polymers were poly(L ‐lactic acid) (molecular weight = 5000), poly(ethylene glycol) (PEG; PEG4000, molecular weight = 3000; PEG6000, molecular weight = 7500; and PEG20000, molecular weight = 20,000), poly(methyl methacrylate) (molecular weight = 15,000), ethyl cellulose (molecular weight = 5000), and PEG–poly(propylene glycol)–PEG triblock copolymer (molecular weight = 13,000). The solubilities of the polymers as coating materials and these medicines as core substance were very low in CO₂. However, the solubilities of these polymers in CO₂ significantly increased with the addition of low molecular weight alcohols as cosolvents. After RESS‐N, polymeric microcapsules were formed according to the precipitation of the polymer caused by a decrease in the solvent power of CO₂. This method offered three advantages: (1) enough of the coating polymers, which were insoluble in pure CO₂, dissolved; (2) the microparticles of the medicine were encapsulated without adhesion between the particles because a nonsolvent was used as a cosolvent and the cosolvent remaining in the mixture was removed by the gasification of CO₂; and (3) the polymer‐coating thickness was controlled with changes in the feed composition of the polymer for drug delivery. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 742–752, 2003     

Enhanced solubility of hydrogen and carbon monoxide in propane‐ and propylene‐expanded liquids

Conventional propylene hydroformylation occurs in a gas‐expanded liquid phase. Reliable knowledge of the phase equilibria of such systems, including the solubilities of CO and H₂ in propylene‐expanded solvents, is essential for rational process design and development. Herein, we report the vapor–liquid equilibrium (VLE) data of the following ternary systems involving CO, H₂, propane, propylene, toluene and NX‐795 at temperatures from 70 to 90°C and pressures up to 1.5 MPa: propane/H₂/toluene, propane/CO/toluene, propylene/H₂/toluene, propylene/CO/toluene, propane/H₂/NX‐795, propane/CO/NX‐795, propylene/H₂/NX‐795 and propylene/CO/NX‐795. The solubilities of H₂ and CO in either propane‐expanded or propylene‐expanded phases are observed to be greater than those in the neat organic solvents, by as high as 78% at 70°C and 1.5 MPa. By modeling the vapor and the liquid phases as pseudo‐binary systems, the Peng‐Robinson equation of state (PR‐EoS) with van der Waals’ mixing rules and binary interaction parameters is shown to satisfactorily predict the experimental VLE data. © 2017 American Institute of Chemical Engineers AIChE J, 64: 970–980, 2018     

On‐line NIR sensing of CO2 concentration for polymer extrusion foaming processes

An on‐line sensor using near infrared (NIR) spectroscopy is developed for monitoring CO₂ concentration in polymeric extrusion foaming processes. NIR absorption spectra are acquired by a probe installed at the foaming extruder die. The calibration curve relating the absorbance spectrum at 2019 nm to the dissolved gas concentration is derived so as to infer dissolved CO₂ gas concentration on‐line from measured NIR spectra. Experimental results show the developed on‐line NIR sensor can successfully estimate dissolved CO₂ concentration in the molten polymer and illustrate that the developed NIR sensing technique is among the more promising methods for quality control of polymeric extrusion foaming processes.     

Polymer plasticization using supercritical carbon dioxide

The plasticizing effect of supercritical CO₂ (scCO₂) during the extrusion of polymers was investigated. A modified extrusion system was used to demonstrate the viscosity‐reducing effect of scCO₂ together with a capability to produce foam‐free extrudate with selected polymers, including poly(vinyl chloride). Samples of extrudate and materials prepared off‐line by using a pressure vessel were characterized by thermal, mechanical, and X‐ray techniques. After gas diffusion from the polymer, there was no long‐term effect on polymer structure and properties. J. VINYL ADDIT. TECHNOL., 2008. © 2008 Society of Plastics Engineers.     

Predicting phase behavior in aqueous systems without fitting binary parameters I: CP‐PC‐SAFT EOS,aromatic compounds

This study examines an accuracy of CP‐PC‐SAFT attached by the 4C cross‐association scheme and zero values of binary parameters in predicting the high temperature‐high pressure phase behavior in aqueous systems of aromatic compounds containing one and two benzoic rings, CO₂ and cis‐decalin. In spite of the noteworthy complexity of these systems and the entirely predictive nature of the current approach, it correctly predicts the topology of phase behavior and typically yields the quantitatively accurate estimations of critical loci and the hydrocarbon–rich liquid phases in wide range of conditions. The available single phase volumetric data are also predicted accurately. Unfortunately, it is not a case of the water–rich phases exhibiting very small hydrocarbon concentrations. Nevertheless, the model is still capable of capturing the solubility minima characteristic for these phases around the room temperature. Predictions of the recent version of Simplified PC‐SAFT proposed by Liang et al. (2014) are also discussed. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4124–4135, 2017     

Modeling of solid–liquid equilibria for polyethylene and polypropylene solutions with equations of state

We modeled solid–liquid equilibria (SLEs) in polyethylene and polypropylene solutions with a Soave–Redlich–Kwong (SRK) cubic equation of state (EOS) and a perturbed‐chain statistical associating fluid theory (PC‐SAFT) EOS. Two types of mixing rules were used with SRK EOS: The Wong–Sandler mixing rule and the linear combination of the Vidal and Michelsen mixing rules (LCVM), both of which incorporated the Bogdanic and Vidal activity coefficient model. The performance of these models was evaluated with atmospheric‐pressure and high‐pressure experimental SLE data obtained from literature. The basic SLE equation was solved for the equilibrium melting temperature instead of for the composition. The binary interaction parameters of SRK and PC‐SAFT EOS were estimated to best describe the experimental equilibrium behavior of 20 different polymer–solvent systems at atmospheric pressure and 31 other polymer–solvent systems at high pressure. A comparison with experimental data showed that SRK–LCVM agreed very well with the atmospheric SLE data and that PC‐SAFT EOS was more efficient in high‐pressure conditions. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Calculation of the solid solubilities in supercritical carbon dioxide using a new G mixing rule

The aim of this study is to develop a new EOS/G^ex-type mixing rule with special attention to calculating the solid solubilities of aromatic hydrocarbons, aliphatic carboxylic acids, aromatic acids, and heavy aliphatic and aromatic alcohols in supercritical carbon dioxide. A volume correction term is applied with a combination of second and third virial coefficients which the equation for the third virial coefficient is quadratic, according to the suggestion by Hall and Iglesias-Silva. In this study, the cubic Peng-Robinson (PR) and Soave-Redlich-Kwong (SRK) equations of state have been used to calculate the solid solubilities of 23 solutes in supercritical CO₂, by using six mixing rules, namely, the Wong-Sandler (WS) rule, the Orbey-Sandler (OS) rule, the van der Waals one fluid rule with one (VDW1) and two (VDW2) adjustable parameters, the covolume dependent (CVD) rule and the new mixing rule. In all cases, the NRTL model was chosen as the excess Gibbs free energy model. The coefficients of the NRTL model and the binary interaction parameters of six mixing rules with two EOSs (PR and SRK EOSs) have been determined for 100 data sets of 23 binary systems over a wide range of temperatures and pressures covering more than 970 experimental data points which are reported in the literature. The results show that the PR EOS with the new mixing rule model is more accurate than the PR and SRK EOSs with the other mixing rules for solid solubility calculations in supercritical carbon dioxide.The regressed interaction parameters of the binary system, without any further modification, were then extended to four ternary mixtures, giving satisfactory results of the solid solubilities in supercritical CO₂.     

Phase behavior of mixture of supercritical CO2 + ionic liquid: Thermodynamic consistency test of experimental data

Various models have been applied composed of the Peng‐Robinson equation of state (PR‐EoS) and the Soave‐Redlich‐Kwong equation of state (SRK‐EoS) associated with three mixing rules including the following: Wong‐Sandler (WS), van der Waals one (vdW1), and van der Waals two (vdW2) for phase behavior modeling of mixtures of supercritical CO₂ + different ionic liquids in vapor–liquid equilibrium (VLE) region. It has been found that the PR EoS implying the WS mixing rule can be used as a reliable thermodynamic model to perform a thermodynamic consistency test on the experimental data of phase behaviors of the supercritical CO₂ + ionic liquid systems (19 commonly‐used ionic liquids have been studied). The results show that 40% of the experimental data seem to be thermodynamically consistent, 55.5% seem to be thermodynamically inconsistent, and 4.5% seem to be not fully consistent. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3892–3913, 2013     

GAS CHROMATOGRAPHIC DETERMINATION AND CORRELATION OF WEIGHT-FRACTION HENRY'S CONSTANTS FOR HYDROCARBON GASES AND VAPORS IN MOLTEN POLYMERS

In the polymer industry, separation equipment is required to separate unreacted monomers and solvents from polymers. In order to design such equipments, solubilities of gases and vapors in molten polymers are needed as fundamental data. It is very helpful if the weight-fraction Henry's constant, which gives solubilities of a solute at concentrated regions of a polymer, can be estimated by a predictive method.

In the present study, a new expression for the free volume term has been derived and is coupled with the UNIFAC model. The present UNIFAC-FV model was applied to common polymer systems. The weight-fraction Henry's constants were calculated for several volatile hydrocarbons and the calculated results were compared with the experimental data determined by a gas chromatographic technique.

The present UNIFAC-FV model with a new free volume expression was found to be helpful in predicting the weight-fraction Henry's constants of hydrocarbon solutes in molten polystyrene, in polypropylene, and in low-density polyethylene. It is advantageous that our model is applicable both supercritical gases and subcritical vapors with no adjustable parameters.     

A new microcellular foam injection‐molding technology using non‐supercritical fluid physical blowing agents

A new foam injection‐molding technology was developed to produce microcellular foams without using supercritical fluid (SCF) pump units. In this technology, physical blowing agents (PBA), such as nitrogen (N₂) and carbon dioxide (CO₂), do not need to be brought to their SCF state. PBAs are delivered directly from their gas cylinders into the molten polymer through an injector valve, which can be controlled by a specially designed screw configuration and operation sequence. The excess PBA is discharged from the molten polymer through a venting vessel. Alternatively, additional PBA is introduced through the venting vessel when the polymer is not saturated with PBA. The amount of gas delivered into the molten polymer is controlled by the gas dosing time of the injector valve, the secondary reducing pressure of the gas cylinder and the outlet (back) pressure of the venting vessel. Microcellular polypropylene foams were prepared using the developed foam injection‐molding technology with 2–6 MPa CO₂ or 2–8 MPa N₂. High expansion foams with an average cell size of less than 25 μm were prepared. The developed technology dispels arguments for the necessity to pressurize N₂ or CO₂ to the SCF to prepare microcellular foams. POLYM. ENG. SCI., 57:105–113, 2017. © 2016 Society of Plastics Engineers     

Solubility of binary liquid mixtures in polymeric materials

Experimental data on the permeation of binary mixtures through polymeric materials show that liquid mixtures can exhibit large, positive synergistic rates. As the permeation rate depends on both solubility and the diffusion coefficient, the existence of a maximum in the steady-state permeation rate vs. the composition curve could be due to an increase in solubility and/or diffusion coefficient. In this study, a theoretical model based on the Flory-Huggins equation was developed to predict the solubility of binary liquid mixtures in polymers. The equation has four adjustable parameters that can be determined from solubilities of pure liquids in the polymer and the vapor-liquid equilibrium data for the binary liquid mixture. The model was tested for two binary liquid mixture/polymer systems. The predicted values of solubilities are close to the experimental data. © 1993 John Wiley & Sons, Inc.     

Preparation and characterization of binary blends composed of poly(dioctylfluorene‐alt‐hexylsulfonylthiophene) and nonconjugated polymers

The solutions and the thin films of poly[9,9‐dioctyl‐2,7‐fluorene‐alt‐2,5–(3‐hexyl‐sulfonylthiophene)] (PFSO₂T) and its binary blends with other nonconjugated polymers such as poly(methyl methacrylate) (PMMA), polycarbonate (PC), and ethylene vinyl acetate copolymer (EVA) can be prepared by different concentrations from a polymer solution. Binary polymer blends can increase the absorbance and photoluminescence intensities in the solid state due to nonconjugated polymers can act as dispersion agents which can reduce the interchain interaction or the aggregation of the conjugated polymers. Photoluminescence intensity of the thin films of fluorescent polymers blending with ethylene vinyl acetate copolymers exhibited six times higher than that of the neat fluorescent polymers. The PFSO₂T/EVA binary blends reveal the least extent of optical degradation of around 20% compared to those binary blends in both absorption and emission intensities after the irradiation under the UV‐light for 20 h. The cross‐sectional morphology of fluorescent polymers blending with ethylene vinyl acetate copolymers reveals little aggregation and better phase separation among the other binary polymer blends. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 44969.     

Effect of CO2 sorption and desorption on the creep response of polycarbonate

In this article, experimental results on the effect of CO₂ sorption and desorption on the creep response of polycarbonate (PC) are presented. Tensile specimens machined from PC sheets were exposed to CO₂ and the absorbed gas mass fraction ranged from 0.045 to 0.12. The creep/creep recovery response of as‐received PC, saturated PC, and saturation‐cycled PC was characterized. It was found that the saturated PC showed a creep behavior similar to heating the PC to its glass transition temperature. The creep compliance of saturation‐cycled PC was found to change with the desorption or aging time. The tests on PC saturated and then desorbed for up to 60 days showed that the effects of exposure to CO₂ on PC creep properties persist long after the gas has left the polymer, and could be permanent. POLYM. ENG. SCI., 45:1639–1644, 2005. © 2005 Society of Plastics Engineers