Solubility of butane and isobutane in molten polypropylene and polystyrene

The solubility of butane and isobutane in molten polypropylene (PP) and polystyrene (PS) was measured at pressures up to 3 MPa and along four isotherms from 438 to 483 K for PP and from 348 to 473 K for PS. The solubility increased with increasing pressure and decreasing temperature. At 438 K and 2 MPa, the solubilities of butane and isobutane in PP were 0.15 and 0.11 g‐gas/g‐polym, respectively. At 423 K and 2 MPa, the solubilities of butane and isobutane in PS were 0.08 and 0.05 g‐gas/g‐polym, respectively. Solubility could be correlated with the Sanchez‐Lacombe equation of state with temperature‐dependent binary interaction parameters to within 4.4% average relative deviation. Henry's constant for these gases in the PP and PS obtained in this work were used to determine correlation equations along with literature data. Polym. Eng. Sci. 44:2083–2089, 2004. © 2004 Society of Plastics Engineers.     

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

Solubilities are reported for carbon dioxide (CO₂) 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 CO₂ 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 CO₂ dissolution into the polymer was predicted with the GCLF EOS and the solubility data under the assumption that CO₂ could dissolve only in the amorphous regions. The trend of the estimated crystallinity with CO₂ dissolution into the polymer was consistent with results in the literature.     

Solubilities and diffusion coefficients of carbon dioxide in poly(vinyl acetate) and polystyrene

Solubilities of carbon dioxide in poly(vinyl acetate) (PVAc) were measured at temperatures from 313.15 to 373.15 K and pressures up to 17.5 MPa. Diffusion coefficients of carbon dioxide in PVAc were also measured at 313.15 K and pressures up to 7 MPa. Solubilities and diffusion coefficients of carbon dioxide in molten polystyrene (PS) were studied at temperatures from 373.15 to 473.15 K and pressures up to 20 MPa. An apparatus using a magnetic suspension balance (MSB) was constructed for the measurements. The solubilities in the PVAc and the PS were in good agreement with literature data. The solubility in both polymers were correlated with the Sanchez and Lacombe equation of state to within an average relative deviation of 3.6 and 1.6% for PVAc and PS systems, respectively. The diffusion coefficients in PS were correlated with free volume theory of Kulkarni and Stern to within 10% of relative average deviation.     

Experimental and theoretical investigation of solubility and diffusion of ethylene in semicrystalline PE at elevated pressures and temperatures

The solubility and diffusivity of ethylene in semicrystalline polyethylene were experimentally measured using a magnetic suspension microbalance. The sorption measurements were carried out at temperatures up to 80°C and pressures up to 66 atm. The experimentally measured solubilities were found to decrease with increasing temperature and increased with ethylene pressure in good agreement with the predictions of the Sanchez–Lacombe lattice‐fluid model. The diffusivity of ethylene in semicrystalline polyethylene films was estimated from the reduced sorption curves using the half‐time method. The experimentally determined diffusivities were compared with theoretical values predicted by a new molecular hybrid model, which combines the characteristic features of the Pace–Datyner diffusion model with those of the Kulkarni–Stern free‐volume model. The ethylene diffusion coefficient was found to increase with temperature and/or the ethylene‐sorbed concentration. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 87: 953–966, 2003     

Pressure‐volume‐temperature behavior of polylactide,poly(butylene succinate), and poly(butylene succinate‐co‐adipate)

Pressure‐Volume‐Temperature (PVT) behavior of three biodegradable polymers, Polylactide, poly(butylene succinate), and poly(butylene succinate‐co‐adipate), was measured at temperatures from 313 to 493 K and pressures up to 200 MPa. The PVF data in molten state were compared with predicted values of a group contribution modified cell model equation of state (GCMCM EOS). It was found that the GCMCM EOS coupled with one specific volume datum at atmospheric pressure could predict the PVT of the polymer melts to within 0.46% in an average relative deviation of specific volume.     

Demixing pressures of hydroxy-terminated poly(dimethylsiloxane)–carbon dioxide binary mixtures at 313.2 K, 323.2 K and 333.2 K

The phase behavior of PDMS(OH)–CO₂ binary mixtures was investigated. Two different molecular weight PDMS(OH) were utilized and the demixing pressures were determined at three temperatures for a wide composition range. Both of these polymers were found to form miscible mixtures with CO₂ at all compositions at pressures lower than 31 MPa in the temperature range 313.2–333.2 K. Depending on the composition of the binary mixtures, two types of phase separation was observed during depressurization; the bubble point and the cloud point. In addition, at specific weight fractions a color change was also observed which was attributed to the mixture critical point. The demixing pressures were observed to increase with temperature and decrease with increasing polymer weight fraction. In addition, higher demixing pressures were obtained for the higher molecular weight polymer mixtures. The bubble point data were modeled by using Sanchez–Lacombe equation of state (SLEoS) and the binary interaction parameters were regressed at the studied temperatures. It was observed that the binary interaction parameters decreased with increasing temperature.     

Phase equilibrium characteristics of supercritical CO2/poly(ethylene terephthalate) binary system

The solubility of carbon dioxide in poly (ethylene terephthalate) (PET) at high pressure and elevated temperature conditions was investigated for a better understanding of the phase equilibrium characteristics of supercritical CO₂/PET binary system and useful data for the process development of the supercritical fluid dyeing. Based on the principle of pressure decaying, a novel experimental apparatus suitable to high pressure and high temperature measurement was established. The solubilities of CO₂ in PET were measured with the apparatus at temperatures of 110, 120, and 130°C and pressures up to 30.0 MPa. The results show that the solubility of CO₂ in PET increases with the increase of pressure and CO₂ density, respectively, at a constant temperature, whereas it decreases with the increase of temperature at a constant pressure. The Sanchez‐Lacombe equation of state (S‐L EOS) was used to correlate the experimental data. The calculated results are in good agreement with the experimental ones. The average absolute relative derivation (AARD) is less than 3.91%. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Experimental and modeling studies on the solubility of sub‐ and supercritical carbon dioxide (scCO2) in potato starch and derivatives

The solubility of CO₂ in native potato starch (NPS) and potato starch acetate (SA) at two different temperatures (50°C and 120°C) and various pressures (up to 25 MPa) was determined using a magnetic suspension balance. Within the experimental window, a maximum solubility of 31 mg CO₂/g_sample for NPS and 79.4 mg CO₂/g_sample for SA was obtained. The CO₂ sorption behavior is highly depending on the temperature and pressure. The solubility data were modeled with the Sanchez Lacombe equation of state (S‐L EOS). The swelling (S_w) values, as predicted using the S‐L EOS, were relatively small and a maximum value of 6.1% was obtained for SA at 25 MPa and 120°C. POLYM. ENG. SCI., 2011. © 2010 Society of Plastics Engineers     

Solubility of hydrofluorocarbon (HFC‐134a,HFC‐152a) and hydrochlorofluorocarbon (HCFC‐142b) blowing agents in polystyrene

Solubilities of blowing agents (HFC‐134a, HCFC‐142b, and HFC‐152a) in polystyrene (PS) were measured at temperatures from 348 to 473 K and pressures up to 3.2 MPa with a volumetric method. For all conditions, the solubility of the blowing agents in PS decreased with increasing temperature. At a given temperature and pressure, the solubility of HFC‐134a, HFC‐152a, and HCFC‐142b in PS increased in that order. Solubilities could be correlated with the Sanchez‐Lacombe equation of state with temperature‐dependent binary interaction parameters to within 3.4% average relative percent deviation. The temperature dependence of the Henry's constants, K_p, for the blowing agents were found to have a linear relationship between ln(1/K_p) and (T_c/T)², where T_c is the critical temperature of the blowing agent.     

Solubility measurements of N2 and CO2 in polypropylene and ethene/octene copolymer

In this set of experiments a magnetic suspension balance (MSB) was employed to measure the apparent solubilities of N₂ and CO₂ in polypropylene (PP) and ethene/octene copolymer melts, while the swollen volume predicted by the Sanchez–Lacombe (SL) equation of state (EOS) was used to account for the buoyancy effect. The swollen volume of the polymer/gas mixture, as well as the gas solubilities for both PP and the ethene/octene copolymer, are discussed. It was observed that the branched molecular structure limited the molecular movement, and therefore the volume swelling of the polymer/gas mixture. In a similar context, the solubility of both N₂ and CO₂ were less in the branched polymer (ethene/octene copolymer) than in the linear PP. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 2945–2953, 2007     

Comparison of Sanchez–Lacombe and SAFT model in predicting solubility of polyethylene in high-pressure fluids

Sanchez–Lacombe and SAFT (statistical associating fluid theory) models are used to describe phase behavior of polyethylene solutions (M_w = 2,150, 16,400, 108,000, and 420,000, and M_wM_n = 1.14, 1.16, 1.32, and 2.66, respectively) in n-pentane and in n-butane at high pressures. In order to test the predictive capability of the two models, all the predictions were conducted without any adjustment of the binary interaction parameter. Even though both models correctly predict the general trends of the phase envelopes and the LCST (lower critical solution temperature) nature of the systems, SAFT gives predictions that are much closer to the experimental data than the Sanchez–Lacombe model. © 1995 John Wiley & Sons, Inc.     

Heat capacity of polymer melts from the polymer chain-of-rotators equation of state

Recently, the chain-of-rotators equation of state derived from the rotational partition function was extended to polymers. Values of the three equation of state (EOS) parameters were obtained from fitting with experimental pressure–volume–temperature data and the parameters were correlated with the structure of the polymer repeat unit. In this article, the residual molar heat capacity derived from an EOS is added to the ideal gas heat capacity from Benson's group contribution method to obtain the polymer molar heat capacity at constant pressure, C_p. Predictions from the polymer chain-of-rotators (PCOR) using correlated parameters are compared with those obtained from PCOR, Sanchez–Lacombe, Flory–Orwoll–Vrij, and the perturbed-hard-sphere chain equations of state using parameters fitted from experimental data. Deviations of calculated C_p from the formula of van Krevelen for liquid polymers are likewise presented. With the correlations developed for its parameters, the PCOR offers the advantage of predicting the C_p for polymer melts from just the knowledge of the polymer's structure. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 67:841–848, 1998     

Predicting the effect of dissolved carbon dioxide on the glass transition temperature of poly(acrylic acid)

The morphology and size of poly(acrylic acid) (PAA) particles produced by precipitation polymerization in supercritical CO₂ (scCO₂) depends on the glass transition temperature (T_g) of the polymer at reaction conditions. In this study, the use of the Sanchez–Lacombe equation of state (SL‐EOS), in conjunction with Chow's equation, to predict the effect of CO₂ pressure on the T_g of PAA was evaluated. Characteristic parameters for PAA were determined by fitting density data. Characteristic parameters for CO₂ were determined by fitting density data in the supercritical region. When the SL‐EOS was used in a purely predictive mode, with a binary interaction parameter (ψ) of 1, the solubility of CO₂ in PAA was underestimated and T_g was overestimated, although the trend of T_g with CO₂ pressure was captured. When was determined by fitting the SL‐EOS to the measured sorption of scCO₂ in PAA, the calculated T_g's agreed very well with measured values. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Pressure–volume–temperature relationships for polymeric liquids: A review of equations of state and their characteristic parameters for 56 polymers

A review of theoretical equations of state for polymer liquids is presented. Characteristic parameters for six equations of state, as well as parameters for the empirical Tait equation, are given for 56 polymers where pressure–volume–temperature (PVT) data over a wide range of conditions could be found in the literature. New PVT data are presented for four polymers: poly(epichlorohydrin), poly(?-caprolactone), poly(vinyl chloride), and atactic polypropylene. All six equations of state provide adequate fits of the experimental specific volume data for the 56 polymers in the low pressure range (up to 500 bar). The modified cell model of Dee and Walsh, the Simha–Somcynsky hole theory, the Prigogine cell model, and the semiempirical model of Hartmann and Haque, were all found to provide good fits of polymer liquid PVT data over the full range of experimental pressures. The Flory–Orwoll–Vrij and the Sanchez–Lacombe lattice–fluid equations of state were both significantly less accurate over the wider pressure range. © 1993 John Wiley & Sons, Inc.     

High‐pressure phase equilibria for a styrene/CO2/polystyrene ternary system

To reveal the possibility of supercritical (SC)‐CO₂‐assisted devolatilization of polystyrene, the equilibrium composition data for the CO₂ phase in a styrene/CO₂/polystyrene ternary system is determined by a semistatic experimental technique. The parameters in the lattice–fluid equation of state of Sanchez and Lacombe are determined for the investigated system. The distribution coefficients of styrene between the polymer and the supercritical fluid phases are investigated experimentally at 318 and 328 K over the pressure range of 12–20 MPa. The binary interaction parameter between styrene and CO₂ is obtained by regression of the vapor–liquid equilibrium data. The interaction parameter between CO₂ and polystyrene is calculated by using the sorption data from the literature, and the interaction parameter between styrene and polystyrene is optimized by using the measured data of this study. The investigation of the distribution coefficients indicates that styrene can be removed from polystyrene by SC‐CO₂ at near room temperature and moderately high pressures. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 85: 1938–1944, 2002     

High-pressure phase behavior in polyethylene/n-butane binary and polyethylene/n-butane/CO2 ternary systems

Solubility of polyethylene molecular weight standards (M_w = 2150, 16,400, 108,000, and 420,000 and M_w/M_n = 1.14, 1.16, 1.32, and 2.66, respectively) has been studied in near- and supercritical n-butane and n-butane/CO₂ mixtures at pressures up to 70 MPa. For each polyethylene/solvent system at selected compositions, demixing pressures have been determined using a high-pressure variable-volume view-cell at temperatures up to 200°C. Solutions in pure n-butane are found to display LCST (lower critical solution temperature)-type behavior. The behavior of the solutions in n-butane/CO₂ mixtures are observed to change from the LCST to the UCST (upper critical solution temperature) with increasing CO₂ content in the binary solvent. Sanchez–Lacombe theory has been used to model these systems. The predictions correctly describe the nature of the phase diagrams for both binary and ternary systems and the calculations are in reasonable agreement with experimental data. © 1994 John Wiley & Sons, Inc.     

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.     

Solubilities of sub‐ and supercritical carbon dioxide in polyester resins

In supercritical carbon dioxide (CO₂) assisted polymer processes the solubility of CO₂ in a polymer plays a vital role. The higher the amount of CO₂ dissolved in a polymer the higher is the viscosity reduction of the polymer. Solubilities of CO₂ in polyester resins based on propoxylated bisphenol (PPB) and ethoxylated bisphenol (PEB) have been measured using a magnetic suspension balance at temperatures ranging from 333 to 420 K and pressures up to 30 MPa. An optical cell has been used to independently determine the swelling of the polymers, which has been incorporated in the buoyancy correction. In both polyester resins, the solubility of CO₂ increases with increasing pressure and decreasing temperature as a result of variations in CO₂ density. The experimental solubility has been correlated to the Sanchez–Lacombe equation of state. POLYM. ENG. SCI. 46:643–649, 2006. © 2006 Society of Plastics Engineers     

Group contribution lattice fluid equation of state for CO2–ionic liquid systems: An experimental and modeling study

The group contribution lattice fluid equation of state (GCLF EOS) was first extended to predict the thermodynamic properties for carbon dioxide (CO₂)–ionic liquid (IL) systems. The group interaction parameters of CO₂ with IL groups were obtained by means of correlating the exhaustively collected experimental solubility data at high temperatures (above 278.15 K). New group parameters between CO₂ and IL groups were added into the current parameter matrix. It was verified that GCLF EOS with two kinds of mixing rules could be used for predicting the CO₂ solubility in ILs, and volume expansivity of ILs upon the addition of CO₂, as well as identifying the new structure–property relation. Moreover, it is the first work on the measurement of the solubility of CO₂ in ILs at low temperatures (below 278.15 K), manifesting the applicability of predictive GCLF EOS over a wider temperature range. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4399–4412, 2013     

On the use of pressure‐volume‐temperature data of polyethylene liquids for the determination of their solubility and interaction parameters

Specific volumes of high‐density and low‐density polyethylene liquids at several elevated temperatures and pressures were measured. The measured specific volumes were then used to estimate the thermal expansion coefficients $\left( {{\rm \alpha = }\frac{{\rm 1}}{v}\left( {\frac{{\partial v}}{{\partial T}}} \right)_P } \right)$ and isothermal compressibility $\left( {{\rm \beta = } - \frac{{\rm 1}}{v}\left( {\frac{{\partial v}}{{\partial P}}} \right)_T } \right)$ of the polymers. Two different approaches were used in which one was simply to fit the raw data by second order polynomials to obtain (?v/?T)_P and (?v/?P)_T, while the other by the Sanchez‐Lacombe (S‐L) equation of state. It was found that the resultant α and β obtained from the above methods differ significantly, indicating that the S‐L equation of state may not be suitable for determining α and β at elevated temperatures. When these two sets of α and β were used to calculate the corresponding solubility parameters and then the Flory‐Huggins interaction parameters (χ) of the polymers, the results also differ considerably. Nonetheless, χ obtained from the first method agrees well with the results obtained from small angle neutron scattering measurements while the S‐L equation of state method does not. The current results suggest that solubility and interaction parameters obtained from pressure‐volume‐temperature experiments depend critically on the manner by which the data analysis is performed. Polym. Eng. Sci. 44:853–860, 2004. © 2004 Society of Plastics Engineers.