Sanchez-Lacombe Equation Of State Research Articles

Density measurements of homogeneous phase fluid mixtures comprising CO2/methanol and CO2/ethanol binary systems and correlation with equations of state

Equations of state (EoS) are powerful tools for estimating a wide variety of physical properties. However, the applicability of parameter sets derived from specific physical properties for the correlation and estimation of various other physical properties has received limited attention. Additionally, the estimation of physical properties using EoS is anticipated to be affected by the association of molecules. The densities of homogeneous phase fluid mixtures comprising carbon dioxide (CO2)/methanol (MeOH) and CO2/ethanol (EtOH) binary systems were measured in the current study using a high-pressure vibration-type density meter equipped with a circulation pump and a variable-volume viewing cell. Homogeneity was ensured by observing the fluid through the viewing window of the variable volume cell. The measurements were carried out at a temperature range of 313–353 K, the CO2 mole-fraction range of 0–80 mol%, and at pressures up to 20 MPa. Subsequently, the as-obtained experimental data were correlated with two EoSs, viz. Sanchez-Lacombe (SL) EoS and Perturbed Chain statistical associating fluid theory (PC-SAFT) EoS. The density correlations between SL and PC-SAFT EoS were almost identical in accuracy. Additionally, the association between CO2 and alcohols in PC-SAFT EoS had no discernible effect on the reliability of the density correlations. The vapor liquid equilibria (VLE) of the CO2/MeOH and CO2/EtOH mixtures were further estimated using parameter sets determined from the density measurements. Both the EoSs demonstrated comparable estimation accuracy; however, the pressure was estimated primarily near the critical region of the mixture, which yielded a lower estimation accuracy. Additionally, the densities of the binary systems were determined using characteristic parameters derived from the VLE correlations. Of the EoSs, the PC-SAFT EoS yielded a good correlation of the VLE, including the region near the mixture's critical region, while taking the association between CO2 and alcohols into consideration. Although few of the correlations were observed to be inferior, the density of the homogeneous fluid mixture was accurately estimated using the two EoSs, with the parameters obtained from the VLE correlations. The findings of the study thus suggest that in order to estimate the density and VLE using EoS-shared parameters, the parameter sets must first be determined using a VLE that exhibits a wide range of conditions affected by the system's associations.

Density, viscosity, and CO2 solubility in ether-functionalized phosphonium-based bis(trifluoromethanesulfonyl)amide ionic liquids

We measured the densities and viscosities of two ionic liquids, triethyl(methoxymethyl)phosphonium bis(trifluoromethanesulfonyl)amide ([P222(1O1)][TFSA]) and triethyl(2-methoxyethyl)phosphonium bis(trifluoromethanesulfonyl)amide ([P222(2O1)][TFSA]), at atmospheric pressure and 273.15–363.15 K. The high-pressure density at the pressures up to 50 MPa was also measured at 298.15–353.15 K. Meanwhile, CO2 solubility in these phosphonium-based ionic liquids was determined using a magnetic suspension balance at 303.15–333.15 K and pressures up to 6 MPa. The experimental density and viscosity at atmospheric pressure were fitted using quadratic and Vogel-Fulcher-Tammann equations, respectively. The high-pressure density was fitted using the Tait equation and Sanchez-Lacombe equation of state. The properties of the two ether-functionalized ionic liquids were compared to those of triethylpentylphosphonium bis(trifluoromethanesulfonyl)amide [P2225][TFSA]. The density at atmospheric pressure increased in the order [P2225][TFSA] < [P222(2O1)][TFSA] < [P222(1O1)][TFSA]. The introduction of the ether group effectively reduced viscosity in the following order: [P222(1O1)][TFSA] < [P222(2O1)][TFSA] < [P2225][TFSA]. The CO2 solubilities in [P222(1O1)][TFSA] and [P222(2O1)][TFSA] were slightly lower than those in [P2225][TFSA]. In contrast, the molality of CO2 (m1) increased in the order [P2225][TFSA] < [P222(2O1)][TFSA] < [P222(1O1)][TFSA]. Ether functionalized phosphonium-based cations are effective in enhancing the physical absorption of CO2, particularly the molality of CO2.

Estimation of the Effects of CO2 and Temperature on the Swelling of PS-CO2 Mixtures at Supercritical Conditions on Rheological Testing.

The use of supercritical CO2 as a blowing agent for polymeric foams instead of traditional blowing agents has been a trend in recent years. To achieve the final desired properties of the polymeric foams, the rheological behavior of the material needs to be reliable. The polymer swelling in the samples for rheological testing affects the results of the viscoelastic properties of the material. This study proposes a new testing methodology to control the accuracy and repeatability of the rheological characterization for PS-SCO2 samples. To develop this methodology, three polystyrene resins with different molecular weight distribution were studied at three temperatures (170, 185 and 200 °C) and three pressures (0.1 MPa, 6.89 MPa and 13.78 MPa). The CO2 concentration was estimated and used in the Sanchez–Lacombe Equation of State (SLEOS) to determine the polymer swelling, as it affects the dimensions of specimens tested in high-pressure rheometers. The correction factors provided a consistent trend in the viscosity with respect to temperature and a decrease of up to 50% in the standard deviation. The results of this study are crucial for an accurate measurement of viscoelastic properties by parallel-plate rheometry.

Measurement of the density of carbon dioxide/toluene homogeneous mixtures and correlation with equations of state

Equations of state (EoS) can be used to estimate a wide variety of physical properties. However, there has been limited verification of the applicability of parameter sets derived from specific physical properties to correlate and estimate various other physical properties. The densities of homogeneous phase fluid mixtures of the carbon dioxide (CO2)/toluene (Tol) binary system were measured and correlated to three equations of state. The density measurements were performed using a high-pressure vibration-type density meter equipped with a circulation pump and variable-volume viewing cell, which guaranteed the homogeneity of the mixtures. The densities were measured at temperatures ranging from 313 to 353 K, pressures up to 20 MPa, and CO2 concentrations from 0 to 80 mol%. The experimental data obtained were correlated to the Tait density equation and three EoS, namely Peng–Robinson (PR), Sanchez–Lacombe (SL), and Perturbed Chain statistical associating fluid theory (PC-SAFT) EoS. Among them, SL and PC-SAFT EoS agree better with the experimental data compared to the PR EoS, presumably due to differences in the pure component parameters used in each EoS. Using parameter sets determined from the density measurements, the vapor liquid equilibrium (VLE) of the CO2/Tol mixtures was estimated. While we were unsuccessful in estimating VLE using the PR EoS, SL and PC-SAFT EoS were successfully used for the estimations. We also attempted to determine the densities from VLE correlations. It was found that SL and PC-SAFT EoS could be used to estimate the density well, whereas the PR was not predictive. From the results of the study, it is clear that for estimating density using EoS, the basic data used for determining the pure component parameters are important.

Pressure-volume-temperature relationships of diisononyl phthalate and phase behavior of carbon dioxide/diisononyl phthalate binary system

The pressure-volume-temperature (PVT) relationships of pure diisononyl phthalate (DINP) were measured at temperatures of 303.15–363.15 K and pressures up to 160 MPa by a variable-volume method. Using a synthetic method that involved observing the bubble point, the phase behavior of the CO2/DINP binary system was also measured. The phase boundaries were determined at temperatures of 313.15–393.15 K and CO2 molar fractions of 0.3–0.9. The characteristic parameters of DINP were obtained by correlating the measured PVT data using the Sanchez-Lacombe equation of state (SL EoS), and the bubble points of the system were correlated using the SL EoS with the determined characteristic parameters. The interaction parameter exhibited temperature dependence, and the introduction of the temperature dependence improved the correlation.

Measurement and modeling of solubilities and diffusion coefficients of carbon dioxide in poly(ethylene-co-acrylic acid)

We measured and modeled the solubilities and diffusion coefficients of carbon dioxide (CO2) in poly(ethylene-co-acrylic acid) (PEAA) over temperatures of 373–473 K and pressures of up to 20 MPa. The measured solubilities of CO2 in PEAA obeyed Henry’s law and decreased with an increase in the acrylic acid content of the copolymer. The Sanchez-Lacombe equation of state could be applied to correlate the measured solubilities. The temperature dependence of the CO2 solubilities in PEAA was found to be similar to that in polyethylene with analysis using Henry’s law. Further, the gas solubility and acrylic acid content were the influential factors for determining the diffusivity of CO2, which could be modeled based on the free volume theory.

Effective interaction between colloids immersed in a polymer blend and their effect on the equation of state of this blend

HypothesisOwing to the entropic interactions between polymers comprising a blend and surfaces of colloids immersed in this blend, the polymer inter-phases are formed between the colloids and blend. These inter-phases that are non-uniform both in density and composition, mediate the effective interaction between colloids immersed in a polymer blend. We surmise that there is an additional non-osmotic mechanism of the polymer mediated interactions specific to polymer blends, which is caused by the compositional non-uniformity of the above colloid-blend inter-phases. TheoryBy developing and making use of the random phase approximation based upon the Sanchez-Lacombe equation of state, we calculate the second virial coefficient of the effective interaction between colloids mediated by a polymer blend. The proposed approach takes into account finite compressibility of a polymer blend, as well as the specific (strong) interactions between dissimilar blend components. Using the obtained results, we derive the equation of state of a polymer blend filled with colloids. FindingsWe prove that the correlations imposed by the variations of the composition of a polymer blend cause a significant contribution to the polymer mediated interaction between colloids immersed in this blend. This contribution dominates over the osmotic contribution in the case of dense polymer blends.

Estimation of diffusion coefficients for multiple penetrant/polyolefin systems based on sorption data

The binary and ternary diffusion coefficients for gas/polymer systems can be estimated from solubility data and an equation of state to the free volume of penetrant/polymer systems. The system free volume can be calculated by the Sanchez Lacombe equation-of-state (SL-EoS), eliminating the need for viscoelastic data in determination of free volume parameters. Furthermore, this approach accounts for polymer swelling. The model gives reliable predictions for both binary and ternary systems of alkanes and alkenes in polyolefins.

Measurement and prediction of phase equilibria of ethylene + methyl acrylate + poly(ethylene-co-methyl acrylate) systems

The solubilities of ethylene in the methyl acetate (MA) solutions of poly (ethylene-co-methyl acrylate) (EMA) were investigated according to conditions applicable to polymerization. The bubble point pressure (BP) for vapor-liquid equilibrium (VLE) and the cloud point pressure (CP) for liquid-liquid equilibrium (LLE) of ethylene + MA + EMA ternary system (weight ratio of MA: EMA, 9: 1) were measured at temperatures of 373 K and 393 K and at pressures up to 25 MPa with a synthetic method. The BP and CP increased with increasing temperature and ethylene weight fraction, especially the slope of CP against ethylene weight fraction was large. The Sanchez-Lacombe equation of state (SL EoS) could correlate VLE data of ethylene + MA and ethylene + EMA systems by fitting a corresponding binary interaction parameters for each binary to within about 4.7% in pressure. The phase equilibria of the ternary system could be predicted with the SL EoS from binary interaction parameters determined from the binary systems.

Polymeric Foaming Predictions from the Sanchez-Lacombe Equation of State: Application to Polypropylene-Carbon Dioxide Mixtures

The author has the right to post and update the article on a free-access e-print server using files prepared and formatted by the author. Any such posting made or updated after acceptance of the article for publication by APS should include a link to the online APS journal article abstract. In all cases, the appropriate bibliographic citation (von Konigslow, K., Park, C. B., & Thompson, R. B. (2017). Polymeric Foaming Predictions from the Sanchez-Lacombe Equation of State: Application to Polypropylene-Carbon Dioxide Mixtures. Physical Review Applied, 8(4), 044009. https://doi.org/10.1103/PhysRevApplied.8.044009) and notice of the APS copyright must be included.

Phase behavior of Carbon dioxide/Trimethoxy(methyl)silane and Methylsilicate 51 system

The phase behaviors of carbon dioxide (CO2)/trimethoxy(methyl)silane (MTMS) and CO2/Methylsilicate 51 (MS-51: methylsilicate tetramer) binary systems were determined. The experiments were performed using a synthetic method by observing the bubble point. The phase boundaries were determined at temperatures of 313.2 K–393.2 K and CO2 molar fractions of 0.2–0.9. The experimentally obtained bubble points of the CO2/MTMS binary system were correlated using the Peng-Robinson equation of state (PR EoS), and the molecular interaction parameters kij and lij were determined. The results of the CO2/MS-51 binary system were correlated using the PR EoS and the Sanchez-Lacombe equation of state (SL EoS). In the SL EoS, two types of mixing rules, originally proposed by Sanchez et al. which uses kij as a fitting parameter and modified by McHugh et al. which uses two fitting parameters kij and lij, were used. For this system, the experimental results were correlated better using the SL EoS than using the PR EoS, and the latter mixing rule was more suitable than the former.

Simulation and Sensitivity Study of Industrial Low Density Polyethylene Tubular Reactor

The development and application of process modelling technology for polymer industry is relatively increasing. Accurate simulation of the polymerisation process can help industrial community to maximise their polymer production with minimal energy and cost. In this study, industrial Low Density Polyethylene (LDPE) tubular reactor process has been simulated using Aspen Plus software. Aspen Polymer (Aspen Plus component) was used to model the free radical polymerisation part of the polymer. The reactor properties, reaction mechanisms and kinetic model for the polymerisation process was taken from several referred journals. Sanchez-Lacombe equation of state was used to describe the thermodynamic properties of the process. Based on a comparison with available literature data, the selected equation of state and reaction kinetic model had performed well in simulating tubular reactor temperature profile, polymer molecular weight and monomer conversion. Sensitivity study was also conducted to study the behaviour of controlled parameters in the tubular reactor process. In this study, the effect of initiators flow rate, oxygen flow rate, and Chain Transfer Agent (CTA) flow rate towards ethylene conversion and temperature profile were observed. From the sensitivity study, both initiators and oxygen flow rate had displayed considerable effect on the observed parameters. Among them, the second initiator flow rate displayed the most significant effect. CTA flow rate gave the minimal effect since its main purpose is to modify the polymer molecular properties. This demonstrates the important of proper regulation of second initiator flow rate in order to meet desired polymer conversion while maintaining the reactor temperature.

Viscosity of poly(ethyleneglycol) 200 [PEG 200] saturated with supercritical carbon dioxide

The article presents viscosity measurements on mixtures of poly(ethyleneglycol) 200 (PEG 200) saturated with supercritical CO2, along three isotherms, at approximately 313K, 333K and 348K, and pressures up to 25MPa. The measurements have been performed with a previously described vibrating wire instrument. The results show a steep initial viscosity decrease with increasing pressure of CO2, followed by a flatter zone, extending up to 25MPa. This behavior, which is quantitatively temperature dependent, seems to be closely related to the solubility of CO2 as a function of pressure.The experimental method for the determination of the viscosity requires the density of the samples. For this purpose, the density data for the mixtures were calculated from phase equilibrium studies by Gourgouillon and Nunes da Ponte, using the Sanchez-Lacombe equation of state. The measured viscosity data for CO2 saturated PEG 200 solutions were then correlated using the Kelly-Bueche theory.

Measurement and prediction of phase equilibria of ethylene + vinyl acetate + methanol + poly(ethylene-co-vinyl acetate) systems

This work investigated the solubilities of ethylene in the 10 wt% poly (ethylene-co-vinyl acetate) (EVA) solutions including vinyl acetate (VA) and methanol which are related to production of EVA. The bubble point pressure (BP) for vapor-liquid equilibrium (VLE) and the cloud point pressure (CP) for liquid-liquid equilibrium (LLE) of ethylene + VA + EVA ternary and ethylene + VA + EVA + methanol quaternary systems were measured at temperatures of 313 K, 343 K, 373 K and at pressures up to 20 MPa with a synthetic method. The experimental results revealed that the BP and CP increased with increasing temperature and ethylene weight fraction, especially the influence of ethylene weight fraction on CP was found to be drastic. The Sanchez-Lacombe equation of state (SL EOS) could correlate the BP data of ethylene + VA + EVA ternary and ethylene + VA + EVA + methanol quaternary systems within 3.6% an average relative deviation. The phase equilibria of the EVA + VA + ethylene ternary system could be predicted over wide polymer concentration ranges by the SL EOS with the determined parameters in the correlations. With increasing pressure, phase behavior changed from VLE at low pressure to vapor-liquid-liquid equilibrium (VLLE) and LLE at high pressures.

Methane Adsorption in a Series of IRMOFs Studied by PHSC and Sanchez–Lacombe Equations of State

In this study, the methane adsorption on several kinds of isoreticular metal organic frameworks (IRMOF) has been modeled by applying perturbed hard sphere chain (PHSC) and Sanchez–Lacombe (SL) equation of state. PHSC and SL equation of state have three characteristic parameters calculated using group contribution method. In this study, the methane adsorption on absorbents, namely, IRMOF-6, IRMOF-8, IRMOF-10, IRMOF-14 has been obtained at temperature 298 K and various pressures up to 10 MPa. Finally, results have been compared with the simulated adsorption data points to show the precision of PHSC and SL equation of state in predicting the methane sorption trend.

Prediction of self diffusion coefficients of selected solvents in poly(vinyl alcohol) using lattice-free volume theory

The free volume model is probably the most successful model for predicting the diffusivity of small molecules in polymers. However, the experimental procedure for parameterizing the model is not trivial and in fact extremely time consuming. In this work, we propose a much less time consuming approach for the parameterization step. In particular, we carried out isobaric-isothermal molecular dynamics simulations to generate thermodynamic data of a few selected polymer/solvent systems and used the data to parameterize the corresponding Sanchez–Lacombe equation of state (SLEOS). The characteristic parameters of the SLEOS were then used in the parameterization of the lattice free volume (LFV) model so that diffusivity of the solvents in a polymer was then determined. To illustrate the newly proposed approach, we used poly(vinyl alcohol) and water, ethanol and benzene over a concentration range of 1–20 wt% and a temperature range of 270–370 K. We found that the LFV model was much easier to be parametrized in the aforementioned approach and yielded predictions much better than those of the well-known Mackie-Meares model. We also demonstrated that the two adjustable parameters of the LFV model are related to the size of the solvent molecules and their interaction with the polymer.

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 31MPa in the temperature range 313.2–333.2K. 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.

Free volume in ionic liquids: a connection of experimentally accessible observables from PALS and PVT experiments with the molecular structure from XRD data

In the current work, free volume concepts, primarily applied to glass formers in the literature, were transferred to ionic liquids (ILs). A series of 1-butyl-3-methylimidazolium ([C4MIM](+)) based ILs was investigated by Positron Annihilation Lifetime Spectroscopy (PALS). The phase transition and dynamic properties of the ILs [C4MIM][X] with [X](-) = [Cl](-), [BF4](-), [PF6](-), [OTf](-), [NTf2](-) and [B(hfip)4](-) were reported recently (Yu et al., Phys. Chem. Chem. Phys., 2012, 14, 6856-6868). In this subsequent work, attention was paid to the connection of the free volume from PALS (here the mean hole volume, <v(h)>) with the molecular structure, represented by volumes derived from X-ray diffraction (XRD) data. These were the scaled molecular volume Vm,scaled and the van der Waals volume V(vdw). Linear correlations of <v(h)> at the "knee" temperature (<v(h)>(T(k))) with V(m,scaled) and V(vdw) gave good results for the [C4MIM](+) series. Further relationships between volumes from XRD data with the occupied volume Vocc determined from PALS/PVT (Pressure Volume Temperature) measurements and from Sanchez-Lacombe Equation of State (SL-EOS) fits were elaborated (V(occ)(SL-EOS) ≈ 1.63 V(vdw), R(2) = 0.981 and V(occ)(SL-EOS) ≈ 1.12 V(m,scaled), R(2) = 0.980). Finally, the usability of V(m,scaled) was justified in terms of the Cohen-Turnbull (CT) free volume theory. Empirical CT type plots of viscosity and electrical conductivity showed a systematic increase in the critical free volume with molecular size. Such correlations allow descriptions of IL properties with the easily accessible quantity V(m,scaled) within the context of the free volume.

Comparison of Lattice-Fluid Binary Parameters For Mixtures and Block Copolymers

The aim of this report is to discuss the method of determination of lattice-fluid binary interaction parameters by comparing well characterized immiscible blends and block copolymers of poly(methyl methacrylate) (PMMA) and poly(ϵ−caprolactone) (PCL). Experimental pressure-volume-temperature (PVT) data in the liquid state were correlated with the Sanchez—Lacombe (SL) equation of state with the scaling parameters for mixtures and copolymers obtained through combination rules of the characteristic parameters for the pure homopolymers. The lattice-fluid binary parameters for energy and volume were higher than those of block copolymers implying that the copolymers were more compatible due to the chemical links between the blocks. Therefore, a common parameter cannot account for both homopolymer blend and block copolymer phase behaviors based on current theory. As we were able to adjust all data of the mixtures with a single set of lattice-binary parameters and all data of the block copolymers with another single set we can conclude that both parameters did not depend on the composition for this system. This characteristic, plus the fact that the additivity law of specific volumes can be suitably applied for this system, allowed us to model the behavior of the immiscible blend with the SL equation of state. In addition, a discussion on the relationship between lattice-fluid binary parameters and the Flory–Huggins interaction parameter obtained from Leibler's theory is presented.

Mathematical Modeling of Acid-Catalyzed 1,3-Propanediol Polymerization

A reaction mechanism for the polymerization of 1,3-propanediol is proposed for two acid catalysts. Population and mass balance equations are derived for small molecules and for polymeric species of chain distributions distinguishable in terms of protonation state and end group functionality. Since the sulfuric acid catalyzed process has two types of polymer linkages, the derivation of the moment equations is challenging. The reverse reactions are also accounted thus creating a moment closure problem. A mass transfer model is developed to predict reaction mixture water content. The Sanchez-Lacombe equation of state is used to calculate phase behavior and species partitioning. Optimization of selected parameters is accomplished by comparison to laboratory data resulting in a fully predictive model.