Solubility prediction of gases in polymers using fuzzy neural network based on particle swarm optimization algorithm and clustering method

A four‐layer fuzzy neural network (FNN) model combining particle swarm optimization (PSO) algorithm and clustering method is proposed to predict the solubility of gases in polymers, hereafter called the CPSO‐FNN, which combined fuzzy theory's better adaptive ability, neural network's capability of nonlinear and PSO algorithm's global search ability. In this article, the CPSO‐FNN model has been employed to investigate solubility of CO₂ in polystyrene, N₂ in polystyrene, and CO₂ in polypropylene, respectively. Results obtained in this work indicate that the proposed CPSO‐FNN is an effective method for the prediction of gases solubility in polymers. Meanwhile, compared with traditional FNN, this method shows a better performance on predicting gases solubility in polymers. The values of average relative deviation, squared correlation coefficient (R²) and standard deviation are 0.135, 0.9936, and 0.0302, respectively. The statistical data demonstrate that the CPSO‐FNN has an outstanding prediction accuracy and an excellent correlation between prediction values and experimental data. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013     

Poly-1-hexene,synthesis and solubility in dense carbon dioxide

Several poly-1-hexene samples were prepared using different Ziegler-Natta catalysts, and their solubilities in dense carbon dioxide (CO₂) were studied. Despite the varied molecular weight distributions (MWD) in the polymers, a surprising correlation was found between intrinsic viscosity and dense CO₂ solubility. Due to the ability of dense CO₂ to extract low-molecular weight fractions preferentially, it is recommended that narrow MWD polymers be used, as far as possible, for dense CO₂ solubility determinations.     

CO2‐assisted polymer processing: A new alternative for intractable polymers

CO₂‐assisted polymer processing is proposed as an alternative route for intractable and high molecular weight polymers based on the plasticization effects of CO₂ and its direct effect on the melting behavior of semicrystalline polymers. A modified processing system was used to process a variety of polymers in the presence of high‐pressure CO₂. The system includes an extruder that was modified to allow for high pressures created by the injection of CO₂. The new design includes a modified feed section that allows a given mass of polymer to interact with CO₂ before and during the extrusion process. The inherent shear mixing and the presence of CO₂ allow for a specific control over the extrudate morphology. Results suggest that this alternative design provides a new and easy route to melt process high melt viscosity polymers of commercial importance, such as polytetrafluoroethylene (PTFE), fluorinated ethylene propylene copolymer (FEP), and syndiotactic polystyrene (s‐PS). The increased processability of these systems in CO₂ is related to the plasticization effect of CO₂ that was quantified through a depression in the glass‐transition temperature according to the Chow model. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 93: 1501–1511, 2004     

Evaluation of CO2-philicity and thickening capability of multichain poly(ether-carbonate) with assistance of molecular simulations

Phenyl-centered tri-chain poly(ether-carbonate) (TMA-PEC), phenyl-centered double-chain poly(ether-carbonate) (TPA-PEC), and phenyl-centered four-chain poly(ether-carbonate) (TFA-PEC) were synthesized to act as CO₂ thickener. Their solubility in CO₂ was measured by cloud point pressure. In order to explore the material characteristics that affect the solubility, dynamic simulations were used to analyze intermolecular polymer interactions, and the interaction between polymers and CO₂. It was found that TPA-PEC and TMA-PEC has better solubility than TFA-PEC in CO₂ among the three polymers while the thickening effect is poor, TFA-PEC possess the best viscosity thickening effect while the solubility in CO₂ is unfavorable. The silicone unit 1,1,1,3,5,5,5-heptamethyl-3-(3-[oxiran-2-ylmethoxy] propyl)trisiloxane modified TFA-PEC (TFA-PEC-SAGE) combine good solubility and good thickening ability together. The molecular simulations show that TPA-PEC and TMA-PEC have weaker intermolecular interactions and TPA-PEC and TMA-PEC have stronger interaction with CO₂ which are beneficial to the solubility.     

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     

The perfluoropolymer upper bound

Perfluoropolymers have fundamentally distinct thermodynamic partitioning properties compared to those of their hydrocarbon counterparts. However, current upper bound theory assumes hydrocarbon solubility behavior for all polymers. Herein, the fundamental presupposition of invariance in solubility behavior to upper bound performance is critically assessed for perfluoropolymers and hydrocarbon polymers. By modifying solubility relationships, theoretical perfluoropolymer upper bounds are established, showing a positive shift of the upper bound front as a result of beneficial solubility selectivities for certain gas pairs, including N₂/CH₄, He/H₂, He/N₂, He/CH₄, and He/CO₂. Within the framework of the solution–diffusion model, an analysis is presented to compare two independent approaches often pursued in efforts to surpass the polymer upper bound: (a) achieving solubility selectivity via perfluoropolymers and (b) improving diffusion selectivity via rigid hydrocarbon polymers. This analysis demonstrates the significant benefit that can be achieved by considering both the chemical composition and morphology of solid-state macromolecules when designing membrane materials.     

Application of compressed carbon dioxide in the incorporation of additives into polymers

It has been found that carbon dioxide remarkably accelerates the absorption of many low molecular weight additives into a number of glassy polymers. This effect is due to the high diffusivity, solubility, and plasticizing action of compressed CO₂ in polymers. The transport of CO₂ and the effects of CO₂ pressure on the transport of other low molecular weight compounds in polymers have been studied by a simple gravimetric method: Polymer film samples were contacted in a pressure vessel with compressed CO₂, or with CO₂ plus various organic liquids or solids, and the sample weight was followed with a fast-response electronic balance during subsequent desorption at atmospheric pressure. Upon release of the pressure, absorbed CO₂ rapidly diffuses from the polymer, while the other compounds desorb much more slowly. The amount of additive absorbed can be determined from the plateau weight of the sample after most of the CO₂ has escaped. Extensive kinetic and equilibrium data are reported for the model system poly(vinyl chloride)/dimethyl phthalate/CO₂, and a number of other examples of CO₂-assisted additive absorption are given. This “infusion” process, in effect, amounts to the partitioning of the additive between the CO₂- and polymer-rich phases; consequently, the relative solubility of the additive in CO₂ and in the polymer is a major factor governing the amount of additive absorbed. Data reported here illustrate the generality and potentially broad applicability of CO₂-assisted polymer impregnation.     

Gas sorption in poly(butylene terephthalate). A critical test of the influence of molecular gas data

To test the molecular parameters concerning gas sorption in polymers, the concentration of CO₂, N₂O, CO, N₂, CH₄ and the noble gases Ne, He in glassy poly(butylene terephthalate) films (PBTP) has been studied gravimetrically with a recording microbalance at 25°C. The sorption isotherms exhibit downward curvature to the pressure axis. As neither solubility nor adsorption can explain the experimental results, analysis was carried out based on the dual-sorption model: gas dissolution and microvoid filling are considered as independent sorption mechanisms. The parameters of the dual-sorption model for the mentioned penetrants are determined. The results indicate that for parameter correlation the Lennard-Jones potential parameters give a rough idea, but size exclusion of gases in small diameter microvoids is proposed and special chemical interactions must be considered.     

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 and diffusivity of CO2 in carboxylated polyesters

The solubility of CO₂ in saturated polyester resins at different temperatures (306 and 343 K) and pressures (0.1-30 MPa) has been measured using a magnetic suspension balance. The solubility data were used for estimating the binary diffusion coefficients. The results show a good solubility of CO₂ in polymers, up to 0.64 g CO₂/g polymer. The diffusion coefficients of supercritical CO₂ in polymers have generally high values and are in the range from 0.156 × 10⁻⁸ to 10.38 × 10⁻⁸ cm²/s. DSC and XRD analyses of the semi-crystalline polymer samples indicate that amorphous degree of polymers after exposure to CO₂ is increased. The observed structural effects are dependent on pressure, temperature and time of exposure to CO₂.     

Studies on the interactions of CO2 with biodegradable poly(dl-lactic acid) and poly(lactic acid-co-glycolic acid) copolymers using high pressure ATR-IR and high pressure rheology

Amorphous poly(dl-lactic acid) (P_dlLA) and poly(lactic acid-co-glycolic acid) (PLGA) polymers have been used to fabricate porous scaffolds for tissue engineering applications via a supercritical foaming technique. The chemical composition of the polymers and the morphology (pore size, porosity and interconnectivity) of the scaffolds are crucial because they influence cell filtration, migration, nutrient exchange, degradation and drug release rate. To control the morphology of supercritical foamed scaffolds, it is essential to study the interactions of polymers with CO₂ and the consequent solubility of CO₂ in the polymers, as well as the viscosity of the plasticized polymers. In this paper, we are showing for the first time that well known and useful biodegradable polymers can be plasticized easily using high pressure CO₂ and that we can monitor this process easily via a high pressure attenuated total reflection Fourier transform infrared (ATR-IR) and rheology. High pressure ATR-IR has been developed to investigate the interactions of CO₂ with P_dlLA and PLGA polymers with the glycolic acid (GA) content in the copolymers as 15, 25, 35 and 50% respectively. Shifts and intensity changes of IR absorption bands of the polymers in the carbonyl region (∼1750 cm⁻¹) are indicative of the interaction on a qualitative level. A high pressure parallel plate rheometer has also been developed for the shear viscosity measurements of the CO₂-plastisized polymers at a temperature below their glass transition temperatures. The results demonstrate that the viscosities of the CO₂-plasticized polymers at 35 °C and 100 bar were comparable to the values for the polymer melts at 140 °C, demonstrating a significant process advantage through use of scCO₂. The data from the high pressure rheology and high pressure ATR-IR, combined with the sorption and swelling studies reported previously, demonstrate that the interaction and the solubility of CO₂ in PLGA copolymers is related to the glycolic acid content. As the glycolic acid ratio increases the interaction and consequent solubility of CO₂ decreases. The potential applications of this study are very broad, from tissue engineering and drug delivery to much broader applications with other polymers in areas that may range from composites and polymer synthesis through to injection moulding.     

Modeling of CO2 equilibrium solubility in a novel 1‐Diethylamino‐2‐Propanol Solvent

In this work, the equilibrium solubility of CO₂ in a 1‐diethylamino‐2‐propanol (1DEA2P) solution was determined as a function of 1DEA2P concentration (over the range of 1–2 M), temperature (in the range of 298–333 K), and CO₂ partial pressure (in the range of 8–101 kPa). These experimental results were used to fit the present correlation for K₂ (Kent‐Eisenberg model, Austgen model, and Li‐Shen model). It was found that all of the models could represent the CO₂ equilibrium solubility in 1DEA2P solution with ADDs for Kent‐Eisenberg model, Austgen model, and Li‐Shen model of 6.3, 7.3, and 12.2%, respectively. A new K₂ correlation model, the Liu‐Helei model, was also developed to predict the CO₂ equilibrium solubility in 1DEA2P solution with an excellent ADD of 3.4%. In addition, the heat of absorption of CO₂ in 1DEA2P solution estimated by using the Gibbs‐Helmholtz equation was found to be ?45.7 ± 3.7 kJ/mol. Information and guidelines about effectively using data for screened solvents is also provided based on the three absorption parameters: CO₂ equilibrium solubility, second order reaction constant (k₂), and CO₂ absorption heat. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4465–4475, 2017     

In situ FTIR measurement of carbon dioxide sorption into poly(ethylene terephthalate) at elevated pressures

Knowledge of the sorption rate and solubility of CO₂ in polymers are of great importance for developing technologies utilizing high‐pressure and supercritical CO₂‐assisted processes. Many conventional techniques for measuring gas sorption have inherent complications when used at elevated pressures. In this work, we demonstrate the use of near‐IR spectroscopy as an accurate method to measure CO₂ sorption kinetics and solubility in PET at elevated pressures. Sorption kinetics and solubility are measured at 0, 28, and 50°C between pressures of 57.1 and 175.2 atm. Both initially amorphous and initially partially crystalline samples of PET are studied, and the effects of the initial crystallinity are determined. In addition, the effects of CO₂ processing on the final crystallinities of our samples are measured. Crystallization was induced in PET at 28 and 50°C over the range of pressures studied. However, at 0°C, no detectable crystallization occurred in PET, even in the presence of high pressures of CO₂. The method demonstrated in this work could easily be extended to directly measure CO₂ sorption in other polymers. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 764–775, 2000     

Influence of tert-amine groups on the solubility of polymers in CO2

There is a need to develop new, non-fluorous polymers that are highly soluble in CO₂. Experimental evidence indicates that tertiary amine and pyridine groups may exhibit favorable Lewis acid-Lewis base type interactions with CO₂. It is therefore reasonable to assume that incorporation of tertiary amines into the side chain or backbone of non-fluorous polymers may impart a degree of CO₂-solubility to the polymer. We present experimental results for eight different tert-amine-containing polymers. Of these polymers, only propyl dimethylamine-functionalized poly(dimethylsiloxane) is soluble in CO₂ at temperatures and pressures accessible in our experiments, but even this polymer is less soluble than non-functionalized poly(dimethylsiloxane) at the same chain length. We have performed ab initio calculations on tertiary amine-containing moieties representative of some of the polymers examined experimentally. Our calculations confirm that amine-CO₂ interactions are indeed energetically favorable. However, we also find that the moiety self-interactions are typically more favorable than the CO₂-moiety interactions. This indicates that the lack of solubility of amine-containing polymers in CO₂ is a direct result of strong polymer-polymer interactions.     

A novel equation of state (EOS) for prediction of solute solubility in supercritical carbon dioxide: Experimental determination and correlation

Solubility data of organophosphorous metal extractants in supercritical fluids (SCF) are crucial for designing metal extraction processes. We have developed a new equation of state (EOS) based on virial equation including an untypical parameter as BP/RT, reduced temperature and pressure for prediction of solute solubility in supercritical carbon dioxide (SC CO₂). Solubility experimental data (solubility of tributylphosphate in SC CO₂) were correlated with the two cubic equations of state (EOS) models, namely the Peng–Robinson EOS (PR‐EOS) and the Soave–Redlich–Kwong EOS (SRK‐EOS), together with two adjustable parameter van der Waals mixing and combining rules and our proposed EOS. The AARD of our EOS is significantly lower than that obtained from the other EOS models. The proposed EOS presented more accurate correlation for solubility data in SC CO₂. It can be employed to speed up the process of SCF applications in industry.     

Effects of carbon nanofiber on the dissolution and diffusion of CO2 in polypropylene nanocomposites

The effects of nanofiller with elongated structure on the dissolution and diffusion behaviors of CO₂ in polypropylene (PP)/carbon nanofiber (CNF) composites were investigated in this work. The solubility of CO₂ in PP and PP composites containing 5 wt% and 10 wt% CNF was measured by using magnetic suspension balance (MSB) combined with the experimental swelling correction by using a self-designed high-temperature and -pressure view cell at the temperatures of 200 and 220 °C and pressures up to 20 MPa. The diffusion coefficient of CO₂ in PP and PP composites was also determined from the sorption line at CO₂ pressures ranging from 5 to 10 MPa. It was found that the solubility and diffusivity of CO₂ in PP/CNF composites increased with increasing the filler content, which should be mainly attributed to the change of the distribution of free volume in the polymer matrix besides the small amount of adsorption capacity of CO₂ in CNF. A modified Henry model incorporated with Langmuir adsorption factor was proposed to correlate the solubility of CO₂ in the PP/CNF composites with an average relative deviation less than 3%. A new model based on free volume theory incorporated with the diffusion driving force factor was established to correlate the experimental diffusion coefficient of CO₂ in the PP/CNF composites within an average relative deviation of 2%.     

Solubility and diffusivity of CO2 in polypropylene/micro-calcium carbonate composites

This work is aimed at studying the effects of the fillers and interface bonding condition between the fillers and polymer matrix on the solubility and diffusivity of CO₂ in polypropylene (PP)/Micro-calcium carbonate (MicroCaCO₃) composites. The solubility of CO₂ in PP and its composites containing 5% and 10% MicroCaCO₃ was determined precisely by using magnetic suspension balance (MSB) combined with experimental swelling correction at 200 and 220 °C and CO₂ pressures up to 22 MPa. It was found that the solubility of CO₂ in the PP/MicroCaCO₃ composites without the interface compatibilizer increased with increasing the filler content, while the CO₂ solubility remained almost unchanged in PP composites with compatibilizer. The Henry's law and a modified Henry's law were used to well correlate the solubility of CO₂ in the PP composites with and without the interface compatibilizer, respectively. The diffusion coefficient of CO₂ in the PP composites was found to decrease with increasing the filler content. The mutual diffusion coefficients of CO₂ in the PP composites can be correlated within an average relative deviation of 10% by the free volume model proposed by Kulkarni and Stern with a parameter accounting for the barrier effect of the filler.     

Recent advances in polymeric membranes for CO2 capture

Membrane and membrane process have been considered as one of the most promising technologies for mitigating CO₂ emissions from the use of fossil fuels. In this paper, recent advances in polymeric membranes for CO₂ capture are reviewed in terms of material design and membrane formation. The selected polymeric materials are grouped based on their gas transport mechanisms, i.e., solution‐diffusion and facilitated transport. The discussion of solution‐diffusion membranes encompasses the recent efforts to shift the upper bound barrier, including the enhanced CO₂ solubility in several rubbery polymers and novel methods to construct shape-persisting macromolecules with unprecedented sieving ability. The carrier-bearing facilitated transport membranes are categorized based on the specific CO₂-carrier chemistry. Finally, opportunities and challenges in practical applications are also discussed, including post-combustion carbon capture (CO₂/N₂), hydrogen purification (CO₂/H₂), and natural gas sweetening (CO₂/CH₄).