Solubility Of Gases In Polymers Research Articles

A microscopic computational model based on particle dynamics and evolutionary algorithm for the prediction of gas solubility in polymers

Solubility is one of the key physicochemical properties of foaming materials and plastic membrane materials, which are commonly used in the processing, preparation, and modification of various new materials. It is challenging to develop a good dissolution behavior calculation model. A novel particle dynamics evolutionary algorithm (DP-PD-EA) is developed to simulate the movement of molecules in the process of dissolution at the microscopic scale. DP-PD-EA deeply combines particle dynamics with evolutionary algorithm so that particles evolve iteratively under the action of the potential energy field. The prediction experiments of the solubility of supercritical carbon dioxide (SCCO2) in three polymers confirmed that DP-PD-EA had the better prediction performances than other models. The proposed model can be used in the solubility calculation of foaming materials and has theoretical and practical values in many fields, such as the prediction of physical/chemical properties and the calculation of multi-scale theory.

COSMO-based models for predicting the gas solubility in polymers

We like to highlight the extension of COSMO-based models (COSMO RS-FV and COSMO SAC-FV) to the prediction of gas solubility in polymers, including polymerized ionic liquids (PILs) for the first time. To verify the applicability of COSMO-based models, the predicted values for gas solubility in both common polymers (CH4/N2 + PEG) and PILs (CO2 + P[MATMA][BF4]/P[VATMA][BF4]) were evaluated based on previous experimental data. It was confirmed that the COSMO-RS (Klamt) model performs better than the COSMO-SAC model for common polymers, whereas the COSMO-RS (ADF-Lei 2018) exhibits the best predictions for PILs. The moderately accurate predictions of COSMO-based models demonstrate the high potential for predicting gas solubility in polymers.

A modified non-equilibrium lattice fluid model based on corrected fractional free volume of polymers for gas solubility prediction

We propose a model based on non-equilibrium lattice fluid (NELF) theory and corrected fractional free volume of polymers to effectively and accurately predict the solubility of gases in different polymers. The method to achieve this purpose is based on the utilization of NELF model infinite dilution solubility coefficient (S0) as the base of predictive calculations. To account for the isolated pore in the polymer matrix in density estimation, a fractional free volume correction factor (β) was introduced in NELF model. The modified NELF model was successfully applied for prediction of solubility of C3H8 and CO2 in polyethylene oxide (PEO) and CO2 in polyethylene terephthalate (PET), isotactic polypropylene (i-PP), polyetherimide (PEI), polymethyl methacrylate (PMMA) and polyethyl methacrylate (PEMA) with adjustments in β value and depth of diffusion of gases in polymer matrix (ζ) at different pressures and temperatures. This work involves multi-objective optimization using genetic algorithm of MATLAB toolbox with adjusted settings. It applies to find the optimum temperature at which the minimum standard deviation of β for different gas-polymer systems is obtained. β showed the same trend of change with temperature as the constrained pressure imposed on the amorphous phase in semi-crystalline polymers. A cubic correlation for standard deviation for β versus temperature was obtained which was able to anticipate the changing trend of β at different temperatures. The chi-square test results verified that compared with original NELF model, a more accurate model for prediction of gas solubilities in polymers has been proposed.

Predicting gas solubility in semi-crystalline polymer solvent systems by consistent coupling of Sanchez-Lacombe EOS with a continuum mechanics approach

Solubility of gases in polymers plays a crucial role in several industrial sectors. This spans from chemical, pharmaceutical to polymer industry. While, in last years thermodynamic models have been successfully developed to predict the solubility of fluids in polymers, which are above the melting temperature or in a glassy state, thermodynamic models for predicting the fluid solubility in semi-crystalline polymer solvent mixtures are rare and even controversially discussed in literature. In this work a new theoretical framework based on a consistent coupling of SL-EOS with a continuum mechanics approach is developed to explain phenomena occurring due to gas solubility in semi-crystalline polymers on the one hand and predict gas solubility in semi-crystalline polymer solvent mixtures with a high accuracy on the other hand. Herein, the framework is applied to a n-butane/linear low density polyethylene mixture as well as to an i-butane/linear low density polyethylene mixture. The solubility of n-butane in the respective polymer is predicted for various temperature and pressure states, where the polymer is due to temperature variations in the molten as well as in the semi-crystalline state. A very good agreement between predicted and experimental solubility data could be achieved.

Prediction of CO2 Solubility in Polymers by Radial Basis Function Artificial Neural Network Based on Chaotic Self‐adaptive Particle Swarm Optimization and Fuzzy Clustering Method

AbstractTo replace costly and time‐consuming experimentation in laboratory, a novel solubility prediction model based on chaos theory, self‐adaptive particle swarm optimization (PSO), fuzzy c‐means clustering method, and radial basis function artificial neural network (RBF ANN) is proposed to predict CO2 solubility in polymers, hereafter called CSPSO‐FC RBF ANN. The premature convergence problem is overcome by modifying the conventional PSO using chaos theory and self‐adaptive inertia weight factor. Fuzzy c‐means clustering method is used to tune the hidden centers and radial basis function spreads. The modified PSO algorithm is employed to optimize the RBF ANN connection weights. Then, the proposed CSPSO‐FC RBF ANN is used to investigate solubility of CO2 in polystyrene (PS), polypropylene (PP), poly(butylene succinate) (PBS) and poly(butylene succinate‐co‐adipate) (PBSA), respectively. Results indicate that CSPSO‐FC RBF ANN is an effective method for gas solubility in polymers. In addition, compared with conventional RBF ANN and PSO ANN, CSPSO‐FC RBF ANN shows better performance. The values of average relative deviation (ARD), squared correlation coefficient (R2) and standard deviation (SD) are 0.1071, 0.9973 and 0.0108, respectively. Statistical data demonstrate that CSPSO‐FC RBF ANN has excellent prediction capability and high‐accuracy, and the correlation between prediction values and experimental data is good.

QSPR prediction of the solubility of CO2 and N2 in common polymers

In this work, a quantitative structure–property relationship (QSPR) model is presented for solubility prediction of carbon dioxide and nitrogen in polyethylene, polypropylene, polystyrene, polyvinyl acetate and poly(butylene succinate) at different temperatures and pressures. The five most important descriptors which are related to the structure of the gas molecules and the repeating unit of polymers were selected by means of a genetic function approximation (GFA) from a set of more than 1600 descriptors. The selected descriptors in addition to the temperature and pressure were used as the inputs for the artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS) models to develop the required non-linear relationships. These non-linear models were assessed by some internal and external validation methods. The obtained results indicated the excellent ability of ANN and ANFIS for prediction of solubility of gases in polymers.

Prediction of gas solubility in polymers by back propagation artificial neural network based on self-adaptive particle swarm optimization algorithm and chaos theory

A novel prediction method based on chaos theory, self-adaptive particle swarm optimization (PSO) algorithm, and back propagation artificial neural network (BP ANN) is proposed to predict gas solubility in polymers, hereafter called CSPSO BP ANN. The premature convergence problem of CSPSO BP ANN is overcome by modifying the conventional PSO algorithm using chaos theory and self-adaptive inertia weight factor. Modified PSO algorithm is used to optimize the BP ANN connection weights. Then, the proposed CSPSO BP ANN (two input nodes consisting of temperature and pressure; one output node consisting of gas solubility in polymers) is used to investigate solubility of CO2 in polystyrene, N2 in polystyrene, and CO2 in polypropylene, respectively. Results indicate that CSPSO BP ANN is an effective prediction method for gas solubility in polymers. Moreover, compared with conventional BP ANN and PSO ANN, CSPSO BP ANN shows better performance. The values of average relative deviation (ARD), squared correlation coefficient (R2) and standard deviation (SD) are 0.1275, 0.9963, and 0.0116, respectively. Statistical data demonstrate that CSPSO BP ANN has excellent prediction capability and high accuracy, and the correlation between predicted and experimental data is good.

Prediction of the gas solubility in polymers by a radial basis function neural network based on chaotic self‐adaptive particle swarm optimization and a clustering method

ABSTRACTA novel model based on a radial basis function neural network (RBF NN), chaos theory, self‐adaptive particle swarm optimization (PSO), and a clustering method is proposed to predict the gas solubility in polymers; this model is hereafter called CSPSO‐C RBF NN. To develop the CSPSO‐C RBF NN, the conventional PSO was modified with chaos theory and a self‐adaptive inertia weight factor to overcome its premature convergence problem. The classical k‐means clustering method was used to tune the hidden centers and radial basis function spreads, and the modified PSO algorithm was used to optimize the RBF NN connection weights. Then, the CSPSO‐C RBF NN was used to investigate the solubility of N2 in polystyrene (PS) and CO2 in PS, polypropylene, poly(butylene succinate), and poly(butylene succinate‐co‐adipate). The results obtained in this study indicate that the CSPSO‐C RBF NN was an effective method for predicting the gas solubility in polymers. In addition, compared with conventional RBF NN and PSO neural network, the CSPSO‐C RBF NN showed better performance. The values of the average relative deviation, squared correlation coefficient, and standard deviation were 0.1282, 0.9970, and 0.0115, respectively. The statistical data demonstrated that the CSPSO‐C RBF NN had excellent prediction capabilities with a high accuracy and a good correlation between the predicted values and the experimental data. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 130: 3825–3832, 2013

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

AbstractA 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

Simple gases to replace non-environmentally friendly polymer foaming agents. A thermodynamic investigation

Foaming constitutes one of the most important industrial activities in polymer engineering to produce efficient thermal insulating materials. In particular, rigid insulating boards are produced worldwide on a large scale using blowing agents which eventually are released in the environment where they adversely impact the natural friendly stratospheric ozone layer. Concomitantly, the chemicals used as blowing agents contribute to the creation of the unfriendly tropospheric ozone layer generating the disastrous green house effect around our planet. The traditional foaming intermediates currently named freons, like chlorofluorocarbons (CFCs) currently used as blowing agents as well as the hydrochlorofluorocarbons (HCFCs) often considered as alternative blowing agents, must be banned from industrial processes and new (friendly) foaming agents have to be suggested and evaluated in terms of both easy engineering and environmental neutrality. Undoubtedly thermodynamics plays a major role in assessing the effective capability of those chemicals. Some CFCs still accepted and other possible simple gases like carbon dioxide and nitrogen have been considered. The in-depth thermodynamic investigation has been made possible thanks to new experimental developments to determine gas solubility in polymers and associated swelling as well as the thermodynamic properties of (gas + polymer) systems, including the thermophysical properties of polymers under gas sorption. Pertinent data have been generated for such properties over extended T and p ranges.

Equation of state for square-well chain molecules with variable range II. Extension to mixtures

An equation of state (EOS) developed in our previous work for square-well chain molecules with variable range is further extended to the mixtures of non-associating fluids. The volumetric properties of binary mixtures for small molecules as well as polymer blends can well be predicted without using adjustable parameter. With one temperature-independent binary interaction parameter, satisfactory correlations for experimental vapor–liquid equilibria (VLE) data of binary normal fluid mixtures at low and elevated pressures are obtained. In addition, VLE of n-alkane mixtures and nitrogen + n-alkane mixtures at high pressures are well predicted using this EOS. The phase behavior calculations on polymer mixture solutions are also investigated using one-fluid mixing rule. The equilibrium pressure and solubility of gas in polymer are evaluated with a single adjustable parameter and good results are obtained. The calculated results for gas + polymer systems are compared with those from other equations of state.

Prediction of Gas Solubility in Polymers by Molecular Dynamics Simulations

Prediction of Gas Solubility in Polymers by Molecular Dynamics Simulations

Application of a New Lattice-Fluid Equation of State Based on Chemical-Association Theory for Polymer Systems

In our previous work, a new lattice-fluid equation of state (LF-EoS) was developed and successfully applied to normal fluid systems and ionic liquid systems. In this work, this LF-EoS is further extended to describe thermodynamic properties of polymer systems. First, the model parameters for polymers were determined by fitting experimental pVT data of polymers over a wide temperature and pressure range. Then, the LF-EoS was applied for calculating vapor−liquid equilibrium (VLE) of polymer−solvent systems using one adjustable binary parameter κ12. The solubility of gas in polymer can be calculated up to a high pressure. Moreover, a new parameter Cr was introduced to describe the effect of composition of mixtures on chain length parameter r, and several typical liquid−liquid equilibrium behaviors of polymer solutions can be successfully reproduced.

Sorption, Dilation, and Partial Molar Volumes of Carbon Dioxide and Ethane in Cross-Linked Poly(ethylene oxide)

Experimental gas solubility and sorptive dilation data are reported for carbon dioxide and ethane in a cross-linked poly(ethylene oxide) rubber prepared by photopolymerization of poly(ethlyene glycol)diacrylate. Five different operating temperatures (253 ≤ T (K) ≤ 308) were considered, with a maximum gas pressure of 2.16 MPa (21.3 atm). The importance of taking sorptive dilation into account in the determination of gas solubility in polymers by the pressure−decay method was demonstrated. Sorption isotherms in terms of gas fugacity were described by the Flory−Huggins model. In the case of ethane, the Flory−Huggins interaction parameter was a decreasing function of temperature. In contrast, for carbon dioxide, a single parameter represented all isotherms. Dilation and sorption data were combined to calculate the partial molar volume (PMV) of the gases in the polymer, which was an increasing function of temperature. The PMV data were compared to the available literature data for other rubbery polymers and li...

Fluid phase behavior modeling of CO2 + molten polymer systems using cubic and theoretically based equations of state

AbstractPhase equilibrium data of CO2 + molten polymer systems are of great relevance for chemical engineers because these are necessary for the optimal design of polymer final‐treatment processes. This kind of processes needs information about gas solubilities in polymers at several temperatures and pressures. In this work, CO2 solubilities in molten polymers were modeled by the perturbed chain‐statistical associating fluid theory (PC‐SAFT) equation of state (EoS). For comparison, the solubilities were also calculated by the lattice gas theory (LGT) EoS, and by the well‐known Peng‐Robinson (PR) cubic EoS. To adjust the interactions between segments of mixtures, there were used classical mixing rules, with one adjustable temperature‐dependent binary parameter for the PC‐SAFT and PR EoS, and two adjustable binary parameters for the LGT EoS. The results were compared with experimental data obtained from literature. The results in terms of solubility pressure deviations indicate that the vapor–liquid behavior for CO2 + polymer systems is better predicted by the PC‐SAFT model than by LGT and PR models. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers.

Correlation between solubility of hydrocarbons in polymers and polymer structure

A fractal model allowing a sufficiently exact quantitative description of gas solubility in polymers is developed. The solubility coefficient is determined by the following two factors: size and orientation of dissolving-gas molecules and interaction of these molecules with the polymer structure. The latter factor has the most pronounced effect on the solubility coefficient.

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

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

Prediction and Correlation of High-Pressure Gas Solubility in Polymers with Simplified PC-SAFT

Using simplified PC-SAFT we have modeled gas solubilities at high temperatures and pressures for the gases methane and carbon dioxide in each of the three polymers high-density polyethylene (HDPE), nylon polyamide-11 (PA-11), and poly(vinylidene fluoride) (PVDF). In general the results are satisfactory, using in most cases a single, temperature-independent value of the binary interaction parameter. In the cases of methane in HDPE and PVDF, a temperature-dependent binary interaction parameter was required. New pure component polymer parameters for PA-11 and PVDF were obtained using a recently developed prediction scheme which does not rely on binary experimental data.

Direct measurement of gas solubilities in polymers with a high‐pressure microbalance

AbstractSolubility and diffusion data are presented for methane and carbon dioxide gases in high‐density polyethylene. The polymer was cut from extruded piping intended for use in offshore oil and gas applications. The measurements were carried out with a high‐pressure microbalance. The properties were determined from 25 to 50°C and from 50 to 150 bar for methane and from 20 to 40 bar for carbon dioxide. In general, a good agreement was obtained with similar measurements reported in the literature. The solubility followed Henry's law (linear) dependence with pressure, except at high pressures for methane, for which negative deviations from Henry's law behavior were observed. The diffusion coefficients for each of the gases in the polymer were also measured with the balance, although the uncertainty was greater than for the solubility measurements. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 91: 1476–1488, 2004

Simultaneous measurement of the solubility of gases in polymers and of the associated volume change

A new instrument to measure simultaneously the solubility of gases in polymers and the associated volume changes of the polymer is presented. The quantity of penetrating fluid introduced in the system is evaluated by pressure decay measurements in a calibrated volume, while a vibrating-wire force sensor is employed to weigh the polymer sample during sorption inside the high-pressure equilibrium cell. The combined use of the two techniques is required by the nature of the sorption process, since the effects of swelling and solubility processes cannot be isolated by performing one single gravimetric or pressure decay measurement. The knowledge of the equation of state of the gas is required, as well as an estimation of its viscosity. The present instrument accepts polymer samples of about 5 g, and operates at temperatures up to 473 K and pressures up to 100 MPa. The technique was validated by measuring the sorption of nitrogen in polystyrene. The instrument showed a sensitivity of the order of 1 mg of dissolved gas and is capable of detecting a volume change of 0.05% of the initial volume of the polymer. The same principles exposed in the present work can be adapted to other kinds of sorption studies.