Hybrid model for the diffusion of simple and complex penetrants in polymers

A hybrid model, which combines the characteristic features of the Pace–Datyner molecular model with those of the Kulkarni–Stern free‐volume model, was developed to assess the effect of temperature, penetrant concentration, and polymer crystallinity on penetrant diffusivity. The predictive capabilities of the proposed model were tested by a direct comparison with experimental data. The diffusivity of ethylene and propylene vapors in semicrystalline polyethylene and isotactic polypropylene was experimentally measured using a magnetic suspension microbalance. Sorption kinetic measurements were carried out at temperatures up to 80°C and pressures up to 80 atm. The diffusivity was found to increase with temperature and penetrant concentration. Apparently, there was a very good agreement between the theoretical values predicted by the new hybrid diffusion model and the experimentally determined diffusivities. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2007     

Ethylene and 1‐hexene sorption in LLDPE under typical gas‐phase reactor conditions: Experiments

The sorption of ethylene and 1‐hexene and their mixture in three poly(ethylene‐co‐1‐hexene) samples is measured gravimetrically at temperatures 70, 90, and 150°C and pressures 0–30 bar. Gravimetric sorption measurements are supplemented with microscopic observations of swelling of polyethylene particles caused by sorption and the extent of swelling is found to be significant. Experimental data are compared with predictions of PC‐SAFT (perturbed chain—‐statistical associating fluid theory) equation of state. Comparison of sorption data in semicrystalline polymer (measured at 70 and 90°C) and amorphous polymer (at 150°C) demonstrates the constraining effect of semicrystalline structure. Solubilities of penetrants in investigated samples are not observed to depend on the content of 1‐hexene in copolymers. The solubility of the mixture of ethylene and 1‐hexene is smaller than the sum of solubilities of individual components at 70 and 90°C. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 1124–1136, 2006     

Measurement and prediction of diffusion coefficients of supercritical CO2 in molten polymers

The solubility and diffusivity of supercritical carbon dioxide (sc‐CO₂) in low‐density polyethylene (LDPE), high‐density polyethylene (HDPE), polypropylene (PP), ethylene‐ethylacrylate copolymer (EEA) and polystyrene (PS) were measured at temperatures from 150°C to 200°C and pressures up to 12 MPa by using the Magnetic Suspension Balance (MSB), a gravimetric technique for gas sorption measurements. The solubility of CO₂ in each polymer was expressed by Henry's constant. The interaction parameter between CO₂ and polymer could be obtained from the solubility data, and it was used to estimate the Pressure‐Volume‐Temperature relationship and the specific free volume of polymer/CO₂ mixtures. The diffusion coefficients were also measured by the MSB for each polymer. The resulting diffusion coefficients were correlated with the estimated free volume of polymer/CO₂ mixture. Combining Fujita's and Maeda and Paul's diffusion models, a model was newly developed in order to predict diffusion coefficients for the polymers studied. Polym. Eng. Sci. 44:1915–1924, 2004. © 2004 Society of Plastics Engineers.     

Modeling solubility of gases in semicrystalline polyethylene

An absorption model of gases in semicrystalline polymer was built that was based on the activity coefficient theory in polymer solution and associated with crystallinity dependent on temperature. The solubility of ethylene, isopentane, and n‐hexane in three types of polyethylene (PE) were obtained by the use of a pressure‐decay method at temperatures of 333–363 K and pressures of up to 2 MPa, 80–300 KPa, and 19–100 KPa, respectively. Experimental data from three gases in each PE sample were used for the single‐parameter fitting, and fitting error was within about 12%. It was found that a single parameter was merely dependent on the properties of PE used. It was shown that, unlike with the Flory–Huggins model and the UNIFAC–M‐H method, correlation between the crystallinity of the semicrystalline polymer and temperature had to be taken into account in order for the solubility data of alkane, olefin, and aromatic hydrocarbons in polyethylene to fit well, especially in the temperature range near the melting point of the polymer. The four free‐energy contributions to the total gas activity were experimentally determined to be about 47%–60% combined, the free‐volume contribution about 12%–25%, and the elastic effect about 22%–35%, but the interactional contribution was zero. The contributions changed with the size of the gas molecules. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 1737–1744, 2007     

Thermal diffusivity and conductivity of crystalline polymers

The thermal diffusivity and conductivity of the isotropic and drawn samples of five semicrystalline polymers—nylon 6, poly(ethylene terephthalate), poly(butylene terephthalate), polybutene-1, and poly(4-methylpentene-1)—were measured by the flash method over the temperature range 100–350 K. The temperature dependence of the thermal diffusivity was found to follow a simple phenomenological pattern, while a more detailed understanding of the temperature dependence and the effect of orientation on thermal conductivity was obtained by using the modified Maxwell model.     

Thermal diffusivity of polyolefins by temperature wave analysis

The thermal diffusivities of 25 kinds of polyolefin films, including high‐density polyethylene, low‐density polyethylene, linear low‐density polyethylene, polypropylene, 4‐methylpentene, and ethylene–octene copolymer, were determined by temperature wave analysis in a continuous temperature scan. The thermal diffusivity decreased with increasing temperature, and the temperature dependence was steeper in the solid state than in the melt state. A supercooling phenomenon was observed in the crystallization process during cooling. The thermal diffusivity of polyethylene in the solid state was in a good correlation with the density at room temperature, and a higher temperature coefficient was observed in high‐density polyethylene with a higher thermal diffusivity. The influence of the catalyst system on the thermal diffusivity was also observed in the ethylene–octene copolymer. The thermal diffusivity was sensitive to the precise change in the microstructure of the crystalline polyolefin, which was influenced not only by the chemical structure but also by the thermal history. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 99: 1104–1110, 2006     

Free‐volume microprobe study of iodine diffusion in polymers

The effect of iodine sorption on the free‐volume of three polymers, namely, acrylonitrile–butadiene–styrene, poly(ethylene terephthalate) and polycarbonate have been investigated by the positron annihilation lifetime technique. Diffusion coefficients have been evaluated from the sorption curves using Crank's solution for Fick's second law of diffusion. The positron results are explained in terms of iodine filling the free‐volume holes, swelling and conformational changes. It has also been found that the diffusion process in acrylonitrile–butadiene–styrene and poly(ethylene terephthalate) deviates from Fick's law of diffusion whereas in polycarbonate, the diffusion process obeys Fick's law. Further, for polymers in which diffusion deviates from Fick's law, the sorption process has been separated into diffusion‐controlled (Fickian) and relaxation‐controlled (non‐Fickian) parts using the dual‐mode sorption model. Interestingly, the present results show that the polymers which deviate from Fickian diffusion also deviate from Fujita's free‐volume theory of diffusion and vice versa. The positron results also indicate that sorbed iodine in the polymer acts as an inhibitor of ortho‐positronium. © 2001 Society of Chemical Industry     

Sorption and diffusion of water vapor in poly(ethylene terephthalate) film

The sorption and diffusion of water vapor in poly(ethylene terephthalate) (PET) film were measured by applying a thermogravimetric analyzer (TG‐DTA), which customarily has been used to detect the weight loss of a sample with the increase of temperature under a given atmosphere. In this case, we detected the weight gain of PET film by sorption of water vapor under a given humidity at a constant temperature. Sorption‐rate curves were successfully obtained in spite of the low solubility of PET film and the presence of Fickian‐type curves. The solubility was better described according to the dual‐mode sorption model. The diffusion coefficients were determined in their initial slopes by the short‐time method. We found that the diffusion coefficient depended on vapor pressure. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 76: 67–74, 2000     

Ethylene solubility and diffusion in low-density polyethylene and ethylene copolymers

Evolution rate measurements were conducted to determine the solubility and the diffusion constants of ethylene in three semicrystalline polymers: low-density polyethylene (LDPE), ethylene-ethyl acrylate (EEA), and ethylene–vinyl acetate (EVA) copolymers. The apparatus for such measurements utilizes a flame ionization detector interfaced to a computer for continuous monitoring of the ethylene evolution from the polymer pellets. Solubilities are obtained by calculating the total ethylene evolved over a 12–48-hr period. Analysis of the evolution rate data in terms of the nonsteady-state diffusion equation for spheres yields the diffusivity. The ethylene solubility and diffusion constants in EVA and EEA are very similar to those in LDPE. This is due to compensating effects of decreased crystallinity and increased cohesive energy density with the incorporation of bulky polar groups into the polymer chain.     

反相气相色谱法测定小分子溶剂在聚乙烯粒子中的无限稀释扩散系数

基于经典线性非平衡色谱过程的矩分析理论,用反相气相色谱法测定了323.15～358.15 K温度范围内二氯甲烷、三氯甲烷、四氯甲烷3种不同相对分子量的同系物小分子及正己烷在聚乙烯粒子中的无限稀释扩散系数。采用聚合物粒子直接填充的色谱柱,考察了温度、同系物小分子分子量及聚乙烯结晶度对扩散系数的影响。实验结果表明,对同一种小分子溶剂/聚乙烯体系,扩散系数均随温度升高而增大。不同相对分子量的同系物小分子在同一种聚乙烯中扩散系数随分子量增加而减小,聚乙烯结晶度增加也会导致扩散系数减小。采用文献中所报道的Krevelen扩散系数预测模型的计算值与实验测量值较为吻合,表明本文所采用的以聚合物粒子直接填充色谱柱的反相气相色谱扩散分析具有一定的可靠性。     

Determination of sorption kinetic parameters using the relaxation‐dependent solubility model in the methanol vapor—Poly(methyl methacrylate) system

The relaxation‐dependent solubility model was applied to simulate the experimentally observed sorption kinetic behavior of the PMMA–vapor MeOH system at 25°C, to obtain the main transport parameters. Application of the model in series of successive sorption kinetic runs covering small concentration intervals revealed certain trends in the concentration dependence of the diffusion coefficient of the system, not detectable by a previous simpler analysis of the data. Following excess free volume fill up, relaxation frequencies exhibit a weak exponential dependence on concentration. The functional dependence of the thermodynamic diffusivity on the concentration, deduced from the aforementioned simulation procedure, was tested and found to reproduce reasonably well the series of sorption kinetic runs covering considerably larger concentration intervals. In addition, this analysis indicates a strong dependence of the relaxation mechanism on the concentration interval. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 2278–2288, 2006     

Theoretical analysis and experimental study on SO2 adsorption onto pistachio‐nut‐shell activated carbon

The adsorption study of SO₂ onto the activated carbon prepared from pistachio‐nut shell was studied theoretically and experimentally. A single‐particle sorption model known as concentration‐dependent surface diffusivity micropore, surface and macropore diffusion control model incorporating micropore, macropore and surface diffusions, together with a nonlinear isotherm at the micropore mouth, has been derived and solved by a finite difference method. The effects of different types of nonlinear isotherms and concentration dependent surface diffusivities have been thoroughly studied. The effects of adsorbate concentration and temperature on adsorption were studied experimentally. Good agreement was found between the model predictions and the experimental results. The value of the tortuosity factor and the extracted diffusion coefficients obtained are consistent with their corresponding values reported. © 2008 American Institute of Chemical Engineers AIChE J 2009     

Semi-empirical model of toluene transport in polyethylene membranes based on the data using a new type of apparatus for determining gas permeability, diffusivity and solubility

Solubility, diffusivity and permeability of toluene vapors in low-density polyethylene (LDPE) membranes of various thicknesses (approximately 48, 93, 138 and 187 μm) at different temperatures 30, 40 and 50 °C in the range of relative vapor pressure p/p⁰=(0.05; 0.95) were measured using new type of permeation apparatus. Moreover, special construction of the new cell enables determination of the permeant amount sorbed in the membrane in the steady state operation of vapor permeation.The simple semi-empirical model of toluene transport in a polyethylene membrane based on relation between experimentally obtained effective diffusion coefficients and concentration dependent diffusion coefficients evaluated from experiments on a new permeation apparatus was proposed. The model enables estimation of toluene fluxes, sorption in the steady state of vapor permeation and concentration profiles in a polyethylene membrane from equilibrium sorption isotherms and effective diffusion coefficients. Very good agreement between experimental and calculated values from the proposed model was obtained.     

Diffusion and sorption of organic liquids through polymer membranes. I. Polyurethane versus n-alkanes

Sorption and diffusion studies of n-alkanes through a commercial polyurethane membrane have been investigated in the temperature interval of 25–60°C. Liquid diffusivity through polyurethane was measured by using the immersion/weight gain method and the diffusion mechanism was explained in terms of the Fickian model. The activation energies of sorption and diffusion processes have been estimated and used to investigate the thermodynamic interactions between polyurethane chains and n-alkanes. Furthermore, sorption data were used to estimate the molar mass between crosslinks of the network polymer.     

Diffusion of ethylbenzene in molten polystyrene

Mutual diffusion coefficients are measured for the ethylbenzene-polystyrene system for the temperature range of 115.5°–178°C and for concentrations as high as 70 wt-% ethylbenzene. Experiments were carried out using a quartz spring sorption apparatus which was modified for high-temperature measurements. The diffusivity data are compared with the predictions of a recently developed free-volume theory of polymer-solvent diffusion.     

Sorption and desorption of tetrachloroethylene in fluoropolymers: Effects of the chemical structure and crystallinity

In 18 fluoropolymers with different repeating‐unit structures and crystallinities, the solubility, diffusivity, and permeability at 70°C of a polarizable nonpolar solute (tetrachloroethylene) were studied. The transport properties were mostly controlled by the polarity of the polymer and to a lesser degree by the polymer crystallinity. The highest permeability was observed in the dipole‐containing ethylene–chlorotrifluoroethylenes because of their high tetrachloroethylene solubility. The lowest permeability was observed in the hydrogen‐bonding poly(vinylidene fluoride) polymers because of the combination of low solute solubility and solute diffusivity. The tetrachloroethylene diffusivity was solute‐concentration‐dependent, and sorption curves were S‐shaped, indicating that the solute surface concentration was time‐dependent. The rate at which the surface concentration approached the saturation level was proportional to the product of Young's modulus, the square of the thickness of the dry polymer, and the logarithm of the solute diffusivity. Data for the water‐hyperbranched polymer and limonene–polyethylene conformed to the same relationship. Therefore, this provides a new tool for predicting the solute‐surface‐concentration time dependence from data obtained by independent measurements. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 87: 1474–1483, 2003     

Diffusion and sorption of organic liquids through polymer membranes. VIII. Elastomers versus monocyclic aromatic liquids

Sorption and diffusion of five monocyclic aromatic liquids—three halogenated benzenes, nitrobenzene, and aniline—with five engineering polymers—ethylene propylene diene ter-polymer, nitrile butadiene rubber, styrene butadiene rubber, natural rubber, and neoprene—have been investigated in the temperature interval of 25–60°C. Solvent diffusivity into polymer membranes was determined from the immersion/weight gain experiments. Permeability coefficients were also calculated from the diffusion and sorption data. A temperature dependence of sorption and transport was also investigated to estimate the activation parameters. The experimental results and computed quantities were used to study the type of transport mechanism and the nature of polymer-solvent interactions.     

Gas transport properties of poly(ethylene‐2,6‐naphtalene dicarboxylate) films: Influence of crystallinity and orientation

H₂ and CO₂ transport properties were investigated on semicrystalline poly(ethylene‐2,6‐dicarboxylate naphtalene) (PEN) films and biaxially stretched films and analyzed in terms of solubility and diffusion. The decrease of the permeability observed on the thermally crystallized samples has been described by Maxwell's law. No change of the sorption properties of the amorphous phase has been noticed as a function of the thermal treatment and the evolution of the diffusion coefficient has been related to a tortuosity effect. The low permeability measured on the biaxially stretched film is related to both a change of the free volume sizes distribution and a tortuosity effect. The interesting barrier properties of the biaxially stretched film are kept even after annealing the film at 250°C. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 1849–1857, 2003     

Water sorption in poly(ethylene furanoate) compared to poly(ethylene terephthalate). Part 2: Kinetic sorption

Diffusion coefficients for water in amorphous poly(ethylene furanoate) (PEF) and poly(ethylene terephthalate) (PET) were studied at 35 °C over the entire water activity range. PEF exhibits a ∼5× reduction in diffusion coefficient averaged over the entire concentration interval compared to PET. Fickian diffusion was observed for water in both polyesters up to ∼0.6 activity, after which the presence of non-Fickian relaxations required treatment using the Berens–Hopfenberg modeling framework. Penetrant plasticization at high activity was found for both PEF and PET, as evidenced by a positive correlation between diffusion coefficient and increasing water concentration. Arrhenius interpretation of diffusion coefficients measured at 15, 25, 35, and 45 °C allowed calculation of the activation energies of diffusion for PEF and PET, which were similar at 47.1 ± 2.8 kJ/mol and 46.4 ± 3.0 kJ/mol, respectively. This study complements prior work pertaining to the equilibrium water sorption properties in both polyesters, and subsequently provides a detailed investigation of the water diffusion process in these materials.     

Moisture diffusion properties of HFPE‐II‐52 polyimide

Moisture diffusion properties of the polyimide HFPE‐II‐52 were determined using weight gain, weight loss, and swelling experiments over a temperature range of 25–200°C. Below 100°C, diffusivity was measured using standard weight loss and weight gain methods. Above 100°C, diffusivity is found by weight loss experiments performed by placing moisture saturated samples in an oven and recording weight loss dynamically. The diffusivity of the polyimide was found to obey the Arrhenius relation over the entire range of temperature. Weight gain experiments were performed to determine the equilibrium level of moisture absorbed by the polyimide as a function of relative humidity. Swelling experiments were performed to measure swelling strain as a function of moisture absorption. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 3471‐3479, 2006