On the diffusion of gases in partially crystalline polymers (original) (raw)
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Gas diffusion in partially crystalline polymers part I: Concentration dependence
Journal of Polymer Science Part B: Polymer Physics, 1996
In this work, a phenomenological model for the gas diffusion in partially crystalline polymers using differential effective medium theory is presented. By making an analogy with the power law known as Archie's law which relates the d.c. conductivity of a brine saturated porous rock to its porosity; we show that gas diffusion through semicrystalline polymers can be described in a similar way. It is assumed that the diffusion coefficient in the crystalline region is zero, while in the amorphous region it is given by a free volume model, and an effective diffusion coefficient Deff, is obtained using the mentioned analogy. The variation of Deff upon concentration is analyzed through its free volume dependence. The crystallinity dependence is considered through an average chain immobilization factor (p), which is explicitely derived. Finally, the results of this model are compared with experimental data given by Kreituss and Frisch, obtaining a good agreement. 0 1996 John Wiley & Sons, Inc. Keywords: diffusion through polymeric films Archie's law effective medium theory concentration dependence Geophysics, 4 3 , 1 2 5 0 (1978).
Gas Transport in Glassy Polymers: Prediction of Diffusional Time Lag
Membranes
The transport of gases in glassy polymeric membranes has been analyzed by means of a fundamental approach based on the nonequilibrium thermodynamic model for glassy polymers (NET-GP) that considers the penetrant chemical potential gradient as the actual driving force of the diffusional process. The diffusivity of a penetrant is thus described as the product of a purely kinetic quantity, the penetrant mobility, and a thermodynamic factor, accounting for the chemical potential dependence on its concentration in the polymer. The NET-GP approach, and the nonequilibrium lattice fluid (NELF) model in particular, describes the thermodynamic behavior of penetrant/polymer mixtures in the glassy state, at each pressure or composition. Moreover, the mobility is considered to follow a simple exponential dependence on penetrant concentration, as typically observed experimentally, using only two adjustable parameters, the infinite dilution penetrant mobility L10 and the plasticization factor β, b...
Diffusion in polymeric systems–A review on free volume theory
Progress in Organic Coatings, 2017
This review paper deals the history and development of various theories to predict the diffusion in polymeric systems. The basis and application of various theories with the prediction capabilities are discussed. The most commonly used theory is Vrentas and Duda free volume theory with excellent agreement with experimental data report so far. This theory predicts the data very accurately in rubbery region. However, few modifications have come up in this theory to predict the diffusion above the glass transition with a little success. Relation between Fujita −Kishimoto theory [15] and Vrentas and Duda Theory [11,12] is
Diffusion in glassy polymers: A model using a homogenization method and the effective medium theory
Journal of Polymer Science Part B: Polymer Physics, 1992
Glassy polymers are considered as inhomogeneous with regions in which the gas sorption follows Henry's law and others where it follows Langmuir's law. It is assumed that the linear dimensions of these regions are small compared with the macroscopic length of interest but large compared with the mean free path of the penetrant gas molecules. Applying an homogenization method it is shown that the average flux is directly proportional to the concentration gradient in the polymer. This relationship can be expressed in terms of an effective diffusion coefficient Deff, which depends on the details of the microstructure. D,ff is evaluated in the framework of the effective medium theory and compared with experimental data for diffusion of five vapors in ethylcellulose.
Gas Diffusion in Glassy Polymers by a Chain Relaxation Approach
Macromolecules, 2003
Plasticization of glassy polymers by small molecules was approached by the "concentrationtemperature superposition" principle. The major effect of the plasticization by small molecules is on the reduction of the glass transition temperature. The present study suggests that the dependence of diffusion coefficients of small molecules on the penetrant concentration can be affected by the reduction of the glass transition of the penetrant/polymer system caused by a plasticization effect of the penetrant. With a WLF type shift factor, the concentration-dependent diffusion coefficient can be predicted. It is found that the calculated diffusion coefficient correlates very well to the experimental data. This study also proposes a prediction of time-lag values from the solubility and permeability measurements. Moreover, the diffusion coefficients for gases in glassy polymers can also be predicted using the time-lag values alone. The proposed diffusion model represents satisfactorily experimental data reported in the literature for CO 2 in poly(ethylene terephthalate), in polycarbonate, and in polyacrylate. The prediction of diffusion coefficient in glassy polymers is seen to agree well with the experimental data, whereas the prediction of time-lag values is less accurate due to the error propagation in solubility measurement, permeability measurement, and time-lag measurement, respectively.
Macromolecular Symposia, 2010
Summary: Diffusion of n‐hexane in poly(ethylene‐co‐1‐hexene)s with 15–75 wt.% crystallinity was studied by desorption experiments analyzing data using the Fickian equations with a concentration dependent diffusivity. The effect of the impenetrable crystalline phase on the penetrant diffusivity (D) is described by D = Da/(τβ), where Da is the diffusivity of the amorphous polymer, τ is the geometrical impedance factor and β is a factor describing the constraining effect of the crystals on the non‐crystalline phase. For a polymer with 75 wt.% crystallinity, τβ varied markedly with penetrant concentration (v1a) in the penetrable phase: 1000 (v1a = 0) and 10 (v1a = 0.15). This penetrant‐uptake had no effect on the gross crystal morphology, i.e. β must be strongly dependent on v1a. Samples saturated in n‐hexane exhibited a penetrant‐induced loosening of the interfacial structure, as revealed by an increase in crystal density that require an increased mobility in the interfacial component ...
Journal of Membrane Science, 1998
Three types of novel correlations for activation energies of gas permeation E P and diffusion E D in amorphous glassy polymers are considered and their application for prediction of the E P and E D values for different gases are examined. The ®rst one is based on application of the group contribution method. Combined consideration of the equation of free volume and Arrhenius equation results in the correlation of E P and E D with free volume V f and fractional free volume (FFV). At last, the correlations between E P and the permeability coef®cient at a certain reference temperature P(T ref ), as well as E D versus D(T ref ), are based on the ful®lment of the so-called compensation effect between activation energies and preexponential factors in activated processes. Examples of applicability of the correlations considered and recommendations for their use in prediction of the E P and E D values are given for transport of various gases in glassy polymers and separately in amorphous glassy polyimides. #
Elementary prediction of gas permeability in glassy polymers
The transport model proposed by Minelli and Sarti for the representation of gas and vapor permeability in glassy polymers has been extensively applied to various systems, and the model results are thoroughly analyzed. The approach is based on fundamental theory for the diffusion of low penetrant species in polymers, in which the diffusivity is considered as the product of the molecular mobility, and a ther-modynamic coefficient, accounting for the concentration dependence of the chemical potential. The model relies on the thermodynamic description of the penetrant/polymer systems provided by the NonEquilibrium Thermodynamics for Glassy Polymers (NET-GP) approach. The penetrant mobility is assumed to depend exponentially on penetrant concentration, and the model contains two parameters only: mobility coefficient at infinite dilution and plasticization factor. The model parameters obtained from the analysis of the permeability behaviors of various systems have been examined and general correlations are derived. The mobility coefficient is indeed correlated to the properties of the pure penetrants (penetrant molecular size) and pure polymer (fractional free volume and characteristic energy). This allows the derivation of a simple and general expression for the prediction of the permeability of any penetrant species in glassy polymers in the range of low penetrant pressures, as well as the selectivity of any gas pair. Remarkably, the model predictions are able to represent quite accurately the experimental data available in the literature. Furthermore, the plasticization factor is correlated to the swelling produced by the penetrant into the glassy polymer matrix, obtaining thus a reliable tool for the estimation of the pressure dependence of gas permeability on upstream pressure.