Analysis of the Humid Gas Permeation in Glassy Polyimides: A Modeling Approach

Analysis of the humid gas permeation in glassy polyimides:

a modeling approach

 

Luca Ansaloni¹, Caroline Tsvigu², Matteo Minelli^1,3,

Marco Giacinti Baschetti¹, Giulio Cesare Sarti¹

 

¹Dipartimento di Ingegneria Civile Chimica, Ambientale e dei Materiali

Alma Mater Studiorum - Università di Bologna, Bologna, Italy

²Department of Chemical Engineering, Loughborough University, Leicestershire, UK

³Centro Interdipartimentale di Ricerca Industriale Meccanica Avanzata e Materiali

Alma Mater Studiorum - Università di Bologna, Bologna, Italy

 

 

In membrane gas separation applications, the presence of minor compounds in the feed stream is frequent and their influence has to be accounted for a proper description of the membrane performances.^1,2 Water vapor is commonly found in real application³ and it can affect significantly the membrane gas transport properties, depending on the hydrophilic or hydrophobic character of the material. In the first case, water sorption is able to induce a significant swelling of the membrane matrix causing a marked increase of the permeation coefficient of gaseous species in humid condition.^4,5 In case of hydrophobic or weakly hydrophilic materials, on the other hand, the permeability is not affected or tends to decrease, increasing the water content in the feed and in the system.^6,7

Polyimides are known to be hydrophobic materials, and, in view of the low affinity with water, exhibit rather low water uptakes.^8–10 However, in spite of that, a remarkable effect of water on their permeating behavior has been observed, as the permeability of many different gases showed a significant decrease in presence of the water vapor.^6,7,11

In the present work, the effect of water vapor on the gas transport properties of two different glassy polyimides, 6FDA-6FpDA and Matrimid, has been investigated. Four penetrants with different kinetic and thermodynamic characteristics have been studied (CH₄, N₂, CO₂ and He) through a barometric technique. A monotonic decrease of permeability at increasing water activity was observed for all penetrants in both polyimides, with changes even larger than 50% with respect to the values obtained in the dry polymer systems. Due to the higher condensability of water, a strong competitive sorption effect seems to take place during the permeation process, dominating any possible plasticization of polymer chains, related to the water vapor uptake.

Based on these considerations, a simple but effective model has been proposed to analyze the experimental results.

Due to their higher condensability, the water molecules are likely competing with the gaseous penetrants to be absorbed in the polymer matrix and this produces an overall reduction of the fractional free volume (FFV). When water is present in the process, the free volume available for the gaseous species to diffuse across the membrane is significantly reduced compared to the dry conditions, thus negatively affecting their permeation coefficient.

The reduction in FFV, at increasing water concentration in the membrane matrix, is directly related to the amount of water contained in the matrix and can be estimated directly from the sorption isotherms through simplifying assumptions or by a suitable modeling approach.

In the present work, the solubility of different gases and water vapor in the polymer matrix is described by means of the non-equilibrium thermodynamic model (NELF, Non Equilibrium Lattice Fluid)¹². Starting from the pure components parameters of the Sanchez-Lacombe EoS (ρ*, T* and p*, representing the characteristic density, temperature and pressure respectively), this model is able to profitably describe the solubility of mixed solutes in glassy polymers¹³, making possible to estimate the water content and volume fraction in the different experimental conditions.

Moreover, using the lattice fluid parameters for the two polyimides^8,14, it has been possible to evaluate the effect of the presence of water vapor in the sorption behavior of different gases, comparing the results obtained from the model to the pure gas sorption data available in literature^15,16.

Once this information is obtained, the variation of the diffusion coefficient at different water vapor concentration in the membrane matrix is evaluated within the free volume framework, with the well-know exponential expression, which relates the penetrant diffusion with the free volume available for its diffusion thought the polymer.¹⁷

Finally, the permeability is described as product of the solubility and the diffusion coefficient, through the solution-diffusion mechanism. In spite of its theoretical simplicity, the model proposed is able to describe consistently and accurately the experimental data, showing a good agreement with the behavior observed at all different temperatures and water activities.

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