(217fi) 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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