The role of solubility partition coefficient at the mixed matrix interface in the performance of mixed matrix membranes

Abstract

The impact of the solubility partition coefficient at the matrix–filler interface on the effective diffusivity of mixed matrix systems has been calculated using effective medium theory. These predictions are able to explain trends in mixed matrix membrane performance reported in the literature. In particular, partition coefficients which favor sorption of the penetrants in the matrix phase over the dispersed phase, will lead to an increase in the selectivity of the MMM compared to that of the matrix, but will decrease the effective diffusion of the penetrant. On the other hand, partition coefficients, which favor sorption in the dispersed phase have the potential to enhance both selectivity and diffusion, although, to observe this particular effect, the volume fraction of the dispersed phase in the MMM needs to be above a certain threshold.

Introduction

Mixed matrix membranes have the potential to achieve significant improvement in membrane performance in gas separations by combining a continuous polymer bulk phase with a highly selective and/or permeable dispersed inorganic phase [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18]. It has been shown that the matching of the permeabilities of the matrix and the filler is an important factor in the design of mixed matrix membranes [13]. For example if the matrix permeability is either too high or too low in comparison to the filler, the selectivity of the mixed matrix system will not improve in comparison to the neat polymer. In this paper we propose that an additional property that needs to be matched in the two-component system is that of the solubility partition coefficient at the mixed matrix interface. Strathmann et al. have demonstrated the importance of the partition coefficient by using numerical simulations to predict the penetrant concentrations in a polymeric matrix filled with permeable particles [3]. Their results showed that the apparent permeability of the dispersed phase is actually lower than the intrinsic permeability of the dispersed phase when the flux through the filler particles is restricted by the polymer phase. This is true because the driving force over the heterogeneous membrane, expressed as the concentration gradient, is not the same as the driving force over the particles and the polymer phase when measured separately. In fact, a discontinuity in concentration exists at the interface between the matrix and the particle. This phenomenon has a direct implication on the effective permeability of the mixed matrix membrane.

Aside from numerical simulations, numerous analytical models have been utilized in an attempt to predict the membrane performance of mixed matrix membranes as a function of the intrinsic transport properties of the components and the volume fraction of the dispersed phase [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20]. These models, such as Maxwell, Bruggeman, Pal and Feske provide a simple quantitative framework for estimating the effective permeability of a mixed matrix system. Because of their simplicity, though, application of these models to variety of mixed matrix systems can lead to inconsistent results [21]. Most of these discrepancies can be attributed to poor interfacial contact between the molecular sieve and glassy polymers, high loading conditions and large filler aspect ratios, which do not meet the assumptions associated with the simple predictive models. However, even effective permeabilities of mixed matrix systems with idealized interfacial conditions may not conform to the various theoretical models [21]. For example, both the Bruggeman and the Maxwell Models gave poor predictions for Matrimid^@/carbon molecular sieve mixed matrix membranes, overestimating the gas permeabilities of CO₂ and O₂ gases [20]. The lower-than-predicted permeabilities have been attributed to an inhibition of polymer chain mobility at the polymer-sieve interface. Koros et al. was able to account for this phenomenon by introducing an additional interfacial “rigidified” region at the matrix/filler interface with separate intrinsic properties in the Maxwell model [14], [15], [20]. Shimekit et al. [19] have modified the Pal model with the “rigidified interface” as well, to obtain an improved agreement with experimental data for several mixed matrix systems. Although the fit of such modified models with the experimental data is better, the additional parameters, such as the volume fraction of the rigidified interfacial layer and its intrinsic permeability are additional adjustable parameters that cannot be determined independently with high degree of accuracy.

Finally, with the exception of Vu et al. [20], who have employed the Dual Mode/Partial Immobilization Model to model the gas permeabilities of an Ultem^@ continuous phase in a CMS/Ultem^@ matrix, most applications of the various mixed matrix models do not account for the gas solubility differences of the two components making up the mixed matrix system. In fact, most transport models for composite media, such as the Maxwell model effectively predict diffusion coefficients (the equivalent of conductivity in the flux equation) [22], not permeabilities, which have a thermodynamic component. Yet, when these transport models are applied to real systems, it is the permeability that is used in the fitting process. This approach implicitly assumes that the solubility partition coefficient is essentially equal to one, thus implying that there is no thermodynamic resistance at the interface. However, this condition may not be necessarily met, even when the permeabilities of the two components are comparable. Indirect experimental evidence for this can be inferred from the work of Tantekin-Ersolmaz et al., [23] who have examined the role of zeolite particle size on the performance of polymer–zeolite mixed matrix membranes. Their work has clearly demonstrated that the permeability of the mixed matrix system decreases with decreasing particle size of the dispersed component while keeping the overall particle volume fraction constant. This result suggests that the larger interfacial area present in dispersions with smaller particles actually magnifies the mass-transfer resistance arising from the penetrant having to desorb from the matrix phase and resorb in the dispersed phase.

In this paper we utilize the effective medium theory according to Davis [24] to demonstrate the role of the solubility partition coefficient at the phase-boundary on the effective transport properties of mixed matrix membranes. The reason why we have chosen the effective medium theory is that it allows us to predict diffusion coefficients for components experiencing different concentration gradients.