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Article

Estimating CO2/N2 Permselectivity through Si/Al = 5 Small-Pore Zeolites/PTMSP Mixed Matrix Membranes: Influence of Temperature and Topology

1
Department of Chemical and Biomolecular Engineering, Universidad de Cantabria, Av. Los Castros s/n, 39005 Santander, Spain
2
Instituto de Tecnología Química, Universitat Politècnica de València-Consejo Superior de Investigaciones Científicas, Av. de los Naranjos s/n, 46022 Valencia, Spain
*
Author to whom correspondence should be addressed.
Membranes 2018, 8(2), 32; https://doi.org/10.3390/membranes8020032
Submission received: 11 May 2018 / Revised: 7 June 2018 / Accepted: 15 June 2018 / Published: 16 June 2018
(This article belongs to the Special Issue Mixed Matrix Membranes)

Abstract

:
In the present work, the effect of zeolite type and topology on CO2 and N2 permeability using zeolites of different topology (CHA, RHO, and LTA) in the same Si/Al = 5, embedded in poly(trimethylsilyl-1-propyne) (PTMSP) is evaluated with temperature. Several models are compared on the prediction of CO2/N2 separation performance and then the modified Maxwell models are selected. The CO2 and N2 permeabilities through these membranes are predicted with an average absolute relative error (AARE) lower than 0.6% taking into account the temperature and zeolite loading and topology on non-idealities such as membrane rigidification, zeolite–polymer compatibility and sieve pore blockage. The evolution of this structure–performance relationship with temperature has also been predicted.

1. Introduction

Carbon capture strategies are still envisaged as one of the major challenges for preventing CO2 emissions to the atmosphere from anthropogenic sources. Membrane separation technology is often presented as an energy efficient and economical alternative to conventional capture technologies although not yet passing through the stage of pilot plant scale [1]. Polymer membranes for CO2 separation are especially constrained by a performance ‘upper bound’ trade-off between gas permeability and selectivity, which becomes especially significant for treating large volumes of flue gas. The simultaneous improvement on membrane permeability and selectivity is very attractive for industrial applications. Mixed matrix membranes (MMMs), which consist of the introduction of small amounts, usually below 30 wt %, of a special filler providing properties such as a molecular sieve, ion-exchange and robustness in a processable polymer matrix [2], are surpassing this upper bound [3,4,5,6,7]. More than homogenous distribution, the main challenge of MMM fabrication is achieving a good adhesion and compatibility between the inorganic filler and the polymer, avoiding the voids and defects that deteriorate separation performance [8].
Polyimide materials have been, firstly, studied for gas separation because of their stability and selectivity. However, permeability is usually low for CO2 separation [9]. The first and most widely used fillers are zeolites since the pioneering work of Zimmermann et al. [10]. Recently, zeolite 5A was introduced in Matrimid to prepare MMMs for CO2/CH4 separation, after particle surface modification to obtain a defect-free membrane [11]. Amooghin et al. [12] reported the ion exchange effect of Ag+ in zeolite Y-filled Matrimid MMMs led to a CO2 permeability increase of 123% from 8.64 Barrer in pure Matrimid to 18 Barrer in 15% AgY-filled MMM, where 1 Barrer is defined as 10−10 cm3(STP) cm cm−2 s−1 cmHg−1.
A simple approach to produce high permeability and selectivity membranes without the use of modifiers that complicate the synthesis procedures is the variation of the inorganic particles composition themselves to influence the polarity in comparison with the selected polymer matrix. In the case of zeolites, this is represented by the Si/Al ratio and determines many properties of the material, including ion exchange capacity [13]. Thus, for the development of high perm-selective membrane materials for CO2 separation, we focused on the most permeable polymer, poly(trimethylsilyl-1-propyne), PTMSP, and observed that the adhesion with LTA fillers and therefore CO2/N2 separation properties were best with a low Si/Al ratio even upon increasing temperature [14]. The strong influence of zeolite topology on CO2 adsorption has also been acknowledged [15], giving the possibility to locally tune the energy interactions, promoting size and shape selectivity and clustering. However, this effect is not always straightforward because most zeolites cannot be synthesized in pure silica form or at similar Si/Al compositions. Exceptions to this rule are LTA (ITQ-29) [16] and CHA [17]. To avoid this and to see that the lower Si/Al favored the compatibility with glassy hydrophobic PTMSP [14], we fixed an intermediate value of the Si/Al ratio to 5, in order to study the influence of the zeolite filler topology using different small pore zeolites (LTA, CHA, RHO) in the CO2/N2 separation of PTMSP-based MMMs in the temperature range 298–333 K [18]. These MMM surpassed the Robeson’s upper bound at 5 wt % loading even at increasing temperature, but the separation of CO2/N2 mixtures with a 12.5 wt % CO2 content resulted in a real separation factor much lower than the intrinsic selectivity of the membrane material.
Besides the large number of research and publications devoted to new MMM material combinations for gas separation, there is also a growing literature on the development of systematic approaches to describe gas transport through MMMs [19,20,21]. The MMM performance has been evaluated as a function of the membrane morphology imposed by the filler loading and several models have been compared lately [22,23,24,25]. They all present several limitations such as not being valid but at low filler loadings, a large number of adjustable parameters, or not being able to predict the non-idealities common in MMM morphologies that influence their gas separation performance. The most accurate models reported so far are those proposed by Moore et al. [26] and Li et al. [27], accounting for the void interphase, which describes the compatibility between the zeolite filler and the polymer continuous matrix, and the polymer chain rigidification caused by the effect of the inorganic particles embedded in the polymer matrix, in the first case. The second one distinguishes the transport of fast and slow gas molecules, respectively, and introduces the effect of pore blockage that may become important when the dispersed phase is a porous particle as zeolites are [25]. In fact, partial pore blockage has been recently proven to be the dominant effect when porous zeolites are used as fillers in Matrimid, impeding the increase of permeability with increasing dispersed phase loading [28], in agreement with most studies dealing with low permeability polyimides like Matrimid, polysulfone (PSf), and polyethersulfone (PES). The effect of temperature in the performance of those models is seldom reported [29,30].
Thus, in this work the gas permeation through MMMs prepared from small pore zeolites of different topology and constant Si/Al = 5 in PTMSP is evaluated by modified Maxwell models including the void thickness, chain immobilization and pore-blockage effects, and their variation with temperature.

2. Materials and Methods

The MMMs were prepared by a solution-casting method from PTMSP (ABCR, Gelest) previously dissolved in toluene, and CHA, RHO and LTA zeolites of Si/Al = 5 prepared at the Instituto de Tecnología Química (UPV-CSIC) as reported in our previous work [18]. The characteristics of the zeolite fillers used in this work are summarized in Table 1. The membranes were stored in plastic Petri dishes and they were immersed in methanol for a few minutes before gas permeation experiments to remove the effect of aging [31]. The density of the PTMSP pure membranes is 0.75 g/cm3.
Figure 1 shows the high magnification scanning electron microscope (SEM) images of 5 wt % CHA, LTA, and RHO/PTMSP MMMs. As reported in a previous work [18], the smaller LTA particles are dispersed throughout the whole membrane thickness, of which a small glimpse can be seen in Figure 1a, while the larger CHA and RHO zeolites form a bottom layer of particles bound together by the polymer, as observed in Figure 1b for a CHA/PTMSP MMM. In the case of RHO, this adhesion is so strong that individual crystals are not easily discerned in Figure 1c. In this work, we want to focus on the compatibility and adhesion between the filler and the polymer, as the main challenge in MMM fabrication [34,35], thus it is important to notice in Figure 1 that even the largest particles at the bottom of the membrane are apparently well adhered with the polymer continuous matrix.
The thickness of every MMM is measured experimentally at 5 points over the membrane surface for each membrane sample using a IP-65 Mitutoyo digital micrometer (Kawasaki, Japan) with a precision of 0.001 mm. The average thickness for all the MMMs tested in this work was 75 ± 14 µm.
The single gas permeation of N2 and CO2 was measured in that order, using a home-made constant volume set-up described elsewhere [14,18], in the temperature range 298 to 333 K and a feed pressure of 3–4 bar and atmospheric permeate pressure. The average values of the permeabilities and selectivities obtained previously and used in this work are collected in Table A1 in Appendix A.

3. Results and Discussion

3.1. Comparison of Known Mixed-Matrix Membrane Model Predictions

First, well-known models for predicting MMM permeation (Appendix B) have been compared in terms of the percentage average absolute relative error (AARE) with the permeability of CO2 and N2 through MMMs, as
AARE ( % ) = 100 N i = 1 N | P i c a l c P i e x p P i e x p |
where N is the number of experimental data points [23].
A Maxwell model often represents the ideal case with no defects and no distortion of separation properties. Table 2 summarizes the AARE values obtained with the models most commonly encountered in the literature, averaged for the whole range of temperature studied in our laboratory to allow comparison.
According to Table 2, N2 permeability values cannot be predicted by the series, parallel, Maxwell and Higuchi models with acceptable error in all the range of temperature under study. The prediction accuracy of CO2 permeability varies as a function of the zeolite topology. Regarding CO2 permeability, the series and parallel model approaches fit the 5 wt % CHA/PTMSP MMM performance at 323 K, with a lower average AARE for this membrane. The CO2 permeability of LTA/PTMSP MMMs can be described by parallel, Maxwell and Higuchi models in the whole range of operating temperatures and LTA loadings, while the series model only fits the experimental data at low loading. As for the RHO/PTMSP MMM, this is only valid up to 10 wt % RHO loading in the PTMSP matrix. This agrees with the data reported for other MMMs prepared with dispersed fillers of RHO topology [36] where the Maxwell equation only describes the CO2 permeability at low loading, as observed for the ZIF-20/Matrimid MMM, being ZIF-20 a zeolite imidazolate framework of RHO topology as well [36]. In the case of our RHO/PTMSP MMMs, all previous models overestimate the experimental permeabilities.
Only the model predictions with AARE lower than 20% are represented in Figure 2, for clarification purposes. The original Maxwell equation overestimates the experimental value for the permeability of all gases and membranes, especially for N2 permeability. This overestimation is more significant at lower operation temperatures, as reported by Clarizia et al. [14]. In this work, this is true for CHA/PTMSP MMMs with the series model, Figure 2a, and the parallel and Maxwell model for LTA/PTMSP MMMs, Figure 2c. These are simplifications of the general Maxwell equation expressed by Equation (B1) to predict the overall steady-state permeability through an ideal defect-free MMM [26]. Those models provide a simple, quantitative framework to predict the transport properties of MMM when the transport properties of the constituent phases are known, especially at low dispersed phase loading. Only more advanced modifications of this Maxwell equation, such as Felske and Lewis–Nielsen, provide enough accuracy for the description of MMM performance, especially in the case of the slow permeating gas, N2, as reflected in Figure 2b,d,f.

3.2. Reduced Mobility Modified Maxwell Model

In order to account for the non-idealities in the membrane morphology accounting for the compatibility that influence the membrane performance [30], polymer chain rigidification and interphase void thickness, the Maxwell model is applied twice to predict the permeability of a pseudo-interphase induced by the interfacial contact between filler and polymer matrix [25], as schematized in Figure 3a.
According to the reduced mobility modified Maxwell model, the effective permeability through the pseudo-insert in Figure 3a, Peff, is calculated first by
P eff = P I [ P d + 2 P I 2 φ s ( P c P d ) P d + 2 P I + φ s ( P c P d ) ]
where ϕd is the filler volume fraction in the polymer matrix, PI is the permeability through the rigidified continuous matrix, calculated as the ratio between the experimental permeability through a pure PTMSP membrane [18] and an adjustable parameter, β, as described in Figure 3a, and Pd is the permeability through the zeolite. In this work, this value has been taken from literature data on CO2 and N2 permeation through pure zeolite membranes of similar Si/Al ratio and topology (Table 3) to avoid the usual dispersion on this parameter when calculated from experimental solubility isotherms [23].
In Equation (2), PI acts as the permeability of the continuous phase, considering as such the interphase, assuming the bulk of the zeolite as the dispersed phase and the affected zeolite interphase with reduced permeability as the continuous phase [39], as represented in the scheme in Figure 3a. ϕs is the volume fraction of the dispersed sieve phase in combined sieve and interphase, given by
φ s = φ d φ d + φ I = r d 3 ( r d + l I ) 3
where ϕI is the volume fraction of the interface, and lI is the thickness of the ‘interface void’. The permeability of the whole MMM is thus estimated by applying the Maxwell equation again, as
P MMM = P c [ P eff + 2 P c 2 φ s ( P c P eff ) P eff + 2 P c + φ s ( P c P eff ) ]
As ϕd + ϕI increases to one, the interphases of neighboring dispersed particles overlap and the overall mixed matrix is rigidified. This occurs preferentially as the zeolite particle loading is increased or the interphase void distance is increased, i.e., voids appear because embedding in the polymer chains becomes more difficult.
Equations (2)–(4) predict the overall performance of MMMs taking into account the case morphologies identified by Moore et al. [26], adapted to distinguish the performance of the fast and slow gas in CO2/N2 separation, and including the influence of temperature. This model is thus based on three adjustable parameters, the interphase thickness, lI, and the chain immobilization factor, β, which depends on the permeating gas molecule [39], whose values are presented in Table 4, Table 5 and Table 6 for the CHA/PTMSP, LTA/PTMSP and RHO/PTMSP MMM, respectively.
As expected, the chain immobilization factor, β, is smaller for CO2 than N2. This confirms that the polymer chain rigidification normally results in a larger resistance to the transport of the gas with larger molecular diameter [27]. The RHO/PTMSP MMM revealed a different trend, although only at 298 K, which may be attributed to the agglomeration of these larger crystal size and smaller pore size particles at the bottom of the MMM. Interestingly, β(CO2) and β(N2) of the three types of MMMs converge to similar values upon increasing temperature. This may be attributed to the compensating effects of polymer flexibility and chain rigidification of the polymer matrix, which are accentuated for the larger size of the RHO particles than LTA and CHA. This agrees with the current statement that in gas separation through MMMs there is not only an optimum in zeolite loading but also in operating temperature [40].
The thickness of the interphase between the zeolite and the polymer matrix, lI (μm), accounts for the compatibility between the zeolite and polymer phases, as well as the defects or voids due to poor compatibility between zeolites and polymer [25]. In this work, the void thickness decreases with increasing zeolite loading and is independent of the type of gas and temperature. It can also be observed that this parameter lI is influenced by the zeolite topology, in the following order: lI (LTA/PTMSP) < lI (CHA/PTMSP) < lI (RHO/PTMSP). This is attributed to the different interaction with the polymer matrix, and the decreasing particle size, in agreement with results obtained for zeolite-APTES/PES MMMs [27]. Those authors obtained as thickness of the rigidified region li = 0.30 µm for a cubic zeolite A (Si/Al = 1) dispersed phase in PES, and values of the chain immobilization factor (β) of 3 and 4, for O2 and N2, respectively. A rigidified thickness of 1.4 µm and chain immobilization factor was reported for ZIF-20/polysulfone MMMs, estimating a Pd = 45 Barrer, in agreement with pore ZIF membranes of similar pore size and topology [41]. Therefore, the magnitude of the adjustable parameters obtained in this work are in the same order of magnitude.
These parameters allow a prediction of the permeability through these MMMs by this model with an error of up to a global AARE below 6 ± 1%, where the maximum errors lie on 10CHA/PTMSP and 10RHO/PTMSP membranes at 298 K.

3.3. Extended Pore-Blockage Reduced Mobility Modified Maxwell Model

Although in this work the channel opening of the zeolites (0.38, 0.41 and 0.36 nm for CHA, LTA and RHO topologies, respectively) lie in the same range as the gas pair molecules to be separated, we have included the analysis of the partial pore blockage effect [25,35] as Li et al. [27] for zeolite A-APTES/PES MMM, adapted in the Scheme shown in Figure 3b. This approach consists in applying the Maxwell equation not just twice, but three times, and requires not just three, but six adjustable parameters, in order to define the dispersed phase volume fraction in the pore-blockage and the rigidified region, as well as the immobilization factor for the pair of gases in both sections.
Firstly, the permeability in the pore-blockage affected zone near the zeolite particle surface as represented in Figure 3b, is calculated by
P 3 rd = P blo [ P d + 2 ( P d / β ) 2 φ 3 ( ( P d / β ) P d ) P d + 2 ( P d / β ) + φ 3 ( ( P d / β ) P d ) ]
Secondly, the P3rd permeability calculated by Equation (5) is entered as the new dispersed phase, and the permeability of the rigidified region, Prig, is taken as the continuous phase, to calculate the new Peff, P2nd:
P 2 nd = P rig [ P 3 rd + 2 ( P c / β ) 2 φ 2 ( ( P c / β ) P 3 rd ) P 3 rd + 2 ( P c / β ) + φ 2 ( ( P c / β ) P 3 rd ) ]
Thirdly and lastly, the permeability through the bulk of the MMM is calculated using P2nd as the new permeability for the dispersed phase, turning the previous equations into
P MMM = P c [ P 2 nd + 2 P c 2 ( φ d + φ blo + φ rig ) ( P c P 2 nd ) P 2 nd + 2 P c + ( φ d + φ blo + φ rig ) ( P c P 2 nd ) ]
with
φ 3 = φ d φ d + φ blo
and
φ 2 = φ d + φ blo φ d + φ blo + φ rig
Now, the adjustable parameters are ϕblo and ϕrig, the calculated volume fraction of the pore-blockage affected region, and the rigidified region, respectively, as well as β′ and β, whose values depend on the permeating gas, and identify the partial pore blockage affected and rigidified polymer region, respectively, as given in Figure 3b. Note that β is similar to the chain immobilization factor introduced by the previous reduced mobility modified Maxwell model, discussed in the previous section.
Figure 4, Figure 5 and Figure 6 show the comparison of the prediction of CO2 and N2 permeability using both modified Maxwell models. The experimental results are well described for the Si/Al = 5 zeolites, indicating a good compatibility between intermediate Si/Al zeolites and the glassy PTMSP [14]. The optimized β value is higher for N2 than CO2, for CHA and RHO/PTMSP MMMs. β(N2) values of 0.92 are obtained for the CHA/PTMSP MMMs, independently of zeolite loading, where as they increase from 0.66 to 1.40 for the RHO/PTMSP MMMs. β(CO2) gives smaller values than β(N2), as expected for smaller molecules. β(CO2) follows similar trends as β(N2), being constant for CHA and LTA/PTMSP MMMs, at values of 0.3 and 0.2, respectively, and increasing from 0.26 to 0.94 with increasing loading for RHO/PTMSP MMMs. These values are smaller than 1.6, the value recently published for Sigma-1/Matrimid MMMs, considering also the partial pore blockage effect [28]. The values of β′(CO2) are 0.06 for CHA and RHO/PTMSP MMMs, and below 0.03 for LTA/PTMSP MMMs. The β′(N2) are 70% higher in the LTA and RHO/PTMSP MMMs, and 30% higher than β′(CO2) in the case of CHA/PTMSP MMMs. These results reveal that, although the partial pore blockage is low in small–pore zeolites, it is more significant for the smaller pore size zeolite fillers as CHA or RHO, than LTA.
The models describe well the CO2 and N2 permeability through the Si/Al = 5 zeolite/PTMSP MMMs as a function of zeolite loading, topology and temperature. The CO2 permeability increases with temperature while the N2 permeability slightly increases for CHA and RHO/PTMSP MMMs, behavior similar to pure zeolite membranes, as reflected by the activation energies derived from the Arrhenius equation in the previous work [18], in agreement with other works in literature [42]. The LTA/PTMSP MMMs show a maximum performance at 10 wt % zeolite loading and 323 K, losing permselectivity at higher loading and temperature. The worst AARE for the prediction of experimental permeabilities through the extended partial pore blockage reduced mobility model is 0.6%, for the 5 wt % CHA/MMM at 313 K, which were in some of the best agreement with the first modified Maxwell model. Partial pore blockage may be affecting permeability even with small-pore zeolite fillers in a glassy polymer matrix [28].

4. Conclusions

The experimental CO2 and N2 permeabilities of Si/Al = 5 small-pore zeolites/PTMSP MMM has been compared with modified Maxwell model predictions as a function of zeolite topology (CHA, LTA, RHO), loading (0–20 wt %) and temperature (298–333 K). Three adjustable parameters accounting for the membrane rigidification, void interphase and partial pore-blockage have been optimized at values lower than reported in literature. They reveal the compatibility between Si/Al = 5 zeolites dispersed in the glassy polymer PTMSP, as well as a small influence of partial pore blockage in the case of the smaller pore size CHA and RHO. The CO2 and N2 permeabilities through these membranes are predicted with an AARE lower than 0.6% taking into account zeolite loading and topology on non-idealities such as membrane rigidification and sieve pore blockage and their influence on MMM performance. The evolution of this structure-performance relationship with temperature has also been predicted. The implementation of the Arrhenius dependency of the MMM permeability and the prediction studied in this work constitute a step further towards the understanding of the MMM performance in order to develop new membrane materials and module configurations with potential application in CO2 separation, which will be addressed in a future work.

Author Contributions

Conceptualization, C.C.-C.; Data curation, A.F.-B.; Funding acquisition, A.I.; Investigation, C.C.-C., A.F.-B., S.V. and A.I.; Methodology, C.C.-C.; Supervision, A.I.; Writing—original draft, C.C.-C.; Writing—review and editing, C.C.-C., S.V. and A.I.

Funding

This research was funded by Spanish MINECO—General Secretariat for Research, Development and Innovation under project CTQ2016-76231-C2-1-R at the University of Cantabria, and MAT2015-71842-P, at the Instituto de Tecnología Química.

Acknowledgments

The authors gratefully acknowledge the financial support of the Spanish MINECO—General Secretariat for Research, Development and Innovation under project CTQ2016-76231-C2-1-R at the University of Cantabria, and MAT2015-71842-P, at the Instituto de Tecnología Química. Miguel Palomino is thanked for the acquisition of the SEM images at the Electron Microscopy Service of the Universitat Politècnica de València.

Conflicts of Interest

The authors declare no conflict of interest.

Appendix A

The experimental permeation data obtained in a previous work [18] are collected in Table A1.
Table A1. Experimental data of the different MMMs with increasing order of particle size (LTA, 0.5 µm; CHA, 1 µm; RHO, 1.5 µm).
Table A1. Experimental data of the different MMMs with increasing order of particle size (LTA, 0.5 µm; CHA, 1 µm; RHO, 1.5 µm).
Filler and Loading [18]T (K)P(CO2) (Barrer)P(N2) (Barrer)α(CO2/N2)
5 wt % LTA29871507949
30313,88163722
31312,44881615
32311,770120810
333902630443
10wt % LTA29888139519
30312,92186515
31315,80289218
32316,648107815
33311,02945202.5
20 wt % LTA29810,58717206
30313,17825855
31312,98025195
32311,17539663
33310,96443162.5
5 wt % CHA29822742928
303357532911
313565137215
32311,77240929
33316,14551132
10 wt % CHA298336321116
303362026214
313435121620
323589224124
333648533020
5 wt % RHO298820513256
303838312277
31311,722121410
32312,726108912
33313,324136810
10 wt % RHO29832625926
303599650912
313911171213
32310,30476114
33311,114116610
20 wt % RHO298447912294
303888311738
313778412106
323929313417
333949817046

Appendix B

The MMM performance has been evaluated as a function of the membrane morphology imposed by the filler loading using several models that have been compared lately [20,23,24,25]. Equation (A1) was derived by Maxwell for semi-conductors and is widely accepted as an easy tool for a quick estimation of the performance of MMMs from phase-separated blends [3,30]:
P mmm = P c [ P d + 2 P c 2 φ d ( P c P d ) P d + 2 P c + φ d ( P c P d ) ]
where ϕd is the dispersed phase volume fraction, calculated from the nominal weight fraction of the zeolite in the MMMs, using the density of the PTMSP polymer and the corresponding zeolite density (Table 1).
The minimum value of effective permeability of a given penetrant in a MMM is given by considering a series mechanism of transport through the dispersed and continuous phases (Equation (A2)):
P mmm = P c P d ( 1 φ d ) P d + φ d P c
and the maximum value is taken when both phases are assumed to contribute in parallel to the flow direction (Equation (A3)):
P mmm = φ d P d + ( 1 φ d ) P c
Other important models used for the description of gas permeation in MMMs are the Higuchi, Felske and Lewis–Nielsen, Bruggemann and Pal models [20]. The last two are not presented in this work because they are implicit equations derived from Maxwell and Lewis–Nielsen that have to be solved numerically.
The Higuchi model is applied for a random dispersion of spherical filler particles but lacks mathematical rigor [24]. The main equation for porous zeolite particle fillers is given by:
P mmm = P c [ 1 + 3 φ d P d + 2 P c P d P c φ d K [ ( 1 φ d ) ( P d P c ) P d + 2 P c ] ]
where K is an empirical constant containing shape description, with no physical meaning. In this work, it only adjusts the accepted value of 0.78 for 5 wt % CHA, 5–10 wt % LTA5/PTMSP. 10 wt % CHA/PTMSP is adjusted to K = 0.999 and for the rest of the membranes K varies randomly between 0.0001 and 0.03 at different temperatures.
The Felske model was originally used for the description of the thermal conductivity of composites of core-shell particles (core particle covered with interfacial layer) and also for permeability measurement. It gives almost the same predictions as the modified Maxwell model and it can be reduced to Maxwell’s when the interfacial layer is absent [25]. It is described by Equations (A5)–(A7), as
P mmm = P c [ 2 ( 1 φ d ) + ( 1 + 2 φ d ) ( β / γ ) ( 2 + φ d ) + ( 1 φ d ) ( β / γ ) ]
with
β = ( 2 + δ 3 ) P d 2 ( 1 δ 3 ) P I P c = ( 2 + δ 3 ) P d P c 2 ( 1 δ 3 ) P I P c
and
γ = 1 + 2 δ 3 ( 1 δ 3 ) P d P c
where δ = rI/rd. This model also needs three adjustable parameters, as in the reduced mobility modified Maxwell model.
The Lewis–Nielsen model was originally proposed for describing an elastic modulus of particulate composites, and the following equation can be used to predict the effective permeability in MMMs:
P mmm = P c [ 1 + 2 φ d ( α 1 ) / ( α + 2 ) 1 ψ φ d ( α 1 ) / ( α + 2 ) ]
where
ψ = 1 + ( 1 φ m φ m )
This model might represent a correct definition of the permeability over the range of 0 < ϕd < ϕm. The solution diverges when ϕd = ϕm and it should be noted that when ϕm → 1, the Lewis–Nielsen model reduces to the Maxwell equation (Equation (A1)).

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Figure 1. Scanning electron microscope (SEM) images of the detailed contact between LTA (a); CHA (b); RHO (c) and poly(trimethylsilyl-1-propyne) (PTMSP) in 5 wt % loaded mixed matrix membranes (MMMs). Bars correspond to 6 µm.
Figure 1. Scanning electron microscope (SEM) images of the detailed contact between LTA (a); CHA (b); RHO (c) and poly(trimethylsilyl-1-propyne) (PTMSP) in 5 wt % loaded mixed matrix membranes (MMMs). Bars correspond to 6 µm.
Membranes 08 00032 g001aMembranes 08 00032 g001b
Figure 2. Comparison of CO2 (left) and N2 permeabilities through CHA (a,b), LTA (c,d) and RHO (e,f)/PTMSP MMMs with the predictions by the series (dashed lines), parallel (dotted lines), original Maxwell (dash-dot), Higuchi (dash dot dot), Felske (thin continuous line) and Lewis–Nielsen (thick continuous line) models, as a function of temperature. Zeolite loading: 5 wt % (black), 10 wt % (red), 20 wt % (green).
Figure 2. Comparison of CO2 (left) and N2 permeabilities through CHA (a,b), LTA (c,d) and RHO (e,f)/PTMSP MMMs with the predictions by the series (dashed lines), parallel (dotted lines), original Maxwell (dash-dot), Higuchi (dash dot dot), Felske (thin continuous line) and Lewis–Nielsen (thick continuous line) models, as a function of temperature. Zeolite loading: 5 wt % (black), 10 wt % (red), 20 wt % (green).
Membranes 08 00032 g002aMembranes 08 00032 g002b
Figure 3. Schemes of the modified Maxwell model proposed by Moore et al. [26] (a) and the extended modified Maxwell model proposed by Li et al. [27] (b), both adapted for this work.
Figure 3. Schemes of the modified Maxwell model proposed by Moore et al. [26] (a) and the extended modified Maxwell model proposed by Li et al. [27] (b), both adapted for this work.
Membranes 08 00032 g003
Figure 4. Effect of temperature and zeolite loading on the CO2 (a) and N2 (b) permeability through CHA/PTMSP MMMs: Thin lines correspond to the reduced mobility modified Maxwell model and thick lines to the extended modified Maxwell model. Dash, dot and continuous patterns, and void, half-filled and full symbols, refer to 5 wt %, 10 wt % and 20 wt % zeolite loading, respectively.
Figure 4. Effect of temperature and zeolite loading on the CO2 (a) and N2 (b) permeability through CHA/PTMSP MMMs: Thin lines correspond to the reduced mobility modified Maxwell model and thick lines to the extended modified Maxwell model. Dash, dot and continuous patterns, and void, half-filled and full symbols, refer to 5 wt %, 10 wt % and 20 wt % zeolite loading, respectively.
Membranes 08 00032 g004
Figure 5. Effect of temperature and zeolite loading on the CO2 (a) and N2 (b) permeability through LTA/PTMSP MMMs: Thin lines correspond to the reduced mobility modified model and thick lines to the extended modified Maxwell model. Dash, dot and continuous patterns, and void, half-filled and full symbols, refer to 5 wt %, 10 wt % and 20 wt % zeolite loading, respectively.
Figure 5. Effect of temperature and zeolite loading on the CO2 (a) and N2 (b) permeability through LTA/PTMSP MMMs: Thin lines correspond to the reduced mobility modified model and thick lines to the extended modified Maxwell model. Dash, dot and continuous patterns, and void, half-filled and full symbols, refer to 5 wt %, 10 wt % and 20 wt % zeolite loading, respectively.
Membranes 08 00032 g005
Figure 6. Effect of temperature and zeolite loading on the CO2 (a) and N2 (b) permeability through RHO/PTMSP MMMs: Thin lines correspond to the reduced mobility modified model and thick lines to the extended modified Maxwell model. Dash, dot and continuous patterns, and void, half-filled and full symbols, refer to 5 wt %, 10 wt % and 20 wt % zeolite loading, respectively.
Figure 6. Effect of temperature and zeolite loading on the CO2 (a) and N2 (b) permeability through RHO/PTMSP MMMs: Thin lines correspond to the reduced mobility modified model and thick lines to the extended modified Maxwell model. Dash, dot and continuous patterns, and void, half-filled and full symbols, refer to 5 wt %, 10 wt % and 20 wt % zeolite loading, respectively.
Membranes 08 00032 g006
Table 1. Properties of the zeolite fillers with Si/Al = 5 used in this work.
Table 1. Properties of the zeolite fillers with Si/Al = 5 used in this work.
FillerCrystal Size (µm)Density (g/cm3)Pore Size 1 (nm)Structure 2
LTA0.51.498 [32]0.41 Membranes 08 00032 i001
CHA1.02.0900.38 Membranes 08 00032 i002
RHO1.51.442 [33]0.36 Membranes 08 00032 i003
1 From [18]. 2 The crystallographic structures have been taken from the International Zeolite Database (http://www.iza-structure.org/databases/): View of the planes 100 for LTA and 001 for CHA and RHO, respectively.
Table 2. Percentage of average absolute relative error (AARE) for CO2 and N2 permeation (first and second values in every entry) prediction, highlighting those AARE values lower than 20%.
Table 2. Percentage of average absolute relative error (AARE) for CO2 and N2 permeation (first and second values in every entry) prediction, highlighting those AARE values lower than 20%.
MMMSeriesParallelMaxwellHiguchiFelskeLewis-Nielsen
5CHA/PTMSP17.32/370108/2026106/2006146/2609118/32.424.9/2.14
10CHA/PTMSP24.2/143102/296699.7/290996.8/285480/93610−4/10−5
5LTA/PTMSP20.6/33.311.8/51611.4/49826.3/7082.54/10−30.46/0.01
10LTA/PTMSP40.9/50.014.5/6314.79/21414.6/56067.4/9.043.98/10−5
20LTA/PTMSP45.0 /50.07.11 /2128.28/19810.4/1943.00/10−44.37/10−5
5RHO/PTMSP8.62/12612.7/36212.4/35716.7/3950.85/6·10−41.84/0.6·10−5
10RHO/PTMSP24.0/21657.0/103054.5/100349.3/9470.03/2·10−34.32/0.02
20RHO/PTMSP45.3/52.472.2/94763.8/89244.2/75622.0/5·10−412.3/10−4
Table 3. Permeability data of the pure zeolite dispersed phase, Pd, used for the model predictions.
Table 3. Permeability data of the pure zeolite dispersed phase, Pd, used for the model predictions.
Zeolite Dispersed PhasePd(CO2) (Barrer)Pd(N2) (Barrer)T (K)Reference
CHA (Si/Al = 5) 1880.59293[37]
CHA (pure silica)53955313[38]
LTA (Si/Al = 1)1390.048298[25]
RHO 2623260298[33]
1 Si/Al = 5 as the zeolites used in this work. 2 The CO2 permeabilities reported for ZIF-8 composite values are considered as the Rho here, given the similar sodalite topology.
Table 4. Parameters estimated by the reduced mobility modified Maxwell model for the CHA/PTMSP MMMs.
Table 4. Parameters estimated by the reduced mobility modified Maxwell model for the CHA/PTMSP MMMs.
T (K)5 wt %10 wt %
lI (µm) = 1.39lI (µm) = 0.98
β (CO2)β (N2)β (CO2)β (N2)
2987.4261.24.9086.61
3034.5653.283.4864.0
3132.2542.82.8770.5
3231.0131.411.9750.4
3330.7320.51.0010.2
Table 5. Parameters estimated by the reduced mobility modified Maxwell model for the LTA/PTMSP MMMs.
Table 5. Parameters estimated by the reduced mobility modified Maxwell model for the LTA/PTMSP MMMs.
T (K)5 wt %10 wt %20 wt %
lI (µm) = 0.60lI (µm) = 0.56 ± 0.08lI (µm) = 0.27
β (CO2)β (N2)β (CO2)β (N2)β (CO2)β (N2)
2982.3521.91.8317.41.398.82
3030.9327.11.0012.00.865.84
3131.0118.90.8011.00.855.37
3231.0010.20.728.340.922.72
3331.293.381.062.490.932.08
Table 6. Parameters estimated by the reduced mobility modified Maxwell model for the RHO/PTMSP MMMs.
Table 6. Parameters estimated by the reduced mobility modified Maxwell model for the RHO/PTMSP MMMs.
T (K)5 wt %10 wt %20 wt %
lI (µm) = 1.76lI (µm) = 1.23lI (µm) = 0.79
β (CO2)β (N2)β (CO2)β (N2)β (CO2)β (N2)
2982.060.3110.621.953.361.46
3031.570.352.102.981.281.54
3131.070.301.331.291.431.33
3230.910.281.170.931.120.93
3330.870.171.010.451.080.58

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Casado-Coterillo, C.; Fernández-Barquín, A.; Valencia, S.; Irabien, Á. Estimating CO2/N2 Permselectivity through Si/Al = 5 Small-Pore Zeolites/PTMSP Mixed Matrix Membranes: Influence of Temperature and Topology. Membranes 2018, 8, 32. https://doi.org/10.3390/membranes8020032

AMA Style

Casado-Coterillo C, Fernández-Barquín A, Valencia S, Irabien Á. Estimating CO2/N2 Permselectivity through Si/Al = 5 Small-Pore Zeolites/PTMSP Mixed Matrix Membranes: Influence of Temperature and Topology. Membranes. 2018; 8(2):32. https://doi.org/10.3390/membranes8020032

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Casado-Coterillo, Clara, Ana Fernández-Barquín, Susana Valencia, and Ángel Irabien. 2018. "Estimating CO2/N2 Permselectivity through Si/Al = 5 Small-Pore Zeolites/PTMSP Mixed Matrix Membranes: Influence of Temperature and Topology" Membranes 8, no. 2: 32. https://doi.org/10.3390/membranes8020032

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