Silica Membranes - Industrial

Article pubs.acs.org/IECR

Mass Transport in Hybrid PTMSP/Silica Membranes Michele Galizia,†,§ Maria Grazia De Angelis,*,† Massimo Messori,‡ and Giulio C. Sarti† †

Dipartimento di Ingegneria Civile, Chimica, Ambientale e dei Materiali, Alma Mater Studiorum-Università di Bologna, via U. Terracini 28, 40131 Bologna, Italy ‡ Dipartimento di Ingegneria “Enzo Ferrari”, Università di Modena e Reggio Emilia, via Vignolese 905, 41125 Modena, Italy S Supporting Information *

ABSTRACT: Hybrid silica/poly(trimethylsilyl propyne) (PTMSP) membranes in which the silica particles are generated in the polymer solution with a sol−gel reaction from a tetraethoxysilane (TEOS) precursor were fabricated. The membranes are characterized with microscopic, thermogravimetric, and pycnometric analysis; their sorption and diffusion properties with respect to n-C4 and n-C5 vapors are also measured at 25 °C. A significant reduction of the polymer specific volume, organic vapor solubility, and diffusivity is observed after incorporation of silica, according to a combination of free volume filling and compressive constraints. The behavior of the hybrid membranes (HM) is opposite that of mixed matrix membranes (MMM) obtained by physical mixing of preformed silica nanoparticles into PTMSP solutions, which show, on the contrary, free volume, vapor solubility, and diffusivity values higher than pure PTMSP. The hybrid membranes are characterized by larger silica domains than mixed matrix ones. Remarkably, however, the transport behavior of both types of membranes can be interpreted, by the same theoretical background, on the basis of a single structural parameter, namely the density of the polymer phase. This parameter allows a direct estimation of the variation of free volume and vapor solubility and diffusivity in both types of membranes, through a NELF/free volume approach.

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INTRODUCTION It is well-known that the separation performance of polymeric membranes for gas separation shows an upper bound, as an increase of permeability is often accompanied by a decrease of selectivity and vice versa.1 On the other hand, inorganic materials like zeolites or molecular sieves overcome this limit and show, at the same time, adequately high permeability and selectivity levels: this observation suggested that suitable and high-performing materials for separation processes can be obtained by dispersing inorganic fillers in polymeric materials. Initially the choice of inorganic fillers was limited to porous, selective materials with high intrinsic permselectivity, like zeolites or carbon molecular sieves;2,3 then, in the early 2000s it was found that even the addition of virtually impermeable inorganic particles, like silica and metal oxides, to polymers could result in an enhancement of the gas permeability and in some cases also of the gas selectivity properties.4−11 Such behavior is not predictable via the conventional tools used to calculate the properties of composite materials, like Maxwell’s model,12 as the presence of an impermeable filler should lower the permeability of gases in a polymer matrix, by increasing the tortuosity of the gas diffusive path in the membrane as well as reducing the surface area available for transport. In such matrices, on the other hand, the increase of tortuosity has a minor effect on gas transport, and a general improvement of the transport properties is unexpectedly observed. It is commonly accepted that the enhancement of the gas transport rate in mixed matrix membranes (MMM) mentioned above is due to the fact that the addition of nanosized particles, poorly interacting with the polymer chains, creates additional free volume pockets inside the glassy polymer which are just of the right size suitable to enhance gas permeability without © 2013 American Chemical Society

dramatically compromising selectivity. Thermal, spectroscopic and optical analysis allowed a deep insight into these systems, confirming that the main effect of the filler is the free volume modification, while the long-range chain motions are not hindered, as confirmed by the fact that usually the glass transition temperature of the nanocomposites does not differ much with respect to the pure polymer Tg value.5,11 The additional free volume created by filler insertion can be characterized via density measurements, or via positron annihilation lifetime spectroscopy (PALS). The PALS technique gives only a qualitative measure of the polymer free volume, although it enables one to elucidate the separate effect that the addition of inorganic particles has on free volume domains of different sizes. On the other hand, density can be measured by different methods, and its value can be elaborated with various assumptions in order to estimate the average fractional free volume of the system. If the accuracy of the density measurements is not high enough to appreciate the variations of free volume, as often happens, one can use other indirect methods. The most successful applied so far is the one which uses the solubility data of a probe penetrant inside the membrane matrix,13 and the Non-Equilibrium Lattice Fluid (NELF) model for the solubility, obtaining a proper value of polymer density.14 This model was used to describe the free volume, solubility, and effective diffusivity of fluids inside different glassy matrices filled with fumed silica (FS), namely Special Issue: Massimo Morbidelli Festschrift Received: Revised: Accepted: Published: 9243

October 20, 2013 December 17, 2013 December 18, 2013 December 18, 2013 dx.doi.org/10.1021/ie4035225 | Ind. Eng. Chem. Res. 2014, 53, 9243−9255

Industrial & Engineering Chemistry Research

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poly(trimethylsilyl propyne) (PTMSP),13 Teflon AF 1600 and 2400,11,15 polysulfone,16 and a polymer with intrinsic microporosity (PIM-1).17 In mixed matrix membranes, the systematic increase of permeability is accompanied by a variation of selectivity that is difficult to predict. In certain polymeric matrices, the permeability of the larger penetrant molecules is more strongly enhanced by the addition of fumed silica, as happens for instance by adding fumed silica to PMP7,8 and Teflon AF2400,6 thereby enhancing the vapor selectivity of the matrix, or reversing the size selectivity of the original polymer matrix. In other cases, the permeability of the smaller molecules is enhanced more effectively by the addition of nanoparticles, enhancing the size sieving property of the matrix. The final selective behavior depends on the nature of the filler, on the gas mixture considered, and on the initial properties of the polymer. It has been shown recently for nanocomposites based on fumed silica particles that, as a rule of thumb, the addition of fumed silica is able to enhance the n-C4/CH4 selectivity if the initial polymer selectivity lies below an approximate value of 20.16,17 For higher values of initial polymer selectivity, after the addition of fumed silica the selectivity decreases rather than increasing. Of course, the behavior is different for mixed matrices based on porous selective fillers: in the case of polymers of intrinsic microporosity, filled with ZIF and AIPO, the gas permeability increases after the addition of a filler and generally increases more for the penetrants of smaller molecular size than for the larger ones, thus enhancing the size selectivity.17 In mixed matrices based on nonporous fumed silica, which has no intrinsic permeability or selectivity, the observed permselectivity behavior depends essentially on the effect that the nanofiller incorporation has on the size and distribution of polymer free volume. In general, it can be said that the larger free volume domains are usually enhanced by the addition of fumed silica, while the small free volume domains are less affected.16 The incorporation of silica particles in polymers can be pursued with two different techniques, i.e., either by physical mixing of the preformed silica particles in the polymer solution or by in situ generation of the silica particles via sol−gel reactions which use a precursor for the inorganic phase. In the latter technique, the precursor of the silica phase, usually an alkoxysilane, is added to a polymer solution, and a sol−gel reaction is induced in order to form SiO2 domains in the presence of a catalyst. In this way, several hybrid organic/ inorganic structures can be formed, characterized by an intimate contact and interpenetration between the organic and inorganic phases. Hybrid structures have improved gas barrier properties, which makes them suitable for packaging applications.18−20 As far as the gas and vapor separation is concerned, however, the results obtained by different authors on the hybrid membranes obtained with the sol−gel route were somehow unexpected and not always encouraging. Indeed, the hybrid matrices formed by high free volume glassy polymers, such as PTMSP, showed generally permeabilities lower than the pure polymer, with a reduction factor as low as 1/10 for the mixed gas permeability of n-C4 in a mixture with methane.21 In particular, Gomes et al. synthesized hybrid PTMSP/SiO2 membranes with silica content below 6 wt % using tetrathethoxysilane (TEOS), or mixtures formed by TEOS and other bulkier organoalkoxysilanes. The conversion from silane to silica was often far from being complete for such

samples, with the only exception being the hybrid membrane obtained with pure TEOS. Attempts to increase the amount of silica in the membrane failed either because of incomplete conversion or because the final membrane was heterogeneous. The gas permeability of hybrid membranes was always lower than that of the pure polymer with only one exception, while the selectivity was equal or higher than pure PTMSP for the nC4/CH4 couple.21 We believe that the behavior of such structures has to be more thoroughly investigated and understood and coupled to an extensive physical and chemical analysis. For this purpose, in this work we study the properties of PTMSP/SiO2 based hybrid matrices obtained via sol−gel reaction of TEOS in solutions of PTMSP, with different loadings of SiO2 up to 50 wt %. The membranes are characterized via SEM analysis, TGA, DTA, helium pycnometry and sorption experiments performed using hydrocarbon vapors (n-butane, n-pentane). The physical and mass transport properties of such membranes are then compared to the ones of mixed matrix membranes obtained by mechanically dispersing preformed silica particles into PTMSP, obtained in previous works. The solubility and diffusivity data collected are then modified with the NELF/free volume model developed for mixed matrix membranes.13

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THEORETICAL BACKGROUND Normally, models for composite membranes estimate the permeability and rely on the idea of a series/parallel of different phases with different permeabilities: the most common one is Maxwell’s model, which leads to the following expression for dilute sospensions of impermeable fillers:12 PM = PP

1 − ΦF 1 + ΦF /2

(1)

where PM and PP indicate the permeability of the composite and of the pure polymer, respectively, while ΦF represents the filler volume fraction. Other models account for higher degrees of complexity but as a counterpart make use of a higher number of adjustable parameters.2,22−25 Recently, a different model was proposed and tested, which requires only one parameter to describe the sorption and diffusion behavior of nonswelling gases in fumed silica-loaded glassy matrices,13 namely the density of the glassy polymeric phase, which is univocally related to the average fractional free volume. That model is based on the simple physical idea that the only relevant effect of filler addition is a modification of the average density of the polymeric phase of the composite matrix, thus changing the average free volume of the polymer. The use of the NELF model allows one to estimate the mixed matrix solubility value, given the actual polymer density of the matrix, and a free-volume based correlation leads to estimation of the new effective diffusivity value with one adjustable parameter only.13 The basic assumptions and equations of this approach are summarized below, and the same modeling approach can be applied both to MMM as well as to the hybrid membranes obtained with the sol−gel route, as it will be shown in the following. Density and Fractional Free Volume of Composite Membranes. A semiadditive rule is considered for the composite density ρM, based on which the filler density, ρF, 9244

dx.doi.org/10.1021/ie4035225 | Ind. Eng. Chem. Res. 2014, 53, 9243−9255


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remains unchanged with respect to its pure state, ρF,0 (i.e., ρF ≅ ρF,0). On the other hand, the density of the polymer phase in the mixed matrix state changes due to the presence of the inorganic filler, and its value ρP,MM depends on the filler amount. Therefore, the composite density ρM is given by ρM =

previous works13,27,31 and are included for convenience in the Supporting Information. Obviously, the density of the unpenetrated unswollen polymeric phase is the same for all penetrants and depends only on the filler load in the membrane. When the matrix is swollen by the penetrant, the degree of swelling is quantified with a pressure-independent swelling coefficient ksw, according to the observation that swelling is generally linear with penetrant pressure; that allows one to estimate the polymer density at each pressure as follows, since the inorganic phase is not swelling:

1 1 − wF ρP,MM

+

wF ρF

(2)

where wF is the mass fraction of the filler in the original unpenetrated composite. The fractional free volume (FFV) of the dry polymer phase in the MM state, FFV0P,MM, is estimated with respect to the van der Waals density of the pure polymer, ρvdW P , through the usual procedure: FFV 0P,MM =

ρPvdW

0 − 1.3·ρP,MM ρPvdW

ρP (p) = ρP0 (1 − kswp)

The value of ksw depends on the specific penetrant considered; its determination requires a penetrant-dependent swelling or solubility datum in the loaded polymer, at a relatively high pressure. Effective Diffusivity in Composite Membranes. The presence of the filler affects diffusion into the mixed matrix by increasing the tortuosity of the diffusive path with respect to the pure polymer and by varying the FFV of the polymeric phase; clearly the latter effect is the most relevant. In any event, both effects can be described by proper well-known theories. The effective diffusion coefficient in the composite material at infinite dilution D0M, obtained from experimental measurements of sorption or permeation transients on the composite membrane, is easily related to the corresponding value of the polymer phase, D0P, using a tortuosity factor τ evaluated from Maxwell’s model for spherical particles:

(3)

where the superscript 0 indicates the value obtained in the limit of zero penetrant pressure. The van der Waals density of the polymer can be estimated by a group contribution method and is already available for PTMSP, for which ρvdW = 1.373 g/cm3.26 P The value of ρP,MM (or, equivalently, of FFV0P,MM or of ρM) is an essential input for the subsequent calculations of gas solubility and diffusivity into the composite membranes. Such a value can be estimated, either directly by measuring the composite matrix density ρM and using eq 2, or indirectly from solubility data, as indicated below. Solubility of Composite Membranes. Also in the case of solubility, a semiadditive rule is considered. In particular, the mass of penetrant absorbed in the MMM per unit mass of total solid, ΩM, is evaluated by considering the mass adsorbed on the pure filler per unit mass of filler, ΩF, and the mass absorbed in the polymeric phase of the MMM per unit mass of polymer, ΩP,MM. One thus obtains Ω M = wF·Ω F + (1 − wF) ·Ω P,MM

0 = DM

(8)

A semiempirical law, based on the free volume theory, is then considered for the corresponding diffusion coefficient in the polymeric phase, D0P, as a function of the FFV of the same phase in the unpenetrated phase of the composite (FFV0P,MM):

(4)

ln DP0 = A −

B FFV 0P,MM

(9)

where A and B are empirical parameters specific for the polymer−gas system considered. Therefore, experimental diffusivity data measured in composite membranes can be simply related to the filler fraction and to the free volume of the loaded polymer phase as follows: 0 = DM

(5)

⎞ 1 ⎛ B exp⎜⎜A − ⎟⎟ τ FFV 0P,MM ⎠ ⎝

−1 ⎛ ⎞ ⎛ Φ ⎞ B ⎟⎟ = ⎜1 + F ⎟ exp⎜⎜A − ⎝ 2 ⎠ FFV 0P,MM ⎠ ⎝

The solubility of the penetrant in the glassy polymer phase of the MMM (ΩP,MM) has a different value from the one measured in the pure polymer, due to the modified density, and can be estimated with the NELF model, as a univocal function of the density of the polymer phase at each pressure. In fact, the NELF model, thoroughly described in previous papers,13,14 indicates that there is a unique relationship between solubility and density of the polymer phase, so that

(10)

By considering the ratio between the diffusivity in the composite and the diffusivity in the unloaded pure polymer, we obtain immediately 0 DM

NELF

Ω P,MM = f (T , p , ρP,MM )

−1 Φ ⎞ 1 0 ⎛ DP = ⎜1 + F ⎟ DP0 ⎝ τ 2 ⎠

32

In the NELF/free volume model for composites, it is assumed that the sorption or adsorption capacity of the filler remains equal to its pure component value (ΩF ≅ ΩF,0) based also on the observation that its value is rather small compared to the polymer sorption capacity and also considering that sorption takes place on the surface of the particles, which is not chemically bound to the matrix. For all practical purposes, however, it is observed that silica has a much lower fluid sorption capacity than the polymer matrix inspected, so that one can neglect it and assume Ω M ≅ (1 − wF) ·Ω P,MM

(7)

DP0

(6)

=

⎡ ⎛ ⎞⎤ 1 1 1 ⎟⎟⎥ − exp⎢B⎜⎜ 0 0 τ FFV P,MM ⎠⎥⎦ ⎣⎢ ⎝ FFV P

(11)

where one only adjustable parameter is present, B, together with the quantity FFV0P, which represents the fractional free

The basic equations and parameters of the NELF model, as well as of the LF equation of state,28−30 are reported in 9245



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initially dissolved in toluene (THF in the case of membranes containing 30% and 50 wt % of silica) to obtain a 2% mol solution: then the desired amount of TEOS was added to this solution, together with DBTDL, which is the catalyst of the sol−gel reaction, water, and ethanol. The molar ratio of water/ ethanol/TEOS was 4:4:1. The resulting mixture was heated at the reflux temperature for 5 h under vigorous stirring, in order to ensure a homogeneous mixing, and finally cast on a clean Petri dish covered with parafilm, to guarantee a slow evaporation of the solvents. SEM Analysis. SEM analysis (Quanta 200, FEI, USA) was carried out on hybrid membranes. Little slices along the thickness and on the surface were obtained, and successively they were made conductors by sputtering deposition of about 10 ng of gold through an EMITECH K 550. For the quantitative characterization of the size of the particles formed and for the estimation of the thickness, the SEM images were elaborated with the software ImageJ. Thermal Analysis. Thermogravimetric analysis (TGA) and differential thermal analysis (DTA) tests were simultaneously performed on the membranes produced (Netzsch, model STA 409 CD). The samples (about 20 mg) were heated in air up to 800 °C with a heating rate of 20 °C/min. The analysis allowed to determine precisely the amount of residue at 700 °C, and then to estimate the real filler content in the composites. Density Measurements. The pycnometric density of polymeric and hybrid membranes was determined with a gas displacement pycnometer by Micromeritics, mod. Accupic 1330. This apparatus allows one to measure the volume of a sample by measuring the volume of helium displaced by the sample through a calibrated expansion volume. For every measurement, 10 conditioning cycles were made. It must be mentioned that in the literature the values for PTMSP density range from 0.60 to 1.1 g/cm3. This broad range is due to the fact that in ultra high free volume glassy polymers like PTMSP, the density measured with helium pycnometry (referred to as pycnometric density) is much larger than the so-called geometric density, which can be determined as the ratio between the polymer mass and the external volume of the polymer sample, or with the measurement of the buoyancy force exerted by a nonwetting fluid.33,34 Volkov et al. measured the density of PTMSP using a flotation method with both a nonwetting liquid (water) and a wetting liquid (methanol, ethanol).35 The lower density value experienced (0.75 g/cm3) gives the geometric density, while the highest value, measured in the wetting liquid, provides the pycnometric density, which is slightly above 1 g/cm3. It is self-evident and generally accepted that the geometric density is a much more appropriate value than the pycnometric density for the estimation of the free volume of the polymer and of all the related mass transport properties. Indeed the internal free volume regions accessed by helium during a pycnometric measurement, and not accounted for in the polymer volume, are actually available for the vapor sorption by the polymer. However, the pycnometric density was measured in this work, as it provides reliable and accurate values based on which one may obtain relative density variations between polymer and composite samples. However, in view of the previous considerations, the pycnometric density was not used as the absolute density value to be used in (or compared to) model calculations but just to assess the relative variation of polymer density after incorporation of silica.

volume of the pure unloaded polymer, generally known from independent sources, through either direct measurement or literature data. The permeability can then be estimated according to the solution-diffusion theory. Previous Results on Mixed Matrix Membranes. This class of PTMSP/FS membranes can be obtained by adding the desired amount of silica nanoparticles (up to 50% in weight) to a dilute polymer solution (1−2 wt %) and then mixing with a blender at high speed.5 The membrane is then obtained by slow evaporation of the solvent from the solution. The transport properties of mixed matrix membranes based on PTMSP and nanoscopic, hydrophobic fumed silica of diameter 13 nm were tested thoroughly by Merkel et al.5 Although the authors did not provide density measurements of the composite membranes, they indicated that the polymer free volume is augmented by the presence of silica, as proved also by the increase in the gas permeability, diffusivity, as well as solubility, for all gas species inspected. The gas solubility data obtained by Merkel et al. have been analyzed by using the NELF model for the polymer phase, and it was found that, by calculating the polymer density through the methane solubility values, the density of the polymeric phase of PTMSP/FS membranes decreases almost linearly with increasing the amount of fumed silica.13 In particular, the density of the polymeric PTMSP phase in the mixed matrix membranes is estimated to be equal 0 to 0.718 g/cm3 (FFVP,MM = 0.320) for mixed matrices containing 30% FS and equal to 0.680 g/cm3 for matrices loaded with 50% FS (FFV0P,MM = 0.356), while the density of pure PTMSP is equal to 0.75 g/cm3 (FFV0P,MM = 0.290).13 Such values represent properties of the polymer phase in the mixed matrix state and thus are enabled to describe also the solubility of other gases such as N2, C2H6, C3H8, and n-C4H10, as well as the corresponding diffusivity data according to an exponential law based on the free volume theory (eq 11).13 The behavior and properties of PTMSP/FS membranes will be compared to the one of the hybrid PTMSP/SiO2 membranes inspected in this work.

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EXPERIMENTAL AND MATERIALS Materials. Poly(trimethylsilyl propyne) was purchased by Gelest Inc. (Morrisville, PA, USA). It belongs to the family of so-called superglassy polymers, because it shows a rather rigid structure, very high glass transition temperature, and free volume. The exact value of Tg cannot be measured, because the polymer undergoes a thermal decomposition before reaching Tg: indicatively, Tg is higher than 300 °C. This polymer shows, at the same time, a very low density due to the wide fractions of free volume trapped in its glassy structure. The average fractional free volume (FFV), estimated using eq 3, and considering the density of pure PTMSP equal to 0.75 g/cm3 is equal to 28.5%. Nevertheless, different values can be found in the literature, ranging from 27 to 30%, due to the dependence of density on the thermo-mechanical history of the sample. Tetraethoxysilane, dibutyl tin dilaurate (DBTDL), ethanol (purity >99.8%), and THF were purchased by Sigma Aldrich and used as received to prepare HMs. Finally, n-butane and n-pentane (Carlo Erba, purity >99.6%) were used for sorption experiments as received, without any further treatment. Hybrid Membranes Fabrication. Hybrid membranes containing 10, 20, 30, and 50% in weight of silica were fabricated with the following protocol. The polymer was 9246



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Figure 1. SEM micrographs for hybrid PTMSP/SiO2 membranes. (a) PTMSP+10 wt % SiO2 (surface), (b) PTMSP+10 wt % SiO2 (cross section), (c) PTMSP+20 wt % SiO2 (surface), (d) PTMSP+20 wt % SiO2 (cross section).

Vapor Solubility Measurement. Solubility experiments were performed by using normal butane and normal pentane as penetrants, at 25 °C, in a constant volume/variable pressure device (pressure decay)11 by increasing the vapor partial pressure in a stepwise manner up to 1 bar. The vapor activity is evaluated, assuming the vapor phase as an ideal gas, as the ratio between the vapor absolute pressure and its vapor pressure at the same temperature. The penetrant diffusivity in the film can be evaluated from the sorption kinetics, by considering Fickian diffusion and taking into account the variation of interfacial concentration during the experiment due to the limited volume of the apparatus. The expression for the mass uptake as a function of time in every differential step, Mt, in a limited volume where the variation of the interfacial concentration is due to mass sorption in the membrane, is given by36 M t − M0 =1− M∞ − M 0

∞

∑ n=1

2α(1 + α) −Dqn2t / l 2 e 1 + α + α 2qn2

gaseous phase and the polymer, l is the semithickness of the membrane, while qn represents the positive, nonzero solutions of the equation: tg(qn) = −α·qn. By fitting the experimental data of mass uptake versus time to eq 12, one obtains the average diffusivity value for the concentration interval inspected in the differential sorption step. The permeability isotherms can then be estimated as the product of diffusivity and solubility coefficient evaluated during a differential sorption step, according to the solution-diffusion model. In particular, following such a procedure one has P=

J pI − pII δ

=

C I − C II δ pI − pII

D

δ

=D

C I − C II pI − pII

(13)

where δ indicates the membrane thickness, D is the average diffusivity estimated according to eq 12 in the differential sorption step between initial pressure pI and final equilibrium pressure pII, and CI and CII are the initial and final equilibrium concentration values in the membrane, respectively. The permeability value thus calculated practically corresponds to the one measured during a permeation experiment in which the downstream and upstream pressure are equal to pI and pII, respectively, as long as the differential pressure step is sufficiently small.

(12)

where M0 and M∞ are the initial and final mass uptake in the differential sorption step, respectively, α is the ratio between the volume of the external solution and that of the membrane, corrected for the partition coefficient of vapor between the 9247



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Figure 2. SEM micrographs for hybrid PTMSP/SiO2 membranes. PTMSP+30 wt % SiO2 (a, b) cross section, (c, d) upper membrane surface.

Figure 3. SEM micrographs for hybrid PTMSP/SiO2 membranes. PTMSP+50 wt % SiO2 (a, b) cross section, (c, d) upper membrane surface.

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EXPERIMENTAL RESULTS

domain morphology with increasing the amount of silica. It must also be reminded that different solvents were used for the preparation of samples with lower amounts of silica, which also may cause some differences in the domain dispersion. For the

SEM Analysis. The SEM analysis was performed on samples containing a nominal amount of silica of 10%, 20%, 30%, and 50 wt %, in order to establish the evolution of the 9248



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particles than the ones with lower silica loading. We must remind however that such samples were dissolved in THF, and they seem to have a better morphology than the ones with a lower content of silica, which were dissolved in toluene, maybe due to an effect of the solvent polarity and volatility on particle dispersion. In particular, THF has a higher polarity and a lower boiling point than toluene; this latter aspect may indicate that a faster evaporation of the solvent may avoid the possible agglomeration of silica particles during the solvent casting step. The SEM analysis allowed also estimation of the filler particles dimension for the membranes filled with 30% and 50 wt % silica, while the aggregates in the samples with lower amounts of silica were not analyzable for this purpose. This estimation was made by measuring the main dimension of 110 particles: the results indicate that the average diameter of silica aggregates is 1.2 μm, which is much larger than the one usually found in MMMs, where the dimensions of fumed silica domains are around 100−150 nm.7 However, this result is in line with what was obtained by Gomes et al.,21 who fabricated hybrid PTMSP/SiO2 membranes with the same THF solvent used in the fabrication of the highly loaded samples in this work, but with a lower content of silica (about 6%) and observed a size of silica particles between 0.6 and 1.9 μm. It seems therefore that the size of the silica domains is not a stringent function of the silica fraction, but rather of the solvent and protocol used in the preparation. Whether this is due to the solvent polarity, or to its volatility, or to other aspects is not yet clear and will be the object of future studies.

Table 1. Average Particle Size of Silica Domains and Thickness of the Hybrid Membranes, Determined by SEM Analysis membrane PTMSP+10 PTMSP+20 PTMSP+30 PTMSP+50

wt wt wt wt

% % % %

solvent SiO2 SiO2 SiO2 SiO2

toluene toluene THF THF

particle average size (μm)

1.3 ± 0.4 1.2 ± 0.6

membrane thickness (μm) 133 130 220 190

± ± ± ±

14 5 30 8

samples PTMSP+10 wt % SiO2 and PTMSP+20 wt % SiO2 prepared with toluene, the SEM micrographs showed the presence of a high number of rather large aggregates, both on the surface and in the cross section (Figure 1a−d). In the samples with higher silica content, PTMSP+20 wt % SiO2, the materials presented a fragile fracture in the areas with the higher concentration of silica (Figure 1c, d). On the other hand, the samples with the higher content of silica (30 wt % and 50 wt %), for which micrographs are reported in Figures 2 and 3, respectively, seem to show a much better dispersed morphology, with smaller silica domains. In particular, the sample with 50 wt % SiO2 shows a lattice structure where the silica particles represent the nodes. Such membrane, probably due to precipitation of a silica-rich phase on the bottom of the sample, had a thin bottom layer which detached from the upper part of the sample and was not used for the sorption experiments but just for density measurements. It is somehow surprising to notice that the samples with the higher amount of silica (30 and 50 wt %) have smaller silica

Figure 4. TGA and DTA results for PTMSP hybrid matrices loaded with (a) 10 wt % silica, (b) 20 wt % silica, (c) 30 wt % silica, and (d) 50 wt % silica. 9249



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Table 2. Density of the Membranes sample

pycnometric density (g/cm3)

PTMSP silica gel (from sol gel of pure TEOS) PTMSP+10 wt % SiO2 PTMSP+20 wt % SiO2 PTMSP+30 wt % SiO2 PTMSP+50 wt % SiO2 Fumed Silica (FS) PTMSP+30 wt % FS PTMSP+50 wt % FS

0.990 ± 0.0035 1.66 1.06 ± 0.01a 1.17 ± 0.01a 1.26a 1.44a

calculated additive density (g/cm3)

a

geometric density (g/cm3) 0.755

1.032b 1.077b 1.126b 1.240b 0.935d 1.119d

0.780c 0.843c 1.021c 2.25 0.900e 1.040e

a

Measured in this work with helium pycnometry. bCalculated by considering pycnometric densities (PTMSP: 0.990 g/cm3; SiO2 = 1.66 g/cm3). Calculated from n-butane solubility data in HMs and NELF model (this work). dCalculated by considering geometric densities (PTMSP: 0.75 g/ cm3; FS = 2.2 g/cm3). eCalculated from methane solubility data in MMMs and NELF model.13 c

seen that the pycnometric density values measured for the density of PTMSP/silica hybrid membranes are systematically higher than those estimated from the additive rule. In Table 2, we have reported also geometric density data for mixed matrix membranes based on PTMSP and fumed silica, prepared in the work of Merkel et al.5 In the absence of experimentally measured density data for such mixed matrices, we reported for pure PTMSP the value given by the authors, which can be considered as a geometric density (0.75 g/cm3), and for the mixed matrices the values estimated in a previous work by using the methane sorption isotherms from ref 5 and the NELF model, that are also to be considered as geometric densities.13 It can be immediately noticed from the table that the mixed matrix density values are smaller than the ones estimated using volume additivity, which is opposite to the behavior shown by hybrid membranes. This aspect can be clearly visualized by reporting, as in Figure 5, the relative mixing volume of the polymer/silica mixture, which is positive for the mixed matrix membranes and negative for the hybrid membranes. Therefore, by considering that the silica phase volume remains unvaried with respect to its pure state, which is rather reasonable, it can be stated that the direct incorporation of fumed silica nanoparticles into PTMSP enhances the free volume, by creating additional void pockets, probably preferentially located at the interface between silica and polymer chains. On the other hand, the generation in situ of silica domains via sol−gel reaction reduces the free volume of the polymer, through a mechanism which is not yet clearly documented. However, it can be hypothesized that such a mechanism involves filling of the free volume pockets of PTMSP by means of the silica phase which is formed and, more likely, mechanical constraints on the polymer chains exerted by the silica domains. Indeed, the silica domains generated in situ can be more prone to form a network in which the polymer chains may be trapped, as shown for instance by the SEM pictures of the highly loaded silica membranes. It is indeed known that hybrid organic/inorganic materials obtained via the sol−gel technique show extremely good interpenetration between the polymer and the inorganic phase, which often guarantees good properties to such structures, especially when gas barrier properties are desired.18−20 Solubility in Hybrid PTMSP/SiO2 Membranes. Sorption experiments were performed using n-butane and n-pentane vapors as penetrants at 25 °C. The experimental solubility isotherms for n-butane and n-pentane are reported in Figure 6 as a function of penetrant activity. In Figure 6a and b, we report the data directly measured by the pressure decay apparatus per

Figure 5. Relative mixing volume of hybrid matrices PTMSP/SiO2 obtained in this work and mixed matrices PTMSP/FS. Values are estimated using density data reported in Table 2.

The thickness and average particle size values are reported in Table 1. Thermal Analysis. The thermal scans obtained from TGA and DTA scans are reported in Figure 4. The analysis of the results indicates that the real amount of silica is very close to its nominal value with a maximum deviation of 2%. The only exception is represented by the sample with the highest TEOS loading, whose final amount of SiO2 was found to be 39 wt % instead of the calculated value of 50 wt %: however such a deviation was due to a loss of material in the preparation step and not to an incomplete conversion. Such a sample was not used in the measurement of the mass transport properties due to its nonperfect homogeneity. Density. As already mentioned, the pycnometric density of PTMSP assumes values systematically higher than the geometric density, as often happens for high free volume polymers. The pycnometric density value measured in this work for PTMSP is equal to 0.990 g/cm3. On the other hand, the density which could be estimated from the measurement of sample weight and volume and the one prevailing from literature studies is equal to about 0.75 g/cm3.5 The latter value (geometric density) will thus be used for modeling purposes. The pycnometric density values will be used only to determine the relative volume variation with the amount of silica added as well as with the type of matrix inspected. For reference sake, in Table 2 the values of pycnometric density are reported, together with the corresponding density calculated with an additive law, considering a value of 1.66 g/cm3 for the pure silica phase density and to 0.990 g/cm3 for PTMSP. It can be 9250



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Figure 6. n-C4 (a) and n-C5 (b) solubility in PTMSP and hybrid PTMSP/SiO2 membranes at 25 °C. n-C4 (c) and n-C5 (d) solubility in PTMSP and in the polymeric phase of hybrid PTMSP/SiO2 membranes at 25 °C. n-C4 and n-C5 solubility in (e) PTMSP and PTMSP+20 wt % SiO2 membranes; (f) PTMSP+10 wt % SiO2 and PTMSP+30 wt % SiO2. Data for n-C4 sorption in pure PTMSP and PTMSP+50 wt % FS mixed matrix membranes are taken from ref 5.

unit mass of composite membrane (g/gsolid): it can be seen that the solubility of both vapors decreases with an increasing amount of silica loaded in the hybrid membrane. In Figure 6c and d, we report the solubility of the membranes per unit mass of the polymer phase only (g/gpol), obtained according to eq 5. That information presents more specifically the variation of the mass sorption of the polymeric phase due to the presence of silica particles in the HM. Interestingly, the solubility in the polymer phase of both penetrants at fixed activity decreases regularly with increasing the amount of silica. This behavior is completely opposite to what was obtained in MMM by adding fumed silica nanoparticles to toluene solutions of PTMSP, in which the absorption capacity of the polymer phase increased with an increasing amount of silica. On the other hand, the reported behavior of the hybrid membranes is perfectly consistent with what was observed with

density measurements, i.e., a contraction of the polymer specific volume which reduces the solubility in the matrix. It is interesting to notice that the hybrid membrane maintains the solubility selectivity with respect to the larger molecules: indeed in all cases the solubility of n-C5 is larger than the solubility of n-C4 at fixed activity, as shown in Figure 6e and f. The vapor selective behavior is typical of PTMSP and is kept unvaried, at least qualitatively, by the hybrid matrices at all loadings. That is important as the addition of silica is often noticed to modify the selectivity behavior. Diffusivity in Hybrid PTMSP/SiO2 Membranes. The effects of the filler loading on the diffusivity of n-butane and npentane in hybrid membranes are qualitatively similar to those observed for solubility; indeed, the effective diffusivity systematically decreases when the filler fraction increases, as shown in Figure 7. The data relative to n-C4 diffusivity are compared to 9251



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Figure 7. Experimental diffusivity isotherms in HMs: (a) n-C4; (b) n-C5. Data for n-C4 diffusivity in pure PTMSP and PTMSP+50 wt % FS mixed matrix membranes are taken from ref 5. Data are taken at 25 °C.

Figure 8. Experimental permeability isotherms in HMs: (a) n-C4; (b) n-C5. Data for n-C4 permeability in pure PTMSP and PTMSP+50 wt % FS mixed matrix membranes are taken from ref 5, where solubility and diffusivity data were digitized and elaborated according to eq 13. All data taken at 25 °C.

as is apparent from Figure 8. The permeability values show a decreasing trend with vapor activity, in the range inspected: this behavior is quite usual in high free volume polymers like PTMSP. By considering the infinite dilution permeability data, and in particular the relative permeability variation induced by filler addition, P0M/P0P, the behavior of the different types of matrices is immediately pointed out in Figure 9, which shows the permeability of n-C4 at 25 °C as a function of silica weight fraction both in mixed matrix membranes containing PTMSP and fumed silica,5 as well as in hybrid matrices based on PTMSP and SiO2 obtained via sol−gel from TEOS. In the same figure, also data from ref 21 and relative to HM samples are reported for comparison. The plot also reports the prediction of Maxwell’s model for the permeability variation with composition: clearly, that model overestimates markedly the data relative to hybrid matrices and at the same time largely underestimates the behavior of mixed matrix membranes. Comparison with Model Calculations. Solubility. The comparison between the NELF model predictions and the solubility isotherms of n-C4 and n-C5 in the hybrid membranes prepared in this work is shown in Figure 10. The parameters used for the model are reported in Table 3: the pure component lattice fluid parameters are taken from previous works, while the polymeric phase density values for the hybrid membranes are adjusted on the experimental solubility data. Density data obtained from pycnometry indeed were not

Figure 9. n-C4 permeability variation as a function of silica mass fraction in composite PTMSP membranes obtained via direct incorporation of fumed silica (MMMs) and via sol−gel from TEOS (HMs). Comparison with Maxwell’s model prediction and literature data5,21 are also shown.

the ones obtained by Merkel et al.5 in mixed matrix membranes with increasing amounts of fumed silica. Although the trend of the diffusivity isotherms is similar for all membranes, the mixed matrices show higher diffusivity values with respect to hybrid membranes and to pure PTMSP itself. Permeability. The permeability in hybrid PTMSP/SiO2 membranes undergoes a systematic decrease with silica content, 9252



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Figure 10. Comparison between the solubility isotherms of n-C4 (a) and n-C5 (b) in PTMSP/SiO2 hybrid membranes.

Table 3. List of Parameters Used in the Model matrix

ρ* (g/cm3)

T* (K)

p* (MPa)

ρ0P,MM (g/cm3)

FFV0P,MM

0.750 0.770 0.795 0.875

0.290 0.270 0.247 0.171

13

PTMSP PTMSP+10 wt % SiO2 PTMSP+20 wt % SiO2 PTMSP+30 wt % SiO2 penetrant n-C438 n-C511 matrix PTMSP PTMSP+10 PTMSP+20 PTMSP+30 PTMSP PTMSP+10 PTMSP+20 PTMSP+30

wt % SiO2 wt % SiO2 wt % SiO2 wt % SiO2 wt % SiO2 wt % SiO2

1.25

416

405

0.720 0.749 kij

430 451

290 305 ksw (MPa−1)

0

0

0.90 0.20 0.20 0.20 4.00 2.30 1.90 0.80

penetrant

n-C4H10

n-C5H12

Figure 12. n-C4 and n-C5 infinite dilution diffusivity in the hybrid PTMSP/SiO2 membranes versus 1/FFV0. n-C4(b) and n-C5(c) diffusivity variation induced by the addition of silica in hybrid membranes versus their silica content: comparison between experimental data and model values.

Figure 11. Variation of polymer phase relative density with the silica weight fraction in hybrid membranes, as estimated from pycnometric measurements and from NELF model and organic vapor solubility data.

suitable, as explained in the previous section, for the modeling of solubility and transport behavior. From model calculations, one observes that the density of the polymeric phase increases gradually with an increasing amount of silica in the hybrid membrane. Correspondingly, the fractional free volume of the polymer decreases. This is an interesting finding which also indicates that, for hybrid membranes obtained with the present

Figure 13. n-C4 infinite dilution diffusivity in the polymer phase of hybrid PTMSP/SiO2 membranes and mixed matrix PTMSP/FS membranes13 versus 1/FFV0.

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CONCLUSIONS Hybrid glassy membranes based on PTMSP and silica with loadings up to 50% were obtained via sol−gel reaction from TEOS and different solvents. The conversion of silanes to silica is practically complete and the membranes density increases with increasing the amount of silica, indicating a progressive decrease of the PTMSP excess free volume with increasing silica amount. The thermal properties of the membranes are slightly affected by the addition of silica. The size of the silica domains is rather large in the case of membranes loaded with the lower amounts of silica (10% and 20 wt %), which were obtained using toluene as a solvent, while domains in the range of 1 μm are seen with membranes loaded with higher amounts of silica (30 and 50 wt %), which were obtained with THF as a solvent, consistently with literature results. Solubility and diffusivity of n-C4 and n-C5 vapor were measured in the hybrid membranes, and a progressive reduction of solubility, diffusivity, and permeability with increasing silica loading is observed with respect to pure PTMSP. This behavior is opposite to what is observed in mixed matrix membranes where the silica nanoparticles are added via mixing, where both solubility and diffusivity increase due to an increased free volume of the polymer matrix. In hybrid matrices, the polymer free volume is constrained and filled by the silica phase, while in mixed matrices the silica particles create additional free volume. The experimental solubility data were successively compared with the NELF model estimation: the modeling results agree more than satisfactorily with the experimental data. The relative variation of polymer phase density estimated with the NELF model is also in good agreement with the variations in pycnometric density measured in the composite matrices. In addition, also the apparent diffusivity of the composite matrices is strongly correlated to the same FFV obtained from the modeling of solubility data. Finally, by reporting in a single diagram the experimental diffusivity data relative to MMMs and HMs, a unique exponential mastercurve can be drawn which fits reasonably well both series of data, confirming that the NELF/free volume model assumptions can actually explain the behavior of both types of composite membranes. In general, for all the composite membranes based on PTMSP and silica, the results obtained indicate that the solubility and transport behavior depend only on the average fractional free volume in the polymer phase, and no specific information on the size and morphology of the silica domains is required.

protocol, the sorption behavior is a simple function of the silica content and does not require any detailed information concerning size and morphology of the silica domains. The swelling coefficients are also adjusted on the solubility data in an intermediate pressure value, showing that the addition of silica lowers the swelling capacity of the matrix. That is also consistent with the fact that the solubility in hybrid membranes is lower than that measured in the pure polymer. The binary interaction parameter was fixed equal to 0 (default value) for both n-C4 and n-C5 as it is common for this penetrant− polymer couple.38 The relative variation induced by the addition of silica on polymeric density is reported in Figure 11, which displays both the values obtained from the use of pycnometric densities and from densities obtained by using the NELF model and vapor solubility data. It can be seen that a good agreement is evident between the two sets of relative density values, confirming the physical solidity of the model applied. Diffusivity. The density values obtained from solubility data in HMs allow the estimation of the FFV in the polymeric phase for each kind of membrane at different filler contents. The FFV can be then used to correlate the experimental diffusivity data obtained from sorption kinetics. In Figure 12, the diffusivity in the polymeric phase of the membrane (D0P = τD0M in the model) for n-butane is reported as a function of the reciprocal FFV, where D0M is extrapolated from experimental diffusivity data and τ is calculated on the basis of Maxwell’s model. The good linear correlation existing between the diffusivity and the reciprocal FFV is consistent with the free volume theory: in particular, the diffusivity at infinite dilution follows a linear decrease with the reciprocal FFV with a correlation coefficient R2 equal to 0.94 and 0.98 in the case of n-C4 and n-C5, respectively. These findings confirm that the NELF free volume model describes reasonably well both the case of mixed matrix membranes, as already shown in previous works,11,13,15−17 and hybrid membranes. It is also possible to estimate the ratio between the diffusivity in filled and pure PTMSP, D0M/D0P, for different penetrants, using the values of parameter B obtained for each penetrant at a fixed temperature, as the slope of line which best interpolates D0P as a function of FFV−1. The results of the model calculations are indeed in good agreement with the experimental evidence: in particular, in HMs a progressive decrease of diffusivity is noticed with filler loading. Moreover, by plotting the diffusivity data of both hybrid and mixed matrix membranes in a single plot (Figure 13), versus the reciprocal of the polymer FFV, it can be noticed that the data can be reasonably correlated by a single mastercurve to a value of R2 of about 0.91. That is particularly significant and suggests that the different behaviors observed in MMMs and HMs have the same nature and are related to the effects induced by the inorganic filler on the polymer fractional free volume. Such effects are of opposite sign in MMMs and HMs and thus determine the opposite features observed for MMMs and HMs in mass transport phenomena. This result indicates clearly that only average fractional free volume is required to describe average diffusivity, solubility and permeability in the composite matrices, without the need of any information about size and morphology of the silica domains or of the FFV domains.

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ASSOCIATED CONTENT

S Supporting Information *

Table A: NELF model parameters and equations. This information is available free of charge via the Internet at http://pubs.acs.org/.

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]. Present Address §

Department of Chemical Engineering, The University of Texas at Austin, Austin, Texas, United States Notes

The authors declare no competing financial interest. 9254



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ACKNOWLEDGMENTS Partial support from the University of Bologna and from the University of Modena-Reggio Emilia is gratefully acknowledged.

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