Gas and Vapor Transport in Mixed Matrix Membranes Based on

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Ind. Eng. Chem. Res. 2010, 49, 11920–11935

Gas and Vapor Transport in Mixed Matrix Membranes Based on Amorphous Teflon AF1600 and AF2400 and Fumed Silica M. C. Ferrari, M. Galizia, M. G. De Angelis, and G. C. Sarti* Dipartimento di Ingegneria Chimica, Mineraria e delle Tecnologie Ambientali (DICMA), Alma Mater Studiorum-UniVersita` di Bologna, Via Terracini 28, 40131 Bologna, Italy

The enhancement of gas and vapor transport rates induced by the addition of fumed silica nanoparticles to fluorinated glassy polymers is interpreted and quantitatively modeled considering the additional free volume created by incorporation of filler. That effect can be evaluated accurately from gas solubility data, using the NELF model. The solubility of CH4 and CO2 in matrices of Teflon AF1600 and AF2400, filled with variable amounts of fumed silica nanoparticles, was measured at 35 °C; the solubility of n-C4 and n-C5 vapors, as well as their diffusivity and the dilation induced in the same polymer matrices, was also measured at 25 °C. The fractional free volume (FFV) values, estimated on the basis of CH4 solubility data, were used to predict the solubility of the other penetrants inspected, with excellent agreement with experimental data. In addition, a single empirical correlation can be drawn, for both AF1600 and AF2400-based mixed matrices, between the infinite dilution diffusivity of vapors and the FFV value calculated from solubility data. Similarly, a simple correlation valid for both matrices is obtained as well for the dependence of diffusivity on penetrant concentration. Finally, use of the NELF model also allows an estimate of the swelling induced by the sorption process on the basis of virtually one simple data point of gas solubility. Introduction The easy processability of polymeric membranes would favor their employment in the large scale production of gas separation modules. On the other hand, their separation ability is low compared to more rigid molecular-sieves media that have still extremely high costs of production. Dispersing an inorganic selective phase in a polymeric membrane1 may lead to composites that merge the peculiar characteristic of both materials, achieving an important improvement in the modules performance. These composites are conventionally called mixed matrix membranes (MMM) and are obtained by the addition of an inorganic phase such as zeolites, carbon molecular sieves, or silica particles, into a polymeric matrix such as polyimides, polysulphone, amorphous Teflon, PTMSP, and PMP that already shows a good selective behavior.1–3 In the case of the addition of nonporous nanosized particles to high-free-volume glassy polymeric matrices,2,3 the filler does not contribute to transport directly, because it is actually impermeable, but it changes the molecular packing of the polymer chains, resulting in an improvement of the permeation and, in some cases, of the separation properties of the glasses. Measurements of gas transport in Teflon AF2400 loaded with nonporous hydrophobic fumed silica (FS) nanoparticles show3 an increase in gas permeability due to the inorganic filler, and this enhancement is even more pronounced for larger penetrants, leading to a drop in the size selectivity of the composite. The sorption isotherm, reported as mass of penetrant per unit mass of membrane, is not affected much by the presence of the inorganic filler, while the diffusion coefficient is significantly increased by the addition of nanoparticles and causes the increase in permeability. Since a penetrant is adsorbed only on the surface of nonporous fumed silica, the observed sorption behavior can be ascribed to the packing structure of the polymeric matrix which is modified by the filler: the sorption capacity of the polymer increases, compensating for the lower sorption in the volume occupied * To whom correspondence should be addressed. E-mail: [email protected].

by the impermeable particles. The introduction of an inorganic filler in an organic material creates additional free volume close to the interface between the two phases. In the case of glassy phases loaded with nanoparticles, such an effect apparently causes a local increase of solubility in the polymeric phase, which practically compensates for the reduced sorption capacity of the filler, so that a minor influence on the total sorption behavior is observed; on the other hand, a high impact is produced on diffusivity, which is much more sensitive to FFV and turns out to increase even in the presence of obstacles on the diffusive path of the penetrant molecules. From positron annihilation lifetime spectroscopy (PALS) measurements, it is known that there are two different populations of nanovoids in high-free-volume glassy polymers; the addition of FS further increases both the size of larger holes and their fraction.2-3 The NELF model for solubility4,5 was recently applied6 to predict the enhancement in diffusivity due to the addition of fumed silica nanoparticles to high-free-volume matrices as PTMSP and Teflon AF 2400, accounting for the contribution to permeability of diffusivity and solubility separately. In this work, mixed matrices based on amorphous Teflon AF2400 and AF1600 were tested extensively with different penetrants, in order to obtain experimental values for all the relevant transport properties; the method based on the NELF model was then applied to describe the experimental data and predict gas separation performance of the membranes for different penetrants. The procedure followed enables us to obtain the relevant transport properties in MMM on the basis of rather limited experimental data, contrary to what has been the current practice thus far. In fact, solubility isotherms for all gases and vapors can be obtained from the isotherms of a single test gas, plus one single data point at high pressure, for swelling penetrants; for the diffusion coefficients, the results obtained indicate that the infinite dilution diffusivity is a function of the FFV of the

10.1021/ie100242q  2010 American Chemical Society Published on Web 04/09/2010

Ind. Eng. Chem. Res., Vol. 49, No. 23, 2010

polymer phase of the MMM, obtained separately from the solubility isotherms. Theoretical Background The selectivity Rij between two penetrants i and j is usually used to evaluate the performance of a membrane in gas separation. When the downstream pressure is significantly lower than the upstream value, the selectivity is expressed as Ri,j )

Pi Di Si ) RDRS ) Pj Dj Sj

(1)

where Pi is the permeability of the ith penetrant and can be calculated from diffusivity, Di, and solubility coefficient, Si, on the basis of the solution-diffusion model and of Fick’s law for the diffusive mass flux. To our knowledge, no models have been proposed thus far that can predict correctly the mass transport properties of composite materials, including those containing high-freevolume glassy polymers; such a tool would be particularly useful to calculate the permeation and selectivity behavior for different filler loading and different penetrants, starting from a rather reduced set of data, thus decreasing the amount of experimental work needed for every new combination of filler particles, polymers, and penetrants. On the contrary, the models available consider just permeability and, in particular, they predict a decrease in permeability as rigid particles are added to the matrix, due to the increase in the tortuosity of the path followed by the penetrant molecules during the diffusion through the membrane. One of the most widely used is the Maxwell model,7 initially derived for the permittivity of a dielectric composite, that is certainly not applicable to the case of amorphous Teflon loaded with fumed silica. A new method6 has been recently developed, based on the NELF model for solubility, that can predict the behavior of solubility and diffusivity separately from which the permeability can be reliably calculated; that procedure will be briefly recalled hereafter and applied to the MMM considered in the present work. NELF Model. The NELF model4,5,8 can be used to calculate the sorption isotherm in glassy polymers since it relates with an explicit expression the penetrant solubility and the glassy polymer density. It is based on the nonequilibrium thermodynamics for glassy polymers (NET-GP) approach9 that extends the lattice fluid (LF) equation of state10 for amorphous phases to the nonequilibrium states typical of glassy polymers. In this framework, the properties of pure components are calculated using the same characteristic parameters (p*, F*, T*) of the Sanchez and Lacombe theory10 and the mixture properties are obtained through the mixing rules of the same model.11 The pure components characteristic parameters can be calculated fitting the LF equation to PVT data above Tg for the polymer and to either PVT or vapor-liquid equilibrium data for the penetrant. The number of lattice sites occupied by a molecule in its pure phase, ri0 is given by10 ri0 )

Mi p*M i i ) RT*F F*V i * i i * i

(2)

where Mi is the molar mass of component i and V*i is the volume occupied by a mole of lattice sites of pure substance; ri0 is usually set to infinity for the polymer species. The mixture characteristic parameters can be calculated through a mixing

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rule with only one adjustable binary parameter, Ψ, affecting the binary characteristic pressure p*12 that represents the energetic interactions per unit volume between gas and polymer molecules:11 p*12 ) Ψ√p*11p*22

(3)

A first order approximation can be used setting Ψ ) 1 when no specific data for the mixture are available. To describe the properties of glassy phases, the polymer density F2 is also needed besides the usual state variables (temperature, pressure, and composition), and that is the only quantity that can account for the departure from equilibrium. Under weak conditions, the following general results are obtained: (i) The phase equilibrium conditions are obtained when the chemical potential of the penetrant, subscript 1, in the external gas phase and in the mixture with the glassy polymer are equal: PE Eq(g) µNE(s) (T, p, ΩPE (T, p) 1 1 , F2 ) ) µ1

(4)

where the superscript PE stands for pseudoequilibrium conditions, and Ω1 represents the penetrant to polymer mass ratio. (ii) the chemical potential in the solid, nonequilibrium glassy phase is defined as µNE(s) ) 1

( ) ∂Gtot ∂n1

(5)

T,P,n2,F2

and is given by an explicit expression.4,5 To calculate solubility isotherms in glassy phases, one thus needs to use the values of the characteristic parameters of the pure components, that may be found in specific collections, and the density of the glassy polymer, F2, which depends on the experimental conditions and on the history of the samples. For nonswelling penetrants, the density of the membrane at every pressure can be considered equal to its initial value; in the case of swelling agents, information on the density of the membrane at every pressure condition can be retrieved from parallel dilation experiments. Dilation isotherms are not so commonly available or measured; however, it has been seen12–14 that in most cases there is a linear dependence of the polymer density on the partial pressure of the swelling penetrant, and therefore a swelling coefficient, ksw, can be used to account for volume dilation: F2(p) ) F20(1 - kswp)

(6)

where F20 is the density of the pure unpenetrated glassy polymer. Considering this behavior, in the absence of specific dilation data, the parameter ksw can be adjusted virtually on one only solubility datum at high pressure, providing also an estimate of the swelling isotherm of the matrix at all other pressures, through eq 6.15 Using eq 6 with eq 5, the equilibrium condition between an external gas and the glassy phase contains the two polymer parameters F20 and ksw, and is thus of the following type: 0 Eq(g) µNE(s) (T, p, ΩPE (T, p) 1 1 , F2 , ksw) ) µ1

(7)

NELF-Based Modeling of Gas Transport in Mixed Matrix Membranes. Solubility. The NELF model can be applied to calculate sorption isotherm of composite glassy matrices considering separately the contributions of the two phases: the total solubility

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can be decomposed into the sum of two contributions, one due to the polymeric phase and one due to the filler: Ci,M )

ni,F + ni,P ) ΦFCi,F + (1 - ΦF)Ci,P V

(8)

where ΦF is the volume fraction of the filler, Ci,M is the gas solubility per unit volume of unpenetrated mixed matrix, and Ci,F and Ci,P are the gas solubilities in the filler and in the polymer, per unit volume of unpenetrated filler and per unit volume of unpenetrated polymer, respectively. (For simplicity sake we used the notation of eq 8 even though in most cases the contribution of the filler is due to surface adsorption with surface concentration qi,F and surface area per unit volume aF′′′, so that Ci,F ) aF′′′qi,F.) For most common composites, the sorption capacities of the polymer and the filler in the composite material are considered unaffected by the transformation from the state of pure components to that of mixed matrix and therefore a simple additive rule is commonly employed. However, mixed matrices of high-free-volume glassy polymers and impermeable nanofillers do not show this simple behavior because the addition of the inorganic rigid phase affects the actual density of the polymer and its swelling conduct. Defects at the polymer/filler interface lead to a higher FFV that can be attributed completely to the polymer phase. The sorption or adsorption capacity of the filler is typically rather small compared to the total solubility and, also, the process takes place on the surface of the particles which is not chemically bound to the matrix; thus it is reasonable to assume that no appreciable changes in the penetrant uptake onto the inorganic filler take place, with respect to the pure solid state, which can be written as follows: Ci,F ) Ci,F0

(9)

Equation 8 thus becomes: Ci,M ) ΦFCi,F0 + (1 - ΦF)Ci,P

(10)

The solubility isotherm, Ci,P of the penetrant in the glassy polymer phase of the MMM can be obtained from eq 10, using the experimental values of the solubility in the MMM, Ci,M, and in the pure filler, Ci,F0 at each pressure. The value of Ci,P can also be predicted through the NELF model, once the density F2 of the polymer phase is known: in the low pressure range one can use the density F20 of the pure unpenetrated polymer phase of the MMM, as long as volume dilation can be neglected, while, in the general case, one has to use the actual dilation isotherm or eq 6. Unfortunately, it is not easy to measure the density of the polymer phase in a mixed matrix condition, and only very rare data are available in the open literature. For this reason, experimental solubility data on one model penetrant are required to determine F20: in particular, its value is adjusted, in the NELF model, in order to match the low pressure solubility data of the model penetrant in the polymeric phase, Ci,P, obtained from eq 10. In the case of significant dilation, also the swelling coefficient has to be adjusted to obtain the best fit of the model curve to the experimental solubility isotherms in the polymer phase: unlike F20, this is a penetrant-dependent parameter, that is derived by considering just the data at high pressure,15 where dilation is larger and perceptible. The unpenetrated density of the polymeric phase is obviously the same for all the penetrants, and the value calculated for the test gas can be used to predict the solubility of all the other

solutes in the same mixed matrix in the low pressure range where the swelling is not relevant. The swelling coefficient, on the contrary, is related to the specific penetrant-polymer pair and to obtain its value a solubility datum at relatively high pressure is needed15 for the specific penetrant considered. One can thus calculate the swollen value of the polymer density F2 from the NELF model, finally obtaining ksw by applying eq 6. From the value of the unpenetrated polymer density, one can immediately calculate the fractional free volume as follows: FFV )

0 V2 - 1.3VW FW 2 2 - 1.3F2 ) V2 FW 2

(11)

where V2Wand F2Ware the van der Waals specific volume and density of the repeating unit of the polymer, respectively, that can be calculated with the group contribution method.16 The fractional free volume is calculated with respect to the occupied volume, estimated as 1.3V2W, according to Bondi’s rule.16 Such values are already available for the matrices here of interest; in particular for AF1600 one has F2W ) 3.380 g/cm3,17 and for AF2400 F2W ) 3.322 g/cm3.6 In summary, the procedure proposed to calculate the solubility isotherms of gases and vapors in glassy mixed matrix membranes formed by loading a nonporous nanoparticle filler is based on the following steps: (a) select a test penetrant, possibly nonswelling, and measure the solubility isotherms in the MMM, Ci,M, as well as the adsorption isotherm, Ci,F0, onto the pure filler; (b) use eq 10 to calculate the solubility isotherm of the test penetrant in the polymer phase of the MMM, Ci,P; (c) use the NELF model to retrieve the unpenetrated polymer density F20 of the polymer phase of the MMM, from the solubility isotherm Ci,P; (d) use the NELF model, with F20 as input, to calculate the solubility isotherms of any other penetrant of interest: in the low pressure range, or in the entire pressure range, for nonswelling solutes; (e) to complete the solubility isotherm for swelling gases and vapors in the entire pressure range, measure the solubility value at least at one relatively high pressure and repeat steps a-c above to get the value of the polymer phase density, F2, at the pressure considered; (f) use the values of F2 and F20 calculated above to obtain, from eq 6, the swelling coefficient ksw of the penetrant considered; (g) use ksw and F20 to complete the solubility isotherm of the swelling gas or vapor of interest. Diffusivity. It has been seen6 that the influence of the penetrant concentration on the diffusion coefficient in composite membranes can be well represented by an exponential law of the following type: Di,M ) Di,M(0) exp(βCi,P)

(12)

where Di,M(0) is the infinite dilution diffusion coefficient in the mixed matrix, Ci,P the average concentration of penetrant in the polymer phase, and β is a temperature-dependent parameter, characteristic of the polymer-gas couple. Considering only the infinite dilution diffusivity Di,M(0), the swelling effects due to Ci,P can be ignored, and the effects of the characteristics of the mixed matrix alone, that is, FFV and tortuosity, can be isolated and analyzed. The presence of the filler influences the infinite dilution diffusion coefficient of the mixed matrix in two ways: (i) the particles are impermeable and act as obstacles on the path of the gas molecules through the membrane, and this factor reduces the diffusivity; (ii) the nanofiller induces a higher FFV in the polymeric matrix, and this effect enhances diffusivity.


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For the first effect, Di,M(0) is an apparent diffusion coefficient that can be related to the corresponding value of the polymer phase, Di,P(0), using a tortuosity factor τ 1 Di,M(0) ) Di,P(0) τ

(13)

where τ can be evaluated from the Maxwell model17 actually derived for spherical particles: τ)1+

ΦF 2

(14)

Figure 1. Scheme of the modeling approach used for the mixed matrices transport behavior.6

A semiempirical law, based on the free volume theory,18 is usually considered for the infinite dilution diffusion coefficient in the polymeric phase, Di,p(0), as a function of the FFV of the same phase: ln(Di,P(0)) ) A -

B FFVM0

(15)

where A and B are temperature dependent parameters, specific of the polymer-gas system considered, and FFVM0 is the FFV of the unpenetrated polymer phase of the MMM. Considering the effect of the fractional free volume shown in eq 15, eq 13 becomes Di,M(0) )

(

1 B exp A τ FFVM0

)

Figure 2. Molecular structure of (a) Teflon AF and (b) nonporous fumed silica before and after treatment to have a hydrophobic surface.

(16)

which relates the apparent infinite dilution diffusion coefficient in the mixed matrix to the FFV of the unpenetrated polymeric phase; such a value can be obtained using the NELF model and the procedure recalled previously, based on the solubility data of a test penetrant. Considering experimental data for at least two values of FFVM0, estimated from the sorption isotherm of the reference vapor for two different filler loadings, we can calculate parameters A and B, and eq 16 can then be used to predict Di,M(0) for any other value of filler loading. If we then consider the ratio between the diffusivity in the composite and the diffusivity in the unloaded pure polymer, we obtain

[(

Di,M(0) 1 1 1 ) exp B 0 Di,P(0) τ FFVP FFVM0

)]

(17)

where there is only one adjustable parameter, B, together with the quantity FFVP0, which represents the fractional free volume of the unloaded pure polymer, generally known from the literature. Finally, from diffusivity and solubility values, we can estimate also the permeability through the solution-diffusion model, and the proposed procedure to estimate the transport properties in mixed matrices can be summarized as in the scheme of Figure 1. Experimental Section Materials. Teflon AF1600 and AF2400 are two perfluorinated glassy copolymers obtained by random copolymerization of 2,2bis(trifluoromethyl)-4,5-difluoro-1,3-dioxole (BDD) and tetrafluoroethylene (TFE). In Teflon AF2400 the mole fractions of the two monomers are 87% and 13%, respectively. Its glass transition temperature is 240 °C, and its density is equal to 1.74 g/cm3;6 the polymer has an excellent chemical resistance and

Figure 3. (a) Pressure decay apparatus for vapor and gas sorption; (b) optical apparatus for dilation experiments.

high gas permeability. In Teflon AF1600 the same monomers have different mole fractions (65% of BDD and 35% of TFE) and the density is 1.84 g/cm3,19 while the glass transition is 163 °C. Both copolymers were purchased from Dupont (Philadelphia, PA). The filler used (nonporous fumed silica TS-530, Cabot Corp.) has been chemically treated with hexamethyldisilazane, in order

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Figure 4. (a) TEM image of a mixed matrix of AF1600 + 25 wt % of FS and (b) DSC characterization for pure AF1600 and a mixed matrix AF1600 + 25 wt % of FS. Table 1. Density of the Composite, Of the Polymer Phase and FFV of the Samples Studied, As Evaluated in N2 Atmosphere at 25°C with a MSB Balance

AF1600 AF1600 + 10% FS AF1600 + 25% FS

composite FMMM (g/cm3)

Fadditive (g/cm3)

polymer phase F20 (g/cm3)

FFVM0

1.844 ( 0.029 1.871 ( 0.206 1.886 ( 0.054

1.874 1.921

1.844 ( 0.029 1.841 ( 0.223 1.801 ( 0.065

0.291 ( 0.011 0.280 ( 0.080 0.275 ( 0.021

to replace hydroxyl surface groups with hydrophobic trimethylsilyl groups. The particles have an average diameter of 13 nm and a density of 2.2 g/cm3.2 The structures of the repeating units of the copolymers investigated and of the inorganic filler used are shown in Figure 2. Membranes were obtained according to the procedure proposed by Merkel et al.:3 a solution of 1 wt % of polymer in perfluoro-N-methyl-morpholine (PF5060, supplied by 3M) is cast on a glass plate, and the solvent is allowed to evaporate. Fumed silica is added to the polymer solution in the case of mixed matrices, and the mixture is blended for 2-3 min at 18000 rpm in a Waring two-speed laboratory blender and then cast onto a Petri dish covered with an aluminum foil, allowing a slow solvent evaporation. The films were completely dried within 48 h from preparation, and they did not undergo any further treatment before sorption experiments. The final thickness of the films ranged between 60 and 140 µm. Mixed matrices with different filler loadings were prepared, with 10% and 25 wt % of FS for AF1600, and 25% and 40 wt % of FS for AF2400. The vapors used in the experiments, n-butane and n-pentane, were supplied by Sigma-Aldrich and have a purity in excess of 99.6%, while the gases (CO2 and CH4, supplied by Sol) have a purity of 99.998% and 99.995%, respectively. Density Determination. The density of the polymer phase of the membrane is a key parameter to determine the transport properties in the composite matrix; indeed, the density value F20 is used to calculate the solubility isotherm through the NELF model, and to determine the fractional free volume that is required to correlate the diffusivity values by means of the free volume theory, according to eqs 11 and 15. It has been noticed that conventional methods used to determine density are often not accurate enough for the determination of the FFV in mixed matrices.2 In this work, we

relied upon the density value estimated from gas sorption data, according to the procedure described above; however, density measurement were also accurately performed for the sake of direct comparison with predicted data. In this work we used a method that is based on the determination of the buoyancy force acting on the sample immersed in a gaseous atmosphere. The sample weight was measured in vacuum and in a nitrogen atmosphere at 7.5 bar and 35 °C within a magnetic suspension balance (MSB), Rubotherm. To account for the fact that nitrogen is not completely inert, but an albeit small part of it is absorbed into the membrane, the following iterative procedure was used: the film density was first evaluated from the MSB reading and the value obtained was used to calculate the mass uptake value with the NELF model, using the relevant parameters for the system which are already available from previous works;19 then the sorption contribution was subtracted from the weight of the sample to calculate the new polymer density value. The procedure was iterated a few times until convergence and internal consistency was attained: normally, no more than three iterations were necessary for the required accuracy. TEM and DSC Characterization. TEM experiments on samples of mixed matrices based on Teflon AF1600 were carried out by courtesy of the Research Center “C. Buonerba” of Polimeri Europa, Mantova, Italy. The sample was cut in thin (0.5 µm) slices with an automated diamond blade. The glass transition of the same samples was characterized by DSC analysis. DSC runs were performed in a nitrogen atmosphere with a heating rate of 20 °C/min, from room temperature to 230 °C. Gas and Vapor Sorption. Solubility and diffusivity of vapors and gases were measured using two different types of pressure decay apparatuses. In the pressure decay technique, a known amount of vapor is fed into the sample chamber and the mass uptake is evaluated by measuring the pressure decrease in the


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by two manometers (Sensotec Super TJE), the first one having a full scale of 200 absolute psi, the second one of 500 absolute psi. Both manometers have an accuracy equal to 0.05% of the full scale value and they can be connected separately to the experimental chamber in different pressure intervals within the same isothermal experiment, in order to maintain a good level of sensitivity at any pressure. The rest of the apparatus is exactly equal to the low-pressure apparatus previously described. 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. The expression for the mass uptake as a function of time in step (i), Mt(i), for the mass sorption in a limited volume where the variation of the interfacial concentration is due to mass sorption in the membrane, is given by:20 (i) M(i) t - M0

M∞(i) - M(i) 0

∞

)1-

+ R) ∑ 1 +2R(1 R+Rq

2

2

n)1

exp(-Dqn2t/l2)

n

(18)

Figure 5. (a) Solubility isotherms of CH4 in Teflon AF1600, AF1600 + 10 wt % FS, and AF1600 + 25 wt % FS and adsorption onto pure silica at 35 °C; (b) solubility isotherms of CH4 in Teflon AF2400, AF2400 + 25 wt % FS, and AF2400 + 40 wt % FS and adsorption onto pure silica at 35 °C; (c) density of the polymeric phase of Teflon AF1600 and 2400 with different amounts of fumed silica as a function of filler/polymer mass ratio, as evaluated with direct measurements of composite density and eq 20, and as evaluated with NELF model and CH4 sorption data.

gaseous phase; the equilibrium solubility is equal to the final, asymptotic value of the mass uptake. Subsequent sorption tests are performed by increasing the external pressure in a stepwise manner. For vapor penetrants, the measurements were conducted at pressures below 1 bar; pressure is measured with an absolute capacitance manometer (f.s. value 1000 mbar, accuracy 0.15% of the reading), and the activity is calculated as the ratio between the equilibrium pressure and the vapor pressure at the experimental temperature. The system was placed in an air-thermostatted chamber where the temperature is fixed to within (0.1 °C. A scheme of the equipment is shown in Figure 3a. For gas sorption experiments, the same principle is exploited using also a different apparatus where the pressure is monitored

where M0(i) and M∞(i) are the initial and final mass uptake in step (i), respectively, and R is the ratio between the volume of solution and that of the membrane, corrected for the partition coefficient of vapor between the gaseous phase and the polymer, l is the semithickness of the membrane, while qn variables are the positive, nonzero, solutions of the equation: tg(qn) ) -Rqn. By fitting the experimental data of mass uptake versus time to eq 18, one obtains the average diffusivity value within the concentration interval inspected in the differential sorption step. Vapor Swelling. Swelling experiments were performed in a dedicated optical apparatus. The system, shown in Figure 3b is composed of a special sample compartment, formed by a stainless steel cell with two borosilicate glass windows in the opposite sides, to allow optical access for the measurements. The cell is connected to a reservoir containing the penetrant vapor and the pressure transducer, and to a second flask for the storage of liquid penetrant. A vacuum system, with a liquid nitrogen trap and a vacuum pump, is used to evacuate the apparatus before and after each experiment. The sensing element is an optical micrometer (Keyence LS-7030-M) endowed with a high speed linear CCD sensor that ensures accuracy of 1 µm and reproducibility within 0.15 µm in the measurements. The micrometer is fixed on two manual roto-translational optical stages, one for the horizontal alignment of transmitter and receiver with the sample, and one devoted to guarantee that the sample and the light beam are mutually orthogonal. To control the temperature, the experimental cell is surrounded by two heating tapes that can reach temperatures up to 200 °C; all the instrumentation is inserted in a thermostatic hood to eliminate the fluctuations of room temperature that might affect the response of the electronic devices. Results and Discussion TEM and DSC Characterization. The mixed matrix membranes were first characterized with optical techniques in order to inspect particles dispersion inside the sample. In particular, we were focused on the analysis of the MMM based on Teflon AF1600, for which no data have been reported in the literature. For the case of AF2400, a thorough characterization of samples prepared with the same protocol as the one followed in the present work revealed a good dispersion of mixed matrices loaded with mass fractions of silica up to 40%.3 In the present work it was found out that also the mixed matrices of fumed silica and Teflon AF1600 exhibit a good dispersion: in Figure

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4a, a TEM image of a mixed matrix of AF1600 + 25% wt of FS is reported, where the darker areas represent the organic domain. It can be seen that the nanoparticles are uniformly distributed inside the membrane with domains dimensions in the range between 30 and 50 nm. The good dispersion is also indicated by the fact that the samples are rather transparent. Merkel and coauthors also observed that the addition of fumed silica particles to AF2400 does not vary significantly the polymer Tg which remains at about 240 °C also with the various filler loadings.3 This behavior was motivated by the fact that the presence of FS particles does not alter the long-range segmental dynamics important to the glass transition but only the chain packing, as it is also supported by the fact that polymer chains and filler undergo insignificant interactions. The DSC experiments carried out in this work on samples of pure AF1600 and a mixed matrix of AF1600 + 25% FS (Figure 4b) showed that the glass transition temperature is very slightly affected by the addition of the impermeable filler, and varies from 163 to 162. 2 °C. Density Determination. The density values measured for the different MMM used are reported in Table 1. The results obtained show also that the density of the composite actually is lower than the value calculated by a simple additive rule based on the pure component densities. This behavior was also observed by Merkel et al.2 in the case of mixed matrices based on PMP, and it is a direct consequence of the additional free volume created by the incorporation of filler into the polymer. The actual average density of the polymeric phase, F20, is evaluated by considering volume additivity between the two phases of the composite, and taking the density of silica particles equal to its pure component value:

ωF 1 - ωF 1 ) + FMMM FF F20

(19)

For convenience, also the values of FFV of the unpenetrated polymer phase of the composite have been reported in Table 1, calculated using eq 11. The values obtained are listed in Table 1 and will be compared to the values estimated from CH4 sorption isotherm with the use of the NELF model. Gas and Vapor Sorption in Mixed Matrices Based on AF1600 and AF2400. The solubility isotherms for methane in pure AF2400 and its mixed matrices are shown in Figure 5 in grams of penetrants per gram of total solid, as typical example of the data collected with the pressure decay technique. The adsorption onto pure fumed silica particles is also reported in Figure 5. The average overall solubility in the composite, per unit mass of solid, is not affected by the addition of filler and is practically the same of the unloaded polymer, indicating that the main quantitative contribution to the variation of permeability after the particles insertion is due to diffusivity changes. If we assume the pseudoadditive approximation expressed by eq 10, the solubility data can be plotted in terms of grams of penetrant absorbed per unit mass of polymer phase, versus penetrant partial pressure. In Figure 6 the sorption isotherms of CH4 and CO2 in all the membranes are reported and compared to the simulations of the NELF model, obtained with values of the parameters reported in Table 2. In Figure 6 also the data for the two vapors, n-butane and n-pentane, are reported. The binary parameters used in the modeling are very similar to those obtained in a previous work19 for these penetrant/polymer pairs and were kept constant for the same penetrant, for all filler loadings. The swelling coefficient was set to zero for methane,

Figure 6. Experimental solubility of (a) CH4, (b) CO2 at 35 °C. and (c) n-C4,21 (d) n-C5,21 at 25 °C in the polymeric phase of Teflon AF2400-based MMM and comparisons with NELF model calculations. Open symbols indicate the solubility data points used to estimate ksw.


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Table 2. NELF Model Parameters for Polymers, Penetrants and Their Mixtures F* (kg/L)

T* (K)

p*(MPa)

F20 (g/cm3)

FFVM0(eq 11)

Matrix AF240019 AF240025FS AF240040FS

2.13

624

250

1.740 1.714 1.690

0.319 0.329 0.339

AF160019 AF160010FS AF160025FS

2.16

575

280

1.840 1.820 1.790

0.292 0.300 0.312

n-C419 n-C521 CO219 CH419

0.720 0.749 1.515 0.500

430 451 300 215

penetrant

kij

ksw (MPa-1)

CH4

0.05

0 0 0 0 0 0

AF2400 AF240025FS AF240040FS AF1600 AF160010FS AF160025FS

CO2

0

0.012 0.035 0.045 0.018 0.020 0.032


n-C4

0.14

0.40 0.40 0.48 0.17 0.22 0.22


n-C5

0.15

0.91 1.23 1.99 0.56 0.73 1.75


Penetrant

that is a nonswelling penetrant, while it was adjusted on one high-pressure solubility datum for the other swelling penetrants, which is indicated as an open symbol in the figures. To evaluate the variation of FFV of the polymeric phase induced by the addition of filler, the polymer density value in the mixed matrix state was estimated by fitting the NELF model on the solubility isotherms of CH4, that is a small and nonswelling penetrant and is suitable to serve as test probe for a reliable estimate of density and the free volume of the polymer phase. It can be seen from Table 2 that the density values of the polymer phase calculated from methane sorption data decrease with increasing FS content, as otherwise expected. In particular, the FFV value of AF2400-based MMM increases by a factor of 3% when adding 25% of fumed silica nanoparticles, and by a factor of 6% when adding a quantity of nanoparticles corresponding to 40% of the total weight. A similar behavior is observed by adding silica nanoparticles to the denser matrix of AF1600: a +1% variation of FFV is calculated for matrices containing 10 wt % of FS and an increase of 7% in FFV for matrices containing 25% of fumed silica. Moreover, the density values estimated with the NELF model are extremely appropriate for predicting the solubility of all the other penetrants inspected (CO2, n-C4, n-C5) in the same mixed matrices, as it is shown in Figure 6 for the case of AF2400based materials and in Figure 7 for those based on AF1600. To

290 305 630 250 matrix

describe the complete sorption isotherm of these penetrants, over the entire pressure range inspected, one needs to adjust also another parameter to the experimental data of each penetrant, that is, the swelling coefficient ksw. Indeed, the latter quantity is not merely an empirical fitting parameter since it has a precise physical meaning and represents the extent of swelling induced by each penetrant at fixed pressure. Its value obtained through application of the NELF model will be compared to experimental swelling results to check with independent data the reliability of the model and of the procedure followed. Diffusivity. The diffusion coefficient was calculated in every differential sorption step in the pressure decay experiments by fitting Fick’s law to the transient data of the mass sorbed. Mass uptake data were collected for the sorption of the two vapors inspected, n-butane and n-pentane. It is shown in Figure 8 that the addition of FS particles enhances the apparent diffusion coefficient for both matrices, contrary to the common and simplistic thought that the addition of impermeable particles decreases diffusivity due to the tortuosity increase. This behavior was already reported for mixed matrices based on high-freevolume polymers like amorphous Teflon, PTMSP, and PMP,2,3 and it is reasonably associated to the increased presence of large free-volume elements in mixed matrices as demonstrated by PALS measurements reported in the same works. In this respect, these composites behave differently from traditional composite

11928


Figure 7. Experimental solubility of (a) CH4, (b) CO2 at 35 °C and (c) n-C4, (d) n-C5 at 25 °C in the polymeric phase of Teflon AF1600-based MMM and comparisons with NELF model. Open symbols indicate the solubility data points used to estimate ksw.

materials, in view of the small size of inorganic domains in the membrane, that are able to modify the polymer packing on a short-range scale. Also, the weak interactions between polymeric chains and silica domains may favor the formation of voids at the polymer/filler interface, which contribute to the overall increase of FFV. The enhancement in the diffusion coefficient is observed for both of the penetrants inspected, and the extent of the increase depends on the vapor type and is larger for the lower molecular weight vapor (Figure 8). The diffusion coefficient is also a function of the average penetrant concentration in the matrix during the differential sorption step, and in particular it increases with the concentration according to an exponential law. This behavior occurs because the penetrant diffusive jumps in polymers depend, to a certain extent, on polymeric chain motions, which are made more frequent by the swelling and plasticization induced by penetrant sorption. The positive variation of the diffusion coefficient with penetrant concentration is accounted for by parameter β of eq 12: interestingly, the value of β decreases regularly with the increase of filler loading. This behavior, which was observed before in similar materials3 can be due to different factors. The filler addition may cause stiffening of the polymer structure, lowering the chains mobility and, consequently, the swelling induced by the penetrant in the mixed matrix with respect to the pure polymer at fixed penetrant concentration. This explanation is somehow weakened by the results of Tg measurements, that indicate that nanometric silica does not affect the glass transition of the polymer, which is a measure of the chain mobility. Further discussion will be performed in the following

paragraph, through comparison with direct swelling measurement. The free volume initially present in the matrix can also have a significant effect on the value of β, as it will be discussed in the correlations section. Dilation. The dilation experiments were performed for the case of n-butane and n-pentane sorption, by monitoring the elongation in one planar direction, and considering isotropic swelling. The swelling observed is attributed entirely to the polymeric phase, because the inorganic phase does not undergo any swelling. The curves of volume dilation versus penetrant pressure are not reported here for the sake of brevity; it can be pointed out, however, that the dilation depends linearly on the penetrant partial pressure, as it was also observed for unloaded polymers,12–14 at least up to the pressure of 0.12 MPa. The values of ksw obtained experimentally are equal to 0.34, 0.49, and 0.97 MPa-1 for the sorption of n-C4 in pure AF2400, AF2400 + 25% FS, and AF2400 + 40% FS, respectively. The values are similar to those obtained by modeling sorption isotherms with NELF model (i.e., 0.40, 0.40, and 0.48 MPa-1 for the three matrices, respectively) with the exception of the matrix with the higher loading of FS. The maximum pressure at which the experimental swelling data were considered for linear interpolation is equal to 0.12 MPa. In this range the correlation coefficients, R2, for the linear curve interpolating the data is equal to 0.97, 0.96, and 0.98 for the data relative to pure AF2400, AF2400 + 25% FS, and AF2400+ 40% FS, respectively. Swelling coefficients of n-C5 in AF2400-based mixed matrices increase from 0.68 to 0.98 and 1.35 MPa-1 going from the pure polymer to matrices with 25 and 40 wt % of FS,


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Figure 8. Average diffusivity of (a) n-C421 and (b) n-C521 in Teflon AF2400-based mixed matrices at 25 °C, versus average penetrant concentration. Average diffusivity of (c) n-C4 and (d) n-C5 in Teflon AF1600-based mixed matrices at 25 °C, versus average penetrant concentration.

respectively: these values are qualitatively consistent with those obtained with the NELF model and listed in Table 2 (i.e., 0.91, 1.23, and 1.99 MPa-1, respectively). The correlation coefficients, R2 for the linear behavior of the experimental volume dilation data versus the pressure is equal to 0.96, 0.99, and 0.99 for n-C5 in pure AF2400, AF2400 + 25% FS, and AF2400 + 40% FS, respectively. The maximum pressure inspected is equal to 0.045 MPa-1 for pure AF2400 and AF2400 + 40% FS and to 0.025 MPa for AF2400 + 25% FS. The value of ksw found for CO2 in AF2400 with the NELF model (0.012 MPa-1) is exactly equal to the experimental value which was found for this system in a previous work.19 For n-C4 sorption in AF1600-based mixed matrices, the measured swelling parameter ksw goes from 0.18, to 0.24 and 0.22 MPa-1 increasing the weight fraction of silica from 0 to 10 and 25%, respectively; consistently, the NELF model calculates values of ksw that go from 0.17 MPa-1 for the unloaded polymer to a constant value of 0.22 MPa-1 for the loaded polymers. The maximum pressure reached during experimental dilation runs is equal to about 0.1 MPa for all systems. The correlation coefficient of the straight line interpolating the experimental dilation data, R2, is equal to 0.97, 0.99, and 0.98 for n-C4 dilation in pure AF1600, AF1600 + 10% FS, and AF1600 + 25% FS, respectively. The swelling coefficient of n-C5 is more significant and goes from 0.63, to 0.65 and 0.79 MPa-1 for the same matrices, with an increase in the content of silica, qualitatively in line with the values calculated from application of the NELF model, which are 0.56, 0.73, and 1.75 MPa-1, respectively. For

experiments with n-C5, the maximum pressure reached is around 0.04 MPa. The values of R2 for the linear curve interpolating the data is equal to 0.98, 1.00, and 0.98 for n-pentane-induced swelling in pure AF1600, AF1600 + 10% FS, and AF1600 + 25% FS, respectively. It is interesting to notice, also, that the value of ksw found for CO2 in AF1600 with the NELF model (0.018 MPa-1) is perfectly in line with the experimental value which can be found in the literature (0.017 MPa-1).19 The comparison between experimental and predicted values of ksw allows the conclusion that using the solubility data of a probe gas as input to the NELF model has the ability to predict qualitatively and also quantitatively the effect of silica addition on the vapor swelling induced in the mixed matrices. To show in more detail the effect of silica addition on the polymer swellability, we plotted in Figure 9 the volume dilation as a function of the penetrant concentration in the polymeric phase, obtained from the sorption experiments. In the case of AF2400 (Figure 9a,b), the dilation versus concentration curves of all the membranes containing different filler loadings practically overlap with one another, indicating that the swelling is not much affected by the introduction of nanoparticles. This is not true for the case of n-butane in AF2400 + 40% FS where, on the contrary, the deviation from the data for pure polymer is significant, especially at high concentrations of vapor. It is also interesting to notice that, for AF2400 the swelling induced by n-butane appears more significant than that induced by n-pentane, at fixed composition.

11930


Figure 9. Dilation induced by (a) n-C4 and (b) n-C5 in AF2400-based mixed matrices at 25 °C versus penetrant concentration. Dilation induced by (c) n-C4 and (d) n-C5 in AF1600-based mixed matrices at 25 °C versus penetrant concentration. Table 3. Comparison between the Pure Polymer Density Values Retrieved from the NELF Model and Those Experimentally Determined from Direct Density Measurements, and the Corresponding Maximum Deviations on the Solubility Calculations; for Swelling Penetrants the Swelling Coefficient Used Is Retrieved from the NELF Model

mixed matrix pure AF1600

AF1600 + 10% FS AF1600 + 25% FS

Maximum deviation on 0 0 F2 from F2 from solubility using NELF model measurements experimental (g/cm3) (g/cm3) penetrant density CH4 CO2 n-C4 n-C5 CH4 CO2 n-C4 n-C5 CH4 CO2 n-C4 n-C5

1.84

1.844

1.82

1.841

1.79

1.801

+2% +2% +3% +4% +10% +10% +16% +18% +5% +5% +7% +8%

Considering the volume dilation data for AF1600 (Figure 9c,d), the swelling induced by n-C4 is slightly smaller than that due to n-C5 sorption at the same mass fraction; it is also clear that, for both penetrants, the swelling decreases, although slightly, with increasing filler content, and such a trend is more evident in the case of n-C5 sorption. This behavior is opposite compared to what is observed for AF2400 and indicates that

for this polymer the addition of rigid nanoparticles slightly increases the plasticization resistance of the polymer and may also play a role, to some extent, in the trend observed for the β values that decrease with increasing filler content. The different behavior observed between AF1600- and AF2400-based MMM appears reasonably associated with the different initial free volume of the two materials, although deeper investigations are needed to support this conclusion more strongly. After discussing the differences between experimental values of polymer phase density, F20, and of the swelling coefficients, ksw, with the corresponding values obtained from application of the NELF model, it may be interesting now to inspect what is the difference in the solubility isotherms of MMM resulting by the use of the values determined experimentally instead of those retrieved from the NELF model. Indeed use of the values determined experimentally is in principle to be preferred; nonetheless, this route is often not feasible since the density values are rarely available to within the desired precision, not only because of the accuracy required for the determination of the MMM density itself but also for the additional errors associated with the determination of the actual mass fraction of the filler and with its possible nonuniformity in the film. The difficulty in obtaining meaningful density values in these composites was already commented in ref 2. On the other hand, the volume dilation isotherm upon penetrant sorption is hardly


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Table 4. Comparison between the Swelling Coefficient Values Retrieved from the NELF Model and Those Experimentally Determined from Volume Dilation, And the Corresponding Maximum Deviations on the Solubility Calculations penetrant n-C4

n-C5

ksw from NELF model (MPa-1)

ksw from measurements (MPa-1)

0.40 0.40 0.48 0.17 0.22 0.22 0.91 1.23 1.99 0.56 0.73 1.75

0.34 0.49 0.97 0.18 0.24 0.22 0.68 0.98 1.35 0.63 0.65 0.79

available, and the swelling coefficients, ksw, are commonly unavailable from direct experimental evidence. In the present case the values of F20 and ksw are available for AF1600-based MMM both from application of the NELF model and from direct experimental measurements, so that we can estimate the difference on the solubility calculated using the two different values. In Table 3 one can see that there is a high sensitivity on the F20 values, as it was already pointed out for the NELF model in previous works, however deviations in the solubility isotherms are contained to within a reasonably moderate range, with the maximum deviations between 10% and 18% for AF1600 + 10% FS. The effects of the swelling coefficient on the solubility calculated are shown in Table 4; indeed the values of ksw

maximum deviation on solubility using experimental ksw +3.9% -5.3% -21.0% -1.0% -1.2% +6.0% +6.0% +13.0% -3.2% +2.6% +27%

(@ (@ (@ (@ (@ 0 (@ (@ (@ (@ (@ (@

p p p p p

) ) ) ) )

0.096 0.096 0.096 0.085 0.067

MPa) MPa) MPa) MPa) MPa)

p p p p p p

) ) ) ) ) )

0.035 0.037 0.034 0.020 0.029 0.029

MPa) MPa) MPa) MPa) MPa) MPa)

matrix AF2400 AF240025FS AF240040FS AF1600 AF160010FS AF160025FS AF2400 AF240025FS AF240040FS AF1600 AF160010FS AF160025FS

measured and retrieved may be appreciably different from one another, but the solubility values are sensitive rather to the actual polymer density, and thus the maximum deviations shown for the solubility isotherms are again rather contained in general; the maximum deviations are observed for the case on n-C5 in AF1600 + 25% FS. Correlations for Diffusivity. The FFV calculated from the sorption isotherm of the test penetrant (CH4) through the NELF model can also be used to correlate the diffusivity data collected during sorption experiments. In Figure 10, the values of infinite dilution diffusivity in the polymeric phase, DM0τ, with DM0extrapolated from experimental data and τ estimated with eq 14, are plotted as a function of the

Figure 10. Infinite dilution diffusion coefficient of (a) n-C4 and (b) n-C5 in the polymeric phase of mixed matrices based on AF2400 and AF1600 as a function of FFV; β coefficient for diffusion of (c) n-C4 and (d) n-C5 in the mixed matrices based on AF2400 and AF1600 as a function of FFV.

11932


Figure 11. Average permeability of (a) n-C421 and (b) n-C521 in Teflon AF2400-based mixed matrices at 25 °C, versus average penetrant concentration. Average permeability of (c) n-C4 and (d) n-C5 in Teflon AF1600-based mixed matrices at 25 °C, versus average penetrant concentration.

reciprocal of the fractional free volume, 1/FFV, according to the semiempirical free-volume law (eq 15). As shown in Figure 10a for diffusion of n-butane in both AF2400 and AF1600, there is a strong correlation between DM0τ and 1/FFV; furthermore, the same exponential correlation can be used for mixed matrix materials based on Teflon AF1600 and AF2400, with a correlation coefficient R2 of 0.89. This behavior is reasonable since the polymeric matrices have the same chemical structure, and the main difference between the two is the amount of free volume present in the matrix, which is the key parameter governing the penetrant diffusion. Similar behavior is observed for n-pentane diffusion, where considering the data for both polymer matrices the correlation coefficient R2 is 0.93; the values of the parameters A and B of eq 15 differ from the case of n-butane, shown in Figure 10b, as expected for this type of correlations. These results strongly support the physical interpretation offered with the present approach and confirm the validity of a solubility-based method to retrieve the fractional free volume values necessary for the modeling of the transport properties in mixed matrices membranes. Finally, the behavior of the coefficient β was also studied, which represents the dependence of the diffusion coefficient on the penetrant concentration in eq 12, as a function of the fractional free volume of the matrix. It is generally accepted that the vapor diffusivity increases with penetrant concentration, especially for swelling penetrants and for polymers characterized by moderate values of free volume. This behavior is due to the fact that the diffusive jumps of penetrants in polymers become more frequent if the matrix is plasticized by the presence of a penetrant. Also, the swelling induced by the penetrants increases

the free volume available for diffusion. As a consequence, diffusivity increases with increasing penetrant concentration. It is interesting to notice that the β values for the materials inspected in this work is also related to the FFV (Figure 10c,d) through an exponential law: β ) E exp(-F × FFVM0)

(20)

The above correlation is rather novel and interesting: it implies that, the higher the initial free volume in the matrix, the lower the value of β, that is, the less significant is the effect of penetrant concentration on diffusion. Also in this case, a single master curve can be drawn for the two polymer matrices with a correlation parameter R2 of 0.87 in the case of n-C4 and of 0.82 in the case of n-C5. The parameters E and F are both positive and depend, reasonably, on the penetrant type. That behavior can be intuitively explained by the fact that if the initial free volume is larger, the diffusivity is relatively high and consequently the lower is the dependence of the frequency of the effective diffusive jumps on the variations of polymer motions and on the variations in free volume. Therefore, the diffusion-enhancing effect that accompanies the increase of penetrant concentration, through swelling and plasticization, is lower for the higher free volume matrices. The above correlation also implies that the values of β decreases with increasing silica content in the matrix. Although this behavior can be thought, more intuitively, to be due to a “rigidification” induced by silica in the polymeric matrices, direct swelling data shown previously do not confirm this explanation, at least in the case of AF2400, because the volume dilation measured does not decrease with


11933

Figure 12. (a) Ideal n-C5/n-C4 selectivity plotted as a function of n-C5 permeability; (b) n-C4-CH4 solubility selectivity in AF1600 (b) and in AF2400 (c).

increasing silica content. In the case of Teflon AF1600, on the other hand, a certain decrease of dilation with increasing silica content is observed, but it may not be sufficient to explain the significant variation of β observed. Our interpretation is that the effect of silica is mainly that of increasing the free volume of the polymer, rather than affecting its rigidity. The above interpretation is also consistent with the observed independence of Tg on the silica content. Permeability and Ideal Selectivity. As usual, gas and vapor permeability can be also calculated from the diffusivity and solubility data collected in the sorption experiments. To this aim, we have calculated the permeability associated to an infinitesimally small differential step in transmembrane pressure; that enables us to use the local diffusivity value at the local concentration prevailing in the film, and requires, on the other hand, the use of the local solubility coefficient, dCi/dpi, as one immediately recognizes from the definition of permeability: Ci2 - Ci1 Di Ji Ci2 - Ci1 δ Pi ) ) ) Di pi2 - pi1 pi2 - pi1 pi2 - pi1 δ δ

(21)

where δ indicates the membrane thickness and the subscripts 1 and 2 label downstream and upstream interfaces, respectively. When the transmembrane pressure difference is infinitesimally small one has Pi ) Di lim

pi2fpi1

Ci2 - Ci1 dCi ) Di pi2 - pi1 dpi

(22)

The permeability values have thus been calculated from diffusivity and solubility data according to eq 22. Considering n-C4 and n-C5, it is clear from Figure 11 that the addition of filler nanoparticles increases the permeability of both penetrants, essentially following the increase of the diffusion coefficient caused by the presence of fumed silica in the membrane. From the knowledge of the permeability isotherms, the behavior of the ideal selectivity of the composite can be predicted through eq 1. It is observed in Figure 12a that, for the case of the n-C4/n-C5 pair, the matrices considered are vaporselective, namely they are more permeable to the more condensable penetrant, and the selectivity increases with increasing penetrant pressure. The case of 25% of FS in AF2400 is peculiar, since a change in selectivity is observed: the membrane is n-butane selective at low activity and becomes n-pentane selective at higher activity values. It is also very clear from the plots shown in Figure 12a that the selectivity of the matrices, at fixed permeability, decreases with increasing filler content while the permeability of n-C5 increases. From the solubility data it is also possible to calculate the ideal solubility selectivity for the pair methane/n-butane that is of more practical interest. It can be seen in Figure 12b,c that the addition of inorganic filler nanoparticles does not influence the solubility selectivity except for the case of 25% FS in AF1600. This experimental evidence confirms that the permeability behavior of the mixed matrices is mostly influenced by diffusivity that is more significantly affected by the loading of nanoparticles of FS.

11934


Of course, the ideal values of selectivity presented above from pure vapor measurements could be different from the actual case of mixed gases, in which interactions take place between the penetrants, and the transport of both penetrants is affected by the matrix swelling. Conclusions Mixed matrix membranes based on fluorinated, high-freevolume matrices (amorphous Teflon AF1600 and AF2400) show attractive gas transport performances, especially if compared to pure polymeric membranes. This study was devoted to MMMs formed by loading nonporous inorganic nanoparticles of hydrophobic fumed silica in both amorphous Teflons. In particular two classes of membranes based on amorphous Teflon, AF1600 and AF2400, and fumed silica were experimentally characterized to evaluate solubility, diffusivity, and swelling due to different penetrants. The data were modeled with a new approach that allows the predictions of solubility isotherms of every penetrant on the basis of data for one single probe gas. Based on the methane sorption data in mixed matrices with different silica loadings, the NELF model allows an estimation of the density of the unpenetrated polymer phase, and hence its fractional free volume. The method reveals that, consistently with what is expected, the density of the polymeric phase decreases with increasing filler content due to modification of the polymer chain packing and formation of void interfaces between silica and polymer induced by weak interactions between the two phases. The values of density thus retrieved allow a prediction of the solubility of CO2, n-C4, and n-C5 in the same mixed matrices, with the use of only one adjustable parameter, that is, the swelling coefficient ksw, for the estimate of medium pressure sorption data where swelling is present. This parameter has to be adjusted for every gas-membrane couple, while all the other parameters, including the binary energetic parameter, are kept constant with the filler content. The swelling coefficient thus estimated is not a merely empirical quantity but gives a good qualitative if not even quantitative estimate of the actual swelling induced in the matrices, as verified through the comparison with experimental swelling measurements of the various materials in the presence of n-C4 and n-C5. The latter data provide a completely new type of information, particularly important for the characterization of the plasticization behavior of mixed matrix materials based on amorphous Teflon. We observed that, at a fixed concentration of vapor, the swelling of AF1600-based matrices decreases slightly with filler content in the range 0-25 wt % of FS. For AF2400, the addition of silica seems not to affect the swelling capacity of the matrix, with an exception represented by the case of n-butane, which induces more swelling in AF2400-40% FS MMM than in pure AF2400. The fractional free-volume values evaluated from methane sorption data can also be used to correlate gas and vapor diffusivity data of n-C4 and n-C5 at infinite dilution in the polymeric phase, through a free-volume-based semiempirical correlation containing two adjustable parameters. The infinite dilution diffusivity data relative to mixed matrices based on AF1600 and AF2400 lie, for a same penetrant, on the same mastercurve. The diffusivity at higher concentration also follows a regular correlation: it can be observed indeed that the parameter representing the exponential dependence of the diffusivity on the penetrant concentration, β, decreases with increasing filler content according to an exponential function of FFV. This result indicates that initial free volume value dictates the diffusion behavior in the entire concentration range.

The penetrant diffusion in matrices with high initial values of FFV does not depend on the increased mobility of polymeric chains, due to penetrant sorption, but remains essentially unaffected by the polymer plasticization and swelling. Indeed, the dependence of β on the filler content seems to be only weakly related to the dependence of the swelling capacity on the filler content. The data allowed also for an estimation of the permeability in the composite materials. The evaluation of the contributions to the permeability can hence be used to determine the ideal selective behavior of the composite membrane. The addition of silica increases the permeability and decreases the ideal selectivity of n-C5 versus n-C4; the ideal solubility selectivity of the n-C4-CH4 couple is unaffected by filler content, with the main effect being associated to the diffusivity. Acknowledgment The financial support of EU Strep NMP3-CT-2005-013644 (MultiMatDesign) is gratefully acknowledged. We are grateful to Dr. Tim Merkel of MTR for providing us some of the samples characterized and for the precious advices. We thankfully acknowledge the assistance of Dr. Dino Ferri of Polimeri Europa, Mantova, for the TEM measurements, as well as of Professor Andrea Saccani of DICASM, University of Bologna, for the DSC measurements. Literature Cited (1) Chung, T.-S.; Jiang, L. Y.; Li, Y.; Kulprathipanja, S. Mixed matrix membranes (MMMs) comprising organic polymers with dispersed inorganic fillers for gas separation. Prog. Polym. Sci. 2007, 32, 483–507. (2) (a) Merkel, T. C.; Freeman, B. D.; Spontak, R. J.; He, Z.; Pinnau, I.; Meakin, P. Ultrapermeable, reverse-selective nanocomposite membranes. Science 2002, 296, 519–522. (b) Merkel, T. C.; He, Z.; Pinnau, I.; Freeman, B. D.; Meakin, P.; Hill, A. J. Effect of nanoparticles on gas sorption and transport in poly(1-trimethylsilyl-1-propyne). Macromolecules 2003, 36, 6844–6855. (3) Merkel, T. C.; He, Z.; Pinnau, I.; Freeman, B. D.; Meakin, P.; Hill, A. J. Sorption and transport in poly(2,2-bis(trifluoromethyl)-4,5-difluoro1,3-dioxole-co-tetrafluoroethylene) containing nanoscale fumed silica. Macromolecules 2003, 36, 8406–8414. (4) Doghieri, F.; Sarti, G. C. Nonequilibrium lattice fluids: a predictive model for the solubility in glassy polymers. Macromolecules 1996, 29, 7885–7886. (5) Sarti, G. C.; Doghieri, F. Predictions of the solubility of gases in glassy polymers based on the NELF model. Chem. Eng. Sci. 1998, 19, 3435– 3447. (6) De Angelis, M. G.; Sarti, G. C. Solubility and diffusivity of gases in mixed matrix membranes containing hydrophobic fumed silica: correlations and predictions based on the NELF model. Ind. Eng. Chem. Res. 2008, 47, 5214–5226. (7) Maxwell, C. Treatise on Electricity and Magnetism; Oxford University Press: London, 1873. (8) Giacinti Baschetti, M.; De Angelis, M. G.; Doghieri, F.; Sarti, G. C. Solubility of gases in polymeric membranes, in Chemical Engineering: Trends and DeVelopments; Galan, M. A.; d.Valle, E. M., Eds.; Wiley: Chichester, UK, 2005; pp 41-61. (9) Doghieri, F.; Quinzi, M.; Rethwisch, D. G.; Sarti, G. C. Predicting gas solubility in glassy polymers through non-equilibrium EOS. In AdVanced Materials for Membrane Separations; ACS Symposium Series 876; Pinnau I., Freeman, B. D., Eds.; American Chemical Society: Washington, DC, 2004; pp 74-90. (10) Sanchez, I. C.; Lacombe, R. H. An elementary molecular theory of classical fluids. Pure fluids. J. Phys. Chem. 1976, 80, 2352–2362. (11) Sanchez, I. C.; Lacombe, R. H. Statistical thermodynamics of polymer solutions. Macromolecules 1978, 11, 1145–1156. (12) Wissinger, G.; Paulaitis, M. E. Swelling and sorption in polymerCO2 mixtures at elevated pressures. J. Polym. Sci., Part B: Polym. Phys. 1987, 25, 2497–2510. (13) Jordan, S.; Koros, W. J. Free volume distribution model of gas sorption and dilation in glassy polymers. Macromolecules 1995, 28, 2228– 2235.

Ind. Eng. Chem. Res., Vol. 49, No. 23, 2010 (14) Fleming, G. K.; Koros, W. J. Carbon dioxide conditioning effects on sorption and volume dilation behavior for bisphenol A-polycarbonate. Macromolecules 1990, 23, 1353–1360. (15) Giacinti Baschetti, M.; Doghieri, F.; Sarti, G. C. Solubility in glassy polymers: Correlations through the nonequilibrium lattice fluid model. Ind. Eng. Chem. Res. 2001, 40, 3027–3037. (16) van Krevelen, W. Properties of Polymers; Elsevier: Amsterdam, 1990. (17) Polyakov, A. M.; Starannikova, L. E.; Yampolskii, Yu. P. Amorphous Teflon AF as organophilic pervaporation materials. Transport of individual components. J. Membr. Sci. 2003, 216, 241–256. (18) Cohen, M. H.; Turnbull, D. J. Molecular transport in liquids and glasses. J. Chem. Phys. 1959, 31, 1164–1169. (19) De Angelis, M. G.; Merkel, T. C.; Bondar, V. I.; Freeman, B. D.; Doghieri, F.; Sarti, G. C. Gas sorption and dilation in poly(2,2-bistrifluo-

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romethyl-4,5-difluoro-1,3-dioxole-co-tetrafluoroethylene): Comparison of experimental data with predictions of the nonequilibrium lattice fluid model. Macromolecules 2002, 35, 1276–1288. (20) Crank, J. The Mathematics of Diffusion, 2nd ed.; Oxford University Press: Oxford, U.K., 1975. (21) Ferrari, M. C.; Galizia, M.; De Angelis, M. G.; Sarti, G. C. Vapor sorption and diffusion in mixed matrices based on Teflon AF 2400. In Membrane Gas Separations; Freeman, B. D., Yampolskii, Yu. P., Eds.: J. Wiley & Sons Ltd.: submitted for publication.

ReceiVed for reView February 1, 2010 ReVised manuscript receiVed February 26, 2010 Accepted March 9, 2010 IE100242Q

Gas and Vapor Transport in Mixed Matrix Membranes Based on

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