Estimation of Langmuir and Sips Models Adsorption Parameters for

Article pubs.acs.org/jced

Estimation of Langmuir and Sips Models Adsorption Parameters for NaX and NaY FAU Zeolites Pasquale F. Zito,† Alessio Caravella,† Adele Brunetti,‡ Enrico Drioli,†,‡ and Giuseppe Barbieri*,‡ †

The University of Calabria, Department of Environment and Chemical Engineering, Via Pietro BUCCI, Cubo 44A, 87036 Rende CS, Italy ‡ National Research Council, Institute on Membrane Technology (ITM-CNR), Via Pietro BUCCI, Cubo 17C, 87036 Rende CS, Italy S Supporting Information *

ABSTRACT: The single-gas adsorption properties of various species (H2, CH4, CO2 CO, H2O) involved in quite important industrial processes, such as methane steam reforming and water gas shift reaction, are evaluated for Faujasite NaX and NaY zeolites. To carry out such an investigation, a multivariate regression analysis (using Levenberg−Marquardt algorithm) is adopted, fitting experimental adsorption isotherms from the literature with the Langmuir and Sips models. A number of experimental isotherms is used to enlarge as much as possible the validity range in terms of temperature and pressure. The evaluated parameters are compared with those available in the open literature, in order to provide a further confirmation of the results of the present work. Such a comparison is required to extend the literature information and, where necessary, to cover the current lack of adsorption data for the considered zeolite. The chosen functionality of the adsorption parameters with temperature and pressure should be useful in a wide range of applications.

1. INTRODUCTION Zeolites are aluminosilicates with three-dimensional, microporous and crystalline structures. Their microporosity and properties can be effectively used for several applications, like selective adsorption, catalysis, ion exchange, and gas and liquid separation. Zeolite structure consists in a tetrahedral TO4 (T = Si or Al), in which each T atom is connected to four other T atoms by T−O−T bonds, in order to create pores and channels.1,2 An isolated SiO4 should have a negative charge of −4, whereas in all zeolite structures this unit is neutral, owing to their interconnections.2 On the other hand, the AlO4 units are negatively charged and, thus, exchangeable cations are located into the channels to balance this charge. Zeolites can be classified into small (6-, 8-, or 9-membered rings), medium (10membered rings), large (12-membered rings), and ultralarge structures (14-, 18-, or 20-membered rings), based on the pores size.2 Moreover, they are classified with a three-letters identification code adopted by the International Zeolite Association.3 The FAU-type zeolites (faujasites) are involved in a number of industrial applications, owing to their high stability, large pore volume, and surface area.4 In particular, FAU membranes show excellent performances in water/organic mixture separation,5 as well as in gas separation. Kita et al. (1997)6 carried out pervaporation experiments through NaY zeolite using different liquid mixtures, such as water/ethanol, methanol/benzene, methanol/MTBE, ethanol/ © XXXX American Chemical Society

benzene, and ethanol/cyclohexane. Quite high separation factors are observed for all mixtures, especially for methanol/ MTBE (7600). Kusakabe et al. (1997)7 investigated the CO2/ N2 selective permeation in a FAU Y-type, achieving a selectivity in the range of 20 to 100 at 30 °C. Hasegawa et al. (2001)8 synthesized different ion-exchanged Y-type zeolite membranes, obtaining CO2/N2 permeation selectivities for equimolar mixtures between 19 and 40 at 35 °C. Moreover, Kusakabe et al. (1999)9 also tested other different binary mixtures, such as CO 2 /H2 , CH 4 /H 2 , C 2 H 6 /H 2 , and C 3 H 8 /H 2 , obtaining separation factors of 27.8, 1.7, 5.3, and 9.7, respectively. Bernardo et al. (2008)10 studied CO selective oxidation through Y-type zeolite reducing CO to 10−20 ppm. The performances of a FAU NaX zeolite are reported by Belmabkhout et al. (2007)11 for a CO2/CO mixture at two different temperatures, changing the gas compositions. In particular, they operated column breakthrough experiments at 323 K and 373 K, reaching a maximum value of CO2/CO selectivity of 65 K at 323 K. Moreover, they observed that selectivity is not affected by changes in gas compositions at 323 K, whereas it decreases with increasing CO2 composition at 373 K, varying from 51 to 34. The FAU zeolites have a three-dimensional structure consisting in sodalite units (β-cages) which are linked together Received: March 7, 2015 Accepted: September 10, 2015

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DOI: 10.1021/acs.jced.5b00215 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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by six-membered double rings d6R (see Figure 1)12 to give large cavities with diameter of around 12.5 Å (supercages)

taken from the literature considering both Langmuir and Sips adsorption models. More details about the whole procedure are reported in Caravella et al. (2015) for silicalite64 and DD3R.65 In the form of the used adsorption models, the temperature dependence of saturation loading is also considered. To this regard, the saturation loading is a quantity that depends not only on the number of adsorption sites on the surface but also on the interaction among molecules. In general, a higher energetic state of molecules on the zeolite surface (i.e, a higher temperature) can significantly reduce the number of molecules able to form a complete monolayer at saturation conditions. To take into account this effect, some empirical expressions from Do (1998) are used.66

2. EXPERIMENTAL DATA AVAILABLE IN THE OPEN LITERATURE As mentioned above, the experimental isotherms used for parameters calculation are taken from various available sources in order to make the applicability of our results as wide as possible. Figure 2 shows a sketch of adsorption properties data Figure 1. Schematic view of the structure of faujasite (ref 12).

interconnected by windows of 7.4 Å.3,12−14 They can be divided into X- and Y-type, depending on the Si/Al ratio. The former has the Si/Al ratio in the range of 1 to 1.5, whereas the latter has typical range of 1.5 to 3.14−17 Therefore, the X-type structure contains more aluminum and, thus, more extraframework cations are necessary to balance these charge defects (Na+, Li+, K+, Cs+, Ba2+). The extra-framework cations occupy preferentially the sites I, I′, II, III, and III′.18 Their distribution in these sites as a function of the number of cations per unit cell has been extensively studied.19−26 The FAU chemical formula can be written as Si192−xAlxMxO384, in which M is an abovecited cation and x values can vary from 0 to 96, obtaining different Si/Al ratio.26 In particular, NaX or NaY-types with a Si/Al of 1 or 2.4, respectively, are obtained (M = Na) when x is equal to 92 or 56. Jhung et al. (2007)27 studied the effect of aluminum and cation concentration on H2 adsorption in FAU, MFI, and MOR zeolites, finding that an increase of Si/Al ratio causes a decrease of adsorption capacity in all zeolites. Kazansky et al. (1998)28 measured the hydrogen adsorption isotherms on FAU zeolites with different Si/Al ratios, obtaining a higher adsorption capacity for the NaX zeolite with the Si/Al ratio of 1.05 and a lower one for the NaY with an Si/Al of 2.40. The contribute of the present paper consists in giving/ identifying the optimal values of the respective parameters of both Langmuir and Sips adsorption models, utilizing a number of appropriate experimental data available in the open literature as sources.1,4,11,28−63 Therefore, the estimated parameters cover a wide range of temperature and pressure in terms of adsorption isotherms of some light gases, that is, H2, CH4, CO2, CO, H2O. The explicit functionality of the adsorption parameters of these models with the temperature and pressure is provided and, thus, the parameters resulting from this paper allow the direct calculation of the adsorption properties by scientists and other end-users at the desired operating conditions. This allows the suitability of these materials to be identified for their application in various technological fields by a preliminary evaluation “at a glance”. This evaluation was carried out using the Levenberg− Marquardt algorithm to perform a nonlinear multivariate regression analysis of experimental adsorption isotherms

Figure 2. Overview of the published experimental isotherms used in the present work for NaX and NaY zeolites.

of some important species, that is, H2, CH4, CO2, CO, H2O available in the open literature1,4,11,28−63 and used in this work for the NaX and NaY zeolites, respectively. These data were measured at temperature ranging from 77 K to 543 K. Table 1 reports the information for a total of 107 adsorption isotherms of the above-cited gases and the corresponding temperature and pressure ranges. Depending on the species considered, the maximum used pressure ranged from 3.3 kPa to 6306 kPa. The Si/Al ratio of the different references for both NaX and NaY zeolites are reported in Table 2. The isotherms available in the open literature are preliminarily compared each other to verify the consistency among the different experimental data following the same procedure as that reported elsewhere.64 Therefore, some experimental data67−76 were analyzed but not included in the calculation owing to the discrepancy among the adsorption isotherms. This is probably due to the different morphological and physical properties of the various zeolites B



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(2007),11 who expressed the isotherms in absolute adsorbed amount, provide quite similar adsorption isotherms, thus confirming that a relevant difference between excess and absolute adsorbed amount would be observed just for H2 at pressures close to the saturation conditions. As a further check, a comparison between the Sips saturation loadings obtained by Tedds et al. (2011)29 and that obtained in the present work using all adsorption isotherms shows that the difference is very small. In fact, Tedds et al. (2011)29 obtained an absolute Sips saturation loading of 14.2 mol kg−1, whereas a value of 13.1 mol kg−1 is obtained from its data expressed in excess adsorbed amount. 2.1. Data Available for NaX. Tedds et al. (2011)29 measured the adsorption isotherms of H2 up to 15 bar in a wide temperature range (between 77 K and 237 K). The data at 77 K are in a good agreement with those measured by Kazansky et al. (1998)28 and Prasanth et al. (2008).30 The adsorption measurements at higher temperature are taken from Belmabkhout et al. (2007),11 which studied the adsorption isotherms of CH4, CO2, CO, and H2 in a wide range of temperature (303 K to 473 K) and pressure (0 kPa to 1200 kPa) by a static gravimetric method. The experimental data of CH4 are available within 275 K to 473 K and 0 kPa to 5674 kPa.11,32−36 In particular, Loghlin et al. (1990)31 measured the equilibrium adsorption of light nalkanes on Linde 5A and 13X (= NaX) pellets in a temperature range of 275 K to 350 K and up to 1439 kPa, for CH4. Zhang et al. (1991)32 tested five types of X zeolites (NaX, MgX, CaX, SrX, and BaX) ranging from 298 K to 343 K. Cavenati et al. (2004)33 reported the adsorption of CH4, CO2, and N2 on zeolite 13X, obtaining a preferential adsorption of CO2 with respect to the other species. Pillai et al. (2010)34 studied the adsorption of CH4, CO, and N2 on different X-types zeolites at 303.2 K obtaining a higher adsorption capacity for CO and CH4 with respect to that of N2. Furthermore, Sethia et al. (2014)35 performed the equilibrium adsorption measurements of CH4 and N2 on NaX and other X zeolites, changing the cesium content. Finally, Dunne et al. (1996)36 measured the adsorption isotherms of various gases in NaX, including CH4 at 304 K. As for CH4 and CO2, the experimental measurements are carried out in a wide range of temperature (273 K to 473 K) and pressure (0 kPa to 1246 kPa) by different authors.1,11,37−40 Khelifa et al. (2004)37 evaluated adsorption isotherms from 273 K to 393 K at intervals of 30 K. Walton et al. (2006)1 studied the adsorption of CO2 at 298 K on both X and Y sodium zeolites and some of their exchanged forms with alkali metal cations. Wang et al. (2009)38 measured the adsorption of water vapor and carbon dioxide on 5A and 13X zeolite beads and silica gel granules in a volumetric apparatus, covering a wide temperature range. Finally, experimental data at 293 K and 353 K are reported by Kazansky et al. (1999)39 and Choudhary et al. (1995),40 respectively. Less information is available for CO, for which adsorption isotherms at four temperatures are taken from Belmabkhout et al. (2007)11 The first isotherm (at 303 K) is also compared to some isotherms obtained by Pillai et al. (2010),34 this providing a further robustness of these experimental data. The H2O adsorption isotherms are available up to relatively high temperature values (543 K). Dzhigit et al. (1969)41 measured the isotherms at 296 K for different zeolites (LiNaX2, NaX, KNaX, RbNaX, and CsNaX), in which K, Rb, and Cs are present along with Na. Further adsorption data are provided at

Table 1. Overview of the Operating Conditions Ranges Concerning the Published Experimental Adsorption Isotherms Used in the Present Work Tminimum

Tmaximum

Pmaximum

K

K

kPa

H2 CH4 CO2

77 275 273

373 473 473

CO H2O

303 296

473 543

H2 CH4 CO2 CO H2O

77 200 273 77 298

303 343 473 340 303

species

references

number of isotherms

NaX 1500 11, 28−30 5674 11, 31−36 1246 1, 11, 33, 37−40 1031 11, 34 74 41−45 NaY 4000 46−48 6306 4, 49−51 3000 1, 40, 51−55 45 56−59 3.3 44, 60−63

12 17 20 5 14 4 8 18 4 5

Table 2. Si/Al Ratio of the Various Zeolites Taken into Account for the Experimental Adsorption Isotherms NaX component H2

CH4

Si/Al

reference

Si/Al

reference

1.25 1.05 1.53 1.18 1.25

11 28 29 30 11 31 32 33 34 35 36 1 11 33 37 38 39 40 11 34

2.76 2.30

46 47 48

2.20 2.40 2.40 2.40

4 49 50 51

2.35 2.40 2.40 2.31 2.54

1 40 51 52 53 54 55 56 57 58 59 60 61 44 62 63

1.30

CO2

1.18 1.18 1.23 1.23 1.25 1.21

CO

H2O

NaY

1.00 1.30 1.25 1.18

1.38 1.38 1.18 1.53

41 42 43 44 45

2.50 2.40 2.37 2.40 2.67 2.69 2.43 2.30

tested, as well as different pre- and post-treatments to which the zeolites were subjected. Before examining the details of the used experimental data, it is necessary to specify that, in general, adsorption measurements produce data in terms of excess of adsorption amount. In the present work, there are several experimental data expressed in absolute adsorbed amount, that is, Cavenati et al. (2004)33 and Choudhary et al. (1995),40 as well as several others expressed in terms of amount excess. Some of these data, compared with those obtained from Belmabkhout et al. C



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These parameters are the elementary “bricks” of the models, and their good estimation indicates the evaluation quality within the considered ranges of temperature and pressure. The use of values of adsorption parameters outside the operating range considered for regression is also possible with higher degree of uncertainty. However, even in the “worst” case, these parameters can give a “first” indicative values. 3.1. Adsorption Isotherms. Figures S1 to S5 and Figures S6 to S10 (see Supporting Information) show the results of the regression analysis in terms of adsorption isotherms of the considered species, (H2, CH4, CO2 CO, H2O) for NaX and NaY, respectively. The isotherms were calculated for both Langmuir and Sips models utilizing the models parameters previously estimated in this work, which are reported and discussed in more detail in Sections 3.2 and 3.3. Therefore, these figures show the overall result coming at the end of the whole parameter estimation procedure. In addition, the same figures show the experimental data from the literature for comparison purpose. To give to the reader the possibility to appreciate the results quality, the isotherms data are shown for low- and highpressure ranges in the left-hand and right-hand side plots, respectively, for all species except for CH4, CO, and H2O on NaX (Figures S2, S4, and S5 in Supporting Information) and for H2O on NaY (Figure S10 in Supporting Information), for which such a division is not necessary. In most cases, the isotherms calculated using the parameters previously estimated in this work, consisting in one set for each Langmuir and Sips models, reproduce satisfactorily the corresponding isotherms taken from the open literature. The results for NaX are reported in Figures S1−S5 (Supporting Information). It can be observed that the adsorption isotherms are satisfactorily described by both the considered models for the majority of the considered species, as indicated by the R2 values of the Langmuir and the Sips model, respectively (0.9795 and 0.9917 for H2, 0.9860 and 0.9902 for CH4, 0.9513 and 0.9808 for CO2, 0.9956 and 0.9967 for CO, 0.9195 and 0.9495 for H2O). This indicates that the chosen functionalities of the various adsorption parameters with temperature provide a satisfactory result except for CO2 and water, for which both models are not fully able to describe the overall experimental trends. As already said before, the difference between the two models in terms of description of the experimental data is not evident from the figures. However, Sips values of R2 are higher than the Langmuir ones for all the species and, thus, the Sips model describes better than the Langmuir one the experimental data. Figures S6−S10 report the considered experimental adsorption isotherms of the considered species along with the respective model curves. As mentioned above and for the same reasons, also for NaY each figure is split into a low- (left-side) and high pressure plot (right-side), with the only exception of H2O (Figure S10), for which the experimental isotherms are only available at low-pressure values. Also for NaY, the adsorption isotherms are satisfactorily described by both the considered models, as indicated by the values of R2 (0.9916 and 0.9998 for H2, 0.9960 and 0.9966 for CH4, 0.9595 and 0.9844 for CO2, 0.9962 and 1.000 for CO, and 0.9391 and 0.9933 for H2O by adopting the Langmuir and the Sips model, respectively). Also in this case, the Sips model describes the experimental data slightly better than the Langmuir one. 3.2. Determination of Langmuir and Sips Model Parameters for NaX. The optimal values of the adsorption

296 K by Chuikina et al. (1975),42 who also analyzed isotherms of water vapor at 373 K in NaX compared to KNaX. Data at 298 K were obtained gravimetrically by Hunger et al. (2006),43 whereas others at 300 K are given by Di Lella et al. (2006),44 who reported the data of Dzhigit and co-workers. Barrer et al. (1959)45 measured the adsorption isotherms for the NaX faujasites from 303 K to 543 K. 2.2. Data Available for NaY. Raj et al. (2012)46 measured adsorption isotherms of H2 at 77 K and 303 K, using a static volumetric system. The same results were previously obtained at 77 K by Langmi et al. (2003)47 and Yaremov et al. (2008).48 Regarding CH4, the experimental adsorption isotherms are taken from a number of sources4,49−51 under different operating conditions and covering a wide range of temperature and pressure. In particular, Talu et al. (1993)4 measured the CH4 isotherms in various Y zeolites at different temperatures, providing data for NaY at 298 K, 313 K, 323 K, 333 K, and 343 K. Adsorption data are obtained by volumetric and microcalorimetry measurements at 200 K and 300 K by Deroche et al. (2010)49 and Maurin et al. (2006),50 respectively. Ghoufi et al. (2009)51 investigated the CH4 and CO2 adsorption in conditions of both single gas and binary mixture at 303 K by both experimental tests and Monte Carlo simulations. It is for CO2 that the highest number of isotherms is available.1,4,51−55 Shiralkar and Kulkarni (1984)52 studied CO2 adsorption in various Y zeolites in the range of 273 K to 423 K. Maurin et al. (2007)53 combined adsorption tests and simulation in both NaY and LiY zeolites from 323 K to 473 K. Shao et al. (2009)54 synthesized NaY zeolite particles using a hydrothermal method and measured the adsorption of CO2 and N2 at various temperatures. Furthermore, Hasegawa et al. (2001)55 prepared Y-type zeolite membranes on the inner surface of porous a-alumina tubes to investigate CO2−N2 permeation. The Y-types crystallites were used for adsorption tests within 308 K and 423 K. The adsorption isotherms of CO are also available in a wide range of temperature, (77 K to 340 K) but in a quite narrow pressure range.56−59 Cairon et al. (2012)56 studied the adsorption isotherm at very low temperature (77 K) and pressure (up to 100 Pa). Experimental results at higher temperatures are reported by Egerton et al. (1970),57 who investigated the behavior of NaY and six samples of CaY at 273 K. Moreover, Boddenberg et al. (1995)58 studied the adsorption of CO and xenon in different Y zeolites at 298 K. The experimental data at 340 K are taken from Hartmann et al. (1994).59 The H2O isotherms are available in a generally narrower temperature range for NaX zeolites (298 K to 303 K) up to pressure values close to saturation.44,60−63 In particular, Bellat et al. (2009)60 measured adsorption−desorption isotherms of water at 298 K, showing the existence of a hysteresis loop only in relatively low-pressure range. The experimental data are in agreement with those reported by Sychev et al. (2001)61 at the same temperature and Di Lella et al. (2006)44 at 300 K. The adsorption isotherms at 303 K are taken from Boddenberg et al. (2002)62 and Pires et al. (2003).63

3. RESULTS AND DISCUSSION The results of this paper are first presented in terms of adsorption isotherms (section 3.1) and then in terms of parameters of the Langmuir and Sips models (sections 3.2 and 3.3). D



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parameters evaluated with the Langmuir model are reported in Figure 3. The R2 values are reported just for one case, as they

Figure 3. Calculated optimal values of the Langmuir model parameters for the considered species on NaX. Saturation loading Cμs0, parameter b0, heat of adsorption QAds,Langmuir, empirical parameter χ.

are the same for all the parameters (multivariate regression). The confidence intervals are quite narrow for all the parameters of each species (except b0 of H2O), and thus, the parameters estimation is accurate. The functionality of the saturation loading with temperature depends on the value of the empirical parameter χ (see the Supporting Information). From the regression results, it can be observed that the saturation loading is temperature-dependent for all the considered species, as they have χ values significantly different from zero. Figure 4 shows the optimal values of the adsorption parameters of the Sips model. All the Sips saturation loadings at the reference temperature are higher than those of Langmuir. Moreover, the Sips temperature dependence of Cμs (given by the parameter χ) is quite similar to the Langmuir one just for H2, whereasregarding the other speciesthe two models show a different trend. In particular, CO2, CO, and H2O show a stronger temperature dependence of Cμs with the Langmuir model, whereas CH4 is stronger with the Sips one. Moreover, the Sips model forecast that CO saturation loading does not depend on temperature, owing to the estimated value of χ close to zero. The general trend is that confidence intervals for H2, CH4, and CO2 are narrow, whereas they depend on the parameter considered in case of CO and H2O. In particular, regarding these two species, narrower confidence intervals are obtained for Cμs0, b∞,Sips, heat of adsorption and n0, whereas a higher uncertainty is evident for χ and α. However, considering the only two parameters that can be compared (Cμs0 and χ), the confidence intervals obtained with the Sips model are wider than those obtained with the Langmuir one. 3.3. Determination of Langmuir and Sips Model Parameters for NaY. The same types of figures made for the NaX zeolite are made for the NaY one as well. Figure 5 shows the optimal values of the key-adsorption parameters evaluated with the Langmuir model. Quite narrow confidence

Figure 4. Calculated optimal values of the Sips model parameters for the considered species on NaX. Saturation loading Cμs0, Sips affinity constant at infinite temperature b∞,Sips, heat of adsorption QAds,Sips, empirical parameter χ, empirical exponent n0, empirical parameter α.

Figure 5. Calculated optimal values of the Langmuir model parameters for the considered species on NaY. Saturation loading Cμs0, parameter b0, heat of adsorption QAds,Langmuir, empirical parameter χ.

intervals are calculated for the parameters of CH4 and CO2, this indicates good parameter accuracy. However, in general, the confidence intervals of all of the components are narrow for E



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The other parameters of the Sips model have different meanings from those of the Langmuir one and, thus, cannot be directly compared. In the case of the Sips model, confidence intervals of Cμs0, b∞,Sips and n0 are quite narrow for all the components, whereas their width depends on the species considered for the other parameters. 3.4. Isosteric Heat of Adsorption: Discussion and Comparison with the Literature. In this section, the calculated parameters are compared to some literature values, considering that the information scarcity of some adsorption parameters (i.e., saturation loading) of the species makes the results from our investigation quite important in covering such an information lack. The relationship between isosteric heat of adsorption and heat of adsorption is provided by the van’t Hoff equation.66 Using the Sips model, the following expression for the isosteric heat of adsorption as a function of fractional loading is obtained eq 164

saturation loadings only, whereas they can be narrow or wide for the other parameters, depending on the species considered. The highest confidence intervals are those of H2O. By observing the functionality of the saturation loadings with temperature, we can conclude that also in this case all species show a strong temperature dependence except CH4, whose dependence is lower, because of the lower value of χ. Analogously to what done for the Langmuir model, Figure 6 shows the optimal values of the parameters of the Sips model.

⎡ θ ⎤ Q Iso,Sips = Q Ads,Sips − αRT0n2 ln⎢ ⎣ 1 − θ ⎦⎥ +n

χR gT 2 ⎡ 1 ⎤ ⎢ ⎥ T0 ⎣ 1 − θ ⎦

(1) 64

As already reported elsewhere, it can be observed that when the parameter α is close to zero, meaning that n assumes a value close to the unity, the Sips isosteric heat of adsorption tends to coincide with the Langmuir one, as expected. Additionally, if the parameter χ is close to zerothis indicating a very weak functionality with temperaturethe Sips heat of adsorption is in fact the isosteric heat of adsorption calculated at a fractional loading of 0.5. It is also worth noting that values of θ > 0.5 implies a negative contribution of the second term of the right-hand side of eq 1, whereas the opposite occurs for θ < 0.5. Figures 7 to 11 show the trends of the Sips isosteric heat of adsorption versus the loading for each species. According to the model equations, flat trends of isosteric heat of adsorption, and thus flat trends of heat of adsorption, are found in all the cases where the parameter α is calculated to be very close to zero and n0 is close to the unity. In fact, by substituting α = 0 and n0 = 1 in eq 1, the isosteric heat of adsorption is coincident to heat of adsorption, this in turn resulting in the isosteric heat of adsorption independence of the fractional loading. Generally speaking, the higher the loading, the lower the isosteric heat of adsorption. This occurs because at higher loadings the species−species interactions become comparable with the zeolite−species ones. In fact, the species−species interactions are dipole−dipole type or van der Waals-type, which are basically poorly activated processes (i.e., isosteric heat of adsorption close to zero). Therefore, the massive presence of a species (i.e., high loading) generally causes the apparent isosteric heat of adsorption to decrease. However, this effect is generally sufficiently small that the isosteric heat of adsorption can be considered practically constant in a wide loading range with a good approximation. Actually, both of these tendencies are observed for the gas species considered in the present work. In fact, the H2 isosteric heat of adsorption shows the former type of decreasing trend reported above in the NaX zeolite, whereas it shows the latter type of flat trend in the NaY. The same is observed for CH4. If considering that both H2 and CH4 are essentially no-polar species, we could make a preliminary guess for which the higher is the hydrophilic character of the zeolite; the lower is the

Figure 6. Calculated optimal values of the Sips model parameters for the considered species on NaY. Saturation loading Cμs0, Sips affinity constant at infinite temperature b∞,Sips, heat of adsorption QAds,Sips, empirical parameter χ, empirical exponent n0, empirical parameter α.

In particular, the values of saturation loadings at the reference temperature T0 obtained with the Sips model are slightly higher than those obtained with the Langmuir one for H2, CO2, and CO, whereas a slightly lower value and the same value are obtained in the case of CH4 and H2O, respectively. Also in this case, the temperature dependence on the saturation loading reveals that, for all the species considered, the saturation loading depends significantly on temperature. Moreover, the comparison between the Langmuir and Sips values of χ states that the behavior of the saturation loadings with temperature is different for almost all species considered. In particular, a stronger temperature dependence of the saturation loading calculated by the Langmuir model is obtained for H2, CO2, and H2O, whereas slightly stronger temperature dependence by the Sips one is obtained for CH4. Finally, the behavior is similar for CO, owing to the two χ values quite close to each other. F



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Figure 9. Isosteric heat of adsorption of CO2 versus loading on NaX (a) and NaY (b) zeolites: red lines, isosteric heats of adsorption evaluated with eq 1; brown lines, heats of adsorption calculated for the Sips model.

Figure 7. Isosteric heat of adsorption of H2 on NaX (a) and NaY (b) zeolites: red lines, isosteric heats of adsorption evaluated with eq 1; brown lines, heats of adsorption calculated for the Sips model.

Figure 10. Isosteric heat of adsorption of CO versus loading on NaX (a) and NaY (b) zeolites: red lines, isosteric heats of adsorption evaluated with eq 1; brown lines, heats of adsorption calculated for the Sips model.

Figure 8. Isosteric heat of adsorption of CH4 on NaX (a) and NaY (b) zeolites: red lines, isosteric heats of adsorption evaluated with eq 1; brown lines, heats of adsorption calculated for the Sips model.

tendency of the isosteric heat of adsorption of nonpolar gas species to change with loading. As for the other species considered (i.e., CO2, CO, and H2O), an important decrease of isosteric heat of adsorption with increasing loading is observed, in both regression results and experimental data used for comparison in order to put in evidence the discrepancies and similarities also between literature data from different sources, whenever possible. Tedds et al. (2011)29 evaluated the H2 isosteric heat of adsorption on NaX as a function of loading obtaining a

decrease similar to that of this work, as shown in the Figure 7a. Jhung et al. (2007)27 report the H2 isosteric heat for a FAU zeolite (Si/Al = 2.81) variable with the amount of the adsorbed species in the range of 6.4 kJ/mol to 7 kJ/mol. Their values were found to be slightly higher than those obtained in our investigation (Figure 7b). The trend of the isosteric heats of adsorption for CH4 and CO2 for NaX (Figures 8a to 9a) is compared with the experimental values obtained by Dunne et al. (1996)36 and the G



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NaX, the trend of the curves representing isosteric heat of adsorption versus loading (Figure 11a) is similar to those evaluated in the literature,41,44 but the isosteric heat of adsorption values are quite lower. On the other hand, for NaY, each curve of the water heat of adsorption is characterized by a very steep slope (Figure 11b), this owing to the high values of both α and n0. Moreover, the heat of adsorption based on the Sips model for NaY is quite higher than the corresponding value of NaX. From a more physical point of view, this is related to the stronger bond between water and NaX sites compared with the NaY case owing to the higher hydrophilic character of the latter. 3.5. Saturation Loadings: Discussion and Comparison with the Literature. An important comparison can be carried out among the molecular loadings at different temperatures, obtaining a good agreement among the calculated values in this work and literature data. In particular, Langmi et al. (2003)47 measured the hydrogen uptake at 15 bar and 77 K in various materials including NaX and NaY. In the case of NaY, the value of the measured loading (9.05 mol·kg−1) is very close to those evaluated in this simulation with the two (8.85 mol·kg−1 and 9.25 mol·kg−1, respectively). On the other hand, in the case of NaX, the two models provide values −10.46 mol·kg−1 and 10.75 mol·kg−1, respectively, slightly higher than that measured (8.95 mol·kg−1). Talu et al. (1993)4 reports the methane adsorption capacity of 3.96 mol·kg−1 at 298 K and 5200 kPa for NaY zeolite. The Langmuir and Sips models provide the values of 4.07 mol·kg−1 and 4.02 mol·kg−1 under the same conditions. Regarding CO2, Choudhary et al. (1995)40 reported the Langmuir saturation loadings of 6.72 mol·kg−1 and 7.69 mol· kg−1 for NaX and NaY at 305 K, respectively, whereas the values of this work are 6.30 mol·kg−1and 7.34 mol·kg−1 at the same temperature. Moreover, Shao et al. (2009)54 obtained the Sips saturation loading of 8.97 mol·kg−1 at 303 K, which is practically the same as the value estimated in the present work (8.91 mol·kg−1) at the same temperature. Saha et al. (2009)70 correlated the experimental adsorption isotherms of CO in the zeolite 13X using the Langmuir model. The value of its saturation capacity at 237 K is 5.51 mol·kg−1, whereas we extrapolated a capacity of 4.27 mol·kg−1 at the same temperature. The Langmuir saturation capacities of water evaluated in this work at 298 K are 18.91 mol·kg−1 for NaX and 20.27 mol·kg−1 for NaY. Hunger et al. (1997)79 determined the adsorbed amounts with a simultaneous thermal analysis apparatus, obtaining 16.55 mol·kg−1 and 16.25 mol·kg−1, respectively. Moreover, Beta et al. (2004)80 obtained the NaX and NaY water loadings of 18.10 and 16.90 mol kg−1, respectively. To provide a direct use to end-users and compare the results from Langmuir and Sips models, Tables S1 to S10 in Supporting Information report the same information already shown in Figures 3 to 6 for each considered species in terms of more detailed numerical values.

Figure 11. Isosteric heat of adsorption of H2O versus loading on NaX (a) and NaY (b) zeolites: red lines, isosteric heats of adsorption evaluated with eq 1; brown lines, heats of adsorption calculated for the Sips model.

calculated values obtained by Belmabkhout et al. (2007)11 and Pulin and Fomkin (2004).77 The results show that the evaluated trends are in good agreement with those reported in the literature for both the components. However, in the case of CO2 (Figure 9a), this work provides a stronger dependence on amount adsorbed of isosteric heat with respect to the literature data. Yaremov et al. (2013)78 studied the isosteric heat dependence on coverage for CH4, CO2, CO, and N2 in different materials. In the case of NaY, a different trend of isosteric heat versus loading is obtained for CO2 with respect to that of the other species. On the one hand, the isosteric heat of CH4, CO, and N2 decreases with the pore occupancy but, on the other hand, that of CO2 increases with the coverage, differently from what found in both Shao et al. (2009)54 and in the present study. A direct comparison between the Yaremov et al. (2013)78 results and the isosteric heat evaluated in this work is carried out for CH4 (Figure 8b) and CO (Figure 10b). In particular, Figure 8b shows a good agreement between the values of Yaremov et al. (2013),78 slightly dependent on the loading, and the constant value obtained in the present work. Figure 10b shows a good agreement between the literature isosteric heat78 and the evaluated curve at77 K. Shao et al. (2009)54 also report the CO2 isosteric heat of adsorption as a function coverage (Figure 9b), obtaining a trend similar to the present work at low molecular loading (< 2 mol·kg−1) followed by a strong drop at higher adsorbed amount. As reported in Figure 10a, the experimental values of the CO heat of adsorption evaluated by Pillai et al. (2010)34 are quite similar to those of this work. Figure 11 shows the water isosteric heat of adsorption on NaX and NaY evaluated in this work and, for comparison, the Sips heat of adsorption based and the differential heats of adsorption obtained by Dzhigit and co-workers41,44 and Boddenberg et al. (2002),62 respectively. The behavior is different for the two zeolites. In fact, regarding

4. CONCLUSIONS The four parameters of the Langmuir adsorption model as well as the six parameters of the Sips one were evaluated by a multivariate nonlinear regression using all the pure component experimental isotherms available, at our knowledge, in the open literature. The values of saturation loadings evaluated with the Langmuir model are in general close to those obtained with the Sips one, showing different temperature dependence. A H



Article

n0, Empirical exponent in the Sips model at the reference temperature, − P, Pressure, Pa QAds,Lang, Heat of adsorption based on the Langmuir model, J·mol−1 QAds,Sips, Heat of adsorption based on the Sips model, J·mol−1 QIso,Lang, Isosteric heat of adsorption based on the Langmuir model, J·mol−1 QIso,Sips, Isosteric heat of adsorption based on the Sips model, J·mol−1 Rgas, Gas constant, 8.314 J·mol−1·K−1 T, Temperature, K T0, Reference temperature, K

comparison with the few parameters values available in the literature confirms the accuracy of the present calculations. An evident temperature dependence of saturation loading was found for all species, this owing to the values of the empirical parameter χ that is significantly different from zero. The only exception is the behavior of CO on NaX, for which the Sips model does not provide temperature dependence. Moreover, the isosteric heat of adsorption evaluated from the van’t Hoff equation is compared with some literature data, in which the functionality with coverage is taken into account. The results show a good agreement for all the species. The evaluated parameters can be effectively used, for example, as input in selective adsorption and for simulation of multicomponent mass transport through zeolite membranes. The adsorption isotherms, which include all together the model parameters, calculated using the result of this work show a really good agreement with the isotherms took from the literature. Therefore, the estimated parameters for the Langmuir and Sips models can be used with a high confidence in wide operating ranges because of the large amount of literature data for both adsorption and permeation in these zeolites.

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Greek Letters

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.5b00215. Langmuir and Sips model parameters and equations, adsorption isotherms. (PDF)

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α, Empirical parameter in eq S7, − χ, Empirical parameter in eqs S5 and S10, −

AUTHOR INFORMATION

Corresponding Author

*Tel.: +39 0984 492029. Fax: +39 0984 402103. E-mail: g. [email protected]. Funding

This project has received funding from the European Union; Seventh Programme for research, technological development and demonstration under grant agreement no. NMP3-LA2011-262840 “DEMCAMER − Design and Manufacturing of Catalytic Membrane Reactors by Developing New Nanoarchitectured Catalytic and Selective Membrane Materials” (www.demcamer.org). Notes

The authors declare no competing financial interest.

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ABBREVIATIONS a, Sticking coefficient, − bLang, Langmuir affinity constant, Pa−1 bSips, Sips affinity constant, Pa−1/n b0, Parameters defined in eq S4, K0.5 Pa−1 b∞,Lang, Langmuir affinity constant at infinite temperature, Pa−1 b∞,Sips, Sips affinity constant at infinite temperature, Pa−1/n Cμ, Molecular loading, mol·kg−1 Cμs, Saturation molecular loading, mol·kg−1 Cμs0, Saturation molecular loading at the reference temperature, mol·kg−1 kd∞, Desorption rate constant at infinite temperature, mol· s−1·m−2 M, Molar mass, kg·mol−1 n, Empirical exponent in the Sips model, − I



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Estimation of Langmuir and Sips Models Adsorption Parameters for

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