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Confinement-induced infrared absorption by H2 and N2 gases in a porous silica aerogel
Journal of Quantitative Spectroscopy & Radiative Transfer 182 (2016) 193–198
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Journal of Quantitative Spectroscopy & Radiative Transfer journal homepage: www.elsevier.com/locate/jqsrt
Confinement-induced infrared absorption by H2 and N2 gases in a porous silica aerogel J. Vander Auwera a,1, C. Boulet b, Y. Carré c, L. Kocon c, J.-M. Hartmann d,n a Service de Chimie Quantique et Photophysique, Université Libre de Bruxelles, C.P. 160/09, 50 Avenue F.D. Roosevelt, B-1050 Brussels, Belgium b Institut des Sciences Moléculaires d’Orsay (ISMO), CNRS (UMR 8214), Université Paris-Sud, Université Paris-Saclay, Orsay F-91405, France c Commissariat à l’Energie Atomique et aux Energies Alternatives, Division des Applications Militaires, le Ripault, F-37260 Monts, France d Laboratoire Interuniversitaire des Systèmes Atmosphériques (LISA), CNRS (UMR 7583), Universités Paris-Est Créteil et Paris Diderot, Institut P.-S. Laplace, Université Paris-Est Créteil, 94010 Créteil Cedex, France
a r t i c l e i n f o
abstract
Article history: Received 27 April 2016 Received in revised form 27 May 2016 Accepted 29 May 2016 Available online 3 June 2016
Transmission spectra in the fundamental bands of H2 and N2 gas inside the pores of a silica aerogel sample were recorded at room temperature and for several pressures using a Fourier transform spectrometer. They first show that, as the absorption is proportional to the pressure, it is due to the interactions of the molecules with the inner surfaces of the pores and not to the dipole induced during gas-phase molecule–molecule collisions. Furthermore, the analysis of the widths and areas of the observed absorption structures indicate that, for the considered aerogel sample, most of the absorption is likely due to “free” molecules moving within the pores with a weak contribution of adsorbed molecules. & 2016 Elsevier Ltd. All rights reserved.
Keywords: Infrared absorption H2 and N2 gases Porous silica aerogel Surface-induced absorption
1. Introduction While isolated homonuclear diatomic molecules, such as H2 and N2, absorb (weakly) in the infrared through narrow optical transitions due to their vibrating quadrupole moment, much broader features are observed when these molecules interact with their environment. In the pure gas phase, this is due to the short-lived dipole induced by intermolecular interactions that gives rise to the so-called Collision Induced Absorption which is proportional to the squared density for pure gas. This process has been extensively studied [1–3], both experimentally and theoretically (e.g. [4–7] for H2 and [8–11] for N2), and it significantly participates in the spectra of planetary n
Corresponding author. E-mail address: [email protected] (J.-M. Hartmann). 1 Senior research associate with the F.R.S.-FNRS (Belgium).
http://dx.doi.org/10.1016/j.jqsrt.2016.05.032 0022-4073/& 2016 Elsevier Ltd. All rights reserved.
atmospheres [2]. Similarly, when these molecules are adsorbed on, or close to, a solid surface, the electric field of the latter polarizes the molecule, hence creating a dipole and therefore an infrared spectrum. In fact, the interest of spectroscopy for the study of adsorption phenomena in natural as well as synthesized porous media arose a long time ago [12]. As example, the infrared absorption of H2 and D2 adsorbed in NaA zeolites has been the subject of many experimental and theoretical studies (see [13] and references therein). Similarly, physisorbed N2 on Al2O3 surfaces was also detected by high sensitivity IR spectroscopy [14]. In 2002, induced IR absorption of molecular H2 trapped in solid C60 was observed at room temperature [15]. This study revealed that H2 is rotating almost completely freely while at the same time, undergoing localized 3-dimensional translational motion within the box formed by the C60 molecules. More recently, there has been a new interest in the analysis of spectra recorded at room temperature in various porous materials, a situation where
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many of the confined molecules remain in the gas phase and are not adsorbed. In most of such studies (e.g. [16– 19]), the investigated molecules possess a dipole moment so that the observed absorptions are dipole-allowed, but, very recently, the induced spectrum of H2, was observed [20] for the first time at room-temperature in nanoporous aerogel. This observation raises the following question: Is the absorption due to molecules freely moving within the pores, due to adsorbed ones, or due to both? In order to clarify this issue, we have extended this previous study by considering both the H2 and N2 molecules (in addition to CO which is used to probe the aerogel porosity) and recording spectra for various pressures using a high resolution Fourier transform spectrometer. The remainder of this paper is divided into three main parts. Experimental details are given in Section 2 while the data analysis procedure and its results are described in Section 3. The values of the parameters retained to characterize the observed absorptions (peak position, width, area) are discussed in Section 4.
2. Experimental The experimental spectra were recorded with a high resolution Bruker IFS 120 (upgraded to 125) HR Fourier transform spectrometer, using the 14.5 mm long stainless steel cell, pressure gauges and temperature sensors described in [19]. The instrument was fitted with a tungsten source, a KBr beamsplitter, a low pass optical filter and an InSb detector cooled down to 77 K. The low pass filter had a cut-off wavenumber near 3700 cm–1 for CO and N2 and 5400 cm–1 for H2. The infrared radiation beam was transmitted through the aerogel sample, placed inside the cell closed by CaF2 windows. Unapodized spectra of CO, N2 and H2 were recorded with the experimental conditions listed in Table 1. Transmittance spectra were obtained for each pressure as the ratio of the sample spectrum and the average of empty cell spectra recorded before and after at low resolution [maximum optical path difference (MOPD)¼9 cm]. The aerogel sample used, shown in Fig. 1, is basically a truncated cone with a length of 13.2 70.1 mm and diameters from 14.9 70.1 to 15.8 70.1 mm. It has been synthesized by the sol–gel polymerization of a silicon alkoxide TEOS (tetraethylorthosilicate). TEOS was polymerized in two steps, using nitric acid as a hydrolysis catalyst followed by ammonia as a condensation catalyst. The resulting alcogels were then dried with carbon dioxide under supercritical conditions, and silica aerogels were obtained with a density of 0.1 g/cm3. The silica aerogel used in this study was sintered one hour at 940 °C to the density of 0.8 g/cm3 (in agreement with the measured weight of 1.93 g, and volume of 2.44 cm3 of the sample used). Note that, with the silica density of 2.2 g/cm3, this implies that the percentage of porosity is about 64%, but that part of this empty volume may not be connected to the outside. Finally note that the observed absorptions by H2 and N2 are very weak so that the resulting spectra are relatively noisy and subjected to baseline (100% transmission)
variations due to slight changes of the IR source intensity between the recordings made with and without gas. This results in non negligible uncertainties on the data retrieved (see below) from their analysis.
3. Analysis 3.1. CO spectrum analysis and aerogel porosity In a first step, in order to get information on the open porosity of the aerogel sample and on the average pore size, we have treated the CO spectrum exactly as done in Ref. [19]. Briefly, the measured transmission of the fundamental band has been least-square fitted assuming Lorentzian line shapes and using the line intensities given in the HITRAN database [21]. For each absorption line ℓ, we then retrieved the optical path length Lℓ in the open pores (which contain CO gas) , and the spectral positions and half width at half maximum Γ ℓ of each line. The results obtained for the transitions lying in the region of (relative) transparency of the aerogel (the R branch, since silica strongly absorbs below 2100 cm 1), are plotted in Fig. 2. As observed previously [19], they are practically independent of the line, leading to average values of L ¼ 7:58 7 0:11 mm and Γ ¼ 0:102 70:006 cm 1 (with uncertainties set to twice the rms of the results in Fig. 2). First note that the measured sample thickness e (e¼13.2 mm, see Fig. 1) leads to a percentage of opened porosity of 100L/e¼57%. This value is compatible with that, of 64%, of the empty volume determined (see Section 2) from the weight and volume of the sample. Furthermore, as suggested in [22,23] and recently demonstrated [24], a single collision of a molecule with a surface is sufficient to destroy the rotating dipole coherence and broaden the line. In this case, and if one assumes long cylindrical pores of diameter d, as done in [19,25], one has d ¼ ðv=cÞ= 2πΓ ðcm1 Þ where v is the mean translational speed of the considered gas (here CO) and c is the speed of light. For the retrieved value of Γ ¼0.102 cm 1 (see Fig. 2b), this leads to d¼ 25 nm. 3.2. N2 and H2 spectra analyses Let us now turn to the H2 and N2 spectra and first mention that measurements carried out for N2 (which shows the narrowest “Q branch”, see Table 2) with various spectral resolutions (see Table 1) lead to practically the same spectra. We have thus retained those which show the best S/N ratio and/or the smallest inconsistencies with the baseline (empty cell spectrum) recording. For their treatment, we first deduced the absorbances from the measured transmissions and then divided them by the optical path length L determined from the CO lines, yielding the absolute absorption coefficient α(σ,P). The latter was then divided by the pressure P of the corresponding recording, leading to a pressure normalized value α0(σ)¼α(σ,P)/P. The results, plotted in Figs. 3 and 4 for N2 and H2 show that these pressure-normalized values are independent of P. This rules out that they are due to the dipole induced during binary collisions between gas
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Table 1 Useful spectral range (“Range” in cm–1), diameter of the entrance aperture of the interferometer (“Iris” in mm), maximum optical path difference achieved (“MOPD” in cm), number of interferograms averaged (“Count”), and sample temperature (“T”) and pressure (“P”), respectively.
CO N2
H2
Range
Iris
MOPD
Count
T/K
2100–2250 2100–2700
1.50 1.50 1.50 1.50 1.50 2.00 2.00 2.00 2.00 2.00 2.00 1.30 1.30 1.30 1.30 1.30
225 0.45 0.45 0.45 9.0 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9
706 5000 5000 10,000 20,300 37,900 40,000 40,000 35,000 18,500 20,000 37,300 39,500 38,000 37,900 37,400
295 295 295 295 294 294 294 294 294 294 294 294.5 294.5 294.5 294.5 294.5
3900–4400
P/hPa (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (10) (10) (10) (10) (10)
29.9 514 904 1285 1018 510 707 895 902 1092 1292 502 705 900 1122 1292
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reported in Table 2 with uncertainties conservatively set to twice the standard deviation of the values obtained from the five spectra.
4. Discussion (3) (3) (6) (7) (5) (3) (4) (5) (5) (6) (7) (3) (4) (5) (6) (7)
4.1. Half widths First consider the values of the HWHM of the absorption peaks for H2 and N2, which are 15 and 3.3 cm 1, respectively (note that the first is in reasonable agreement with that determined under similar conditions in [20]). The ratio of these two values is 4.5 70.8 (where the uncertainty was determined assuming no correlation between the potential errors on the H2 and N2 measurements). Let us assume that the molecules responsible for the observed absorption are freely moving in the vicinity of the pore inner surfaces. In this case, the broadening observed being due to the life time of the induced dipole, we would obtain a HWHM ratio of vH2 ðTÞ=vN2 ðTÞ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi M N2 =MH2 where vX 2 ðTÞ is the mean translational speed of molecule X2 and M X 2 is its mass. The value of this ratio is 3.7, reasonably close to the value (4.5 70.8) deduced from experiment and practically within its uncertainty. This is a first indication that the absorption may be due to “free” molecules (with a minor contribution of adsorbed ones) while they are approaching (or departing from) the pores inner surfaces. 4.2. Areas For the analysis of the areas below the measured absorption, let us assume that the absorption is due to the ! polarization of the molecules by the electric field E existing nearby the inner surfaces of the pores. In this case, if all molecular orientations are taken into account, the area below the absorption is given by [13,26]: AX 2 ¼ BN X 2 σ X 2 ðα2X 2 þ 0:2γ 2X 2 ÞE2
Fig. 1. The aerogel sample (units on the ruler are cm).
phase molecules, since the latter leads to an absorption proportional to P2. This is further confirmed by calculations of this process using the data from [3], which show that it leads to absorptions several orders of magnitude smaller than the measured ones. This leads to the first conclusion that the observed spectra are entirely due to the interactions of the molecules with the inner surfaces of the pores. In order to go further, the spectra in Figs. 3 and 4 have been analyzed in order to retrieve several parameters that characterize them, that are: the value α0Max(cm 1/atm) and spectral position σMax(cm 1) of the peak absorption, the half width at half maximum Γ0(cm 1) of the “Q-branch like” peaking narrow structure at the center of the spectrum, and the area AExp(cm 2/atm) below the spectrum in the spectral range of the two figures. These values are
ð1Þ
where B is a constant, NX2 is the number of X2 molecules involved, and σX2 is the vibrational frequency. αX2 and γX2 are the vibrational matrix elements of the isotropic and anisotropic components of the molecular polarizability, respectively, the values of which for the fundamental band are given in Table 3. From Eq. (1) and the values of Tables 2 and 3, one obtains: AH2 ¼ B 2576N H2 E2
and
so that their ratio is AH2 =AH2
AN2 ¼ B 412NN2 E2 ; ð2Þ ¼ 6:25 NH2 =N N2 . Using the
Exp ratio of the experimentally determined areas AExp H 2 =AN2 ¼
4:1 7 1:5 thus leads to ðN H2 =NN2 Þ ¼ 0:66 7 0:24 . If we first assume that the absorption is entirely due to “free” molecules moving within the aerogel cavities in the field due to the inner surface of the pores, NH2 =N N2 should be equal to unity, which is close to the upper limit of the experimentally determined value. On the opposite, if we assume that the absorption results only from molecules trapped in some adsorption sites on the inner surface of
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Fig. 2. Optical path length L (a) and half width at half maximum (b) retrieved from the CO R(J) lines from J ¼1 to J¼19. The indicative error bars in (a) and (b) correspond to 7 2 and 7 5% respectively. Table 2 Parameters describing the observed absorptions of Figs. 3 and 4, i.e.: the peak positions σMax, its amplitudes α0Max and its halfwidths at half maximum Γ0, and the area AExp below the absorption in the spectral range of the two figures. Mol
σMax (cm 1)
103α0Max (cm 1/atm)
Γ0 (cm 1)
AExp (cm 2/atm)
H2 N2
4142.2 70.2 2326.3 70.1
4.7 7 0.15 5.2 7 0.25
14.9 71.3 3.3 70.5
0.377 0.09 0.0917 0.024
Fig. 4. Pressure-normalized absorption coefficient in the region of the fundamental H2 band deduced from spectra recorded for five different pressures between 502 and 1292 hPa. Table 3 Vibrational matrix elements of the isotropic and anisotropic components of the molecule polarizability (in atomic units).
Fig. 3. Pressure-normalized absorption coefficient in the region of the fundamental N2 band deduced from spectra recorded for five different pressures between 514 and 1292 hPa.
the pores, NH2 =N N2 should be equal to the ratio K H2 =K N2 of the Henry constants driving the adsorption process in the considered range of pressures. To the best of our knowledge such constants are not known for the type of material (porous aerogel with pores of 25 nm diameter) used in this study, and we thus cannot totally exclude that it could be
α01 γ 01
H2 [27]
N2 [28]
0.74 0.61
0.375 0.428
Table 4 Comparison of the Henry constants of H2 and N2: two examples. Ref.
Material
Dimension of the pores (nm) T
[29] Zeolite Na-4A 2.5 [30] Zeolite 5A 99
K H2 =K N2
300 0.25 293 0.09
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equal to about 0.7. However, for other materials for which calculations and/or measurements exist, this ratio has always been found to be much smaller than 0.7 as shown by the two examples of Table 4. Indeed, even for the smaller pore size of 2.5 nm (and it is well known that the Henry constant decreases with the pore dimension) the value of K H2 =K N2 ¼0.25 is clearly outside of our experimental confidence interval of 0:66 7 0:24. Therefore, for the “high” temperature of the present study, the most probable explanation, similar to that experimentally demonstrated for CO (which is isoelectronic to N2 and for which no spectral signature of adsorbed gas was detected), is that the observed absorption is mostly due to H2 or N2 molecules “freely” moving inside the pores (possibly with a minor contribution of those trapped in adsorption sites). 4.3. Peak positions Let us finally discuss the positions of the absorption peaks for H2 and N2, which are 4142.2 and 2326.3 cm 1, respectively, the first being in very good agreement with that determined under similar conditions in [20]. These two values differ (shifts of about 18 and 4 cm 1, respectively) from the frequencies of the maximum of the induced Q branch in the gas phase, around 4160 cm 1 for H2 (as deduced from the ab initio quantum calculated spectra of [31]) and 2330 cm 1 for N2 (as deduced from the experimental spectra of [32]). This is, of course, a consequence of the interactions between the molecules and the inner surfaces of the aerogel pores. It is not easy to compare the present results with previous ones in which the molecules are physisorbed on various surfaces. A first reason is the temperature since most of the results for adsorbed molecules were obtained at low temperature. A second reason is the scattering of these previous results, depending on the materials, the adsorbant surface, etc. For instance, for H2 adsorbed in porous Vycor glass at 18 K, a shift of 30 cm 1 has been observed for the Q(1) line [33]. In contrast, for H2 adsorbed in NaA zeolite a large vibrational shift was observed at 90 K, around 80 cm 1 (depending on the exact nature of the zeolite) [34]. For physisorbed N2, the situations also may be very diverse. When N2 is adsorbed in NaA zeolite, the Q branch frequency is shifted to 2339 cm 1 ( þ9 cm 1) at 185 K [26]. Similar measurements were also made for N2 adsorbed on Al2O3 surfaces exhibiting, only for temperatures lower than 200 K, a band located at 2331 cm 1 ( þ1 cm 1) [14]. Finally, it must be pointed out that an explicit calculation of the shift requires a more sophisticated model than the simple one used above in order to derive some orders of magnitudes of the numbers of molecules. Indeed, while the induced dipole depends on the field near the inner surface of the pores, allowing therefore to build a very simple model, on the opposite, the shifts are known to depend on both the field and the field gradients [13], thus requiring a much more sophisticated approach, far beyond the limits of the present work.
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5. Conclusion We have recorded transmission spectra in the fundamental bands of CO, H2 and N2 gas inside the pores of a silica aerogel sample at room temperature and for several pressures, using a Fourier transform spectrometer. The absorption by CO is used to retrieve information on the pore sizes and on the optical path length within the gas inside the aerogel. This enables the determination of the absolute value of the absorption coefficients by H2 and N2. These show that, the absorption being proportional to the pressure, the absorption spectra are due to the interactions of the molecules with the inner surfaces of the pores and not to the dipole induced during gas-phase molecule– molecule collisions. Furthermore, the analysis of the widths and areas of the observed absorption structures indicate that most of the absorption is likely due, for the considered aerogel, to “free” molecules moving within the pores with a weak contribution of adsorbed molecules. The fact that adsorbed molecules may also participate cannot be ruled out but we believe that their contribution is minor. For a further check of this result, obtained here at room temperature for pores of diameter d E25 nm, complementary experiments for other temperatures and/or other materials and/or different pores sizes would be of considerable interest. Indeed, one expects that all these parameters have a significant influence of the relative amounts of adsorbed and “free” molecules.
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Contents lists available at ScienceDirect
Journal of Quantitative Spectroscopy & Radiative Transfer journal homepage: www.elsevier.com/locate/jqsrt
Confinement-induced infrared absorption by H2 and N2 gases in a porous silica aerogel J. Vander Auwera a,1, C. Boulet b, Y. Carré c, L. Kocon c, J.-M. Hartmann d,n a Service de Chimie Quantique et Photophysique, Université Libre de Bruxelles, C.P. 160/09, 50 Avenue F.D. Roosevelt, B-1050 Brussels, Belgium b Institut des Sciences Moléculaires d’Orsay (ISMO), CNRS (UMR 8214), Université Paris-Sud, Université Paris-Saclay, Orsay F-91405, France c Commissariat à l’Energie Atomique et aux Energies Alternatives, Division des Applications Militaires, le Ripault, F-37260 Monts, France d Laboratoire Interuniversitaire des Systèmes Atmosphériques (LISA), CNRS (UMR 7583), Universités Paris-Est Créteil et Paris Diderot, Institut P.-S. Laplace, Université Paris-Est Créteil, 94010 Créteil Cedex, France
a r t i c l e i n f o
abstract
Article history: Received 27 April 2016 Received in revised form 27 May 2016 Accepted 29 May 2016 Available online 3 June 2016
Transmission spectra in the fundamental bands of H2 and N2 gas inside the pores of a silica aerogel sample were recorded at room temperature and for several pressures using a Fourier transform spectrometer. They first show that, as the absorption is proportional to the pressure, it is due to the interactions of the molecules with the inner surfaces of the pores and not to the dipole induced during gas-phase molecule–molecule collisions. Furthermore, the analysis of the widths and areas of the observed absorption structures indicate that, for the considered aerogel sample, most of the absorption is likely due to “free” molecules moving within the pores with a weak contribution of adsorbed molecules. & 2016 Elsevier Ltd. All rights reserved.
Keywords: Infrared absorption H2 and N2 gases Porous silica aerogel Surface-induced absorption
1. Introduction While isolated homonuclear diatomic molecules, such as H2 and N2, absorb (weakly) in the infrared through narrow optical transitions due to their vibrating quadrupole moment, much broader features are observed when these molecules interact with their environment. In the pure gas phase, this is due to the short-lived dipole induced by intermolecular interactions that gives rise to the so-called Collision Induced Absorption which is proportional to the squared density for pure gas. This process has been extensively studied [1–3], both experimentally and theoretically (e.g. [4–7] for H2 and [8–11] for N2), and it significantly participates in the spectra of planetary n
Corresponding author. E-mail address: [email protected] (J.-M. Hartmann). 1 Senior research associate with the F.R.S.-FNRS (Belgium).
http://dx.doi.org/10.1016/j.jqsrt.2016.05.032 0022-4073/& 2016 Elsevier Ltd. All rights reserved.
atmospheres [2]. Similarly, when these molecules are adsorbed on, or close to, a solid surface, the electric field of the latter polarizes the molecule, hence creating a dipole and therefore an infrared spectrum. In fact, the interest of spectroscopy for the study of adsorption phenomena in natural as well as synthesized porous media arose a long time ago [12]. As example, the infrared absorption of H2 and D2 adsorbed in NaA zeolites has been the subject of many experimental and theoretical studies (see [13] and references therein). Similarly, physisorbed N2 on Al2O3 surfaces was also detected by high sensitivity IR spectroscopy [14]. In 2002, induced IR absorption of molecular H2 trapped in solid C60 was observed at room temperature [15]. This study revealed that H2 is rotating almost completely freely while at the same time, undergoing localized 3-dimensional translational motion within the box formed by the C60 molecules. More recently, there has been a new interest in the analysis of spectra recorded at room temperature in various porous materials, a situation where
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many of the confined molecules remain in the gas phase and are not adsorbed. In most of such studies (e.g. [16– 19]), the investigated molecules possess a dipole moment so that the observed absorptions are dipole-allowed, but, very recently, the induced spectrum of H2, was observed [20] for the first time at room-temperature in nanoporous aerogel. This observation raises the following question: Is the absorption due to molecules freely moving within the pores, due to adsorbed ones, or due to both? In order to clarify this issue, we have extended this previous study by considering both the H2 and N2 molecules (in addition to CO which is used to probe the aerogel porosity) and recording spectra for various pressures using a high resolution Fourier transform spectrometer. The remainder of this paper is divided into three main parts. Experimental details are given in Section 2 while the data analysis procedure and its results are described in Section 3. The values of the parameters retained to characterize the observed absorptions (peak position, width, area) are discussed in Section 4.
2. Experimental The experimental spectra were recorded with a high resolution Bruker IFS 120 (upgraded to 125) HR Fourier transform spectrometer, using the 14.5 mm long stainless steel cell, pressure gauges and temperature sensors described in [19]. The instrument was fitted with a tungsten source, a KBr beamsplitter, a low pass optical filter and an InSb detector cooled down to 77 K. The low pass filter had a cut-off wavenumber near 3700 cm–1 for CO and N2 and 5400 cm–1 for H2. The infrared radiation beam was transmitted through the aerogel sample, placed inside the cell closed by CaF2 windows. Unapodized spectra of CO, N2 and H2 were recorded with the experimental conditions listed in Table 1. Transmittance spectra were obtained for each pressure as the ratio of the sample spectrum and the average of empty cell spectra recorded before and after at low resolution [maximum optical path difference (MOPD)¼9 cm]. The aerogel sample used, shown in Fig. 1, is basically a truncated cone with a length of 13.2 70.1 mm and diameters from 14.9 70.1 to 15.8 70.1 mm. It has been synthesized by the sol–gel polymerization of a silicon alkoxide TEOS (tetraethylorthosilicate). TEOS was polymerized in two steps, using nitric acid as a hydrolysis catalyst followed by ammonia as a condensation catalyst. The resulting alcogels were then dried with carbon dioxide under supercritical conditions, and silica aerogels were obtained with a density of 0.1 g/cm3. The silica aerogel used in this study was sintered one hour at 940 °C to the density of 0.8 g/cm3 (in agreement with the measured weight of 1.93 g, and volume of 2.44 cm3 of the sample used). Note that, with the silica density of 2.2 g/cm3, this implies that the percentage of porosity is about 64%, but that part of this empty volume may not be connected to the outside. Finally note that the observed absorptions by H2 and N2 are very weak so that the resulting spectra are relatively noisy and subjected to baseline (100% transmission)
variations due to slight changes of the IR source intensity between the recordings made with and without gas. This results in non negligible uncertainties on the data retrieved (see below) from their analysis.
3. Analysis 3.1. CO spectrum analysis and aerogel porosity In a first step, in order to get information on the open porosity of the aerogel sample and on the average pore size, we have treated the CO spectrum exactly as done in Ref. [19]. Briefly, the measured transmission of the fundamental band has been least-square fitted assuming Lorentzian line shapes and using the line intensities given in the HITRAN database [21]. For each absorption line ℓ, we then retrieved the optical path length Lℓ in the open pores (which contain CO gas) , and the spectral positions and half width at half maximum Γ ℓ of each line. The results obtained for the transitions lying in the region of (relative) transparency of the aerogel (the R branch, since silica strongly absorbs below 2100 cm 1), are plotted in Fig. 2. As observed previously [19], they are practically independent of the line, leading to average values of L ¼ 7:58 7 0:11 mm and Γ ¼ 0:102 70:006 cm 1 (with uncertainties set to twice the rms of the results in Fig. 2). First note that the measured sample thickness e (e¼13.2 mm, see Fig. 1) leads to a percentage of opened porosity of 100L/e¼57%. This value is compatible with that, of 64%, of the empty volume determined (see Section 2) from the weight and volume of the sample. Furthermore, as suggested in [22,23] and recently demonstrated [24], a single collision of a molecule with a surface is sufficient to destroy the rotating dipole coherence and broaden the line. In this case, and if one assumes long cylindrical pores of diameter d, as done in [19,25], one has d ¼ ðv=cÞ= 2πΓ ðcm1 Þ where v is the mean translational speed of the considered gas (here CO) and c is the speed of light. For the retrieved value of Γ ¼0.102 cm 1 (see Fig. 2b), this leads to d¼ 25 nm. 3.2. N2 and H2 spectra analyses Let us now turn to the H2 and N2 spectra and first mention that measurements carried out for N2 (which shows the narrowest “Q branch”, see Table 2) with various spectral resolutions (see Table 1) lead to practically the same spectra. We have thus retained those which show the best S/N ratio and/or the smallest inconsistencies with the baseline (empty cell spectrum) recording. For their treatment, we first deduced the absorbances from the measured transmissions and then divided them by the optical path length L determined from the CO lines, yielding the absolute absorption coefficient α(σ,P). The latter was then divided by the pressure P of the corresponding recording, leading to a pressure normalized value α0(σ)¼α(σ,P)/P. The results, plotted in Figs. 3 and 4 for N2 and H2 show that these pressure-normalized values are independent of P. This rules out that they are due to the dipole induced during binary collisions between gas
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Table 1 Useful spectral range (“Range” in cm–1), diameter of the entrance aperture of the interferometer (“Iris” in mm), maximum optical path difference achieved (“MOPD” in cm), number of interferograms averaged (“Count”), and sample temperature (“T”) and pressure (“P”), respectively.
CO N2
H2
Range
Iris
MOPD
Count
T/K
2100–2250 2100–2700
1.50 1.50 1.50 1.50 1.50 2.00 2.00 2.00 2.00 2.00 2.00 1.30 1.30 1.30 1.30 1.30
225 0.45 0.45 0.45 9.0 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9
706 5000 5000 10,000 20,300 37,900 40,000 40,000 35,000 18,500 20,000 37,300 39,500 38,000 37,900 37,400
295 295 295 295 294 294 294 294 294 294 294 294.5 294.5 294.5 294.5 294.5
3900–4400
P/hPa (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (10) (10) (10) (10) (10)
29.9 514 904 1285 1018 510 707 895 902 1092 1292 502 705 900 1122 1292
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reported in Table 2 with uncertainties conservatively set to twice the standard deviation of the values obtained from the five spectra.
4. Discussion (3) (3) (6) (7) (5) (3) (4) (5) (5) (6) (7) (3) (4) (5) (6) (7)
4.1. Half widths First consider the values of the HWHM of the absorption peaks for H2 and N2, which are 15 and 3.3 cm 1, respectively (note that the first is in reasonable agreement with that determined under similar conditions in [20]). The ratio of these two values is 4.5 70.8 (where the uncertainty was determined assuming no correlation between the potential errors on the H2 and N2 measurements). Let us assume that the molecules responsible for the observed absorption are freely moving in the vicinity of the pore inner surfaces. In this case, the broadening observed being due to the life time of the induced dipole, we would obtain a HWHM ratio of vH2 ðTÞ=vN2 ðTÞ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi M N2 =MH2 where vX 2 ðTÞ is the mean translational speed of molecule X2 and M X 2 is its mass. The value of this ratio is 3.7, reasonably close to the value (4.5 70.8) deduced from experiment and practically within its uncertainty. This is a first indication that the absorption may be due to “free” molecules (with a minor contribution of adsorbed ones) while they are approaching (or departing from) the pores inner surfaces. 4.2. Areas For the analysis of the areas below the measured absorption, let us assume that the absorption is due to the ! polarization of the molecules by the electric field E existing nearby the inner surfaces of the pores. In this case, if all molecular orientations are taken into account, the area below the absorption is given by [13,26]: AX 2 ¼ BN X 2 σ X 2 ðα2X 2 þ 0:2γ 2X 2 ÞE2
Fig. 1. The aerogel sample (units on the ruler are cm).
phase molecules, since the latter leads to an absorption proportional to P2. This is further confirmed by calculations of this process using the data from [3], which show that it leads to absorptions several orders of magnitude smaller than the measured ones. This leads to the first conclusion that the observed spectra are entirely due to the interactions of the molecules with the inner surfaces of the pores. In order to go further, the spectra in Figs. 3 and 4 have been analyzed in order to retrieve several parameters that characterize them, that are: the value α0Max(cm 1/atm) and spectral position σMax(cm 1) of the peak absorption, the half width at half maximum Γ0(cm 1) of the “Q-branch like” peaking narrow structure at the center of the spectrum, and the area AExp(cm 2/atm) below the spectrum in the spectral range of the two figures. These values are
ð1Þ
where B is a constant, NX2 is the number of X2 molecules involved, and σX2 is the vibrational frequency. αX2 and γX2 are the vibrational matrix elements of the isotropic and anisotropic components of the molecular polarizability, respectively, the values of which for the fundamental band are given in Table 3. From Eq. (1) and the values of Tables 2 and 3, one obtains: AH2 ¼ B 2576N H2 E2
and
so that their ratio is AH2 =AH2
AN2 ¼ B 412NN2 E2 ; ð2Þ ¼ 6:25 NH2 =N N2 . Using the
Exp ratio of the experimentally determined areas AExp H 2 =AN2 ¼
4:1 7 1:5 thus leads to ðN H2 =NN2 Þ ¼ 0:66 7 0:24 . If we first assume that the absorption is entirely due to “free” molecules moving within the aerogel cavities in the field due to the inner surface of the pores, NH2 =N N2 should be equal to unity, which is close to the upper limit of the experimentally determined value. On the opposite, if we assume that the absorption results only from molecules trapped in some adsorption sites on the inner surface of
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Fig. 2. Optical path length L (a) and half width at half maximum (b) retrieved from the CO R(J) lines from J ¼1 to J¼19. The indicative error bars in (a) and (b) correspond to 7 2 and 7 5% respectively. Table 2 Parameters describing the observed absorptions of Figs. 3 and 4, i.e.: the peak positions σMax, its amplitudes α0Max and its halfwidths at half maximum Γ0, and the area AExp below the absorption in the spectral range of the two figures. Mol
σMax (cm 1)
103α0Max (cm 1/atm)
Γ0 (cm 1)
AExp (cm 2/atm)
H2 N2
4142.2 70.2 2326.3 70.1
4.7 7 0.15 5.2 7 0.25
14.9 71.3 3.3 70.5
0.377 0.09 0.0917 0.024
Fig. 4. Pressure-normalized absorption coefficient in the region of the fundamental H2 band deduced from spectra recorded for five different pressures between 502 and 1292 hPa. Table 3 Vibrational matrix elements of the isotropic and anisotropic components of the molecule polarizability (in atomic units).
Fig. 3. Pressure-normalized absorption coefficient in the region of the fundamental N2 band deduced from spectra recorded for five different pressures between 514 and 1292 hPa.
the pores, NH2 =N N2 should be equal to the ratio K H2 =K N2 of the Henry constants driving the adsorption process in the considered range of pressures. To the best of our knowledge such constants are not known for the type of material (porous aerogel with pores of 25 nm diameter) used in this study, and we thus cannot totally exclude that it could be
α01 γ 01
H2 [27]
N2 [28]
0.74 0.61
0.375 0.428
Table 4 Comparison of the Henry constants of H2 and N2: two examples. Ref.
Material
Dimension of the pores (nm) T
[29] Zeolite Na-4A 2.5 [30] Zeolite 5A 99
K H2 =K N2
300 0.25 293 0.09
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equal to about 0.7. However, for other materials for which calculations and/or measurements exist, this ratio has always been found to be much smaller than 0.7 as shown by the two examples of Table 4. Indeed, even for the smaller pore size of 2.5 nm (and it is well known that the Henry constant decreases with the pore dimension) the value of K H2 =K N2 ¼0.25 is clearly outside of our experimental confidence interval of 0:66 7 0:24. Therefore, for the “high” temperature of the present study, the most probable explanation, similar to that experimentally demonstrated for CO (which is isoelectronic to N2 and for which no spectral signature of adsorbed gas was detected), is that the observed absorption is mostly due to H2 or N2 molecules “freely” moving inside the pores (possibly with a minor contribution of those trapped in adsorption sites). 4.3. Peak positions Let us finally discuss the positions of the absorption peaks for H2 and N2, which are 4142.2 and 2326.3 cm 1, respectively, the first being in very good agreement with that determined under similar conditions in [20]. These two values differ (shifts of about 18 and 4 cm 1, respectively) from the frequencies of the maximum of the induced Q branch in the gas phase, around 4160 cm 1 for H2 (as deduced from the ab initio quantum calculated spectra of [31]) and 2330 cm 1 for N2 (as deduced from the experimental spectra of [32]). This is, of course, a consequence of the interactions between the molecules and the inner surfaces of the aerogel pores. It is not easy to compare the present results with previous ones in which the molecules are physisorbed on various surfaces. A first reason is the temperature since most of the results for adsorbed molecules were obtained at low temperature. A second reason is the scattering of these previous results, depending on the materials, the adsorbant surface, etc. For instance, for H2 adsorbed in porous Vycor glass at 18 K, a shift of 30 cm 1 has been observed for the Q(1) line [33]. In contrast, for H2 adsorbed in NaA zeolite a large vibrational shift was observed at 90 K, around 80 cm 1 (depending on the exact nature of the zeolite) [34]. For physisorbed N2, the situations also may be very diverse. When N2 is adsorbed in NaA zeolite, the Q branch frequency is shifted to 2339 cm 1 ( þ9 cm 1) at 185 K [26]. Similar measurements were also made for N2 adsorbed on Al2O3 surfaces exhibiting, only for temperatures lower than 200 K, a band located at 2331 cm 1 ( þ1 cm 1) [14]. Finally, it must be pointed out that an explicit calculation of the shift requires a more sophisticated model than the simple one used above in order to derive some orders of magnitudes of the numbers of molecules. Indeed, while the induced dipole depends on the field near the inner surface of the pores, allowing therefore to build a very simple model, on the opposite, the shifts are known to depend on both the field and the field gradients [13], thus requiring a much more sophisticated approach, far beyond the limits of the present work.
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5. Conclusion We have recorded transmission spectra in the fundamental bands of CO, H2 and N2 gas inside the pores of a silica aerogel sample at room temperature and for several pressures, using a Fourier transform spectrometer. The absorption by CO is used to retrieve information on the pore sizes and on the optical path length within the gas inside the aerogel. This enables the determination of the absolute value of the absorption coefficients by H2 and N2. These show that, the absorption being proportional to the pressure, the absorption spectra are due to the interactions of the molecules with the inner surfaces of the pores and not to the dipole induced during gas-phase molecule– molecule collisions. Furthermore, the analysis of the widths and areas of the observed absorption structures indicate that most of the absorption is likely due, for the considered aerogel, to “free” molecules moving within the pores with a weak contribution of adsorbed molecules. The fact that adsorbed molecules may also participate cannot be ruled out but we believe that their contribution is minor. For a further check of this result, obtained here at room temperature for pores of diameter d E25 nm, complementary experiments for other temperatures and/or other materials and/or different pores sizes would be of considerable interest. Indeed, one expects that all these parameters have a significant influence of the relative amounts of adsorbed and “free” molecules.
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