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Influence of nanoconfinement on the rotational dependence of line half-widths for 2–0 band of carbon oxide
Chemical Physics Letters 637 (2015) 18–21
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Influence of nanoconfinement on the rotational dependence of line half-widths for 2–0 band of carbon oxide A.A. Solodov a,b,∗ , T.M. Petrova a , Yu.N. Ponomarev a,b , A.M. Solodov a a b
V.E. Zuev Institute of Atmospheric Optics SB RAS, Academician Zuev Square 1, Tomsk 634021, Russia National Research Tomsk State University, Lenina Av. 36, Tomsk 634050, Russia
a r t i c l e
i n f o
Article history: Received 29 May 2015 In final form 26 July 2015 Available online 31 July 2015
a b s t r a c t Absorption spectra of carbon oxide, confined in nanoporous silica aerogel, have been measured within 4100–4400 cm−1 region at room temperature and at several pressures using Bruker IFS-125 HR Fourier spectrometer. Dependence of the half-width (HWHM) values on rotational quantum numbers is studied and compared with the data available in literature. It is found that variations in the half-width values for the confined CO at small quantum numbers are larger than at moderate ones. The influence of confinement tightness on rotational dependence is discussed. © 2015 Elsevier B.V. All rights reserved.
1. Introduction In recent years, the investigations of absorption spectra of gases located in the volume of nano-structural materials take increasing attention of researches [1–11]. Molecules in nanopores are detected both in gas phase and adsorbed on the inner surface [1–4]. Studies of gas-phase molecules confined in nanopore volume [1–10] started not long ago; therefore, there are much less papers devoted to this problem than to the spectra of adsorbed molecules [11–13]. Nevertheless, investigations of confined gas phase molecules are of great interest from the fundamental point of view, because, as opposed to the adsorbed ones, they have a fine rotational structure, allowing obtaining additional information on the interaction with surfaces. As was discussed in [4,5], half-width analysis of the confined gas-phase molecule lines allows assessment of nanopore sizes. The mean free path of gas-phase molecules inside nanopores is limited by their walls. The less gas pressure and pore size is, the more frequently confined molecules collide with the walls than with each other. The dominating role of molecule collisions with nanopore surface results in changes of spectral line parameters as compared to free gas. Increased collision frequency due to limitation of mean free path inside nanopores leads to the broadening of spectral lines [1–10]. For H2 O and D2 O molecules confined in aerogels [14], the shifts of lines relative to the free gas have
∗ Corresponding author at: V.E. Zuev Institute of Atmospheric Optics SB RAS, Academician Zuev Square 1, Tomsk 634021, Russia. E-mail address: [email protected] (A.A. Solodov). http://dx.doi.org/10.1016/j.cplett.2015.07.048 0009-2614/© 2015 Elsevier B.V. All rights reserved.
been observed [1,3]. These shifts do not correlate with values and directions of the line self-shifts known for free-gas water vapor. The influence of rotational energy on line half-widths of confined molecules is weakly studied. The half-widths for confined H2 O and D2 O with different quantum numbers, as discussed in [1,3], vary by values comparable with those for free gases. Another regularity has been found in [2,7,9] for more simple molecules (CO, CO2 , O2 ): line shifts were not observed at all and the half-width dependence on J was found to be very weak. As a result, the authors of these works concluded that each collision of such molecule with the walls, irrespective of rotational state, causes interruption of the radiation absorption process. Our preliminary measurements of absorption spectra of 2–0 carbon oxide band, confined in aerogel with pore sizes of 17 nm, have shown relatively strong dependence of spectral line HWHM on quantum numbers [4,10]. In this work we performed a new research on rotational dependence of line half-widths for 2–0 CO band. The measurements were carried out at several pressures, with better signal to noise ratio, and with more careful treatment of the data as compared to the previous study [4]. The possible causes of difference between our results and those in [9] are discussed. 2. Experimental details Measurements of CO absorption spectra in aerogel nanopores were performed using Fourier spectrometer Bruker IFS 125 HR in the region 4100–4400 cm−1 at spectral resolution of 0.008 cm−1 . The spectrometer was equipped with tungsten light source, CaF2 beamsplitter and InSb detector cooled by liquid nitrogen. The aerogel sample was made at G.K. Boreskov Institute of Catalysis. The
A.A. Solodov et al. / Chemical Physics Letters 637 (2015) 18–21
Figure 1. Fragments of the spectra recorded at the pressures of 50.3, 202, 535, 504 mbar formed by absorption of CO molecules, adsorbed on the surface of aerogel nanopores (wide structureless plinth), and by gas-phase CO molecules (finely structured vibration–rotation transitions). Pressures increase from down to top.
sample length was of 54 mm, the density of 0.25 g/cm3 , the surface area and the pore sizes, determined by the method of nitrogen low-temperature adsorption [15], were of 940 m2 /g and 17 nm, respectively [4]. Before measurements the aerogel sample was put into the vacuum cell of 65 mm length, and pumped out during 6 h with forevacuum pump at temperature ∼100 ◦ C. The absorption spectrum of the pumped-out sample was recorded and was used as a baseline. The procedure of filling aerogel by carbon oxide and the pressure stabilization were significantly faster in these measurements as compared to the water vapor study [1]; the measurements were conducted in an hour after the filling. Since the aerogel surface area is very large, even minor temperature variations can break the adsorption equilibrium [15] and cause the pressure change. In order to stabilize the pressure for a long time recording spectra, the cell was connected with a ballast reservoir of 3000 cm3 . The measurements were carried out at pressures of 50.3, 202, 353 and 504 mbar, at temperatures of 296, 297, 297 and 296 K respectively. The pressure was measured using the MKS Baratron and Vacuubrand DVR-5. In order to increase the signal-to-noise ratio coaddition of 2000 interferograms was done and a filter was used.
19
Figure 2. Processing of carbon oxide P(7) spectral line at pressure of 50.3 mbar by simultaneous fitting of Lorentz (1) and Voigt (2) profiles to experimentally recorded ones. The lower panel shows the respective residuals.
done to determine scaling factors which convert line intensities from HITRAN to that for all spectral lines of 2–0 band of confined and free CO. Further fitting was performed with fixing of corrected intensities of both profiles. This procedure allowed us to reduce the dispersion of half-width values; however, it does not change qualitatively their dependence on rotational quantum numbers. 4. Results and discussion The profile of absorption lines of molecules located inside nanopores is formed by collisions with the surface of nanostructured material ( wall ) and with other molecules in the volume of nanopores ( mol ) (1). According to works [5,9] the contributions of wall and mol to full HWHM are additive: = wall + mol
(1)
In order to check applicability of the formula (1) for nanoporous aerogel we plotted dependences of the full HWHM on the gas pressure for R(1), R(4), R(10) and R(16) spectral lines (Figure 3). If contributions of wall and mol are additive, then the slopes of lines which characterize the dependences of full HWHM on pressure for confined CO should be the same as that for free gas. Also these lines should be Y-shifted by value wall . I.e. in equation of line y = ˛x + ˇ coefficients ˛ and ˇ correspond to self-broadening value
3. Spectral data processing Fragments of the recorded absorption spectra of 2–0 carbon oxide band, confined in aerogel nanopores, are shown in Figure 1. The spectra show a fine structure of vibration–rotational lines of gas-phase CO, located on a wide structureless plinth, corresponding to the absorption of CO, adsorbed on the inner surface of nanopores. More detailed view of individual spectral line is presented in Figure 2. One can see that lines of gas phase consist of two profiles, the narrow one (2), corresponding to the gas located in the gaps between aerogel sample and the cell windows, and the wider one (1), corresponding to the CO absorption in nanopores. The processing of spectral lines was performed in two steps. At the first one the fitting of Lorenz and Voigt profiles to the experimentally recorded ones was performed without fixing of any parameters. During the fitting it was found that residuals are not enough sensitive to variation of the profiles parameters, despite of the difference in their half-widths by an order of magnitude. Therefore, it was necessary to fix some parameters of profiles correctly. At the second step the sets of intensities for both wide and narrow profiles were compared with data available in HITRAN [16]. It was
Figure 3. Dependences of fitted full HWHM of confined CO on pressure for several spectral lines (symbols). These dependences were approximated by linear functions with all fitting parameters to be free (dashed lines) and with fixing the slopes to the self-broadening coefficients in free gas (solid lines).
20
A.A. Solodov et al. / Chemical Physics Letters 637 (2015) 18–21
corresponding to the smallest and largest J, can be assessed from the formula: wall
Figure 4. Dependence of HWHM values on rotational quantum numbers for (1) – CO confined in aerogel, (2) – xerogel (data taken from [9]), and (3) – free gas (selfbroadening coefficients at pressure 50.3 mbar) [16]. For sake of clarity the sets of half-widths for CO, confined in xerogel, and for free gas were multiplied by factors 3.5 and 47 respectively (m = J + 1 for R branch and m = −J for P branch of the CO absorption band).
for free gas and wall respectively. The dependences plotted were approximated by linear functions in two ways. In the first one all fitting parameters were free. In the second way the coefficients ˛ were fixed to the self-broadening values in free gas [16], i.e. only wall values (ˇ) were fitted. Comparison of self-broadening coefficients for confined CO obtained in two ways shows that difference between them does not exceed 5%, hence wall values can be retrieved with the help of Eq. (1) using available in HITRAN self-broadening coefficients for free CO as mol . The fact that the additivity of wall and mol holds for spectral lines with both small and moderate quantum numbers allowed us to conclude that pressure does not impact the wall half-widths dependence on J. More detailed investigation of the half-width dependence on quantum numbers was performed for pressure of 50.3 mbar. Figure 4 shows the wall HWHM values for confined in aerogel CO, found from Eq. (1). Let us compare these values with data available in literature: wall half-width values of CO confined in xerogel nanopores [9], and self-broadening coefficients of free CO calculated for our experimental conditions [16]. The values of these sets strongly differ from each other, therefore, for convenience of comparison two last of them were multiplied by factors 3.5 and 47, respectively. Figure 4 demonstrates similar to a free gas decreasing of HWHM values with quantum numbers for carbon oxide confined in aerogel at m < 4 (where m = J + 1 for R branch, and m = −J for P branch of CO absorption band). The dependence becomes very weak for rotational quantum numbers m > 4, which is similar to the case of xerogel [9]. In order to explain obtained result, let us first recall that collisional HWHM is determined by lifetimes of rotational states involved in the optical transition [17]. Very weak dependence of half-widths on quantum numbers (at m > 4), similar to that found in [9], means that collisions with nanopore wall, independently of CO molecule rotational energy, interrupts absorption of radiation [7]. Increasing of HWHM values with decreasing of quantum numbers (at m < 4) allows us to suggest that the interruption occurs at different distances from the nanopore wall. Indeed, the energy required to change the molecule’s rotational state (E = EJ+1 − EJ ) decreases with J, and interaction of a molecule with surface strongly reduces as the distance from the wall increases. Hence, from all of molecules moving toward the surface, those, which rotational energy is the lowest, change energy level first. The distances from the surface can be estimated as following. The sizes of aerogel nanopores found from half-widths wall
1 A = 2c V
kB T 2mmol
(2)
where c is speed of light; A is area of the nanopore surface; V is nanopore volume, kB is the Boltzmann constant; T is the gas temperature; mmol is mass of the gas molecule (see [5,6] and references therein). Nanopore diameters, estimated from formula (2), vary between 18.4 and 21.7 nm (which is close to 16.5 nm, found by the method of nitrogen low-temperature absorption [4]). Therefore, the distances at which the process of radiation absorption is interrupted (determined as half of the difference between maximum and minimum nanopore’s diameter) can differ by 1.7 nm. We found also that all line centers of CO in aerogel nanopores are shifted as compared to free CO approximately by −0.005 cm−1 . Contrary to the water vapor, confined inside similar aerogel sample [1], CO spectral lines are shifted in the same direction as in a free gas. In xerogel nanopores of 80 nm sizes the line shift was not detected [9]. The difference between collisional half-width dependence on J obtained in this work and in paper [9] can be attributed to the properties and structure of the nanoporous material’s inner surface. They affect both the distance from nanopore wall, at which the interruption of radiation absorption process occurs, and the interaction potential between molecules and surface. One more possible reason for this difference is that the size of nanopores in our study is several times smaller than in [9]. It was estimated above that diameter of pores is an order of magnitude larger than the distances at which molecules interact with the surface. Therefore, impact of the distance on the mean free path of confined molecules, and hence, on half-widths and their rotational dependence, is weaker for larger nanopores. In our case, spectral line parameters of more tightly confined CO molecules have stronger dependence on the ‘gas-surface’ interaction potential.
5. Conclusion Rotational dependence of line half-widths for 2–0 absorption band of CO confined in nanoporous aerogel has been studied. The half-width values obtained vary from 0.173 to 0.204 cm−1 . For lines with smaller values of quantum rotational numbers (m < 4) the dependence is approximately the same as for the free gas, while for m > 4 the dependence becomes significantly weaker. The relatively strong change in the rotational dependence is tentatively attributed to the fact that the interruption of radiation absorption process occurs at different distances from nanopores surface. Our estimation shows, that these distances can differ by 1.7 nm. The CO lines in the volume of aerogel nanopores are shifted relative to their centers in free gas by −0.005 cm−1 . The difference between rotational dependence obtained in this work and that found in [9] can be attributed to tightness of the nanoconfinement and to the structure of surfaces. Nevertheless, the mechanism of formation of individual spectral line half-widths was found to be the same: the contributions of collisions of molecules with surface and with each other are additive and pressure does not impact the wall half-widths dependence on J. The rotational dependence of the line half-widths should be taken into account when assessing nanopore sizes by spectroscopic methods. The results we found are of great interest for further spectroscopic investigation of gases under nanoconfinement: developing existing theories [7,9], simulating spectra of more tightly confined gas-phase molecules, understanding the interaction processes of gases with surfaces, etc.
A.A. Solodov et al. / Chemical Physics Letters 637 (2015) 18–21
Acknowledgments The authors are grateful to A. F. Daniluk for manufacturing the silica aerogel sample and deriving its parameters. This work was supported by the Grant of President, Project MK-7801.2015.2. References [1] Yu.N. Ponomarev, T.M. Petrova, A.M. Solodov, Opt. Express 18 (2010) 26062. [2] J. Vander Auwera, N.H. Ngo, H. El Hamzaoui, B. Capoen, M. Bouazaoui, P. Ausset, C. Boulet, J.-M. Hartmann, Phys. Rev. A 88 (2013) 042506. [3] L. Sinitsa, N. Lavrentieva, A. Lugovskoi, Mol. Phys. 112 (2014) 2468. [4] T.M. Petrova, Yu.N. Ponomarev, A.A. Solodov, A.M. Solodov, A.F. Danilyuk, JETP Lett. 101 (2015) 65. [5] T. Svensson, E. Adolfsson, M. Burresi, R. Savo, C. Xu, D.S. Wiersma, S. Svanberg, Appl. Phys. B 110 (2013) 147. [6] T. Svensson, M. Lewander, S. Svanberg, Opt. Express 18 (2010) 16460. [7] J.-M. Hartmann, V. Sironneau, C. Boulet, T. Svensson, J.T. Hodges, C.T. Xu, Phys. Rev. A 87 (2013) 032510. [8] Yu.N. Ponomarev, T.M. Petrova, A.A. Solodov, A.M. Solodov, JETP Lett. 99 (2014) 619.
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[9] J.-M. Hartmann, C. Boulet, J. Vander Auwera, H. El Hamzaoui, B. Capoen, M. Bouazaoui, J. Chem. Phys. 140 (2014) 064302. [10] T.M. Petrova, Yu.N. Ponomarev, A.A. Solodov, A.M. Solodov, XXIII International Conference on High Resolution Molecular Spectroscopy, 2–6 September, Bologna, Italy, 2014. [11] F.X. Llabreґs i Xamena, A. Zecchina, Phys. Chem. Chem. Phys. 4 (2002) 1978. [12] K. Wolter, O. Seiferth, J. Libuda, H. Kuhlenbeck, M. Baumer, H.-J. Freund, Surf. Sci. 402–404 (1998) 428. [13] L.H. Little, Infrared Spectra of Adsorbed Species, Academic Press, 1966. [14] Yu.N. Kharzheev, Phys. Part. Nucl. 39 (2008) 107. [15] S. Gregg, K. Sing, Adsorption, Surface Area and Porosity Academic, 1982. [16] L.S. Rothman, I.E. Gordon, Y. Babikov, A. Barbe, D. Chris Benner, P.F. Bernath, M. Birk, L. Bizzocchi, V. Boudon, L.R. Brown, A. Campargue, K. Chance, E.A. Cohen, L.H. Coudert, V.M. Devi, B.J. Drouin, A. Fayt, J.-M. Flaud, R.R. Gamache, J.J. Harrison, J.-M. Hartmann, C. Hill, J.T. Hodges, D. Jacquemart, A. Jolly, J. Lamouroux, R.J. Le Roy, G. Li, D.A. Long, O.M. Lyulin, C.J. Mackie, S.T. Massie, S. Mikhailenko, H.S.P. Müller, O.V. Naumenko, A.V. Nikitin, J. Orphal, V. Perevalov, A. Perrin, E.R. Polovtseva, C. Richard, M.A.H. Smith, E. Starikova, K. Sung, S. Tashkun, J. Tennyson, G.C. Toon, V.L.G. Tyuterev, G. Wagner, JQSRT 130 (2013) 4. [17] J.-M. Hartmann, C. Boulet, D. Robert, Collisional Effects on Molecular Spectra, Elsevier Science, 2008.
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Influence of nanoconfinement on the rotational dependence of line half-widths for 2–0 band of carbon oxide A.A. Solodov a,b,∗ , T.M. Petrova a , Yu.N. Ponomarev a,b , A.M. Solodov a a b
V.E. Zuev Institute of Atmospheric Optics SB RAS, Academician Zuev Square 1, Tomsk 634021, Russia National Research Tomsk State University, Lenina Av. 36, Tomsk 634050, Russia
a r t i c l e
i n f o
Article history: Received 29 May 2015 In final form 26 July 2015 Available online 31 July 2015
a b s t r a c t Absorption spectra of carbon oxide, confined in nanoporous silica aerogel, have been measured within 4100–4400 cm−1 region at room temperature and at several pressures using Bruker IFS-125 HR Fourier spectrometer. Dependence of the half-width (HWHM) values on rotational quantum numbers is studied and compared with the data available in literature. It is found that variations in the half-width values for the confined CO at small quantum numbers are larger than at moderate ones. The influence of confinement tightness on rotational dependence is discussed. © 2015 Elsevier B.V. All rights reserved.
1. Introduction In recent years, the investigations of absorption spectra of gases located in the volume of nano-structural materials take increasing attention of researches [1–11]. Molecules in nanopores are detected both in gas phase and adsorbed on the inner surface [1–4]. Studies of gas-phase molecules confined in nanopore volume [1–10] started not long ago; therefore, there are much less papers devoted to this problem than to the spectra of adsorbed molecules [11–13]. Nevertheless, investigations of confined gas phase molecules are of great interest from the fundamental point of view, because, as opposed to the adsorbed ones, they have a fine rotational structure, allowing obtaining additional information on the interaction with surfaces. As was discussed in [4,5], half-width analysis of the confined gas-phase molecule lines allows assessment of nanopore sizes. The mean free path of gas-phase molecules inside nanopores is limited by their walls. The less gas pressure and pore size is, the more frequently confined molecules collide with the walls than with each other. The dominating role of molecule collisions with nanopore surface results in changes of spectral line parameters as compared to free gas. Increased collision frequency due to limitation of mean free path inside nanopores leads to the broadening of spectral lines [1–10]. For H2 O and D2 O molecules confined in aerogels [14], the shifts of lines relative to the free gas have
∗ Corresponding author at: V.E. Zuev Institute of Atmospheric Optics SB RAS, Academician Zuev Square 1, Tomsk 634021, Russia. E-mail address: [email protected] (A.A. Solodov). http://dx.doi.org/10.1016/j.cplett.2015.07.048 0009-2614/© 2015 Elsevier B.V. All rights reserved.
been observed [1,3]. These shifts do not correlate with values and directions of the line self-shifts known for free-gas water vapor. The influence of rotational energy on line half-widths of confined molecules is weakly studied. The half-widths for confined H2 O and D2 O with different quantum numbers, as discussed in [1,3], vary by values comparable with those for free gases. Another regularity has been found in [2,7,9] for more simple molecules (CO, CO2 , O2 ): line shifts were not observed at all and the half-width dependence on J was found to be very weak. As a result, the authors of these works concluded that each collision of such molecule with the walls, irrespective of rotational state, causes interruption of the radiation absorption process. Our preliminary measurements of absorption spectra of 2–0 carbon oxide band, confined in aerogel with pore sizes of 17 nm, have shown relatively strong dependence of spectral line HWHM on quantum numbers [4,10]. In this work we performed a new research on rotational dependence of line half-widths for 2–0 CO band. The measurements were carried out at several pressures, with better signal to noise ratio, and with more careful treatment of the data as compared to the previous study [4]. The possible causes of difference between our results and those in [9] are discussed. 2. Experimental details Measurements of CO absorption spectra in aerogel nanopores were performed using Fourier spectrometer Bruker IFS 125 HR in the region 4100–4400 cm−1 at spectral resolution of 0.008 cm−1 . The spectrometer was equipped with tungsten light source, CaF2 beamsplitter and InSb detector cooled by liquid nitrogen. The aerogel sample was made at G.K. Boreskov Institute of Catalysis. The
A.A. Solodov et al. / Chemical Physics Letters 637 (2015) 18–21
Figure 1. Fragments of the spectra recorded at the pressures of 50.3, 202, 535, 504 mbar formed by absorption of CO molecules, adsorbed on the surface of aerogel nanopores (wide structureless plinth), and by gas-phase CO molecules (finely structured vibration–rotation transitions). Pressures increase from down to top.
sample length was of 54 mm, the density of 0.25 g/cm3 , the surface area and the pore sizes, determined by the method of nitrogen low-temperature adsorption [15], were of 940 m2 /g and 17 nm, respectively [4]. Before measurements the aerogel sample was put into the vacuum cell of 65 mm length, and pumped out during 6 h with forevacuum pump at temperature ∼100 ◦ C. The absorption spectrum of the pumped-out sample was recorded and was used as a baseline. The procedure of filling aerogel by carbon oxide and the pressure stabilization were significantly faster in these measurements as compared to the water vapor study [1]; the measurements were conducted in an hour after the filling. Since the aerogel surface area is very large, even minor temperature variations can break the adsorption equilibrium [15] and cause the pressure change. In order to stabilize the pressure for a long time recording spectra, the cell was connected with a ballast reservoir of 3000 cm3 . The measurements were carried out at pressures of 50.3, 202, 353 and 504 mbar, at temperatures of 296, 297, 297 and 296 K respectively. The pressure was measured using the MKS Baratron and Vacuubrand DVR-5. In order to increase the signal-to-noise ratio coaddition of 2000 interferograms was done and a filter was used.
19
Figure 2. Processing of carbon oxide P(7) spectral line at pressure of 50.3 mbar by simultaneous fitting of Lorentz (1) and Voigt (2) profiles to experimentally recorded ones. The lower panel shows the respective residuals.
done to determine scaling factors which convert line intensities from HITRAN to that for all spectral lines of 2–0 band of confined and free CO. Further fitting was performed with fixing of corrected intensities of both profiles. This procedure allowed us to reduce the dispersion of half-width values; however, it does not change qualitatively their dependence on rotational quantum numbers. 4. Results and discussion The profile of absorption lines of molecules located inside nanopores is formed by collisions with the surface of nanostructured material ( wall ) and with other molecules in the volume of nanopores ( mol ) (1). According to works [5,9] the contributions of wall and mol to full HWHM are additive: = wall + mol
(1)
In order to check applicability of the formula (1) for nanoporous aerogel we plotted dependences of the full HWHM on the gas pressure for R(1), R(4), R(10) and R(16) spectral lines (Figure 3). If contributions of wall and mol are additive, then the slopes of lines which characterize the dependences of full HWHM on pressure for confined CO should be the same as that for free gas. Also these lines should be Y-shifted by value wall . I.e. in equation of line y = ˛x + ˇ coefficients ˛ and ˇ correspond to self-broadening value
3. Spectral data processing Fragments of the recorded absorption spectra of 2–0 carbon oxide band, confined in aerogel nanopores, are shown in Figure 1. The spectra show a fine structure of vibration–rotational lines of gas-phase CO, located on a wide structureless plinth, corresponding to the absorption of CO, adsorbed on the inner surface of nanopores. More detailed view of individual spectral line is presented in Figure 2. One can see that lines of gas phase consist of two profiles, the narrow one (2), corresponding to the gas located in the gaps between aerogel sample and the cell windows, and the wider one (1), corresponding to the CO absorption in nanopores. The processing of spectral lines was performed in two steps. At the first one the fitting of Lorenz and Voigt profiles to the experimentally recorded ones was performed without fixing of any parameters. During the fitting it was found that residuals are not enough sensitive to variation of the profiles parameters, despite of the difference in their half-widths by an order of magnitude. Therefore, it was necessary to fix some parameters of profiles correctly. At the second step the sets of intensities for both wide and narrow profiles were compared with data available in HITRAN [16]. It was
Figure 3. Dependences of fitted full HWHM of confined CO on pressure for several spectral lines (symbols). These dependences were approximated by linear functions with all fitting parameters to be free (dashed lines) and with fixing the slopes to the self-broadening coefficients in free gas (solid lines).
20
A.A. Solodov et al. / Chemical Physics Letters 637 (2015) 18–21
corresponding to the smallest and largest J, can be assessed from the formula: wall
Figure 4. Dependence of HWHM values on rotational quantum numbers for (1) – CO confined in aerogel, (2) – xerogel (data taken from [9]), and (3) – free gas (selfbroadening coefficients at pressure 50.3 mbar) [16]. For sake of clarity the sets of half-widths for CO, confined in xerogel, and for free gas were multiplied by factors 3.5 and 47 respectively (m = J + 1 for R branch and m = −J for P branch of the CO absorption band).
for free gas and wall respectively. The dependences plotted were approximated by linear functions in two ways. In the first one all fitting parameters were free. In the second way the coefficients ˛ were fixed to the self-broadening values in free gas [16], i.e. only wall values (ˇ) were fitted. Comparison of self-broadening coefficients for confined CO obtained in two ways shows that difference between them does not exceed 5%, hence wall values can be retrieved with the help of Eq. (1) using available in HITRAN self-broadening coefficients for free CO as mol . The fact that the additivity of wall and mol holds for spectral lines with both small and moderate quantum numbers allowed us to conclude that pressure does not impact the wall half-widths dependence on J. More detailed investigation of the half-width dependence on quantum numbers was performed for pressure of 50.3 mbar. Figure 4 shows the wall HWHM values for confined in aerogel CO, found from Eq. (1). Let us compare these values with data available in literature: wall half-width values of CO confined in xerogel nanopores [9], and self-broadening coefficients of free CO calculated for our experimental conditions [16]. The values of these sets strongly differ from each other, therefore, for convenience of comparison two last of them were multiplied by factors 3.5 and 47, respectively. Figure 4 demonstrates similar to a free gas decreasing of HWHM values with quantum numbers for carbon oxide confined in aerogel at m < 4 (where m = J + 1 for R branch, and m = −J for P branch of CO absorption band). The dependence becomes very weak for rotational quantum numbers m > 4, which is similar to the case of xerogel [9]. In order to explain obtained result, let us first recall that collisional HWHM is determined by lifetimes of rotational states involved in the optical transition [17]. Very weak dependence of half-widths on quantum numbers (at m > 4), similar to that found in [9], means that collisions with nanopore wall, independently of CO molecule rotational energy, interrupts absorption of radiation [7]. Increasing of HWHM values with decreasing of quantum numbers (at m < 4) allows us to suggest that the interruption occurs at different distances from the nanopore wall. Indeed, the energy required to change the molecule’s rotational state (E = EJ+1 − EJ ) decreases with J, and interaction of a molecule with surface strongly reduces as the distance from the wall increases. Hence, from all of molecules moving toward the surface, those, which rotational energy is the lowest, change energy level first. The distances from the surface can be estimated as following. The sizes of aerogel nanopores found from half-widths wall
1 A = 2c V
kB T 2mmol
(2)
where c is speed of light; A is area of the nanopore surface; V is nanopore volume, kB is the Boltzmann constant; T is the gas temperature; mmol is mass of the gas molecule (see [5,6] and references therein). Nanopore diameters, estimated from formula (2), vary between 18.4 and 21.7 nm (which is close to 16.5 nm, found by the method of nitrogen low-temperature absorption [4]). Therefore, the distances at which the process of radiation absorption is interrupted (determined as half of the difference between maximum and minimum nanopore’s diameter) can differ by 1.7 nm. We found also that all line centers of CO in aerogel nanopores are shifted as compared to free CO approximately by −0.005 cm−1 . Contrary to the water vapor, confined inside similar aerogel sample [1], CO spectral lines are shifted in the same direction as in a free gas. In xerogel nanopores of 80 nm sizes the line shift was not detected [9]. The difference between collisional half-width dependence on J obtained in this work and in paper [9] can be attributed to the properties and structure of the nanoporous material’s inner surface. They affect both the distance from nanopore wall, at which the interruption of radiation absorption process occurs, and the interaction potential between molecules and surface. One more possible reason for this difference is that the size of nanopores in our study is several times smaller than in [9]. It was estimated above that diameter of pores is an order of magnitude larger than the distances at which molecules interact with the surface. Therefore, impact of the distance on the mean free path of confined molecules, and hence, on half-widths and their rotational dependence, is weaker for larger nanopores. In our case, spectral line parameters of more tightly confined CO molecules have stronger dependence on the ‘gas-surface’ interaction potential.
5. Conclusion Rotational dependence of line half-widths for 2–0 absorption band of CO confined in nanoporous aerogel has been studied. The half-width values obtained vary from 0.173 to 0.204 cm−1 . For lines with smaller values of quantum rotational numbers (m < 4) the dependence is approximately the same as for the free gas, while for m > 4 the dependence becomes significantly weaker. The relatively strong change in the rotational dependence is tentatively attributed to the fact that the interruption of radiation absorption process occurs at different distances from nanopores surface. Our estimation shows, that these distances can differ by 1.7 nm. The CO lines in the volume of aerogel nanopores are shifted relative to their centers in free gas by −0.005 cm−1 . The difference between rotational dependence obtained in this work and that found in [9] can be attributed to tightness of the nanoconfinement and to the structure of surfaces. Nevertheless, the mechanism of formation of individual spectral line half-widths was found to be the same: the contributions of collisions of molecules with surface and with each other are additive and pressure does not impact the wall half-widths dependence on J. The rotational dependence of the line half-widths should be taken into account when assessing nanopore sizes by spectroscopic methods. The results we found are of great interest for further spectroscopic investigation of gases under nanoconfinement: developing existing theories [7,9], simulating spectra of more tightly confined gas-phase molecules, understanding the interaction processes of gases with surfaces, etc.
A.A. Solodov et al. / Chemical Physics Letters 637 (2015) 18–21
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