We demonstrate high-resolution tunable diode laser absorption spectroscopy (TDLAS) of water vapor confined in nanoporous alumina. Strong multiple light scattering results in long photon pathlengths (1 m through a 6 mm sample). We report on strong line broadening due to frequent wall collisions (gas-surface interactions). For the water vapor line at 935.685 nm, the HWHM of confined molecules are about 4.3 GHz as compared to 2.9 GHz for free molecules (atmospheric pressure). Gas diffusion is also investigated, and in contrast to molecular oxygen (that moves rapidly in and out of the alumina), the exchange of water vapor is found very slow.
©2010 Optical Society of America
High-resolution tunable diode laser absorption spectroscopy (TDLAS) is a well established method for selective and sensitive gas sensing and accurate measurements of gas concentration, pressure, and temperature. The technique is widely used, e.g. in atmospherical sciences, for combustion diagnostics, and for industrial process monitoring. The use of TDLAS for analysis of gas located inside turbid solids [1–3] is an emerging subfield with numerous interesting application areas. The approach, often referred to as gas in scattering media absorption spectroscopy (GASMAS), has been applied in, e.g. medical diagnostics of the human paranasal sinuses [4–6], characterization and optical porosimetry of pharmaceutical tablets and ceramics [7–9], as well as for monitoring of drying processes  and food packaging .
More recently, it has also been shown that GASMAS can be used to study gases in nanoporous materials . Besides having potential applications in material science for, e.g. studies of heterogenous catalysis, molecular sieving, adsorption and gas dynamics in nanoporous materials, this new domain of laser spectroscopy is also of fundamental spectroscopic interest. In particular, the absorption lines of gases are strongly broadened by frequent wall collisions (gas-surface interactions). For oxygen molecules confined in 20 nm pores of nanoporous bulk alumina, it was found that wall collision broadening is the dominating source of line broadening - even at atmospheric pressure . Normally, pressure broadening due to intermolecular collisions is the main broadening mechanism during measurements at atmospheric pressure. However, considering that the mean free path (i.e. distance between subsequent collisions) of many gases at atmospheric pressure is 50–100 nm , it is not surprising that nano-confinement also will be a major source of line broadening. In addition, as wall collision line broadening strongly depends on the pore size, the phenomenon opens for a new, non-destructive method for pore size assessment.
Wall collision broadening has previously been discussed in connection with low pressure spectroscopy in the microwave region [14–18]. There, measurements in the mTorr pressure regime (10−6 atm) rendered the mean free path between intermolecular collisions so long (centimeters) that wall collisions in the utilized gas cells no longer were negligible. Measurements were, however, dominated by Doppler broadening, and the wall collision component was only in the order of 10 kHz (see, e.g. [17,19]). In general, the strength of the line broadening is related to the rate of wall collisions, f wall, which according to gas kinetics is given by
where τ wall is the average time between wall collisions, A the container area, V the container volume, k the Boltzmann constant, TK the temperature, m the molecular mass, and ν avg the average speed of the molecules. Assuming that collisions cause complete relaxation, the halfwidth of wall collision broadening is approximately Γwall = (2πτ wall)−1. For some time, it was assumed that the lineshape due to wall collisions was Lorentzian, and that the resulting collisional linewidth Γcoll was given by (Γgas and Γwall refering to the HWHM linewidths due to intermolecular and wall collisions, respectively) . It was later theoretically shown that the lineshape due to wall collisions indeed is not Lorentzian [14,15], and that it depends on the container shape. Furthermore, for a parallell plate geometry, it was found that the combined linewidth follows Γcoll = Γgas + r 0(r) × Γwall, where r 0(r) is a coefficient that depends on the relative contribution ratio r = Γgas/Γwall and should be close to unity as long as r > 1  (in this context, it can be mentioned that also sub-Doppler effects have been demonstrated for gases in thin pillbox-type cells [21,22]). However, little is known about other geometries and cases where wall collision broadening dominates. Nor have any direct experimental studies of wall collision lineshapes been published. In microwave spectroscopy, wall collisions have mainly been considered a phenomenon accounted for by minor corrections. The impact of wall collisions has recently also been noted in connection with optical spectroscopy of gases at low pressure gas confined inside the 10 µm core of hollow photonic band-gap fibers [23,24]. High-resolution laser spectroscopy of gases confined in nanoporous materials is thus a new topic. In contrast to the microwave spectroscopy discussed above, wall collision line broadening is here a very prominent effect. So far, the only study involves a near-infrared transition of molecular oxygen (at 760 nm) confined in alumina . While wall collision broadening in the microwave region was in the kHz regime, that study reports on GHz line broadening for molecular confined in nano-cavities. Much is yet to learn about line broadening and lineshapes of confined molecules, and the area constitutes a new challenge for the theory of collisions and spectroscopic lineshapes. In addition, potential applications needs to be identified and explored.
In this work, we demonstrate high-resolution laser spectroscopy of water vapor (H2O) confined in nanoporous alumina (Al2O3) with a pore size of about 70 nm (as given by mercury intrusion porosimetry). The strong multiple scattering of the alumina results in long interaction pathlengths, and allows direct absorption spectroscopy with peak absorption fractions of about 1–3%. For a 6 mm thick sample, the average optical pathlength through pores of the material is almost half a meter. Speckle interference is a major problem in GASMAS in general , and is in this work suppressed by means of laser beam dithering (as suggested in ). We then investigate line broadening due to the tight confinement by studying near-infrared transitions around 935 nm. Since the utilized TDLAS system has not been used for lineshape analysis previously, we also report on its basic performance in this respect (spectroscopy of water vapor at ambient conditions). Furthermore, we report on gas exchange by studying the gas diffusion dynamics after having stored the sample in 100% relative humidity, and also by simultaneously monitor water vapour and molecular oxygen during nitrogen flushing.
2. Experimental details
2.1. High-resolution laser spectroscopy
High-resolution spectra are recorded by employing tunable diode laser absorption spectroscopy (TDLAS). The TDLAS instrument utilized is a fiber-based dual beam system for near-infrared sensing of molecular oxygen (around 760 nm) and water vapor (around 935 nm) . The system was originally designed and used for simultaneous measurements of path integrated O2 and H2O absorption by means of wavelength modulation spectroscopy (WMS). A detailed description of the TDLAS system is found in , and a schematic of the experimental configuration is given in Fig. 1. Briefly, the system is based on two distributed feedback (DFB) diode lasers (Nanoplus). Along the lines described in, e.g. [8,25], both diode laser tuning and data acquisition are controlled by a computer card (NI-6120, National Instruments) with internally synchronized analog outputs (AO) and inputs (AI). The tuning is realized by imposing linear ramps (5 Hz repetition rate) on the diode laser operation current supplied by conventional diode laser drivers. The two DFB diode lasers are pigtailed to single-mode optical fibers (SMF), and in order to allow simultaneous sensing of two gases these are combined into one single fiber. Unfortunately, the early part of the optical system cause unwanted interference noise. To be able to remove these detrimental effects, a beam splitter (BS) is used to create a dual beam configuration. The reference arm allows baseline recordi ngs and is crucial for analysis of sample arm data. Light in both arms are detected by large-area photodiodes (PD), and the resulting photocurrents are amplified and converted to voltage by low-noise transimpedance amplifiers (TIA). The voltage signals corresponding to the reference and sample arms are denoted ur and us, respectively. A relative optical frequency scale is determined by recording the etalon fringes of a solid BK7 etalon (40.75 mm long, having a 2.44 GHz free spectral range at 935 nm).
In the present work, we conduct direct absorption measurements with only the 935 nm diode laser (except for the nitrogen flushing experiment where WMS is used for simultaneous monitoring of both oxygen and water vapor; see Section 3.3). Measurements on porous samples are conducted in transmission. Light is injected into the sample by means of a divergent output of a single-mode optical fiber, and a 5.6 × 5.6 mm2 large-area photodiode (S1337-66BR, Hamamatsu) is used to collect the diffuse light transmitted through the sample.
Since GASMAS deals with spectroscopy of gas located inside porous, highly scattering solids, one needs to handle detection of weak diffuse light, unknown interaction pathlengths and severe speckle interference. As described in , speckle interference is suppressed by means of laser beam dithering. A lens mounted on tracking coils (TC-L) is inserted between the sample and the output of the single-mode fiber (the path through ambient air is about 1 cm, and the corresponding absorption is negligible compared to that from the nanoporous alumina). By feeding the tracking coils with low-frequency noise, the speckle interference is converted into noise that can be averaged out.
2.2. Spectral lines
We study water vapor by utilizing the strongest absorption line in the 940 nm region. This particular line is located at 935.684 nm (10687.36209 cm−1, vacuum wavelength), and is due to the (000) → (201) vibrational transition with the rotational change given by (J,Ka,Kc): (303) → (404). There are four neighboring lines of importance, but these are at least five times weaker. The strongest of them is the line located at 935.608 nm (10688.233710 cm−1). Relevant line parameters of these two transitions are given in Table 1.
2.3. Analysis of high-resolution spectra
The sample arm signal us(ν), where ν denotes relative optical frequency, can be written as a product of a baseline u 0(ν) and a transmission profile T(ν)
Accordingly, experimental data is evaluated by simultaneously fitting a baseline and a transmission profile to us (using non-linear Levenberg-Marquardt optimization). In this work, the baseline model is based on the reference arm signal, ur(ν). Differences in offset and intensity between the two arms are taken into account by introducing two free fit parameters a 0 and a 1. The baseline model is explicitly stated in Eq. 3.
When a HITRAN simulation, Tsim(ν), is used to model the transmission profile, the complete model is given by
where a 0, a 1, k and ν 0 are free fit parameters. While a 0 and a 1 are related to the baseline (c.f. Eq. 3), k is a scale factor introduced to allow adjustment of path-integrated absorbance, and ν 0 a frequency shift needed to match the relative optical frequency.
Due to strong wall collision line broadening , spectra originating from gas confined in the nanoporous alumina cannot be simulated by HITRAN. In such cases, the transmission profile is instead modeled by a certain number of independent Lorentz lineshapes:
Here, ḡ denotes a peak normalized Lorentzian lineshape, and the free fit parameters in this model are: αi being the peak absorbance, Γi being the Lorentz HWHM, and ν 0,i being the line center on the relative optical frequency scale. Using the same baseline model as in Eq. 4, the complete model then beomes
In order to make fitting robust, an initial guess is constructed based on (i) the expected positions of absorption lines, and (ii) the observed peak absorption fraction of the strongest line.
2.4. Calculations of water vapor concentration
The concentration of water vapor in air is calculated using the Arden-Buck equation, 
where TK (K) is the temperature and p (atm) the saturation pressure. A measurement of the relative humidity is needed in order to estimate the actual partial pressure of water vapor. For this purpose, we employ a Testo 608-H1 hygrometer (accuracy of ±3% RH units).
2.5. Nanoporous alumina
The alumina investigated in this work is a nanoporous bulk alumina manufactured by sintering a monodispersive 0.3 µm α-alumina powder at 1000 °C. The sample is 13 mm in diameter and about 6 mm thick. It has previously been used in connection with spectroscopy of confined oxygen molecules . The pore structure has been characterized by mercury intrusion porosimetry, a porosimetry standard . The sample is then put in a container with liquid mercury, and the intruded volume is recorded as the pressure is gradually increased. Larger pores are filled first, and smaller and smaller pores are filled as the pressure is increased (the relation between pressure and pore size is modeled by the Washburn equation ). As shown in Fig. 2, the total porosity is ϕ = 35.4%, and the mercury intrusion data suggest a narrow (±10 nm) pore size distribution around 70 nm. It should, however, be noted that the pore size given by mercury intrusion porosimetry refers to the most narrow dimension of the pore structure, i.e. the pore neck size. In addition, the method assumes sequential filling of pores in decreasing order of size. This means that the effective pore size most likely is underestimated, and that 70 nm cannot be regarded as an absolute truth (the effective pore size is most likely above 100 nm).
The optical properties have been studied with photon time-of-flight spectroscopy (PTOFS) [12,32]. The material is extremely scattering and exhibits a λ −4 Rayleigh-type scattering dependency, where the reduced scattering coefficient µ′s approximately follows 596 cm−1 × (λ/µm)−3.9 (improved expression based on re-evaluation of data from  using a more accurate measure of the sample thickness). The reduced scattering coefficient is thus about 770 cm−1 at 935 nm (i.e. a 1/µ′s ~ 13 µm transport mean free path for photons), while absorption is low (< 0.01 cm−1). The distribution of photon pathlengths for transmission measurements of the alumina material is shown in Fig. 3. The pathlength is calculated from the time-of-flight by assuming a volume-averaged refractive index 1.76 × (1 − ϕ) + 1 × ϕ ≃ 1.49. The experimental data was recorded for a 2.25 mm thick sample at 940 nm, where diffusion-based evaluation [32,33] yields a reduced scattering coefficient of about 750 cm−1. The reason why measurements were not performed on the 6 mm thick sample used for gas spectroscopy is that the corresponding time-of-flight (TOF) distribution would not fit within the 12.5 ns window offered by our 80 MHz repetition rate pulsed laser . Instead, the TOF distribution expected for the 6 mm sample is calculated theoretically  for 935 nm light (770 cm−1 in reduced scattering), taking the experimental arrangement into account (a ~2 mm diameter injection spot size and a 5.6 × 5.6 mm2 square detector). The simulation results in an average photon pathlength of about 105 cm (average TOF of 5 ns). It may appear surprising that transmission through a few millimeters of the investigated alumina gives rise to pathlengths of more than one meter. However, the scattering of the alumina is only moderate when comparing it to the extreme scattering of various disordered materials used in fundamental science of light localization (transport mean free paths of photons down to 0.1 µm have been reported) [34,35].
3. Experimental results
3.1. System test on ambient air
In order to test how well the utilized system is suited for lineshape investigation, we studied high-resolution spectra obtained under well known (ambient) conditions. The raw data generated by the system are shown in Fig. 4.
HITRAN-based evaluation of the data, as described in Section 2.3, is presented in Fig. 5(a). The evaluation is based on a HITRAN simulation for 983 mbar, 295.5 K, a pathlength of 100 cm, and a H2O volume mixing ratio of 5000 ppm. The fitted value of k was 0.977, and suggests a path integrated concentration of about 4900 ppm·m. The Arden-Buck equation for a 295.5 K and 19.8±3% RH results in H2O partial pressure in the 0.0044 to 0.0060 atm range, and path integrated concentrations between 4600 and 6200 ppm·m (for 983 mbar = 0.97 atm). The experimental result is thus well within accuracy of the utilized hygrometer. Furthermore, the good agreement in spectral shape between our experiment and HITRAN shows that our system can be used for lineshape assessment. Note, however, that the residual pattern exhibit non-random structures, indicating non-canceled interference, inaccurate reference values for pressure and temperature, and/or slight inaccuracy in the the frequency scale. On the other hand, the maximum residual is not more than 2 × 10−4 and the signal-to-residual ratio is well above 100.
Since HITRAN cannot take wall collision broadening into account, we will later evaluate measurements on confined water vapor by fitting multiple Lorentzian lines to our data. In order to verify the performance of this procedure, we tested it on the ambient air data. The result is presented in Fig. 5(b), where 5 Lorentzians are simultaneously fitted to the data. Fitted line parameters are given in Table 2. The fact that the lines should exhibit Voigt lineshapes is not of major importance, since the Lorentzian contribution is dominating at atmospheric pressure. For the three strongest lines, fitted spectral positions and linewidths agree well with line parameters stated in HITRAN. The two weakest lines have peak absorption fractions that are not much larger than the residual background. This is reflected by a fairly large deviation in fitted and expected parameters.
3.2. Gas confined in nanoporous alumina
It is very important to note that interference suppression is crucial during laser spectroscopy of gas in turbid media . If our experiments are performed under static conditions (tracking coils turned off), the transmittance spectrum is distorted by a 5 × 10−3 (peak-to-peak) random interference structure (c.f. Fig. 6). This noise is detrimental to spectral analysis, even for the strongest absorption line in our experiments.
Experimental data obtained from a measurement on the nanoporous alumina are presented in Fig. 7, and fitted Lorentzian line parameters are given in Table 3. The measurement was conducted on a sample that had been stored in 100% RH and about 296 K for several hours, and the acquisition time was 60 s. Absorption lines for the confined water vapor is clearly much broader than for free water vapor (for the strongest line, 4.3 GHz versus 2.9 GHz, i.e. a 47% increase in HWHM). The absorption lines are well modeled by Lorentzian lineshapes. This is expected as conventional pressure broadening should dominate (the mean free path between intermolecular collisions are smaller than the pore size, see, e.g. ). The peak absorption fraction is about 3%, and may appear surprisingly strong given that the sample is not more than 6 mm thick. The explanation is the strong multiple scattering of the material, and the related pathlength enhancement (c.f. Section 2.5).
It is interesting to compare the strength of the observed water vapor absorption with the results of photon time-of-flight spectroscopy (PTOFS, c.f. 2.5). This can be done by calculating the interaction pathlength L from the gas absorption data, and comparing it to the pathlength given by PTOFS. The transmission T(ν) is related to interaction pathlength as
where S cm2Hz is the integrated linestrength, g(ν) the area-normalized lineshape function (a function of optical frequency), and N the number density of the absorber. For the strongest water vapor line, as stated in Table 1, we have S = 1.936 × 10−11 cm2Hz. The peak value of a Lorentzian lineshape function is g max = 1=(πΓ), i.e. 7.4026 × 10−11 Hz−1 for the molecules confined in the alumina (Γ = 4.3 GHz). The number density of water vapor is given by c × N 0, where c is the concentration and N 0 the Loschmidt number. The Loschmidt number states the total number density of an ideal gas and depends on temperature (TK) and pressure (p), N 0 = p/(kBTK), where kB is the Boltzmann constant. For our case, TK = 296 K and p = 1 atm, we have N 0 = 2.4794 × 1019 cm−3. Turning to the water vapor concentration, some reasoning is needed. The absorption measurement was made soon after the sample was taken from a sealed environment (100% RH and a temperature of about 296 K). According to Eq. 7, the corresponding saturation pressure of water vapor is 0.0275 atm (a concentration of 27500 ppm, at atmospheric pressure). Given the experiences from investigations of gas dynamics (c.f. Fig. 8), we expect that the effective concentration in the material during our measurement is approximately 3/4 of the saturation pressure (i.e. a concentration of about 21000 ppm). The resulting number density is thus N = 0.021N 0 ≃ 5.2 × 1017 cm−3. We may now estimate the interaction pathlength by solving
Doing so, we find that L is approximately 41 cm. This is in good agreement with the measurement of the photon time-of-flight distribution (c.f. Section 2.5), in which the total photon pathlength was estimated to 105 cm. Given the 35.4% porosity of the alumina, we should thus expect that about 37 cm is through the pores (i.e. close to the 41 cm derived from gas absorption). Note that this reasoning assumes that light has no significant preference to travel in the solid when the heterogeneity is smaller than the wavelength of light. In contrast, recent work on light propagation in macroporous materials show that light is predominantly confined to the solid . The issue thus deserve further attention.
3.3. Gas exchange dynamics
In order to study water vapor transport in the nanoporous alumina, we studied how the water vapor concentration in the alumina relaxes to ambient conditions after the material has been stored in a sealed environment with 100% RH. Fig. 8(a) shows how the water vapour absorption signal slowly decreases with time. The process exhibits non-trivial features and cannot be modeled by a single exponential decay. This is illustrated by the outcome of exponential fitting over the complete data series. On the other hand, the process from 20 minutes and onwards appears to be well modeled by a single exponential. Note also that the relative absorption does not drop to 0.25, as expected from the ambient air relative humidity. This may be explained by an initial rapid decay that is not captured (the insertion of the sample into the setup takes up to one minute), or that 100% RH was not reached within the sample.
The results of the relaxation experiment stand in great contrast to the experiences from spectroscopy of molecular oxygen confined in the alumina. Oxygen has been found to enter and exit the alumina very quickly . In order to further illustrate this difference, we conducted simultaneous sensing of water vapor and oxygen in the nanoporous alumina during a nitrogen flushing experiment. In order to readily be able to separate absorption of the two gases, we employ WMS and use different modulation frequencies at the two wavelengths used. The result of the experiment is given in Fig. 8(b). There, the absorption imprint of the gases are measured by the peak-to-peak value of the intensity-corrected first harmonic WMS signal (1f IC-WMS). The sample was flushed with nitrogen approximately from t = 0 to t = 4 min. The flushing was conducted in open air by directing a ~12 l/min flow of nitrogen towards the sample. The decay in water vapor concentration is clearly very slow, while the decay in oxygen concentration is extremely fast and cannot be resolved by our instrument. Note that the flushing method utilized here was not able to completely replace the air surrounding the sample (previous measurements on the same material show that the signal indeed can be completely removed within seconds ). Despite non-optimal nitrogen flushing, the experiment clearly illustrates the significant difference in gas exchange characteristics. Water vapor is clearly a “sticky gas”.
4.1. Regarding wall collision line broadening
In previous work , it was found that oxygen exhibit a broadening from 1.6 GHz to 2.3 GHz when confined in the same material as investigated here. The corresponding relative increase in linewidth is 45%, and is close to the increase in linewidth for water vapor reported in the present work (47%, going from 2.9 GHz to 4.3 GHz). As the H2O line is almost twice as broad (1.8 times) as the O2 at ambient air conditions, the equal increase in relative linewidth indicates that the wall collision broadening is stronger for H2O than for O2. Since the average speed of H2O is 1.3 times greater than for O2 (590 m/s versus 440 m/s at ambient conditions), this is somewhat expected. Since it is not known how the line shapes and widths due to intermolecular and wall collisions add up, it is, however, difficult to check the quantitative agreement between observations and kinetic theory. Furthermore, the mercury intrusion porosimetry gives us an indication of the most narrow passages in the pore structure, and the 70 nm pore size reported in Section 2.5 is thus, to some extent, an underestimation of the effective pore size. Nonetheless, for H2O at 296 K inside a 100 nm diameter sphere, Γ = (2πτ)−1 in combination with Eq. 1 yields a 1.41 GHz linewidth due to wall collisions. For O2, analogous calculations yields 1.06 GHz. The agreement is thus not unreasonable, but further scrutiny is essential.
In order to progress, two things are important. The first thing is to perform measurements at reduced pressures. This will eliminate the impact of intermolecular collisions, while wall collision broadening should remain equally strong. It will allow investigations of the wall collision lineshape, as well as studies of how it adds to traditional collisional broadening. Secondly, better information about the shape and size of pores must be gathered. The pore neck size, as provided by mercury intrusion porosimetry, may be far from the effective pore size. When interpreting lineshapes of gases tightly confined in porous materials, one should also keep in mind that the lineshape can be influenced also by Dicke narrowing [37,38] as well as by, e.g. van der Waals interactions [39,40].
4.2. Regarding gas diffusion
Despite the fairly simple pore structure (a narrow distribution around 70 nm), the gas exchange process appears non-trivial, and cannot be explained by a single exponential decay. The minor plateau occurring after 6 min is reproducible, and is thus not a measurement error. It is important to realize that the measured absorption is a product of the photon sampling distribution and the gas concentration distribution. This fact complicates interpretation, and needs further attention. Another question is whether adsorption/desorption processes can influence the internal gas concentration. A key in resolving these issues is to construct a GASMAS instrumentation that allows measurements of samples while kept in controlled atmospheres (avoiding manual moving of samples from controlled conditions to ambient conditions, as in the present work).
The authors are grateful to Karin Lindqvist at SWEREA IVF for manufacturing of the alumina, and to Erik Alerstam, Dmitry Khoptyar and Stefan Andersson-Engels for collaboration on PTOFS. This work was supported by the Swedish Research Council through a direct grant and a Linnaeus grant to the Lund Laser Centre.
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