Modulated and Pulsed
Photoacoustics
in Trace Gas Analysis András Miklós, Peter Hess University of Heidelberg (Germany)
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he phenomenon of sound generation after illuminating a material with nonstationary (modulated or pulsed) radiation is called the photoacoustic (PA) effect. Photoacoustic spectroscopy (PAS) is the application of the PA effect for spectroscopic purposes. PAS is a form of optical absorption spectroscopy, but it also can be considered a form of calorimetry because the technique measures the transient internal heating of a sample. The PA effect in gases can be divided into three main steps: heat release in the sample due to optical excitation and subsequent nonradiative decay, acoustic and thermal wave generation in the sample from localized transient heating and expansion, and measurement of the acoustic signal in a PA cell with a microphone. This article discusses the current state of PAS and its prospects for the future. With further development of laser technology, PAS will be a method for rapid determination of trace gases.
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PA effect The effects caused by the absorption of photons are illustrated in Figure 1. When incident photons are absorbed by a molecule, rotational, vibrational, and electronic energy levels are excited. Excited states lose their energy by radiative processes, such as spontaneous or stimulated emission, and/or by collisional relaxation, in which the energy is transformed into translational energy. Radiative emission and chemical reactions do not play an important role in vibrational excitation, because the radiative lifetime of vibrational levels is long compared with the time needed for collisional deactivation at the pressures used in photoacoustics (~1 bar), and the photon energy is too small to induce chemical reactions (1, 2). Thus, the absorbed energy is
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New types of diode lasers are aiding the development of this technique.
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released as heat, appearing as translational (kinetic) energy of the gas molecules. However, in the case of electronic excitation, radiation emission and chemical reaction processes compete efficiently with collisional energy transfer. Chemical reactions also may contribute to the release of heat and thereby may increase the PA effect. For example, if photodissociation occurs, the local increase in the number of molecules and the thermalization of the recoil energy of the fragments generate a local pressure and temperature rise (3). If it is assumed that the thermalization of the absorbed photon energy can be described by a linear relaxation process, the kinetics of heat release due to optical absorption in the sample material can be modeled by a simple rate equation. The heat released per unit volume and time can be determined by solving this rate equation (4). If the nearresonant vibration–vibration (V–V) and the vibration rotation, translation (V–R, T) relaxation processes are the fastest, the deposited heat power density will be proportional to the absorption coefficient and the incident light intensity (A glossary can be found on p 37 A). However, Laser radiation for short laser pulses with correspondModulated, pulsed ingly high light h Absorption intensities and highpower continuousExcitation wave (cw) lasers, optical saturation Vibration, electronic can yield a nonlinear dependence of V–R, T Deactivation deposited heat with light intensity. Heating Sound and therLocalized, transient mal wave generation can be theoretExpansion, contraction ically described by classical disciplines Acoustic wave of physics, such as fluid mechanics and Standing, pulsed thermodynamics. The governing physical equations are the energy, Microphone momentum, and mass conservation FIGURE 1. Detailed scheme of the physical laws. The physical processes occurring after optical excitation. quantities characterizing the PA and Modulated or pulsed laser radiation leads to the population of rotational, vibrational, and electronic states. photothermal Collisional deactivation by R–T; V–R, T; and E–V, R, T processes are the processes generates a localized transient heating. The temperature (T ), resulting expansion launches standing or pulsed acoustic waves, which are detected with a microphone. pressure (P ), den-
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sity (ρ), and the three components of the particle velocity vector v. Because the five equations (equations of mass and energy conservation, and three equations for the conservation of the components of momentum) are not sufficient to determine the above six quantities, a sixth equation is added describing the thermodynamic equation of state in the form ρ = ρ(P, T ). By eliminating the variables T, ρ, and v, a linear wave equation can be derived for the sound pressure. This wave equation always has two independent solutions: a propagating acoustic wave with wavelengths in the centimeter to meter range, which is only weakly damped, and a diffusive thermal wave (5). Because the latter wave has a very small wavelength (in the submillimeter region) and is strongly damped, it can be observed only in the vicinity of the exciting light beam. Therefore, thermal and acoustic waves show different behaviors and, because they separate in space, can be investigated independently. In trace gas analysis, the acoustic signal is typically detected. The energy released in the material over time (power density) as a result of all the processes generating translational energy is the source of the thermal and acoustic waves. The spatial size and shape of the source volume depend on the light-beam geometry and on the pathlength in the gas. Similarly, the time dependence of the heat source is determined by the time dependence of the laser excitation and the relaxation dynamics of the analyte. In modulated PAS, the intensity (or the wavelength) of the incident light beam is modulated in the audio frequency range (10–104 Hz) to generate the PA signal. The amplitude of the periodic pressure change is proportional to the timevarying component of the released heat power density and inversely proportional to the modulation frequency. The PA signal also depends on the boundary conditions determined by the type and geometry of the PA cell. The PA chamber can be considered a linear acoustic system, which responds in a characteristic way to a photoexcitation process. Although the detectors usually can be used for both modulated and pulsed excitation PAS, the two cases will be presented separately.
Photoacoustic signal analysis The main parts of a photoacoustic gas analyzer are shown in Figure 2. The laser radiation passes through the PA cell and enters a power monitor. Continuous-wave laser radiation is modulated by a mechanical chopper or an electrooptic device. The excited sound wave is detected by an electret or condenser microphone with a sensitivity in the 1- to 100-mV/Pa range. The microphone signal is either measured by a lock-in amplifier or digitized and evaluated directly by a PC. All cavities used as photoacoustic cells have acoustic resonances. If the modulation frequency is much smaller than the lowest acoustic resonance frequency, the cell operates in a nonresonant mode (“nonresonant cell”). In this case, the
sound wavelength is much larger than the cell dimensions, and, therefore, sound cannot propagate. The average pressure in the cell will oscillate with the modulation frequency. The photoacoustically generated pressure can be described by
operating in the resonant mode is the additional amplification of the PA signal by the Q factor of the resonator, which can be as high as 103.
Ultralow gas concentration measurements (γ − 1) αlW P(ω) = _________ i ωV
(1)
High-power, line-tunable IR lasers are currently the best choice for ultrasensitive PA trace gas analysis, because molecular V–R, T relaxation processes are very effective in the IR region. It is clear from Equations 1 and 2 that the PA signal scales withW and α. Therefore, the sensitivity can be increased by exciting states with large transition moments and using higher laser powers. Fundamental vibrational modes with high absorption strengths can be accessed in many important species by line-
in which α is the optical absorption coefficient of the gas at the radiation wavelength, l is optical pathlength,W is the incident light power, i is the imaginary unit, ω is the angular frequency of modulation,V is the cell volume, and γ denotes the adiabatic coefficient of the gas (6). The amplitude of the pressure oscillation (the PA signal) will be proportional to α, l, andW and inversely proporHigh-power, line-tunable IR lasers are currently the tional to ω and V, which means that the PA signal is inversely best choice for ultrasensitive PA trace gas analysis. proportional to an effective cross section defined by V/l. The signal may be quite large for a small cell and low modulatunable CO2 or CO gas lasers. To date, these lasers have tion frequency. Unfortunately, the noise also increases with made possible the lowest analyte concentration measuredecreasing ω and V; thus, the S/N usually will decrease. ments by PAS. For the first ethylene measurements in 1972, The PA signal has a 90° phase lag with respect to W. a CO2 gas laser with a modest power of 1 W was used (8). A cavity with a carefully optimized geometry, such as a nearly perfect cylinder or sphere, is used in quantitative pho- Current state-of-the-art experiments use higher power toacoustics (7). Such an acoustic resonator has several eigen- (>1 W) CO2 and CO lasers, resonant cells with low volumes (
