Anal. Chem. 2006, 78, 5218-5221
Photothermal Gas Analyzer for Simultaneous Measurements of Thermal Diffusivity and Thermal Effusivity Israel A. Esquef,† Ana Paula L. Siqueira,† Marcelo G. da Silva,† Helion Vargas,*,† and Luiz Carlos M. Miranda‡
Universidade Estadual do Norte Fluminense, Campos dos Goytacazes, RJ, Brazil, and Instituto Nacional de Pesquisas Espaciais, Sa˜o Jose´ dos Campos, SP, Brazil
In this paper, we describe a new, simple, and fast photothermal method for simultaneous measurements of two important gas thermal properties: thermal diffusivity and thermal effusivity. The method consists essentially in combining a photoacoustic cell and a thermal wave pyroelectric cell enclosed in a single compact gas analyzer. The photoacoustic cell is kept filled with synthetic air and sealed. The pyroelectric cell is also filled with synthetic air, and after some warm up time, the synthetic air is exchanged to the gas of interest. It is shown that the analysis of the transient and saturation signals of both photoacoustic and pyroelectric cells is capable of measuring the thermal properties with an accuracy of 3%. This particular capability of performing simultaneously the measurements of thermal diffusivity and thermal effusivity allows us to carry on the complete characterization of the thermal properties of gases. In the last years, we have witnessed the development of a number of photothermal techniques for characterization of the thermal properties of liquids and gases. The photothermal techniques are essentially based upon sensing the fluctuation in temperature of a given sample due to nonradiative de-excitation processes following the absorption of modulated light. One of these techniques, which was called thermal wave interferometry (TWI) is based upon the concept of interference of thermal waves, first discussed by Bennett and Patty.1 This possibility was later demonstrated by Shen and Mandelis,2-4 who succeeded in showing the feasibility of the pyroelectric detection of thermal waves propagating across an air gap, between a pyroelectric sensor and a source of thermal waves. These authors showed that, using this thermal wave detection configuration, the thermal diffusivity of air could be measured with very good accuracy. Quite recently we have reported on the use of this technique for investigating the transport properties of hydrocarbon vapors * To whom correspondence should be addressed. E-mail:
[email protected], Phone: 55 (22) 2726-1518. Fax: 55 (22) 2726-1532. † Universidade Estadual do Norte Fluminense. ‡ Instituto Nacional de Pesquisas Espaciais. (1) Bennett, C. A.; Patty, R. R. Appl. Opt. 1982, 21-49. (2) Shen, J.; Mandelis, A. Rev. Sci. Instrum. 1995, 66, 4999-5005. (3) Shen, J.; Mandelis, A.; Aloysius, B. D. Int. J. Thermophys. 1996, 17, 12411254. (4) Shen, J.; Mandelis, A.; Ashe, T. Int. J. Theromphys. 1998, 19, 579-593.
5218 Analytical Chemistry, Vol. 78, No. 14, July 15, 2006
diffusing into the air5-7 and the characterization of the thermal properties of pure liquids,8 as well as the characterization of adulterants in automotive fuels.9,10 This effort culminated with the development of a photothermal gas analyzer (PTGA). In this work, motivated by the success of the previous applications of the TWI technique,7-10 we present an improved, self-contained, compact, portable, gas analyzer combining two wellestablished photothermal techniques for the simultaneous measurement of the thermal diffusivity and thermal effusivity of gas samples. The basic design of this new analytical instrument combines a photoacoustic cell (PA cell) and a TWI pyroelectric cell (PE cell) separately only by an aluminum foil absorber. The basic design of the improved photothermal gas analyzer consists of a sealed cylindrical PA cell, filled with synthetic air. Adjacent to the external face of the Al foil there is a PE sensor positioned at 2-mm distance from the Al foil. This 2-mm gap between the Al foil and the PE sensor is called the PE cell. This entire system is enclosed in a temperature-controlled gas reservoir, so that the atmosphere in the PE cell can be filled with the gas one wants to characterize, the so-called, active gas. Initially, the PE cell is also filled with synthetic air, and after some initial warm up time, the gas in the PE cell is exchanged to the gas of interest. It is shown that this new PTGA design allows us to measure the thermal diffusivity of gas samples through the PE cell and, simultaneously, the thermal effusivity through the PA cell with an accuracy of 3% for both properties. This fact renders the technique to be well suited for thermal conductivity measurements of pure gases or gases mixtures. (5) Lima, J. A. P.; Marin, E.; Silva, M. G.; Sthel, M. S.; Cardoso, S. L.; Takeuti, D. F.; Gatts, C.; Vargas, H.; Rezende, C. E.; Miranda, L. C. M. Rev. Sci. Instrum. 2000, 71, 2928-2932. (6) Lima, J. A. P.; Silva, M. G.; Massunaga, M. S. O.; Marin, E.; Vargas, H.; Miranda, L. C. M. J. Appl. Phys. 2002, 91, 5581-5586. (7) Lima, J. A. P.; Marin, E.; Silva, M. G.; Sthel, M. S.; Cardoso, S. L.; Vargas, H.; Miranda, L. C. M. Rev. Sci. Instrum. 2001, 72, 1580-1582. (8) Lima, J. A. P.; Marin, E.; Correa, O.; Silva, M. G.; Cardoso, S. L.; Gatts, C.; Rezende, C. E.; Vargas, H.; Miranda, L. C. M. Meas. Sci. Technol. 2000, 11, 1522-1526. (9) Lima, J. A. P.; Cardoso, S. L.; Silva, M. G.; Sthel, M. S.; Gatts, C.; Vargas, H.; Miranda, L. C. M. Ind. Eng. Chem. Res. 2001, 40, 6207-6212. (10) Lima, J. A. P.; Silva, M. G.; Massunaga, M. S. O.; Vargas, H.; Miranda, L. C. M. Anal. Chem. 2004, 76, 114-119. 10.1021/ac060517e CCC: $33.50
© 2006 American Chemical Society Published on Web 06/07/2006
Figure 1. Schematic view of the experimental PTGA setup.
EXPERIMENTAL SECTION Photothermal Gas Analyzer. The new PTGA setup consists of a box measuring 50 cm by 36 cm by 50 cm with an 8-in. LCD display and a retractable keyboard weighing ∼10 kg. The core of the gas analyzer is a temperature-controlled closed cylindrical glass cell (48.2 mm diameter, 60.7 mm long), adequately adapted for gas exchange and control of ambient parameters. In this new design, a photoacoustic cell was integrated into the thermal wave generator, between the diode laser collimation lens and the Al foil, as schematically shown in Figure 1. In this small sealed cavity, a highly performance miniature electret microphone (Knowles model EK-3024) was inserted in order to detect the PA signal. The PA signal is synchronously detected using an OL-4000 (Optronics Laboratories) lock-in board. The thermal wave generator consists of a 12-mm-diameter, 15-µm-thick Al foil closing one end of the PA cell. The surface of this Al foil facing the inner tube space is painted with black ink so that it acts as a light absorber. The pumping light beam consists of a 40-mW diode laser (Mitisubishi model ML101J8) operating at 663 nm and electronically modulated at 10 Hz. This pumping light beam is focused on the black-painted surface of the Al foil. Following the absorption of the modulated light beam, the Al foil temperature fluctuates periodically at the modulation frequency of the incident light beam thereby launching thermal waves into the gas-filled cell. The thermal waves thus generated propagate through the PE cell gap causing a temperature fluctuation of the pyroelectric sensor as they reach the gas-sensor interface. The sensing unit consists of an 18-mm-diameter pyroelectric sensor made of a 25-µm-thick poly(vinylidene difluoride) (PVDF) film with Al metallized surfaces. This active glass cell is enclosed coaxially by a second larger cylindrical glass cell (65 mm diameter, 60.7 mm long), such that the space between them is filled with distillated water that flows from a closed-loop controlled cooling system to ensure the adequate temperature control needed for the experiments. The temperature rise at the pyroelectric surface is probed using another OL-4000 (Optronics Laboratories) lock-in board. The whole system is controlled in a PC/104 platform with a dedicated data acquisition and control program. The photoacoustic and pyroelectric signals are essentially determined by the temperature fluctuations at the surfaces of the Al absorber and of the pyroelectric sensor, respectively. These, in turn, are described by the well-known thermal diffusion model for the generation of photothermal signals.10-13 As a general (11) Vargas, H.; Miranda, L. C. M. Phys. Rep. 1988, 161, 43-101.
Figure 2. Geometry of the PTGA cell.
reference and for a more detailed discussion on the theoretical and practical applications of the photothermal techniques we refer to refs 11 and 12. Theoretical Basis. Referring to the geometry schematically shown in Figure 2, the temperature distribution T(x,t) within the gas cells, following the periodic heating of the Al foil at x ) 0, is obtained by solving the thermal diffusion equation for the three media (active gas, Al absorber, and reference gas of the PA cell), assuming that the modulated light beam is fully absorbed at x ) 0. The laser beam is assumed to illuminate uniformly the Al foil in order to minimize the lateral heat diffusion effects. Under these conditions, thermal gradients in the radial direction are negligible and the problem may be adequately treated as a one-dimensional problem. The harmonic component of the temperature fluctuation in the active gas cell is denoted by T(x)ejωt, with ω ) 2πf, where f is the modulation frequency of the pumping light beam. The corresponding temperature fluctuations in the Al absorber and in the reference PA cell gas are denoted as Ta(x)ejωt and T0(x)ejωt, respectively. Performing lengthily but straightforward calculations,9-13 the temperature fluctuation amplitudes, θPA and θPE, at the Al absorber-reference cell interface at x ) 0 and at the active gas cell-pyroelectric sensor interface at x ) L, respectively, can be shown to be given by,
θPA )
β′I0 1 ; k0σ0 (1 + /0)
θPE )
β′I0 1/2 1 e-L(πf/a) k0σ0 (1 + /0) (1)
Here, β′ is the surface absorption coefficient of the Al foil, I0 represents the light intensity, (0) is the thermal effusivity of the active (reference) gas, κ(κ0) is the thermal conductivity of the active (reference) gas, and σ0 ) (1 + j)(πf/R0)1/2 is the complex thermal diffusion coefficient of the reference cell gas, with R0 being its thermal diffusivity. The thermal diffusivity and thermal effusivity are related to the thermal conductivity, κ, specific heat, c, and mass density, F, by R ) k/Fc and ) (kFc)1/2. In arriving at eq 1 we have implicitly assumed that, at the 10 Hz modulation frequency, the Al absorber is thermally thin, namely, La(πf/R0)1/2 , 1, where Ra is thermal diffusivity of the Al absorber of thickness La. For a 15-µm-thick Al foil, for which Ra ) 0.92 cm2/s, this (12) Almond, D.; Patel, J. Photothermal Science and Technology; Chapman and Hall: London, 1996. (13) Rosencwaig, A.; Gersho, A. J. J. Appl. Phys. 1976, 47, 64-69.
Analytical Chemistry, Vol. 78, No. 14, July 15, 2006
5219
Figure 3. (a) Time evolution of the PE signal amplitude, normalized to its initial t ) 0 value, for the air/CO2 exchange. (b) The PA signal levels for air and CO2.
condition is amply satisfied for a 10-Hz modulation frequency. This means that the Al absorber is “transparent” to the deposited heat diffusion and that is why both temperature fluctuation amplitudes in eq 1 do not depend on the absorber properties. It was also assumed that both the reference and the active gases are thermally thick at the working modulation frequency. That is, we have assumed that both L0(πf/R0)1/2 and L(πf/R)1/2 are much greater than unit at the current modulation frequency. For gas cell lengths of the order of (or greater than) 2 mm, this condition is again amply satisfied for the majority of gases. The thermal diffusion model discussed in refs 11-13 shows that, for the thermally thick gas layers we are considering, the resulting pressure fluctuation in the PA cell is proportional to the θPA, namely, δP ) P0θPA/T0L0σθ (where P0 and T0 are the ambient pressure and temperature, respectively), whereas the current fluctuation in the pyroelectric sensor is proportional to θPE. This means that, in terms of the active gas thermal properties, the output voltages of the microphone in the PA cell, SPA, and of the pyroelectric sensor in the active cell, SPE, can be written as
1 ; SPA ) χPA (1 + /0)
1/2
SPE ) χPAeL(πf)
(2)
where the χi(i ) PA and PE) are complex functions containing the frequency response functions of the corresponding transducers and geometrical parameters characterizing the detection systems. Now, at the beginning of the experiment at t ) 0, both cells are filled with synthetic air so that the corresponding signal amplitudes in eq 2 reduce to SPA ) (1/2)χPA and SPE ) χPEeL(πf)1/2. After exchanging the gas in the active gas cell to the gas of interest, the corresponding signals are given by eq 2, so that the normalized signal amplitudes of the PA and PE cells, with respect to the initial signals, can be written as
SPAnorm )
2 ; (1 + /0)
SPEnorm ) eL(πf)
xR0 - 1/xR]
1/2[1/
(3)
These results mean that, starting with both cells filled with the synthetic air and exchanging the active cell gas to the gas of 5220
Analytical Chemistry, Vol. 78, No. 14, July 15, 2006
interest, the PA signal changes its amplitude such that when the active gas is completely filled with the gas one wants to characterize, the signal ratio depends only on the value of its thermal effusivity with respect to that of the reference gas. Similarly, the ratio of the PE signal depends only on the value of the active gas thermal diffusivity with respect to the synthetic air thermal diffusivity. In this way, by simply measuring the PA and the PE signal amplitude ratios, with respect to the originally air-filled cell, both thermal properties of the active gas can be simultaneously measured in a fixed geometry and modulation frequency configuration. RESULTS AND DISCUSSION In this work, we have used synthetic air (20% O2 and 80% N2) as the reference gas and CO2 (99.99%) and methane CH4 (99.5%) as the active gases, whose thermal properties we wanted to determine. All measurements were carried out at ambient temperature (23 °C) and pressure (760 mmHg) using a gas calibration and supplier system. As mentioned before, the experimental procedure consists of measuring the PA signal starting with both cells filled with the synthetic air and, in sequence, acquiring the typical time evolution PE signal due to the exchanging of the reference gas by the active gas, at a controlled flow rate of 4 L/h. At this flow rate, the PE cell is completely filled with the active gas in typically 10 min, at which point the PE signal begins to show a saturation behavior. Immediately after acquiring the PE signal, the PA signal is measured again in this configuration, in which the PE cell is now filled with the active gas. For each investigated gas, a series of at least five independent experimental runs has been carried out. In Figure 3a, we present the time dependence of the normalized PE signal for the case in which the initial synthetic air of the PE cell is exchanged by CO2. As the gas exchange process takes place, the PE signal evolves toward saturation after a time interval of roughly 10 min, when the synthetic air in the active cell is completely exchanged by CO2. At this point, the value of the normalized PE signal is evaluated by taking the average over the last 50 points of the saturation plateau in Figure 3a. The result found was SPEnorm(CO2) ) 0.496 ( 0.001 05. Upon substituting this
Table 1. Values of the Thermal Properties of the Investigated Gases As Obtained from the Proposed Technique and Those Quoted in the Literature at 23 °Ca gas
R (cm2/s)
RLit. (cm2/s)
(mW‚s1/2/cm2‚K)
Lit. (mW‚s1/2/cm2‚K)
κ (mW/cm‚K)
κLit. (mW/cm‚K)
air CO2 CH4
0.109 ( 0.0004 0.247 (0.0002
0.220 0.110 0.242
0.494 ( 0.0071 0.681 ( 0.0172
0.558 0.505 0.693
0.163 ( 0.0029 0.338 ( 0.0056
0.260 0.168 0.334
a
Taken from refs 14 and 15.
value into eq 3, and using the literature value4,14,15 of the thermal diffusivity of synthetic air at T ) 23 °C, namely, Rair ) 0.220 cm2/ s, the thermal diffusivity of CO2 is readily obtained. The value found was RCO2 ) 0.109 ( 0.0004 cm2/s. This value is in good agreement with those reported in the literature,7,14,15 both experimental and theoretical values. The difference between the above value and those reported in the literature is of the order of 0.9%. In Figure 3b, we show the behavior of the PA signal during this experiment. The first plateau in Figure 3b corresponds to the PA signal acquired with both cells filled with the synthetic air, whereas the second one corresponds to the situation in which the active gas cell is completely filled with CO2. The normalized PA signal is calculated by SPAnorm ) < SPA(CO2) > /< SPA(Air) >, which yielded SPAnorm ) 1.061 ( 0.0075. Substituting this value into eq 3, and using the literature value of the air thermal effusivity, we have calculated the CO2 thermal effusivity. The result found was RCO2 ) 0.494 ( 0.0071 mW‚s1/2/cm2‚K. This value is again in good agreement with those reported in the literature,14,15 differing by ∼2.2%. The same procedure was carried out for the case of methane. In Table 1, we summarize the results we have obtained for the thermal properties of these gases. Also included in this table are the values of the thermal conductivities obtained from these measurements of R and , as given by κ ) xR. Finally, a few comments should be made regarding the promised accuracy of the proposed photothermal gas analyzer. As is well known, the thermal diffusivity and thermal effusivity are extremely dependent upon the temperature as well as on the ambient pressure. Thus, to make use of the full advantage of the proposed technique, special attention should be given to keep the
actual measurement conditions under strict control. This means that not only the heat bath temperature but also the incident laser power should be adequately maintained as stable as possible. Excessive laser power may induce undesirable sample heating which, in turn, induces sample thermal expansion and blending, in which case the thermal diffusion model described above is no longer valid.
(14) Lyde, D., Ed. CRC Handbook of Chemistry and Physics, 75th ed.; Chemical Rubber Co: Cleveland, OH, 1995. (15) Reid, R. C.; Praunitz, J. M.; Poling, B. E. The Properties of Gases and Liquids, 4th ed.; McGraw-Hill: New York, 1987.
Received for review March 21, 2006. Accepted May 8, 2006.
CONCLUSION In this paper, we have described a new, simple, and fast photothermal method for simultaneous measurements of two important gas thermal properties: thermal diffusivity and thermal effusivity. It was demonstrated that both thermal diffusivity and thermal effusivity could be detected with good accuracy using the described experimental device. The results presented here open the possibility to perform routine measurements of those thermal properties of pure gases or gas mixtures, including the evaluation of their thermal conductivities. Finally, we add that apart from advantages previously mentioned, it should be emphasized that the proposed technique allows us to perform the measurements of the thermal properties of a gas sample under the same measurement conditions, avoiding eventual experimental discrepancies due to the difference in the measurement conditions, if the measurements would be done separately. ACKNOWLEDGMENT The authors greatly acknowledge Luiz A. M. Meireilles for the technical assistance. This work was partially supported by Brazilian agency CNPq.
AC060517E
Analytical Chemistry, Vol. 78, No. 14, July 15, 2006
5221
