Anal. Chem. 1998, 70, 998-1006
Amperometric Gas Sensor Response Times P. Richard Warburton,* Marcus P. Pagano, Robert Hoover, Michael Logman, and Kurtis Crytzer
Draeger Safety Inc., 101 Technology Drive, P.O. Box 120, Pittsburgh, Pennsylvania 15230-0120 Yi Jin Warburton
Calgon Corporation Inc., P.O. Box 1346, Pittsburgh, Pennsylvania 15230
This work examines the relative importance of diffusion and the electrical time constant of the working electrode on the response time of amperometric gas sensors. The response curve of an electrochemical carbon monoxide sensor to a 200 ppm CO test gas was measured as a function of the added resistance that is in series with the working electrode to increase the time constant. It has been found that the response time increases with additional resistance. The experimental behavior was compared to the values predicted on the basis of Fick’s second law of diffusion and to the values expected on the basis of the electrical properties of the sensor. The behavior of the sensor was explained using an equivalent electrical circuit, describing the time constants of the working electrode. Values obtained from this model were further compared to experimental values obtained from electrochemical impedance spectra. It has been found that the response time of the sensors depends on both the rate of diffusion and the electrical time constants of the working electrode. Since the first amperometric oxygen sensor was developed in 1956 by Clark,1 the use of amperometric sensors has become one of the most common methods for gas detection. Amperometric gas sensors are used to measure a wide range of gases in many media, both liquids and atmospheres, as has been described in several excellent reviews.2-7 One market where electrochemical gas sensors dominate is the monitoring of workplace atmospheres for exposure to toxic gases. The sensors are typically small, relatively rugged, and inexpensive, and they manifest favorable accuracy and precision. Electrochemical gas sensors that continuously detect gases in typical industrial settings at TLV-TWA * Correspondence should be addressed to this author at 1619 Ridge St., Moon Township, PA 15108. (1) Clark, J. C., Jr. Trans. Am. Soc. Artif. Intern. Organs 1956, 2, 41. (2) Seiyama, T., Ed. Chemical Sensor Technology, Vols. 1 and 2; Kodansha Ltd.: Tokyo, 1988 and 1989. (3) Gnaiger, E., Forstner, H., Eds. Polarographic Oxygen Sensors, Aquatic and Physiological Applications; Springer-Verlag: Berlin, 1983. (4) Mari, C. M.; Barbi, G. B. Gas Sensors; Kluwer Academic Publishers: Dordrecht, 1992; p 329. (5) Chang, S. C.; Stetter, J. R.; Cha, C. S. Talanta 1993, 40, 461. (6) Hobbs, B. S.; Tantram, A. D. S.; Chan-Henry, R. Liquid Electrolyte Fuel Cells. In Techniques and Mechanisms in Gas Sensing; Moseley, P. T., Norris, J. O. W., Williams, D. E., Eds.; Adam Hilger: Bristol, 1991. (7) Schuetzle, D., Hammerle, R., Eds. Fundamentals and Applications of Chemical Sensors; ACS Symposium Series 309; ACS: Washington, DC, 1986.
998 Analytical Chemistry, Vol. 70, No. 5, March 1, 1998
exposure levels8 are commercially available from several manufacturers9-11 for a wide range of gases, in both portable and fixed location instruments (e.g., electrochemical gas sensors available from Draeger Safety Inc. include those for Cl2, CO, CO2, HCl, HCN, HF, H2O2, H2S, NH3, CH3NHNH2, NO, NO2, O2, PH3, and SO2). The detection process usually involves oxidation or reduction of the gas to be detected at the sensor’s working electrode, which is held at a constant potential, and the resulting current flow is detected by the external circuit of the gas detection instrument. Commercially available electrochemical sensors for toxic gases are typically composed of an electrolyte and (usually) three electrodes: counter, reference, and working, with the working electrode positioned behind a gas diffusion barrier.12-14 The bias potential of the working electrode is chosen so that the electrochemical reaction is mass transport limited; thus, all the analyte gas which reaches the electrode is either completely oxidized or reduced. Under these conditions, the sensitivity [(steady-state signal - background current)/(gas concentration)] is determined by the rate of diffusion of the gas into the sensor. When the gas is initially applied, it takes a few seconds for the sensor output current to attain steady-state conditions. The response time of the sensor is commonly specified by the T90 or T50 time. T90 is the time for the sensor’s response current to reach 90% of its steady-state value. Similarly, the T50 metric is the time required for the sensor to reach 50% of its steady-state value. Instruments used for monitoring workplace exposure, especially those used for toxic gases, are required to have rapid response times so as to ensure that a warning can be given as quickly as possible if there is a potentially hazardous accumulation of a toxic gas. Consequently, the response time is one of the key performance characteristics, and response times are frequently cited as a specification for a sensor or instrument. Furthermore, response time characteristics are usually specified in most recognized performance standards for gas detection instruments.15 (8) American Conference of Governmental Industrial Hygienists. 1994-1996 Threshold Limit Values for Chemical Substances and Physical Agents and Biological Exposure Indices; ACGIH: Cincinnati, OH, 1996. (9) ISA Directory of Instrumentation 1996 ISA, the International Society for Measurement & Control: Research Triangle Park, NC, 1996. (10) Plog, B. A., Ed. Fundamentals of Industrial Hygiene, 3rd ed.; National Safety Council: Chicago, IL, 1988. (11) Arenas, R. V.; Carney, K. R.; Overton, E. B. Am. Lab. 1993, 25 (July), 25. (12) Mattiesen, H. U.S. Patent 5,183,550, Feb 2, 1993. (13) Blurton, K. F.; Sedlak, J. M. U.S. Patent 4,042,464, Aug 16, 1977. (14) Oswin, H. G.; Blurton, K. F. U.S. Patent 3,824,167, July 16, 1974. S0003-2700(97)00644-6 CCC: $15.00
© 1998 American Chemical Society Published on Web 01/27/1998
Other applications also require short response times, such as medical sensors (oxygen, carbon dioxide) for breath analyses, which may be required to follow changes in breath composition from breath to breath. Clearly, for these applications, the T90 response time of the sensors needs to be a few seconds or less. There is a need, therefore, to design sensors with shorter response times. If this goal is to be achieved, then those factors which affect the response time need to be understood. The response time (T90) of the sensor is widely assumed to depend on the diffusion properties of the sensor;16,17 fast-response electrochemical sensors have been designed by reducing or eliminating the membrane diffusion barrier.18 In addition to diffusion, other factors can determine the response time of a sensor. For example, Chang and Stetter found that the response of nitrogen dioxide amperometric sensors was limited by either the kinetics of the electrode reaction or the rate of nitrogen dioxide test gas diffusion to the electrode, depending on the ratio between the NO2 concentration and the electrode catalyst loading.19 Sedlak and Blurton found a second-order response for the hydrogen sulfide sensors,20 which was also attributed to the electrochemical reaction. Most electrochemical gas sensors contain electrodes manufactured by fixing high surface area precious metal catalysts on a porous PTFE membrane.14,21 The membrane allows the gas to diffuse to the working electrode and also prevents the (usually) liquid electrolyte in contact with the working electrode from leaking out of the sensor. The high surface area electrode is required for several reasons. It promotes catalytic activity, and it also provides a large area for the so-called three-phase interface, which is the region where gas, electrolyte, and electrode are in close proximity. The high surface area of the electrode results in a large apparent capacitance. This capacitance can arise from both charging of the double layer and redox processes on the electrode’s surface. Such a large capacitance, combined with the resistance of the electrode, may be anticipated to result in a large time constant for the sensor. Maclay et al. assumed that the working electrode RC time constant determined the response time of a carbon monoxide electrochemical sensor in their analysis of the response of the sensor in combination with a heated filament to pyrolize the sample gas (e.g., benzene) with a modulated power supply.22 In this report, the relative importance of diffusion and the electrical time constant of the sensor’s electrode on the response curve of the sensor was examined. The controlling factors of the response time were identified by comparing the experimental response time of a carbon monoxide sensor to the response times predicted on the basis of diffusion, as well as by measuring the effect of varying the sensor electrical time constant on the response characteristics. (15) Performance Requirements for Hydrogen Sulfide Detection Instruments (10100 ppm); ANSI/ISA.-S12.15, Part 1, 1990. (16) Bay, H. W.; Blurton, K. F.; Sedlak, J. M.; Valentine, A. M. Anal. Chem. 1974, 46, 1837. (17) Tierney, M. J.; Kim, H.-O. L.; Joseph, J.; Otagawa, T. Sensors 1992, October, 12. (18) Tierney, M. J.; Kim, H.-O. L. Anal. Chem. 1993, 65, 3435. (19) Chang, S. I.; Stetter, J. R. Electroanalysis 1990, 2, 359. (20) Sedlak, J. M.; Blurton, K. F. Talanta 1976, 23, 445. (21) Chand, R. U.S. Patent 4,498,970, Feb 12, 1985. (22) Maclay, G. J.; Stetter, J. R.; Christesen, S. Sens. Actuators B 1989, 20, 277.
EXPERIMENTAL SECTION The results are described, for brevity, for only one sensor, but the results presented are typical of those found for other sensors of this type. The sensor used was a carbon monoxide Pac II sensor, obtained from Draeger Safety, Inc. (Pittsburgh, PA). The sensor was biased (connected to a potentiostat) at +150 mV relative to its reference electrode for several hours prior to use. The sensor was tested immediately prior to use to ensure that its performance was within the specifications for a new sensor. The Pac-style sensors are small sensors (3 cm long and 2 cm diameter), designed for use in portable gas detection instruments. This type of sensor is a high-performance, three-electrode cell with an acidic electrolyte, and it is typical of the type of electrochemical sensor that is widely used for toxic gas detection for workplace safety. In a carbon monoxide sensor, the electrode will typically be platinum black, fixed to a porous PTFE membrane with a PTFE binder, with sulfuric acid as the electrolyte.14 For the CO Pac II sensor studied in this paper, the geometric area of the working electrode is only 0.4 cm2. The real area is estimated to be 1100 cm2 from the platinum oxide reduction peak in the cyclic voltamogram23 at 1 mV/s under nitrogen, or about 2700 times the geometric area, assuming that the platinum oxide forms a complete and single monolayer, the reduction is a two-electron process per platinum, and the surface can be represented by the bulk platinum structure, namely a face-centered cubic structure with unit cell dimensions a ) 0.39231 nm.24 For comparison, a 1.6-mm-diameter polished platinum disk electrode gives a real area about twice that of the geometric area using the same method, suggesting that the ratio of the real to geometric areas for the sensor electrode is approximately 1000 to 1. Sensor gas testing was performed using an EG&G PAR 263 potentiostat interfaced with a PC running EG&G PAR M270 software. This instrument was also used for the cyclic voltammetry and chronoamperometry potential step experiments. The working electrode capacitance was estimated from the area under the current versus time curve of a potential step by using the relationship
C ) dQ/dE where C is the capacitance, dQ is the change in charge passed, and dE is the change in potential. The change in charge was measured for 300 s after the potential step. This measured capacitance probably arises primarily from the charge passed due the faradaic oxidation of the platinum surface to platinum oxide at the operating potential of the sensor (∼1.1 V vs SHE), with only a small component from the double-layer capacitance, since the operating potential of the sensor (0.15 V vs the reference electrode) coincides with the wave in the cyclic voltammogram corresponding to formation of platinum oxide. Electrochemical impedance spectra were obtained with an EIS900 system from Gamry, Inc. Models were fitted to the experimental impedance data using a nonlinear least-squares fitting software program also from Gamry, Inc. The conductance (23) Bard, A. J.; Faulkner, L. R. Electrochemical Methods, Fundamentals and Applications; John Wiley and Sons: New York, 1980. (24) Lide, D. R., Frederikse, H. P. R., Eds. CRC Handbook of Chemistry and Physics; CRC Press: Boca Raton, FL, 1995.
Analytical Chemistry, Vol. 70, No. 5, March 1, 1998
999
between sensor electrodes was measured using a YSI conductivity meter (model 34). Gas mixtures were obtained from compressed gas cylinders (UltraSpec Gases) and blended with dry (liquid N2 boil off) nitrogen gas using a STEC SGD-710 gas divider; the constant flow rate was measured using a Scott rotameter. For the sensor response time tests, the gas was supplied to the sensors via a calibration adapter, which fitted the sensor snugly. The test gas was already flowing at the start of the experiment, and the calibration adapter was placed on the sensor to start the gas exposure. The time to place the calibration adapter in place and for the sensor to start responding was typically less than 2 s. The gas flow rate to the sensor was 200 mL/min, and the free volume of the calibration adapter after the sensor has been inserted is approximately 3 mL. Thus, the time to flush the calibration adapter is about 1 s. For the response time data described below, response times were taken from the time the sensor started responding after the gas was applied. Response times are often measured from the time when the gas is applied to the sensor. However, experimentally it is easier to measure the response time after the sensor starts to respond. Response times calculated by the latter method will be slightly shorter than those calculated by the former method. All experiments were run at room temperature (23 ( 2 °C). Digital simulations of the response time based on Fick’s second law of diffusion were obtained using a personal computer program written by one of the authors (P.R.W.) in Microsoft QBASIC. The diffusion coefficient for carbon monoxide in air through the porous PTFE backing and electrode membranes was determined by measuring the rate of loss of carbon monoxide from a transparent container closed by the membrane. In this experiment, the container was filled with a carbon monoxide in air mixture (typically about 200 ppm) in a well-ventilated area and sealed with a lid containing a piece of membrane of known area (∼10-15 cm2). As the carbon monoxide diffused out of the container through the membrane, the concentration of carbon monoxide inside the container decreased, which was monitored by using a Draeger Safety portable carbon monoxide monitor (either a model 190 or a Pac III instrument) which has a digital display visible through the transparent container. Since all the carbon monoxide which diffused through the membrane is quickly lost to the atmosphere, the external concentration was essentially a constant zero. Thus, the decrease in the internal carbon monoxide concentration follows an exponential decay. A plot of the logarithm of the instrument reading versus time is, therefore, expected to be linear with a slope given by
slope ) DA/(V dx)
where D is the diffusion coefficient of the gas passing through the membrane, A is the area of the membrane, V is the volume of the container, corrected for the volume occupied by the instrument, and dx is the thickness of the membrane. The duration of the experiment should be such that the volume of gas consumed by the sensor (∼0.8 cm3/min based on a sensitivity of 0.1 µA/ppm) is small compared to the total volume of the container. Typical experimental runs lasted about 15 min. There is no membrane gas solubility term, as would be necessary for a 1000 Analytical Chemistry, Vol. 70, No. 5, March 1, 1998
Figure 1. Response of CO sensor to 200 ppm CO/N2. Curves are for 0, 50, 243, and 1000 Ω of added resistance and the calculated diffusion-limited response, respectively. From bottom to top, each curve is offset for clarity.
nonporous membrane, since the gas transport remains primarily diffusion through the air via the porous structure of the membrane and not via dissolution into the membrane itself. This method has several advantages relative to the alternative methods in which the diffusion coefficient is directly proportional to the instrument reading.25 Since the diffusion coefficient is calculated from the slope of the curve, it is not necessary to know the exact initial concentration of the carbon monoxide, and the accuracy of the measurement is improved because the diffusion coefficient is calculated from the slope of a logarithmic graph. RESULTS AND DISCUSSION The purpose of this work was to determine the factors which affect the characteristics of the response of an electrochemical (amperometric) sensor to a test gas. In particular, the goal was to investigate whether the response time of the sensor is limited by the rate of gas diffusion or, alternatively, by the electrical properties of the sensor. The response curve of an electrochemical carbon monoxide sensor to 200 ppm CO was measured, and the response time was also measured after adding additional resistance in series with the working electrode. This response was compared to the response based on Fick’s second law of diffusion, calculated using a numerical method, and to the electrical response of the sensor due to small changes in the working electrode’s potential, both with and without added resistance in series with the working electrode. The behavior of the sensor was modeled using an equivalent circuit. Time constants obtained from this model are compared to values obtained from electrochemical impedance spectroscopy. Gas Testing of the Sensor. With the sensor connected to the potentiostat, the CO test gas was applied and the response current measured. The measurement was repeated with a resistance added in series with the working electrode. Typical response curves for the CO sensor are shown in Figure 1. For each experiment, the response times (T90 and T50) were measured; the results are plotted in Figure 2. For small-valued added resistances ( 200 Ω, the slope of the T90 line increases to another apparently straight line, with a slope of approximately 0.31 s/Ω. Clearly, the sensor response characteristics are more complex than a simple exponential. Since the line in Figure 2a above 200 Ω also appears to form a straight line, it is likely that this behavior can be described by the electrode having a second and larger time constant. Figure 2 shows that adding resistance in series with the working electrode increases the time constant of the sensor response. When Rb is small, this second time constant is not observed, since it is so much larger than the first, and it would only show up as a small drift in the response of the sensor when exposed to the test gas. When Rb is large, the sensor’s first response time constant is slowed until it is of similar magnitude to the second one, and thus the T50 and T90 half-lives are determined by both of these time constants. This behavior may be modeled by describing the sensor as two RC networks in parallel. This will be discussed in more detail below. The ac resistance between each of the three electrodes was measured with a conductivity meter. The resistance of each electrode was, therefore, determined by assuming that the measured values were the sum of the two respective electrode resistances, since the sulfuric acid electrolyte is assumed to have high conductivity. The resistances measured for the three electrodes were working electrode, 15.1 Ω; counter electrode, 9.7 Ω; and reference electrode, 13.6 Ω. This working electrode resistance is about half the resistance value obtained from the response to carbon monoxide in Figure 2. The T50 intercept was extrapolated from the line back to zero and falls close to zero. It is unclear why there is such as large difference between the working electrode resistance values calculated from the T90 data and by the conductivity meter. The electrode capacitance estimated from a 100-mV potential step (0.10-0.20 mV vs the sensor’s reference electrode) after 30 s (T50 ) 0.5 s) was 0.074 F, which is 50% larger than the estimates obtained from the slopes of the lines in Figures 2b and 4b below. The other noteworthy feature of Figure 1 is the marked effect that Rb has on the electrical noise of the sensor output. The response without Rb has a large noise signal (∼10 mA peak to peak), whereas, when Rb is 1000 kΩ, the noise is barely noticeable. The working electrode resistance and capacitance are presumably acting as an RC filter, blocking frequencies higher than the time constant of the circuit. Inserting additional resistance in series with the working electrode has been used previously to reduce the noise in potentiostat circuits for gas sensors. However, the designer has to ensure that the resistor is small enough that the response time of the sensor is not compromised.26 1002 Analytical Chemistry, Vol. 70, No. 5, March 1, 1998
Figure 4. (a) Response times of the sensor due to the application a 10-mV potential step for values of Rb spanning 0-2000 Ω. (b) Expanded area of (a) where Rb is less than 500 Ω.
If, indeed, the response time of the sensor is determined by the electrical properties of the working electrode, the dependence of the gas response time to working electrode resistance should be evident in tests of the electrical properties of the sensor, such as small potential steps applied to the working electrode. Applying a small potential step to the sensor results in a transient current, which decays to zero. This potential step method has been applied previously to characterize electrochemical sensors, and the measurement of the current/charge passed has been used in the literature to provide a function check of the sensor.27 The response time of the sensor in response to 10-mV bias potential step was measured, and it was also found to increase when additional resistance (Rb) was placed in series with the working electrode. The electrical response time of the sensor was determined from a plot of the current versus time after the potential step. Plots of the T50 and T90 response times for the sensor are shown in Figure 4. It may be seen that both the T50 and T90 response times increase approximately linearly with added resistance up to about 200 Ω, but the slope increases for resistances greater than 200 Ω. The slopes below 200 Ω are 0.18 and 0.050 s/Ω for T90 and T50, respectively. For resistances greater than 200 Ω, the slope of the T90 response time increases approximately 5-fold to 0.95 s/Ω, whereas the slope of the T50 response time increases by a smaller factor to 0.07 s/Ω, though it is unclear if this latter slope change is significant. The change in slope for T90 response time (26) Product Data Handbook; City Technology Ltd.: Portsmouth, U.K., March 30, 1992. (27) Jones, G. J. U.S. Patent 5,202,637, April 13, 1993.
Figure 5. Equivalent electrical circuit model used to fit EIS data.
occurs at approximately 200 Ω, after 40 s has elapsed, which is in good agreement with what was observed for the gas response behavior shown in Figure 2. Using the same analysis as for the gas response times, the working electrode resistance and capacitance were calculated. The values from the T90 response time data were Re ) 19.5 Ω and Ce ) 0.078 F, and from the T50 response time, Re ) 14.0 Ω and Ce ) 0.072 F. For the T50 response time, the linear dependence extends down to no added resistance, since there is no other slower process comparable to gas delivery/gas diffusion affecting the T50 response time to carbon monoxide test gas. Comparison of Figure 2 with Figure 4 shows a striking resemblance. Both sets of experiments show a straight line for T90, which changes slope at Rb ) 200 Ω. The values of Re and Ce estimated from the slopes in the two sets of data are of similar magnitude for both T50 and T90. Since the potential step experiment is a purely electrical test, the similarity to the gas response results suggests that the gas response characteristics may also be at least partly controlled by the electrical time constants of the sensor. Electrochemical Impedance Spectra (EIS) of Sensor. As discussed above, the high surface areas of the electrodes used in the construction of these amperometric sensors behave as though they have a high capacitance. To better understand the sensor response, electrochemical impedance spectra were recorded, and equivalent circuit models were fitted to the data, assuming either two or three parallel RC networks. One model used for the fit consists of a parallel combination of two series resistor-capacitor networks (R1,C2 and R2,C2) and an additional resistor (Rbgd) to represent the background current. A second model investigated was composed of a parallel combination of three series resistorcapacitor networks, as shown in Figure 5. These two circuit models were fitted to the experimental data, and the results were compared to determine whether the parameters obtained were significantly different and whether the match between the model and the experimental data could be improved. These models were intended to represent the sensor in ambient atmosphere, without carbon monoxide present, since the intention was to examine the electrical properties of the sensor. The EIS experimental data, together with a fitted curve, are shown in Figure 6. The resulting plot of the EIS data and the equivalent electrical circuit with two RC networks gives good agreement, as shown in Figure 6. The values obtained were R1 ) 12.1 Ω, R2 )1800 Ω, C1 ) 0.052 F, C2 ) 0.092 F, and Rbgd ) 73 000 Ω. The two time
Figure 6. Electrochemical impedance spectrum (impedance as solid circles and phase angle as triangles) for a carbon monoxide sensor, and calculated line for an equivalent electrical circuit model composed of two parallel RC networks.
constants for this set of data are R1C1 ) 0.63 s and R2C2 ) 165 s. The same set of experimental data was also fitted to the circuit model, with three RC networks, as shown in Figure 5, and the values obtained were R1 ) 35.3 Ω, R2 ) 1900 Ω, R3 ) 17.8 Ω, C1 ) 0.00511 F, C2 ) 0.0910 F, C3 ) 0.0483 F, and Rbgd ) 75 900 Ω. From this set of data, the time constants may be calculated: R1C1 ) 0.18 s, R2C2 ) 173 s, and R3C3 ) 1.4 s. The time constants obtained from fitting the data to the two and three parallel RC network models are consistent with each other. Both fits predict a time constant around 170 s, and an approximately 1-s time constant. The capacitances for both models are similar (C2 ) 0.091 F [three RC fit] and C2 ) 0.092 F [two RC fit]); for the approximately 1-s time constant, the capacitances are also similar (C1 ) 0.052 F [two RC fit] and C1 + C3 ) 0.053 F [combined ∼1-s three RC fit]). The magnitude of the capacitance in the approximately 1-s time constant is about two-thirds the total capacitance. Therefore, it may be expected that the first half of the current response to either a potential step or exposure to a test gas either will occur on the ∼1-s time scale or will be limited by another process, such as diffusion. This observation is consistent with the rapid T50 response times that have been described above. The T90 response time is, however, at least partly dictated by the slower time constant and, thus, is expected to be much slower and limited by the electrical properties of the electrode. The magnitude of the charge passed to “charge” this second RC time constant will be proportional to the capacitance; however, the current, and thus the impact on the sensor response, will be relatively small, because of the larger RC time constant compared to the approximately 1-s time constant. The steady-state background current calculated from Rbgd and the normal bias potential (+0.150 V) is ∼2.0 µA. This value is more than twice the expected value for a steady-state background current and probably indicates that there may be another time constant that is larger than the time period of this experiment (10 000 s, or 2.8 h). Comparison of the EIS data to the response of the sensor to carbon monoxide and the potential step shows that all three experiments reveal two primary time constants of the sensor working electrode. The values of R1 and R2 are in reasonable agreement with the values for these parameters obtained for the gas testing and the potential step experiment. The second time Analytical Chemistry, Vol. 70, No. 5, March 1, 1998
1003
Table 1. Diffusion Path Parameters for Pac Sensors Pac sensor component
area (cm2)
length (cm)
diffusion coefficient (cm2/s)
sinter outer airspace inner air space backing membrane electrode membrane
2.7 1.5 0.1 0.2 0.2
0.2 0.1 0.3 0.03 0.01
0.146 0.208 0.208 0.0067 0.0017
diffusion barrier, as shown in Figure 7. The numerical values for each of the diffusion barriers are shown in Table 1. The diffusivity is defined as
di ) DiAi/dx Figure 7. Illustration of diffusion barriers in Pac II sensor (not to scale).
constant from the EIS experiment is approximately 170 s. The EIS data also support the idea that the electrical response of the sensor is not a single-exponential function, but instead it behaves as though there are two distinct sensor response time constants. On applying a test gas to the sensor, the initial response characteristics (T50 and T90) will be determined largely by the smaller time constant in combination with diffusion. The effect of the larger time constant will be seen at longer times, and the sensor will not reach the steady-state value as quickly if there is only the smaller time constant. Instead, there will be a rapid rise approaching the steady-state value, but the sensor response will continue to increase slightly with time. Since the second time constant is 170 s, the sensor will require several minutes before it reaches the final steady-state response. Diffusion Calculations. (i) Steady State. Whether the response curve is determined by diffusion or by the electrical properties of the working electrode, it is known that the steadystate current is controlled by the rate at which gas can diffuse to the electrode. To calculate the rate of diffusion into the sensor, the diffusion path can be treated as a series of adjacent diffusion barriers through which the gas must pass in order to reach the electrode, as shown in Figure 7. The steady-state response can be estimated by equating the flux calculated according to Fick’s first law of diffusion for each of the diffusion barriers, assuming linear diffusion, with Faraday’s law for the electrode reaction. That is,
where Di is the diffusion coefficient, Ai is the cross-sectional area, and dxi is the length of each diffusion barrier (i). The gas must pass through a series of diffusion barriers to reach the electrode. The first diffusion barrier is the sintered polyethylene disk (diffusivity d1), and the next two diffusion barriers are air spaces (diffusivities d2 and d3). The fourth diffusion barrier is a porous PTFE membrane (diffusivity d4), and the fifth diffusion barrier is the electrode membrane (diffusivity d5). The diffusion coefficient for carbon monoxide in air was assumed to be the same as that in nitrogen, which can be found in standard references (0.212 cm2/s, 295.8 K).28 The diffusion coefficient for gases in the sintered disk was assumed to be the same as that in air, scaled by the estimated fractional empty volume (70%). The diffusion coefficients for carbon monoxide in the porous PTFE membranes were measured as discussed in the Experimental Section above. Using this method, the sensitivity is calculated to be 0.12 µA/ ppm CO, which compares well with the experimental value of 0.11 µA/ppm. The sensitivity of a sensor is defined as follows:
sensitivity ) (Ig - Ibgd)/C0
d1d3d4d5 + d2d3d4d5)
where Ig is the current of the sensor at steady state in the presence of the test gas, and Ibgd is the background current, i.e., the steadystate current in clean air without the test gas. For these diffusion calculations, Ibgd is assumed to be zero, and Co is the gas concentration in parts per million. This close agreement between the calculated and experimental sensitivities indicates that, as expected, the steady-state response of the sensors is limited by the rate at which the gas can diffuse into the sensor. The agreement is deceptively good, since the estimated error in the calculation is ∼25%, arising primarily from variability of the porous PTFE membrane from sample to sample. (ii) Dynamic. The dynamic diffusion behavior of a sensor is assumed to be linear and is described by Fick’s second law of diffusion:29
where Co is the concentration of carbon monoxide outside the sensor, and di (i ) 1-5) is the diffusivity of each successive
(28) Cussler, E. L. Diffusion, Mass Transfer in Fluid Systems; Cambridge University Press: Cambridge, U.K., 1984. (29) Shewmon, P. G. Diffusion in Solids; J. Williams Book Co.: Jenks, OK, 1983.
current ) nFφ where n is the number of electrons (two for carbon monoxide oxidation), F is the Faraday constant (9.648 × 105 C/mol), and φ is the flux of gas to the electrode. φ is given by
φ ) Cod1d2d3d4d5 /(d1d2d3d4 + d1d2d3d5 + d1d2d4d5 +
1004 Analytical Chemistry, Vol. 70, No. 5, March 1, 1998
dC/dt ) -D d2C/dx2 Since an analytical solution of the diffusion equations for a system with multiple diffusion barriers is typically very cumbersome as the number of diffusion barriers increases, a numerical approach was used instead. The diffusion-limited response was calculated using a computer-based iterative method using an algorithm based on Fick’s second law of diffusion. This type of algorithm has been previously described.30 The algorithm assumes that Fick’s second law can be numerically approximated by dividing the diffusion path into many small discrete regions, and thus, Fick’s second law can be rewritten to allow the concentration of each region I at time t plus a small time increment dt to be calculated on the basis of the diffusion coefficient D and the concentrations of region I and the adjacent regions I + 1 and I - 1 over a small distance increment dx, as follows:
CI(t + dt) ) CI(t) + D(CI-1(t) - 2CI(t) + CI+1(t))(dt/dx2) To simulate the sensor response, this algorithm was modified. The diffusion coefficient varied along the gas diffusion path, and so the diffusion coefficient was made a function of distance. In addition, the cross-sectional area of the diffusion path into the sensor varied, as shown in both Figure 7 and Table 1. Therefore, the diffusion coefficient at each region was multiplied by the crosssectional area at that region. The diffusion coefficient was further modified to be the average of the two adjacent regions in order to avoid errors introduced by the discontinuities in the diffusion coefficient as a function of distance along the gas path. The algorithm used for the calculations was as follows:
CI(t + dt) ) CI(t) + {((AI-1DI-1 + AIDI)/2)(CI-1(t) CI(t)) + ((AI+1DI+1 + AIDI)/2)(CI+1(t) - CI(t))}(dt/dx2) The calculated response curve for the sensor is shown in Figure 1. The calculated steady-state sensitivity is 0.11 µA/ppm CO, which is in agreement with the experimental and calculated values discussed above. The corresponding calculated T50 response time was 2.4 s, and the T90 response time was 5.0 s. These calculated response times were determined from the time when the gas is “applied” to the sensor, whereas all the experimental response times were measured from the time of first indication of a response. Applying this criterion to the calculated response data reduces the response times by about 0.6 ( 0.1 s. Therefore, for comparison with the experimental data, the calculated response times were computed to be 1.8 (T50) and 4.4 s (T90). These calculated response times compare favorably to the response times measured with the carbon monoxide sensor. As already discussed, the T50 response time appears to be limited by gas delivery or gas diffusion. The T90 response time was earlier stated to be limited by the time constant of the sensor based on the results presented earlier. The response time measured for the T90 was, however, comparable in duration to the calculated response time for a diffusion-limited response. Therefore, it is (30) Southampton Electrochemistry Group. Instrumental Methods in Electrochemistry; Ellis Horwood: Chichester, 1985.
unlikely that the T90 response was limited solely by the time constant of the sensor, and it is more probable that the sensor was under mixed control, especially since the T50 was apparently determined by the rate of gas delivery/gas diffusion. DISCUSSION It may be observed that the electrode capacitances calculated from the gas response are of an order of magnitude similar to the values estimated by fitting the model to the EIS data. It should be noted that, since this model fits the data to either five or seven variables, depending on whether two or three parallel RC elements are used, the fit is expected to be good. With so many variables, the physical significance of the values obtained is less certain. However, this work has not attempted to relate the measured electrode capacitance to electrode surface processes, and, thus, if the values obtained from fitting the data have the correct impedance properties as a function of frequency, they are as valid as any other for this discussion. Consistent results were obtained when a wide range of initial values was used as the starting points for the data fitting routine. Several sources have commented that added resistance in series with the working electrode of toxic gas sensors increases the response time and decreases the noise.6,26 Schneider et al.31 have even used the increase in response time produced by adding resistance in series with the working electrode to delay the response of carbon monoxide sensor for residential instruments to meet the UL 2034 standard.32 This standard sets minimum and maximum response times of carbon monoxide detectors, so as to make the sensor response match the extent of carboxyhemoglobin formation in the blood as carbon monoxide is inhaled. Most amperometric sensors are designed so that their response current in the presence of the analyte gas is limited by diffusion. Several workers have investigated the nature of the dynamic response curve upon the application of a test gas. Bay et al.33 found that the response of a carbon monoxide sensor followed a first-order behavior upon the application of gas. A firstorder response was also found for the nitric oxide and nitrogen dioxide sensors.34 The mechanism producing these first-order response behaviors of the CO, NO, and NO2 sensors was not identified. All these cells were constructed similarly, except for differences in the electrode catalyst materials (platinum for CO, gold for NO and NO2). In these sensors, described in the references from Energetic Science, Inc., the test gas flows across the back of the working electrode membrane; thus, the rate of gas delivery to the electrode membrane is expected to be fast. If the Energetic Science, Inc. carbon monoxide sensor behaves similarly to the sensor examined in this paper, then it is likely that diffusion will be rapid; thus, the electrode time constant is probably controlling the form of the response curve. If the response curve is controlled by either a single or a dominant time constant of the electrode, then an approximate first-order plot is to be expected. (31) Schneider, A. L.; Scheffler, T. B.; Davis, B. K. U.S. Patent 5667,653, Sept 16, 1997. (32) Standard for Safety for Single and Multiple Station Carbon Monoxide Detectors; UL 2034; Underwriters Laboratories Inc.: Northbrook, IL, 1996. (33) Bay, H. W.; Blurton, K. F.; Sedlak, J. M.; Valentine, A. M.; Anal. Chem. 1974, 46, 1837. (34) Sedlak, J. M.; Blurton, K. F. Talanta 1976, 23, 811.
Analytical Chemistry, Vol. 70, No. 5, March 1, 1998
1005
The rate of response based on diffusion has also been calculated for several types of sensors. Zhou and Arnold35 derived an equation describing the diffusion-limited response curve for a fiber-optic sensor for nitric oxide. While this sensor was not electrochemical, the mathematical treatment was similar, since all the NO which diffused through the membrane was quantitatively and rapidly consumed as part of the detection mechanism. Their model consisted of one diffusion barrier (the membrane) and thus considered a side reaction between oxygen and the nitric oxide. Several workers have calculated the response curves for polarographic oxygen sensors with respect to either a metallic electrode in the sample matrix or the electrode behind a membrane. Several of these papers and reviews describe the response curve upon applying a potential to the electrode sufficient to reduce the oxygen for various configurations of electrode, membrane, and cell.5,36,37 Response curves have also been calculated for other types of sensors using equations derived from Fick’s second law of diffusion, including an ethanol sensor using a solid electrolyte.38 Mauer and Matthiessen39 have even described an amperometric sensor with a variable diffusion barrier which allowed control of both the sensitivity and the response time. Clearly, for many amperometric sensors, diffusion determines the nature of the response of the sensor. Even for high surface area toxic gas sensors, such as the carbon monoxide sensor examined in this paper, diffusion is a major determinant of the characteristics of the response. In addition to deriving analytical solutions, numerical methods have also been employed. For example, Sutton et al. used numerical methods to calculate the dynamic response curves of microdisk membrane-covered oxygen sensor electrodes.40 Providing that the analytical solution and the numerical method are performed correctly, it is expected that they will both give the same answer. For the computer program used in this work, an excellent match was found with the well-known analytical solution for linear diffusion to a planar electrode, the Cottrell equation,23 when the appropriate boundary conditions were used. As the number of diffusion barriers increases, the complexity of an analytical solution also increases dramatically, and the use of numerical methods become advantageous. From these few examples, it may be seen that diffusion calculations have been used successfully to model the response curves of many types of electrochemical sensor. For many types of sensors, especially those with fast electrode reactions and smooth metallic electrodes (low electrode capacitance), diffusion is likely to be the determining factor for response times. For other amperometric sensors, the dynamic response characteristics of the sensor may be limited by a number of factors: diffusion, (35) Zhou, X.; Arnold, M. A. Anal. Chem. 1996, 68, 1748. (36) Mancy, K. H.; Okon, D. K.; Reilley, C. N. Proc. Indoor Air 1965, 4, 65. (37) Fatt, I. Polarographic Oxygen Sensors, Its theory of Operation and its Application in Biological Medicine and Technology; Robert E. Krieger Publ. Co.: Malabar, FL, 1982. (38) Millet, P. M.; Durand, R. A. J. Appl. Electrochem. 1996, 26, 933. (39) Maurer, C.; Matthiessen, H. U.S. Patent 5,092,980, March 3, 1992. (40) Sutton, L.; Gavaghan, D. J.; Hahn, C. E. W. J. Electroanal. Chem. 1996, 408, 21.
1006 Analytical Chemistry, Vol. 70, No. 5, March 1, 1998
electrode kinetics, and the electrical time constant of the electrode. The electrode time constant is likely to be significant for those sensors employing very large surface area electrodes. For the carbon monoxide sensor discussed here, the T50 response times are comparable to gas diffusion, and it is likely that gas delivery to the sensor and gas diffusion into the sensor are the dominant rate-limiting steps. For the T90 response time, the time constant of the electrode appears to be the dominant factor in determining the T90 response time on the basis of the results in Figure 2. However, since this observed response time is similar in magnitude to the T90 response time calculated for diffusion, the response is best described as being at least partly under mixed control with diffusion. In analyzing the response of amperometric sensors or designing new sensors, it is important that it not be assumed that the response time is diffusion limited, but other factors such as electrode kinetics and the electrode time constant(s) also need to be considered. CONCLUSIONS The sensor response time was found to depend on both diffusion and the electrode time constants. The T50 response time was determined by gas delivery and gas diffusion, whereas the T90 response time was determined primarily by the electrical properties (time constant) of the sensor but was probably also determined, at least in part, by diffusion. There was reasonable agreement between the estimates for the electrode capacitance and electrode resistance from the gas testing, application of potential steps, and electrochemical impedance spectroscopy. The results of the gas test, potential step test, and EIS could be explained by assuming the presence of two distinct time constants associated with the sensor working electrode, one approximately 1 s and the second about 170 s. The T90 response times were found to be dependent on the time constant of the working electrode, and an equivalent electrical circuit model was developed to describe this behavior. The response time for this sensor was found to be ∼2 (T50) and 4-5 s (T90). Amperometric sensors often use high surface area electrodes which have large capacitances of chemical origin associated with the Faradaic processes of the electrode’s surface. The steady-state gas response of the amperometric sensor examined is limited by gas diffusion. ACKNOWLEDGMENT The authors thank C. Bernstein and G. Sagasser of Dra¨gerwerk AG, R. Pulz and L. Stern of Draeger Safety Inc., and W. Mitchell, M. Geraghty, T. Erdner, and N. Sherwood of Calgon Corp. for their review and permission to publish this manuscript. Received for review June 23, 1997. Accepted December 16, 1997. AC970644Y
