Anal. Chem. 2006, 78, 279-290
Transient Signal Analysis Using Complementary Metal Oxide Semiconductor Capacitive Chemical Microsensors Adrian M. Kummer, Thomas P. Burg, and Andreas Hierlemann*
Physical Electronics Laboratory, Eidgeno¨ssische Technische Hochschule (ETH) Zu¨rich, ETH Hoenggerberg, HPT H4.2, Wolfgang-Pauli-Strasse 16, 8093 Zurich, Switzerland
This work explores the possibility to discriminate analytes based on their nonequilibrium signals in polymer-coated capacitive chemical microsensors. The analyte uptake in the chemically sensitive polymer layers of 3-7-µm thickness has been analyzed using a diffusion model and the dynamic sensor response data. The shapes of the response profiles have been calculated analytically. Despite the simplifications in the model, the observed transient signal profiles could be described accurately. Comparison of the measured diffusion coefficients (on the order of 10-12 m2/s) with literature values measured at similar concentration levels showed good agreement. Concentration-independent diffusion coefficients for several analyte/ polymer combinations (poly(etherurethane)/all analytes; poly(epichlorohydrin)/alcohols) as well as slightly concentration-dependent diffusion coefficients (poly(epichlorohydrin)/toluene or ethyl cellulose/toluene) have been found in the investigated concentration range of tens to hundreds of pascals gas-phase partial pressure. The diffusion times of water and the first aliphatic monohydric alcohols in the polymers are strongly correlated to their molecular size. The discrimination of these substances based on dynamic sensor data of a single sensor could be demonstrated. In particular, the analysis of mixtures of analytes with similar chemical behavior (water/ethanol or methanol/ethanol) by means of analyzing the response profile of single-exposure steps or by applying a series of decreasingly long alternating target gas exposure and carrier gas exposure steps has been performed. Capacitive chemical sensors, which rely on changes in the dielectric properties of a sensing material upon analyte exposure, are promising devices for chemical sensing due to the low power consumption, which favors their usage in hand-held devices. For potential commercialization, low-cost production is essential and can be achieved, e.g., by miniaturization and integration.1-6 * To whom correspondence should be addressed. E-mail: hierlema@ phys.ethz.ch. Phone: ++41 44 633 3494. Fax: ++41 44 633 1054. (1) Kakerow, R.; Manoli, Y.; Mokwa, W.; Rospert, M.; Meyer, H.; et al. Sens. Actuators, A 1994, 43, 296-301. (2) Cane, C.; Gotz, A.; Merlos, A.; Gracia, I.; Errachid, A.; et al. Sens. Actuators, B 1996, 35, 136-140. (3) Qiu, Y. Y.; Azeredo-Leme, C.; Alcacer, L. R.; Franca, J. E. Sens. Actuators, A 2001, 92, 80-87. 10.1021/ac051430g CCC: $33.50 Published on Web 12/02/2005
© 2006 American Chemical Society
Integrating capacitive sensors in complementary metal oxide semiconductor (CMOS) technology is especially interesting as no micromechanical parts such as membranes or cantilevers are needed, rendering the chip more rugged and reducing the number of postprocessing steps and, hence, costs. Interdigitated structures are predominantly used as sensor capacitors.7-10 Plate capacitor-type structures with the sensitive layer sandwiched between a porous thin metal film (permeable to the analyte) and an electrode patterned on a silicon support have also been developed.11,12 The fabrication of capacitors integrated with CMOS circuitry components is described in several references.8,10,13-19 The capacitances usually are measured at an ac frequency of a few kilohertz up to 500 kHz. Initial applications areas of chemocapacitors have been in humidity sensing using polyimide films,7-11,18,19 since the high dielectric constant of water (76.6 in liquid state at 303 K) leads to large capacitance changes. Capacitive humidity sensors are commercially available from, e.g., Sensirion,20 Vaisala,21 and Humirel.22 More recent applications of capacitive sensors include (4) Hierlemann, A.; Baltes, H. Analyst 2003, 128, 15-28. (5) Hagleitner, C.; Hierlemann, A.; Lange, D.; Kummer, A.; Kerness, N.; et al. Nature 2001, 414, 293-296. (6) Hagleitner, C.; Hierlemann, A.; Baltes, H. CMOS single-chip gas detection systems: Part II. In Sensors Update; Baltes, H., Fedder G. K., Korvink, J. G. Eds.; Wiley VCH: Weinheim, Germany, 2003; Vol. 12, pp 51-120. (7) Sheppard, N. F.; Day, D. R.; Lee, H. L.; Senturia, S. D. Sens. Actuators 1982, 2, 263-274. (8) Senturia, S. D. Technol. Dig.-Transducers 1985, 198-201. (9) Glenn, M. C.; Schuetz, J. A. Technol. Dig.-Transducers 1985, 217-219. (10) Denton, D. D.; Senturia, S. D.; Anolick, E. S.; Scheider, D. Technol. Dig.Transducers 1985, 202-205. (11) Delapierre, G. Grange, H.; Chambaz, B.; Destannes, L. Sens. Actuators 1983, 4, 97-104. (12) Shibata, H.; Ito, M.; Asakursa, M.; Watanabe, K IEEE Trans. 1nstrum. Meas. 1996, 45, 564-569. (13) Kang, U.; Wise, K. D. Technol. Dig.-Solid State Sens. Actuator Workshop; Hilton Head, 1998; pp 183-186. (14) Cornila, C.; Hierlemann, A.; Lenggenhager, R.; Malcovati, P.; Baltes, H.; et al. Sens. Actuators, B 1995, 25, 357-361. (15) Steiner, F. P.; Hierlemann, A.; Cornila, C.; Noetzel, G.; Ba¨chtold, M.; Korvink, J. G.; Go ¨pel, W.; Baltes, H. Proc. Transducers 1995, 2, 814-817. (16) Hagleitner, C.; Koll, A.; Vogt, R.; Brand, O.; Baltes, H. Technol. Dig.Transducers 1999, 1012-1015. (17) Koll, A.; Kummer, A.; Brand, O.; Baltes, H. Proc. SPIE Smart Struct. Mater. 1999, 3673, 308-317. (18) Boltshauser, T.; Chandran, L.; Baltes, H.; Bose, F.; Steiner, D. Sens. Actuators, B 1991, 5, 161-164. (19) Boltshauser, T.; Baltes, H. Sens. Actuators, A 1991, 26, 509-512. (20) http://www.sensirion.com/. (21) http://www.vaisala.com/.
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the detection of organic volatiles in the gas phase using polymeric layers,14-17,23-28 or liquid crystals.29 Besides polyimide, which is predominantly used in humidity sensing, other organic polymers have been used as chemically sensitive coatings of polymer-based microsensors (see refs 5, 23, and 30-36). These polymers absorb analyte vapors (bulk absorption), which is a well-characterized process that has linear characteristics and features additivity for sufficiently small analyte concentrations.30 Most polymers exhibit, however, only partial selectivity to the volatile organic compounds (VOCs) to be detected. To achieve the required selectivity, multiple different sensors (sensor arrays) combined with mathematical algorithms for data evaluation such as pattern recognition or multicomponent analysis are used.35,37 For capacitive chemical sensors, humidity is a particularly challenging interference owing to the high dielectric constant of water and because humidity is omnipresent in ambient air at high concentrations.36 With regard to analyte mixtures, the steady-state responses of polymer-based sensors are, in a first approximation, linear and additive at low analyte concentrations, which renders data processing rather simple. Therefore, linear regression algorithms, such as partial least-squares regression (PLSR), are usually a good choice.38 Small nonlinearities occurring at higher concentrations can be handled with nonlinear versions.39-42 The selectivity pattern of the steady-state signals of, generally, a polymer-based sensor or, in particular, a polymer-based capacitive chemical sensor is mainly defined by the interactions between the absorbed analyte molecules and the polymer matrix. Analytes of different chemical groups, e.g., an alkane and an alcohol, are generally easy to discriminate: a polar polymer will preferably absorb the alcohol whereas an unpolar polymer will favor the alkane. For chemically similar analytes, such as analytes of a (22) http://www.humirel.com/. (23) Casalini, R.; Kilitziraki, M.; Wood, D.; Petty, M. C. Sens. Actuators, B 1999, 56, 37-44. (24) Endres, H. E.; Drost, S. Sens. Actuators, B 1991, 4, 95-98. (25) Dickert, F. L.; Achatz, P.; Bulst, W. E.; Greibl, W.; Hayden, O.; Ping, L.; Sikorski, R.; Wolff, U. Proc. SPIE-Int. Soc. Opt. Eng. 1999, 3857, 116-123. (26) Rehacek, V.; Novotny, I.; Tvarozek, V.; Riepl, M.; Hirsch, T.; et al. Proc. ASDAM 1998, 255-258. (27) Josse, F.; Lukas, R.; Zhou, R. N.; Schneider, S.; Everhart, D. Sens. Actuators, B 1996, 36, 363-369. (28) Domansky, K.; Jun, L.; Qiong, W. Li; Engelhard, M. H.; Baskaran, S. J Mater. Res. 2001, 16, 2810-2816. (29) Dickert, F. L.; Zwissler, G. K.; Obermeier, E. Ber. Bunsen-Gesellschaft 1993, 97, 184-188. (30) Hierlemann, A.; Kraus, G.; Weimar, U.; Go ¨pel, W. Sens. Actuators, B 1995, 26, 126-134. (31) Zee, F.; Judy, J. W. Sens. Actuators, B 2001, 72, 120-128. (32) Endres, H. E.; Hartinger, R.; Schwaiger, M.; Gmelch, G.; Roth, M. Sens. Actuators, B 1999, 57, 83-87. (33) Maute, M.; Raible, S.; Prins, F. E.; Kern, D. P.; Ulmer, H., et al. Sens. Actuators, B 1999, 58, 505-511. (34) Koll, A. Ph.D. Thesis No. 13460, ETH Zu ¨ rich, 1999. (35) Go ¨pel, W.; Jones, T. A.; Kleitz, M.; Lundstro ¨m, I.; Seiyama, T. In Chemical and Biochemical Sensors, Vol. 2, Part I; Go ¨pel, W., Hesse, J., Zemel, J. N., Eds.; Sensors, A Comprehensive Survey; VCH Verlagsgesellschaft mbH: Weinheim, Germany, 1991. (36) Kummer, A.; Hierlemann A.; Baltes, H. Anal. Chem. 2004, 76, 2470-2477. (37) Gutierrez-Osuna, R. IEEE Sens. J. 2002, 2, 189-202. (38) Geladi, P.; Kowalski, B. R. Anal. Chim. Acta 1986, 185, 1-17. (39) Wold, S. Chemom. Intell. Lab. Syst. 1992, 14, 71-84. (40) Taavitsainen, V. M.; Korhonen, P. Chemom. Intell. Lab. Syst. 1992, 14, 185194. (41) Frank, I. E. Chemom. Intell. Lab. Syst. 1990, 8, 109-119. (42) Wold, S.; Kettanehwold N.; Skagerberg, B. Chemom. Intell. Lab. Syst. 1989, 7, 53-65.
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homologous series (e.g., the monohydric aliphatic alcohols methanol, ethanol, and propanol), only the size or hydrocarbon chain length of their molecules differs. As a consequence, their sorption extent varies in concordance to their boiling points (larger responses for larger molecules exhibiting lower volatility), but their selectivity patterns with a given set of polymers are almost identical.43 Hence, it is extremely difficult, if not impossible, to distinguish between the substances belonging to the same homologous series even with an array of sensors with different polymers as sensitive layers. A possible solution to this dilemma is to use time-dependent signal response profiles for analyte discrimination. The information content that can be extracted from a transient signal f(t) is considerably higher than that from a steady-state signal f. Whereas a steady-state signal is given by a single number f, the transient signal f(t) is given by a series of multiple single-measurement values after various subsequent time intervals t each. For other sensors, such as metal oxide semiconductor sensors, the use of the transient signal is common;44,45 however, for polymer-based sensors, only few attempts have been made,46,47 since the kinetics of polymer sorption and polymer diffusion processes can be comparably fast depending on the nature of the polymer (rubbery or glassy). Permeation and analyte diffusion characteristics of a variety of polymers have been investigated with different methods48-54 including among others Rayleigh surface acoustic wave devices,55 optical methods,56 and conductivity measurements.57 The fast kinetics as observed with, for example, rubbery polymers require the use of a dedicated setup to effectively probe the subtle sorption kinetics differences of the various organic volatiles. The diffusion-induced, time-dependent concentration profile in a polymer layer is independent of the transducer principle, which is used to determine the analyte concentration. The shape of the resulting response profile, however, does depend on the transducing principle since, in general, different transducers feature different spatial sensitivities within the sensitive polymer layer.36,56,57 In this paper, we want to show that the high-temporalresolution response profile of a capacitive sensor upon a sudden (43) Kummer, A. Ph.D. Thesis No. 13460, ETH Zu ¨ rich, 2004. (44) Kunt, T. A.; McAvoy, T. J.; Cavicchi, R. E.; Semancik, S. Sens. Actuators, B 1998, 53, 24-43. (45) Heilig, A.; Barsan, N.; Weimar, U.; Schweizer-Berberich, M.; Gardner, J. W.; Go ¨pel, W. Sens. Actuators, B 1997, 43, 45-51. (46) Schweizer-Berberich, M.; Go¨ppert, J.; Hierlemann, A.; Mitrovics, J.; Weimar, U., et al. Sens. Actuators, B 1995, 27, 232-236. (47) Nakamura, M.; Sugimoto I.; Kuwano, H. J. Intell. Mater. Syst. Struct. 1994, 5, 315-320. (48) Rogers, C. E. Permeability and Chemical Resistance. In Engineering Design for Plastics; Baer, E., Ed.; Reinhold Publishing Corp.: London, 1964. (49) Rogers, C. Permeation of gases and vapours in polymers. In Polymer Permeability; Comyn, J., Ed.; Elsevier: London, 1988. (50) George, S. C.; Thomas, S. Prog. Polym. Sci. 2001, 26, 985-1017. (51) Marais, S.; Metayer, M.; Nguyen, T. Q.; Labbe, M.; Perrin, L.; et al. Polymer 2000, 41, 2667-2676. (52) Iordanskii, A. L.; Razumovskii, L. P.; Krivandin, A. V.; Lebedeva, T. L. Desalination 1996, 104, 27-35. (53) Wellons, J. D.; Stannett, V. J. Polym. Sci., Part A 1966, 4, 593. (54) Di Landro, L.; Pegoraro, M.; Bordogna, L. J. Membr. Sci. 1991, 64, 229236. (55) Frye, G. C.; Martin, S. J.; Ricco, A. J. Sens. Mater. 1989, 1-6, 335-357. (56) Blair, D. S.; Burgess, L. W.; Brodsky, A. M. Appl. Spectrosc. 1995, 49, 16361645. (57) Feldheim, D. L.; Hendrickson, S. M.; Krejcik, M.; Elliott, C. M.; Foss, C. A. J. Phys. Chem. 1995, 99, 3288-3293.
concentration increase does contain the required information to discriminate between different analytes and, in particular, between analytes belonging to the same homologous series. It will be shown that even the signals of a single sensor allow for successful analysis of such similar analytes as, for example, methanol and ethanol, or water and ethanol in a mixture. The capacitive sensor has been selected intentionally since measurements can be made very rapidly (no extended gate time needed as for resonant sensors), and since the dynamic sensor signal is predominantly due to the presence and concentration of an analyte governed by the polymer absorption and diffusion characteristics. The dynamic sensor signal neither relies on secondary effects such as analyte-induced conductivity changes (conducting polymers), nor is it influenced by accompanying effects such as analyte-induced film plasticization (acoustic-wavebased devices).55 CAPACITIVE SENSOR CHARACTERISTICS Sensing Principle/Steady-State Signals. Polymer films deposited on the interdigitated electrodes of the capacitive sensor serve as sensitive films for the detection of volatile organic compounds (analytes) in air. The analytes are reversibly absorbed in the polymer layer volume. Associated with the absorption is an enrichment of the analyte in the polymer by 2-4 orders of magnitude with respect to the concentrations in the gas phase.58 More information about the absorption mechanism and methods to determine the partition coefficients are detailed in refs 43-59. Upon absorption, the physical properties of the polymer layer change owing to the incorporation of the analyte molecules into the polymer matrix. The two effects changing the sensor capacitance are (a) analyte-induced polymer swelling (volume change) and (b) analyte contribution to the composite dielectric constant (dielectric constant change).14,15,36 Assuming the validity of Henry’s law for low analyte concentrations, swelling and the dielectric constant change are linearly proportional to the amount of absorbed analyte. The proportionality factors have to be determined experimentally for every polymer/analyte combination. They can also be estimated: for swelling with solubility parameters or linear solvation energy relationships58 and for the change in dielectric constant by using rather complex equations.15,36,43,36,60,61 While swelling is always positive, the change in dielectric constant upon analyte absorption, ∆, can be either positive or negative:
∆ ∝ φA(A - poly)
(1)
Here, A is the dielectric constant of the analyte (in liquid state), poly is the dielectric constant of the polymer, and φA is the amount of absorbed analyte expressed as volume fraction. The equation shows that sensor signals are positive for analytes with a dielectric constant larger than that of the polymer and negative otherwise. Further details on the sensing mechanisms can be found in refs 36 and 43. (58) Grate, J. W.; Abraham, M. H. Sens. Actuators, B 1991, 3, 85-111. (59) Grate, J. W.; Kaganove, S. N.; Bhethanabotla, V. R. Faraday Discuss. 1997, 259-283. (60) Akhadov, Y. Y. Dielectric Properties of Binary Solutions; Pergamon Press: Oxford, U.K., 1981. (61) Bo ¨ttcher, C. J. F. Theory of electric polarization, 2nd ed.; Elsevier: Amsterdam, 1973.
Figure 1. Concentration profile of an absorbed analyte as a function of time as analytically calculated for an even polymer layer on a planar surface. The vertical axis represents the vertical position (depth) in the polymer layer. A sharp concentration peak is applied at the time t ) 0. Larger concentrations are represented by darker gray levels. The curves represent equiconcentration lines, given as percentage of the final steady-state concentration.
Figure 2. Schematic of the distribution of the electric field lines and representation of the field line density. The vertical axis represents the position (depth) in the polymer layer. The field line density has a maximum near the transducer surface and then decays with increasing distance from the surface into the polymer layer.
Transient Responses. The overall transient response profile of the capacitive microsensors is determined (a) by the distribution of analyte molecules in the polymer matrix as a function of time, i.e., the sorption and diffusion kinetics of the polymer/analyte combination (Figure 1) and (b) by the sensitivity distribution of the capacitive sensor, i.e., the local strength of the electric field within the polymer layer (Figure 2). Both factors will be discussed below. Transient signal characteristics of polymer-based sensors are strongly dependent on the sorption kinetics of the analytes in the sensitive layer. The sorption speed is described by the diffusion coefficient according to Fick’s laws. Diffusion coefficients, D, depend on the analyte-polymer combination, the temperature, and the analyte concentration, but are generally independent of the pressure.48 The temperature dependence can be represented by Arrhenius-type relations:48-50
D(T) ) D0e-ED/RT
(2)
where ED is the apparent activation energy and D0 is a prefactor. Accordingly, the higher the temperature, the faster the diffusion process and, hence, the shorter the response time of the sensor. Diffusion coefficients may strongly depend on the analyte concentration, especially for higher analyte concentrations. The concentration dependence for a given polymer primarily depends on the molecular size and the solvent power of the analyte as well as on the temperature.48 Analytes, which are good solvents, swell and plasticize the polymer, leading to increased mobilities of both Analytical Chemistry, Vol. 78, No. 1, January 1, 2006
281
polymer segments and analyte molecules.48 An exponential dependence was experimentally found for various analyte polymer combinations:48,49
τ ) h2/D
D(c) ) D(c)0)eγc
zt c , ) hτ cSt 1 - 2
∞
1
∑ (n + 1/2)πe
n)0
-t/τ‚[(n+1/2)π]2
sin
( ( ) )) z
h
n+
1
2
π
(
C(h) ) Cuncoated + s 1 -
)
p p - 1 + eh/q
(6)
where Cuncoated is the capacitance of an uncoated sensor, h the polymer layer thickness, and s, p, and q are fit parameters. The term C(h) can be seen as the integral of the spatial sensitivity from the capacitor surface up to the surface of the polymer layer. Consequently, the spatial sensitivity is proportional to the spatial derivative of C(h). As p is almost unity,36,43 eq 6 can be simplified by setting p ) 1. This leads to an exponential sensitivity distribution, SD, which can be written as
( )
(7)
(4)
(62) Crank, J. The mathematics of diffusion, 2nd ed.; Clarendon Press; Oxford, U.K., 1995. (63) Van Gerwen, P.; Laureys, W.; Huyberechts, G.; Op De Beeck, M.; Baert, K.; Suls, J.; Varlan, A.; Sansen, W.; Hermans, L.; Mertens, R. Sens. Actuators, B 1998, 49, 73-80. (64) Burg, T. Diploma thesis, ETH Zu ¨ rich, 2001.
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If the concentration c is written as a function of relative position, z/h, and relative time, t/τ, this function is unique, i.e., independent of the diffusion constant. As the function is rather complex, it is visualized in Figure 1. The concentration is plotted in different gray levels. The analyte concentration immediately increases at the polymer-gas interface and then spreads into the whole volume. At the bottom of the polymer layer on the transducer surface, the concentration has reached 90% of the saturation value after the diffusion time, τ. The diffusion time depends on the square of the layer thickness. Therefore, for a given diffusion constant, D, the diffusion time can be adjusted over a wide range to a favored value with the layer thickness. However, fine-tuning is difficult due to the square dependence. The initially highly nonuniform concentration profile (Figure 1) indicates the importance of the spatial component of the sensitivity function to predict the transient sensor signal. The sensitivity within the polymer is correlated to the strength of the electric field, which is large near the transducer surface but rapidly decreases with increasing distance from the electrodes (Figure 2). The electric field strength and distribution is usually represented by electric field lines.63,64 The electric field distribution also governs the dependence of the sensor capacitance on the polymer layer thickness, C(h) as is reported in refs 36 and 43,
zh e-(h-z)/q SD , ) SSt hq q(1 - e-h/q)
Here, cSt is the steady-state concentration, h the overall layer
282
(5)
(3)
Here, c denotes the analyte concentration, γ a characteristic constant for each analyte/polymer combination, and D(c)0) the diffusion coefficient for infinite dilution (c f 0). For low enough analyte concentrations, i.e., c , 1/γ, the diffusion coefficient remains approximately constant. Values of γ in the range between 10 and 200 are reported in ref 48 for analyte concentrations given in units of mass fraction in the polymer phase. However, there are also analyte-polymer systems, where the diffusion coefficient is almost independent of the analyte concentration51 or even decreases with increasing concentration.52,53 Diffusion cannot be analytically calculated for arbitrary geometries, especially if the diffusion coefficient depends on the analyte concentrations. Therefore, a simplified model is used. First, it is assumed that the diffusion coefficient is, in the range between zero and the maximum applied concentration, independent of the analyte concentration. This does not hold in general, although it applies to the majority of the investigated analyte-polymer combinations in the tested concentration range (see Results and Discussion), and is a prerequisite for analytical calculation. If D is constant, the response profile caused by a certain analyte has a defined shape, whereas the magnitude of the profile differs in proportion to the applied concentration. Consequently, analytes can be recognized by means of their response profile. If furthermore, in a mixture, D of each analyte is independent of the concentration of all analytes, the transient signal of the mixture is a linear superposition of those of the single analytes. Consequently, linear regression algorithms can be used for a quantitative analysis of the mixture. Second, the complex sensor geometry is simplified. The polymer is considered to be a homogeneous flat layer on a planar surface. For thick layers, this is a reasonable approximation.43 The model is based on the assumption that the diffusion process is decisive for the rate of analyte intake in the sensitive layer and that the concentration in the ambient air increases instantaneously. The analytical solution has been calculated using Ficks laws in refs 55, 62, and 64. The concentration in the polymer, c, as a function of the position, z, and time, t, is given by
() (
thickness, z the distance from the polymer outer surface, and τ the diffusion time, given by
The denominator was introduced to normalize the distribution, so that the total sensitivity in the polymer layer is the steadystate sensitivity of the chemical sensor, represented by the prefactor SSt. q is a parameter describing the vertical decay of the electric field strength36,43,64 with a decay length of 0.5-1 µm for the used electrode geometry. The signal of a capacitive chemical sensor is proportional to the concentration in the polymer, weighted by the local sensitivity. Hence, the product of c and SD is integrated, resulting in a change in capacitance, ∆C, given by
( )
(
)
ht ∆C , ) qτ (-1)n
cStSSt 1 -
∞
2h/q
∑e
-t/τ[(n+1/2)π]2
eh/q - 1 n)0
h q
eh/q
(n + 1/2)π
+1
[( ) ] ( ) n+
1
2
2
π
+
h
2
q (8)
This function, though quite complex, is used, since it fits the observed response profiles well, as will be shown in Results and Discussion (see, e.g., Figure 7). In the case of very thick layers (h . q w h . 1 µm), the sensitivity distribution can be replaced by the assumption that the sensor detects only the analyte concentration at the base of the polymer (eq 4). In this case, eq 8 can be simplified to
(
∆C h f ∞,
t τ
) (
∞
≈ cStSSt 1 - 2
(-1)n
∑ (n + 1/2)π e
)
-t/τ‚[(n+1/2)π]2
n)0
(9) The response profile of a sensor can be used to discriminate analytes with different diffusion times. The discrimination is easier if the sensor exhibits a low limit of determination for the investigated analytes. Several considerations help to estimate how successful a discrimination based on the shape of the analyte response profiles can be. To this end, the response profiles of the pure analytes are first normalized to their steady-state values, which are set to unity. Then, the difference of the normalized response profiles is calculated. The discrimination is easier, when the response profiles of the investigated analytes largely differ. All information of the temporal transient signal, i.e., the whole response profile as a function of time, can potentially be used for the discrimination. To assess the discrimination performance for two arbitrarily selected, different analytes, all difference values taken at the defined intervals during response transient evolution of the two analytes can be summarized or integrated. Under the assumption of using a thick polymer layer, the integral can be simplified, and an analytical calculation is possible, resulting in eq 10. The result reveals that the discrimination performance is
DiscrPerf ∝
∫
(
∞
0
()
()
)
t t ∆C τ1 τ2 ∆τ dt ) cSt1SSt1 cSt2SSt2 2
∆C
(10)
directly proportional to the difference in the absorption times so that the discrimination is difficult, if the diffusion times of both analytes are very similar. The discrimination performance of analytes with similar diffusion coefficients can be improved by increasing the layer thickness, which increases the overall diffusion time. However, this also increases the time required for a measurement so that the desired measurement speed sets the upper limit for the layer thickness. EXPERIMENTAL SECTION CMOS Processing and Sensitive-Layer Deposition. The chemical microsensor chips are fabricated using industrial
0.8-µm double-metal, double-poly CMOS technology at austriamicrosystems (Unterpremsta¨tten, Austria). After completion of the CMOS process steps, polymer films acting as chemically sensitive layers were deposited onto the interdigitated capacitors by spraycoating using an airbrush (Badger, model 200-F) and shadow masks (for details, see ref 17). The microsensors presented here have been coated with the polymers poly(etherurethane), (PEUT, Thermedics Inc., Woburn, MA, glass transition temperature 233 K), ethylcellulose (EC, Sigma-Aldrich, Buchs, Switzerland, glass transition temperature 316 K), and poly(epichlorohydrin) (PECH, Sigma-Aldrich, Buchs, Switzerland, glass transition temperature 251 K). The film thicknesses ranged ∼3 µm for EC and PECH and ∼7 µm for PEUT, which showed to be much more permeable to the organic volatiles than EC and PECH. The polymer thickness was chosen so that all electric field lines were within the polymer: The critical thickness is between 2 and 3 µm and with 3 µm it is ensured that swelling effects are increasing the polymer volume outside the electric field lines and that the signals can be predicted taking into account mainly the changes in the dielectric coefficients of the overall sorption matrix.36 All polymers were cured in saturated solvent atmosphere for up to 2 h after spray deposition and were found to form smooth layers on the interdigitated transducers after this curing process.43 For spraying, the polymers were dissolved in dichloromethane (concentrations, 2 mg/mL). Polysiloxanes that have been extensively used in previous studies, the diffusion characteristics of which have been reported in the literature,55,65 have not been used here since polysiloxanes tend to flow and change film morphology owing to their comparably low viscosity, and with some polysiloxanes, wetting problems on silicon, silicon nitride, or silicon oxide surfaces occur. They form, for example, droplets and nonuniform films (see ref 30) so that it is hard to apply any diffusion model. Sensor Chip. The capacitive transducers consist of 128 finger electrodes of 800-µm length and 1.6-µm width, separated by 1.6µm electrode spacing. Seven sensors and five reference capacitors are monolithically integrated with driving and readout circuitry on a single chip.36 The reference capacitors are similar to the sensor capacitors but are passivated with a thick silicon nitride layer and have not been coated with a polymer layer so that differential measurements between sensor capacitors and reference capacitors become possible. The use of such a differential readout scheme is a consequence of the large parasitic capacitances of each individual capacitor, which largely exceed the capacitance changes induced by analyte absorption into the polymer.6 A multiplexer connects sensors and references to the readout circuitry, a φ-∆ modulator (SD). The SD modulator converts the analog capacitance signal to a digital output signal. The frequency of the output signalsmeasured with an external countersis proportional to the difference of sensor and reference capacitance. The SD modulator is described in detail in refs 6 and 66. For the transient measurements, the clock frequency of the SD modulator was 1 MHz or 500 kHz, and the moving average window was accumulating 25 000 values so that an effective sampling frequency of 40 or 20 Hz resulted. For most experiments, (65) Chandak, M. V.; Lin, Y. S.; Ji, W.; Higgins, R. J. J. Appl. Polym. Sci. 1998, 67, 160-175. (66) Kawahito, S.; Koll, A.; Hagleitner, C.; Baltes, H.; Tadokoro, Y. Trans. 1EE Jpn. 1999, 119-E, 3 138-142.
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283
Figure 3. Schematic of the gas manifold as designed for fast transient signal recording.
a data sampling rate of 20 Hz provided sufficient temporal resolution as will be evident from Results and Discussion. Gas Manifold and Vapor Tests. The gas manifold for transient measurements has to be carefully designed so that the important dynamics of the transient sensor signal reflect the analyte sorption and diffusion characteristics rather than the gas flow dynamics of the setup. This means that all gas switching processes must be fast in comparison to the analyte polymer diffusion and sorption dynamics. To this end, a manifold and flow setup was designed as shown in Figure 3. The most important features are the crossover flow architecture by use of a fast crossover four-way valve, the matched flow resistances of the two output gas lines of the four-way valve, and a small tubing volume between the valve and the sensor measurement chamber. The crossover flow architecture implies that there are two input gas lines, one supplying pure carrier gas and the other supplying carrier gas with defined doses of the volatile analyte, and two output gas lines, one leading to the measurement chamber, the other leading directly to the exhaust. This architecture offers the advantage that both input flows and both output flows are continuously flowing and the build-up time of a certain analyte concentration does not influence the dynamic sensor response. With the dosing line being routed to the exhaust (sensors exposed to pure carrier gas), the desired analyte concentration can be adjusted by means of flow controllers. After sufficient time for concentration stabilization, the crossover valve switches the dosing line to the sensors (carrier gas to the exhaust), which then experience a sudden steep concentration gradient. Using the crossover architecture, it is hence possible to rapidly switch between pure carrier gas and carrier gas containing a defined concentration of a certain analyte. The valve must be very fast. In our case, it was a pneumatically driven four-way crossover valve (B-43YF2, Whitey) with a switching time of less than 0.5 s (maximum speed: 0.2 s for switching by means of pressured air at 8 bar pressure and 0.3 s for switching back by means of a spring). The fast switching of the valve generates pressure waves in the direction of the measurement chamber but also backward in the direction of the supply lines and the flow controllers. On the measurement chamber side, the 284
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system is open, and no effect on the sensor signal was observed. On the side of the flow controllers, additional measures had to be taken since pressure wave-induced artifacts had been observed:64 The flow controllers are very sensitive to pressure transients occurring at either their inlet or their outlet so that an additional empty glass bubbler (large diameter and volume) had to be mounted as a buffer in the dosing line to eliminate these artifacts (Figure 3). Moreover, when switching the four-way valve, any pressure difference in the two output flow lines affects the gas flow dynamics and, consequently, influences the actual concentrations. Therefore, the output line without measurement chamber was designed to exhibit a flow resistance as similar as possible to that with the measurement chamber, and the two output lines of the four-way valve feed into the same exhaust line after the measurement chamber. The overall gas volume between the valve and the sensors was ∼1.6 mL, which entails a time span of ∼0.5 s after switching the valve until the gas reaches the sensor (see Results and Discussion) at the applied flow rate of 240 mL/min. The flow rate also may influence the dynamic sensor signals in case it is rather low. In prestudies, the minimum flow rate that did not affect the analyte transients for the given flow setup was assessed to be 190 mL/ min.64 The CMOS sensors in ceramic dual-in-line packages were mounted in the measurement chamber of the computer-controlled gas manifold.67 The analyte vapors were generated from specifically developed temperature-controlled (T ) 223 to 293 K) vaporizers using synthetic air as carrier gas and then diluted as desired using computer-driven mass-flow controllers. The internal volume of these vaporizers, which distribute the liquid over a largearea, packed-bed type support to maximize surface-to-volume ratio, was dramatically smaller than that of typical gas-washing bottles (“bubblers”).68 By using these vaporizers, the noise in the sensor signals caused by concentration fluctuations or aerosol formation of the liquid analytes is reduced, and the reproducibility of the adjusted gas-phase concentrations is significantly enhanced. The vapor-phase concentrations at the respective temperatures were calculated following the Antoine equation.69 The selected analytes were standard organic solvents and used as purchased from Fluka (Buchs, Switzerland) without further purification. The sensors were mounted into a flow-through cell of a thermoregulated chamber, and the measurements were performed at a temperature of 303 K. Both gas streams (pure carrier gas and carrier gas with analyte) were thermostabilized at the measurement chamber temperature before reaching the crossover valve (Figure 3). Since the dynamic sensor response characteristics strongly depend on the measurement temperature (exponential temperature dependence: the diffusion times at 313 K are ∼50% of the diffusion times at 293 K for the polymers used here64), a careful thermostabilization of the gaseous analytes and the sensors is needed. The response time of the sensors for the given polymer thicknesses (3-7 µm) is on the order of 1 s to 1 min. Typical experiments consisted of alternating exposures to (67) Koll, A.; Kawahito, S.; Mayer, F.; Hagleitner, C.; Scheiwiller, D.; Brand, O.; Baltes, H. Proc. SPIE Smart Struct. Mater. 1998, 3328, 223-232. (68) Bodenho ¨fer, K.; Hierlemann, A.; Schlunk, R.; Go ¨pel, W. Sens. Actuators, B 1997, 45, 259-264. (69) Riddick, J. A.; Bunger, W. B.; Sakano, T. K. In Organic Solvents. In Techniques of Chemistry; Weissberger, A., Ed.; Wiley-Interscience: New York, 1986; Vol. II.
pure synthetic air and analyte-loaded synthetic air. Exposure times of 3-5 min to analyte-loaded gas (to reach thermodynamic equilibrium) were followed by 6-10 min purging the chamber with pure synthetic air. RESULTS AND DISCUSSION Transient signals induced by sudden analyte concentration changes have been investigated to increase the discrimination performance of capacitive microsensors. The time to attain equilibrium and the overall response profile contain important information about the analytes, which enables classification. First, we characterized the setup by means of a self-assembled, monolayer-coated sensor to ensure that the subsequently collected data with the much thicker polymer layers are relevant and reflect polymer/analyte absorption and diffusion properties. Then, the dependence of the diffusion times on the analyte concentration has been assessed. Further investigations have been performed for analyte/polymer combinations with quasi concentrationindependent diffusion characteristics. Afterwards, the analytical model as presented above was validated and used to determine diffusion coefficients from measurements. Finally, mixture analyses based on the transient response profiles were performed. Setup Characterization. To draw conclusions on dynamic signals and diffusion processes in polymeric layers upon a sudden concentration change (step response), it is mandatory that the time to apply the concentration step by means of the gas manifold is considerably shorter than the diffusion time in the polymer layer. To prove this condition to be met for the presented experiments, a sensor coated with a very thin sensitive layer was used. The use of an uncoated sensor was not possible since the amount of analyte adsorbed on the bare device surface did not suffice to generate a clear analyte-induced signal. Therefore, we coated the sensor with a very thin layer of octadecyltrichlorosilane (OTS). OTS covalently binds to the silicon oxide between the sensing electrodes and to the native aluminum oxide covering the aluminum electrodes and forms on both surfaces monomolecular self-assembled monolayers. Although the sensitivity of such a monolayer-covered capacitive sensor is much lower than that of a sensor coated with a thicker polymeric layer, it is sufficiently large to allow for the characterization of the “true concentration step” as experienced by the sensors without the influence of polymer diffusion effects. Figure 4 shows the concentration step profile that has been obtained from the OTS-coated sensor using larger concentrations of ethanol (2400 Pa). Three identical ethanol exposure steps have been averaged to reduce the measurement noise and to produce the curve as displayed in Figure 4. The onset of the sensor response is after ∼0.5 s as predicted by looking at the manifold details given in the Experimental Section. The time, when the crossover valve is switched, represents the origin (zero) of the time scale. The temporal difference between reaching 10 and 90% of the equilibrium signal was measured to be 680 ms, while the difference between reaching 10 and 50% was 150 ms. The same measurement was repeated for methanol and water, the diffusion times of both analytes being much shorter than that of ethanol. No difference in the dynamic signal characteristics in comparison to ethanol could be detected so that all three analytes, ethanol, methanol, and water, show the same dynamic response characteristics, which, in our opinion, represent the setup characteristics. The relatively slow rise time
Figure 4. True-concentration step as measured with a sensor coated with an OTS self-assembled monolayer. The curve represents the average of three step exposures to 2400 Pa ethanol. Averaging was done in order to reduce the noise level. The difference between the 10% and the 50% rise time is 150 ms, that between the 10% and the 90% rise time is 680 ms. The time, when the crossover valve is switched, represents the origin (zero) of the time scale.
Figure 5. Normalized on-peak transient signal of different toluene concentrations in PECH from 50 to 300 Pa in a 3-µm-thick PECH layer.
of the curve in Figure 4 after reaching 80% of the equilibrium value may be due to a decreasing absorption rate as a consequence of the monolayer saturation so that the most reliable and accurate dynamic value is the difference between the 50% and the 10% signal rise time. Concentration Dependence. The dependence of the step response on the analyte concentration also has been assessed. The investigated analytes were monohydric aliphatic alcohols and toluene with concentrations on the order of 10% of the respective saturation vapor pressure. The investigated concentration ranges were the following: methanol, 175-475 Pa; ethanol, 100-400 Pa; 1-propanol, 20-120 Pa; 2-propanol, 50-300 Pa; and toluene, 50300 Pa. The tested polymers were PEUT, PECH, and EC. As an example, Figure 5 shows the sensor signal of on-peaks of different toluene concentrations in PECH. A slightly increased absorption speed for higher analyte concentrations is visible for this analyte polymer combination. This reveals that, for toluene, the diffusion coefficient in PECH increases with the analyte concentration. On the other side, no dependence was found for any investigated alcohol in PECH, nor for any analyte in PEUT. Measured diffusion times were generally much shorter in PEUT than in the two other polymers at comparable layer thickness. The fast diffusion in PEUT and the negligible concentration dependence of the diffusion coefficient is most probably a consequence of the rubber-like nature of PEUT.71 The more soft (70) Van Krevelen, D. W. Properties of Polymers, 3rd ed.; Elsevier: New York, 1990. (71) George, S. C., Thomas, S. Prog. Polym. Sci. 2001, 26, 985-1017.
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Table 1. Characteristic Rise-Time Data and Rise-Time Differences (in s) (10, 50, 80, and 90% of the Equilibrium Value) for 3-µm PECH and 3.1-µm EC as Sorptive Layersa polymer
analyte
t10
t50 - t10
t80 - t10
t90 - t10
OTS PECH
ethanol water methanol ethanol 1-propanol 2-propanol water methanol ethanol 1-propanol 2-propanol
0.78 ( 0.02 0.91 ( 0.02 1.22 ( 0.04 1.44 ( 0.08 2.52 ( 0.25 2.53 ( 0.33 0.92 ( 0.02 0.97 ( 0.02 1.23 ( 0.07 2.12 ( 0.11 2.30 ( 0.06
0.15 ( 0.01 0.33 (0.03 1.22 ( 0.04 3.32 ( 0.07 7.50 ( 0.58 8.64 ( 0.55 0.25 ( 0.02 0.35 ( 0.03 1.16 ( 0.08 6.64 ( 0.83 9.81 ( 1.20
0.41 ( 0.03 0.80 ( 0.06 2.99 ( 0.09 8.67 ( 0.48 18.85 ( 0.69 21.94 ( 2.00 0.71 ( 0.04 0.85 ( 0.06 2.94 ( 0.14 15.61 ( 1.82 23.67 ( 2.51
0.68 ( 0.05 1.23 ( 0.12 4.43 ( 0.23 13.13 ( 0.51 26.61 ( 1.78 31.99 ( 2.92 1.24 ( 0.13 1.24 ( 0.10 4.49 ( 0.30 22.59 ( 2.21 34.01 ( 3.39
EC
a The different analytes included water (55% RH), methanol (475 Pa), ethanol (400 Pa), 1-propanol (120 Pa), and 2-propanol (300 Pa). The data from using the OTS layer are given for comparison; t ) 0 is the moment, in which the crossover valve is switched.
and rubbery the polymers are, the less pronounced is the concentration dependence within the rather small concentration range used for the measurements. Elastomers are normally considered to have sufficiently rapid segmental relaxation times so that relaxation effects do not occur and diffusion follows Fickian kinetics.72 The glass transition temperatures of the three polymers are 233 K for PEUT, 251 K for PECH, and 316 K for EC. For PECH, the comparably large diffusivities are also likely to be a direct consequence of the exceedingly open structure of the polymer. The presence of the Cl group in conjunction with the long alkyl chain on the adjacent backbone carbon forces the polymer backbone into a conformation that confers rather extraordinary rigidity to the chain and loose interactive packing. The resulting polymer, with a large amount of excess volume, presumably permits relatively easy passage of alcohol molecules without requiring significant cooperative movement of polymer chain segments.72 In EC, some concentration dependence was observed for the alcohols, and a strong concentration dependence was found for toluene. Besides the polymer nature that plays a significant role, the concentration influence seems also to be correlated to the size of the analyte molecule, which is in agreement with refs 48 and 70. For all analyte-polymer combinations, for which a concentration influence was observed, the absorption rates increased with increasing analyte concentration. This is consistent with most literature: Concentration-dependent diffusion constants are usually described with an exponentially increasing dependence on the concentration (eq 3).48,70,71 Single-Analyte Discrimination/Diffusion Constants. Individual analytes can be discriminated according to their absorption time for different analyte-polymer combinations and according to the concentration ranges, where the diffusion coefficient is constant, i.e., where the diffusion time is independent of the analyte concentration. Figure 6 shows the response profile of water and some alcohols in PECH. To demonstrate the reproducibility, the signal of two different steps are superimposed for each analyte. The selected analytes (homologous series of alcohols) exhibit very similar chemical behavior. Hence, even with a sensor array coated with different polymers, they are difficult to discriminate by means of (72) Aminabhavi, T. M.; Khinnavar, R. S. Polymer 1993, 34, 5, 1006-1017.
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Figure 6. Normalized on-peak transient signals of different analytes: water (55% RH), methanol (475 Pa), ethanol (400 Pa), 1-propanol (120 Pa), and 2-propanol (300 Pa). The sensor is coated with 3-µm PECH. To demonstrate the reproducibility, two repetitions are superimposed for each analyte.
steady-state signals.43 However, as can be seen, the absorption times differ strongly and allow for discrimination. Measuring the time to reach, for example, 80% of the steady-state concentration, it is, in principle, even possible to differentiate between the two propanols. Rise-time data to reach 10, 50, 80, and 90% of the equilibrium or steady-state values and the respective differences for the different analytes (water (55% RH), methanol (475 Pa), ethanol (400 Pa), 1-propanol (120 Pa), and 2-propanol (300 Pa)) using 3-µm PECH and 3.1-µm EC as sorptive layers are given in Table 1. The data constitute the mean values obtained from five different concentrations for each analyte. The error values in Table 1 have been obtained from calculating the standard deviations of the rise times that were obtained from a total of 10 measurements, 2 for each concentration. For comparison, the data from using the OTS layer (Figure 4), which represent the setup characteristics, are also inserted in the table. In the case of EC, the sensor responses to water and methanol are very similar and so fast that a discrimination of water and methanol based on rise-time analysis is not feasible with the time resolution of the gas manifold and the resulting sharpness of the concentration gradient. The two propanol isomers, however, exhibit a considerable difference in rise time. Best discrimination of the propanols can be achieved in using the different t90 times. The ratio of the difference of the t90 times and the combined standard deviation is larger than 2.8. In the case of PECH, the
Table 2. Diffusion Constants for the Monohydric Alcohols and Toluene in the Two Polymers PECH and PEUT As Calculated from the Fit Parameter τ at the Respective Polymer Layer Thicknessa polymer pA (Pa) PECH pA (Pa) PEUT a
h (µm) 5.4 ( 1% 7 ( 20%
methanol
ethanol
1-propanol
2-propanol
toluene
140 9.0 × 10-12 ( 10% 475 2.3 × 10-11 ( 5%
50 2.0 × 10-12 ( 4% 400 1.27 × 10-11 ( 9%
6.5 0.29 × 10-12 ( 3% 120 8.7 × 10-12 ( 1%
15 0.24 × 10-12 ( 3% 300 8.8 × 10-12 ( 1%
100-300 (0.25-0.3) × 10-12 ( 4% 300 9.5 × 10-12 ( 2%
The diffusion-constant values are given in units of m2/s, and their relative standard deviation is given in %.
Figure 7. Normalized transient signal during on-peak of different alcohols: methanol (475 Pa), ethanol (400 Pa), and 1-propanol (120 Pa). The sensor is coated with 7-µm PEUT. The cross-marks represent the measured signal, the solid lines the fits. Due to the good agreement between measurements and fits, the fit curves are hard to recognize below the cross-marks.
ratio is less than 1.6, and for PEUT, there is not any measurable difference between the two isomers. The curves of the analytes were fitted using eq 8, which seems to depend on four physical quantities, h, q, t, and τ, though it mathematically depends only on two variables: h/q and t/τ. The parameter h/q is identical for all analytes on the same sensor, so that a single value of h/q had been determined for all analytes together in a first step. Then, each curve was fitted with a singlefit parameter, τ, while h/q was kept constant. For the relatively thick layers, the choice of h/q did not significantly influence the determination of τ. All this is mentioned because fitting of any arbitrary function is easy if just enough fit parameters are allowed. Here, only one fit parameter, τ, is actually left. Figure 7 shows the measured response profiles of methanol, ethanol, and 1-propanol using a 7-µm-thick PEUT layer and the respective fits. As already mentioned, a 7-µm-thick layer was used since the organic volatile diffusion in PEUT is very fast, much faster than in the case of PECH or EC (compare Figure 6 and Table 1). The curves of 2-propanol and toluene that strongly overlap with that of 1-propanol are not displayed. In particular, the two propanol isomers are not discernible using the PEUT matrix. Despite the simplifications in the model (see statements before eq 4), the response profiles are almost perfectly fitted. The focus of this work was not to determine diffusion coefficients but to use dynamic parameters of the polymer sorption to discriminate chemically very similar analytes by means of chemical sensors. Nevertheless, some diffusion coefficients have been determined from the dynamic data and will be discussed below. The diffusion coefficients, as calculated from the absorption times (see eq 8), are given in Table 2. For PECH, the layer thickness could be determined with a high accuracy. The diffusion coefficient of toluene in PECH is concentration-dependent (see
Figure 5) so that a relative error on the order of 10-20% is introduced by using eq 4. For PEUT, there is an uncertainty in the determination of the layer thicknesses of 20%; the relations between the different values for PEUT, however, are represented with a low error. Diffusion rates of organic volatiles as determined in the literature for rubbery polymers range from 5 × 10-13 to 8 × 10-11 m2/s (polyurethanes, PECH, nitrile-butadiene rubber using the liquid-phase immersion/weight gain method)72-75 and can be as large as 10-10-10-9 m2/s for alcohols in poly(dimethylsiloxane)s.65 They depend on the nature of the polymer (see the discussion in the section Concentration Dependence) and the chemical and geometric properties of the penetrating analytes. Moreover, the diffusion rates can vary over more than 2 orders of magnitude in dependence of the gas-phase concentration as has been shown for the system toluene/PECH by Etxabarren et al. using inverse gas chromatography (8.5 × 10-14 m2/s for low concentrations to 1.8 × 10-12 m2/s for larger concentrations).74 In a homologous series, the chemical properties are similar but the molecules differ in size, shape, or both. The diffusion coefficients within the series of the investigated alcohols decrease with increasing molecular size (Table 2). Also, the branched-chain alcohols show, in most cases, diffusion coefficients that are lower than those of the nonbranched isomers. The same dependence was found in the literature for the homologous series of aliphatic alcohols in polyurethanes and PECH,72,73 for the alkanes in EC and in santoprene,75 and for alkyl acetates in PECH.76 A simple explanation is the spatial constraints, which cause the diffusion speed of larger molecules to be lower. More sophisticated models also take into account that the molecular structures of alcohols are usually considerably more complex than those of simple organic solvents in terms of conformation since, in the associated form, their molecular sizes are larger than those of the most common polymer repeating units. This entails a rather complex theoretical treatment, which is, however, far beyond the scope of this paper.72 The diffusion constants of the alcohols in PECH given in Table 2 are up to 1 order of magnitude lower than those reported on in ref 72 at 298 K, which include 3.23 × 10-11 m2/s for methanol, 1.35 × 10-11 m2/s for ethanol, 0.71 × 10-11 m2/s for 1-propanol, and 0.87 × 10-11 m2/s for 2-propanol. It has to be noted however, that, for all polymers, the diffusion constants strongly depend on (73) Althai, U. S.; Aminabhavi, T. M. J. Chem. Eng. Data 1990, 35, 298-303. (74) Etxabarren, C.; Iriarte, Etxeberria, A.; Uriarte, C.; Iruin, J. J. J. Appl. Polym. Sci. 2003, 89, 2216-2223. (75) Brandrup, J.; Immergut, E. H.; Grulke, E. A. Polymer Handbook, 4th ed.; John Wiley & Sons: New York, 1999. (76) Aminabhavi, T. M.; Munnolli, R. S. J. Polym. Eng. 1995, 14, 53-74.
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the investigated concentration range, which complicates comparisons. According to ref 48, diffusion coefficients at different concentrations may even vary by up to 3 orders of magnitude. This can explain the differences observed. In particular, the values in ref 72 have been determined by immersing a polymer pellet in the liquid alcohol and by subsequently measuring its weight increase, i.e., at extremely high analyte concentrations so that the diffusion coefficients will tend to be rather high. Literature values as determined in gas-phase measurements at lower concentrations include toluene in PECH (8.5 × 10-14-1.8 × 10-12 m2/s for different concentrations),74 butanol in PECH (2.4 × 10-14 m2/s),74 and methanol in PEUT (6.0 × 10-11 m2/s).77 All these values are rather close to the values as determined in this study (Table 2). Additionally, we measured the n-hexane/EC combination at a similar partial pressure as specified in the literature78 for a more direct comparison. The value determined by our measurements (1.7 × 10-13 m2/s) compares quite well to the corresponding literature values (1.24 × 10-13 and 3.1 × 10-13 m2/s) determined by a gravimetric and a volumetric method.78 This demonstrates the importance of the concentration range, at which the diffusion measurements are performed. A fraction of the discrepancy may also result from the 10% uncertainty in the layer thickness determination, which may introduce an error of up to 20%. In summary, it can be said that the response profiles really are induced by analyte diffusion and that the values given in Table 2 correspond to the diffusion coefficients at the indicated concentration range. These diffusion coefficients are generally in the range to be expected for the rubbery polymers used, and the discrepancy to much higher values determined for some of the polymers in the literature72-75 can be explained by the different concentration ranges. Other reasons for deviations may include the uncertainty in the polymer layer thickness determination or the fact that polymers from different suppliers also may feature slightly different sorption characteristics. Regression with Analyte Mixtures. Analyte mixtures constitute a more realistic scenario than the pure form. At least humidity interference is present in most applications. Determination of analyte concentrations in mixtures is, therefore, important and can be performed by transient signal analysis as will be shown. The fact that the diffusion constants of VOCs in polymeric materials can greatly vary can be exploited to discriminate mixtures using a single sensor. This possibility will be demonstrated in this section. Since the signals upon the absorption of different analytes in the polymers are approximately additive for sufficiently low concentrations,30 linear methods can be used in a first attempt to estimate the composition of a gas mixture based on the dynamic sensor response. Figure 8 shows the dynamic responses of a sensor coated with a thick (7 µm) layer of PEUT upon exposure to a mixture of 300 Pa ethanol and different concentrations of toluene (175, 238, and 300 Pa). Owing to the very thick PEUT layer ( ) 4.8), swelling effects do not contribute to the signal.36 Since the rapidly diffusing ethanol ( ) 24.3) causes the effective dielectric constant of the polymer/analyte composite to increase, while the comparably slow toluene ( ) 2.36) gives rise to a capacitance decrease, an initial strong signal rise is (77) Jansen, B.; Ellinghorst, G. J. Biomed. Mater. Res. 1985, 19, 1085-1099. (78) Hsieh, P. Y. J. Appl. Polym. Sci. 1963, 7, 1743.
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Figure 8. Transient signals recorded for ethanol/toluene mixtures of different compositions. The ethanol concentration was 300 Pa for all measurements, that of toluene increased from 175 through 238 to 300 Pa. Ethanol (24.3) has a higher dielectric coefficient than that of PEUT (4.8); toluene has a lower one (2.36). All three mixtures show distinctly different dynamic signal characteristics; for details, see text.
observed followed by a somewhat slower signal decrease, which is more pronounced for higher toluene concentrations (Figure 8). The equilibrium signal is reached after 10-11 s, and its numerical value is equal to that resulting from a linear superposition of the equilibrium signals of both analytes. The equilibrium signal alone does not provide any information about the mixture composition. However, since the transient evolution times of toluene and ethanol greatly differ, the dynamic signals created by the two analytes in the nonequilibrium regime can be used to extract information about the composition of the mixture by using linear regression methods. The results in Figure 8 demonstrate that a qualitative and quantitative analysis of mixtures can be achieved by transient signal analysis. It is, however, not possible to simply use the pure analytes for calibration and to then try to quantify mixtures based on the dynamic responses to the pure compounds. The sensor has to be calibrated with mixtures in the expected concentration range, since the dynamic mixture signals deviate from a simple linear superposition of the dynamic signals of its pure components so that a substantial amount of calibration measurements is necessary. After calibration, a separate validation set has to be used to prove the performance of the multicomponent analysis model built during calibration. To this end, a sensor was calibrated with 17 concentration steps using a PLSR for each analyte. The analytes included water, ethanol, toluene, and several binary mixtures of these analytes. The sampling frequency was increased to 40 Hz to ensure sufficient temporal resolution. To reduce the influence of the higher noise, caused by the higher sampling frequency, the response profiles were smoothed by a Gaussian filter with a width of 1/6 s. For the prediction model, only the first 10 s of the response profiles were used, because they comprise the important transient information. The number of latent variables used were 6, 9, and 8, for humidity, ethanol, and toluene, respectively. The calibration was validated with a series of concentration steps with mixtures of 300 Pa ethanol and different humidities from 25 to 55%. In Figure 9, the predicted concentrations of water, ethanol, and toluene, the latter of which was not present in this mixture, are plotted as a function of the actual humidity. Three of the displayed mixture compositions also have been used for calibration and are labeled “c”. The prediction of humidity was accurate, whereas that of 300 Pa ethanol and that of the absence of toluene
Table 3. Actual and Predicted Concentrations from a Series of Concentration Steps of Different Duration PLSR
analyte
actual values
ethanol methanol ethanol methanol
prediction
Figure 9. Mixtures of 300 Pa ethanol with different humidities. Predicted analyte concentrations and humidities from transient signals of a sensor coated with 7-µm PEUT. Algorithm: PLSR, calibrated for detection of water, ethanol, and toluene with 17 measurements, three of which are displayed and labeled “c”.
Figure 10. Sensor signals for a series of concentration steps of decreasing lengths from 160 down to 1 s. The envelope of the response profile is highlighted in gray. It is analyte-specific and depends on the analyte absorption and desorption times in the respective polymer.
were less accurate. Nevertheless, it has still been possible to identify and quantify analytes in a mixture despite the chemical similarity between water and ethanol and despite the high humidity contents. The latter cause significantly nonlinear sensor signals, further hampering the prediction of the concentrations. Varying Exposure Duration. A further method to discriminate analytes in mixtures is to provide concentration steps of varying length. Applying long exposure intervals, all analytes will reach absorption equilibrium. For short intervals, only fastdiffusing analytes reach the equilibrium concentration whereas slowly diffusing analytes are hardly discernible. From comparison of the signals of different interval lengths, the composition of a mixture can be obtained. A series of concentration steps alternated with pure air were dosed to a sensor coated with 4-µm PECH. The series consisted of analyte steps of 640-s exposure duration down to 1 s. Figure 10 shows the individual series of measurements of ethanol and methanol. To focus on the region of interest, only the steps shorter than 160 s are displayed. The envelope of the response profile depends on the absorption and desorption time and is characteristic for each analyte. The steps of methanol exhibiting a larger diffusion constant reach saturation even for relatively short exposure duration. For ethanolswith a smaller diffusion constants the signal does not saturate even for medium exposure duration. The finally reached signal height begins to decrease at shorter exposure duration. The sensor was calibrated with an ordinary least-squares regression using one measurement of pure ethanol and one of pure methanol (100 Pa each). The total changes in sensor signal
concentrations(Pa) 100 0 102.8 -2.8
80 20 88.6 11.4
60 40 60.1 39.9
40 60 48.1 51.9
20 80 16.3 83.7
0 100 -2.7 102.7
upon each on- and off-peak were used for calibration, i.e., the envelopes of the series of peaks as highlighted in Figure 10. Validation of the calibration was carried out with different binary mixtures of these two alcohols. The predicted and the true concentrations are listed in Table 3. During this measurement, a total drift corresponding to over 60 Pa alcohol was present. However, drift did not impair the discrimination performance owing to the transient measurement scheme. The sums of the concentrations of both analytes are predicted highly accurate. Errors occur in the prediction of the mixing ratio but they never exceed 10 Pa. The pure analytes are predicted accurately. Concluding, the error of prediction was lower than 10 Pa, which corresponds to 10% of the sum of the concentrations of both analytes. The detection limit for the minority component is, therefore, at a concentration ratio of ∼1:10. For other pairs of analytes, the discrimination performance can be estimated with eq 10. To achieve comparable results, the difference in the diffusion times of the two analytes has to be similar (or higher), and the longest exposure duration has to exceed the higher of the two diffusion times. CONCLUSIONS The time-dependent signal response profiles of capacitive chemical sensors upon sudden concentration increases have been investigated and successfully used for analyte recognition and mixture analysis. Opposed to the conventional use of the steadystate signals only, the transient signals contain much more information about the sensed analytes. The shapes of the response profiles are determined by the diffusion of the analyte in the polymer and have been calculated analytically. Despite the simplifications in the model, the observed transient signal profiles could be described accurately. The comparison of the measured diffusion coefficients with literature values given at the same concentration level showed good agreement. The concentration, at which such values are determined is of high importance since, otherwise, the values may deviate by orders of magnitude. Prior to other investigations, the dynamic characteristics of the gas manifold and experimental setup have been assessed. Moreover, the concentration dependence of the diffusion coefficients has been investigated. The found concentration-independent diffusion coefficients for several analyte/polymer combinations are not a mandatory prerequisite but ensure much easier analyte recognitions and mixture analyses. Linear regression algorithms can be applied, and the number of calibration measurements can be kept low. Additionally, a higher accuracy of the predicted concentration is expected. For these reasons, the existence of such analyte/polymer combinations favors the use of transient signals as successful method for vapor recognition. Analytical Chemistry, Vol. 78, No. 1, January 1, 2006
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As has been shown, the diffusion times of water and the first aliphatic monohydric alcohols in PECH strongly depend on the size of the molecule. Though the discrimination of these substances with a conventional sensor array coated with different polymeric sensitive layers is very difficult, this problem can be solved using dynamic sensor data such as the diffusion time of the analyte with a single sensor. Even the recognition of mixtures of analytes with similar chemical behavior is possible (water/ethanol and methanol/ ethanol, respectively) and was proven with two kinds of measurements. With the first method, the response profile of single exposure steps was analyzed. The second method uses the signal change upon a series of decreasingly long alternating target gas exposure and carrier gas exposure steps. With both methods, the recognition of the investigated analytes was successful. However, it has to be noted that a substantial amount of calibration measurements was necessary in both cases. The demonstrated recognition of analytes on the background of humidity is of special importance due to the omnipresence of humidity in sensor applications and due to the high sensitivity of capacitive sensors toward water. The use of the transient signals also renders the system insensitive to long-term drifts in the sensor signals. Humidity influence and drift are commonly considered the strongest challenges in capacitive chemical sensing.36
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Besides the benefits of transient measurements shown above, it has also to be mentioned that transient signal analysis requires sharp concentration increases. Therefore, the sensor cannot be operated alone, but has to be integrated in a system of, for example, a pump, a filter, and valves, which will increase the costs of the sensor system compared to a sensor alone. It depends on the application and the required recognition ability to judge whether this extra effort is justified. The use of transient signals is a very convenient option when other sensor types are used that anyway rely on transient signals and per se require a system to provide sharp concentration steps, such as calorimetric sensors.5,6 ACKNOWLEDGMENT The authors are very much indebted to Prof. E. T. Zellers, Department of Environmental Health Sciences, University of Michigan, Ann Arbor, for extensive scientific discussion on dynamic measurements using polymeric layers and for proofreading large parts of the manuscript. The authors also thank Professor Henry Baltes, ETH Zurich (on leave) for sharing laboratory resources and for his ongoing stimulating interest in their work. Received for review August 10, 2005. Accepted October 28, 2005. AC051430G
