J. CHEM. SOC. FARADAY TRANS., 1994, 90(5), 751-754 751 Response Kinetics of Polymer-coated Bulk Acoustic Wave Devices on Exposure to Gases and Vapours Neville J. Freeman,* lain P. May and Donald J. Weir GEC-Marconi Hirst Research Centre, Elstree Way, Borehamwood, Hefts, UK WD6 IRX The response of bulk acoustic wave (BAW) devices coated with various polymeric materials to step changes in vapour concentration is shown to be modelled accurately by the sum of two exponentials. It is apparent that the parameters of the exponentials are dependent upon both the coating material used and the gas or vapour present. An automated method of fitting the response kinetics is described. This is shown to allow character- isation of the sensor’s response before steady state is reached and to provide additional information for classi-fication of the analyte.Chemical sensors which use piezoelectric devices such as surface acoustic wave (SAW) and bulk acoustic wave (BAW) devices (e.g. crystal resonators) to transduce changes in a chemically selective coating material are well known.’-4 These piezoelectric devices can form part of oscillators whose frequency of operation is dependent upon a number of factors of which mass loading is one (hence the term mass balance). A number of equations relating mass and frequency change have been derived of which the Sauerbrey equation’ is most commonly employed for BAW devices: Sf= -2.3 x 1O6f;(6m/A) (1) where 6m is the change in mass (g), A is the piezoelectrically active surface area (cm2) andf, (MHz) is the uncoated fre- quency of the BAW device. The use of piezoelectric devices as chemical sensors was proposed as long ago as 19642 for the measurement of humidity.The piezoelectric transducer’s response to vapours is modified by coating the surface with a suitable material such as a gas chromatograph (GC) stationary phase. As vapours concentrate in the surface coating, the change in the coating’s acoustic properties alters (generally reduces) the fre- quency of oscillation. Although much empirical work on the identification of suitable coatings for given applications has been reported in the literat~re~-~ less attention has been paid to the physical changes occurring in polymeric coatings on absorbing vapours and their consequences for the frequency of operation.Recent studies on the response of piezoelectric sensors (both SAW and BAW device^)^,^ have investigated the importance of viscoelastic changes in coatings applied to such devices on absorption of vapours. The term ‘mass balance’ should therefore be used with some caution when referring to coated piezoelectric devices. In the current paper, the response kinetics of piezoelectric crystals with various coatings are modelled and an automatic method of fitting the model is presented. The response is accurately modelled by the sum of two exponentials implying that two concomitant physical processes are occurring. It is shown that this model allows the characterisation of the response before steady state is reached and provides additional information for the classi- fication of the analyte.Experimental Apparatus ated vapours were passed to a mixer module where flow dilution took place as required. Finally the mixed vapour stream was passed into the sensor chamber which was placed in a second water bath (Grant Instruments) held at 25°C. The vapour generation system and sensor chamber were designed to minimise the dead-space in the sensor chamber which was estimated to be ca. 15 cm3. Frequency changes were measured with respect to a reference source (Marconi Instruments 2022D) whose frequency was set above that of the coated crystal. Thus on exposure to the vapour the fun- damental frequency of the crystal falls and the difference between the two increases.A personal computer (Opus PCV) was used to control the experiments and log the data. The experiments consisted of repeats of four distinct phases: initially the sensor chamber was flushed with nitro- gen (60 min), after which the carrier stream was bubbled through the sample liquid for 30 min in order to equilibrate the generated vapour, while the nitrogen purge of the sensor chamber continued. Following the completion of these two phases the sensors were alternately exposed to the sample vapour and purged with laboratory nitrogen for periods shown in the results. The sequence of events was computer controlled by switching a set of solenoid valves (Precision Dynamics). Chemicals Toluene, methanol, chloroform and dichloromethane AnalaR Grade (BDH Ltd.) were used as supplied.Coating materials AT1000, OW01 and Carbowax were obtained from Alltech Ltd. and ethyl cellulose from Aldrich Ltd. Samples of linalol, nitrogen carrier gas control I-I -flow . control sensormixer I chamberI liquid sample IVapours were generated using an automated system (outlined exhaust gas in Fig. 1) in which gas wash bottles were placed in a water Fig. 1 A schematic diagram of the vapour generation system used. bath (Grant Instruments) at 20°C in order to saturate a dry- The sensor chamber is switched between diluted sample vapour and nitrogen carrier stream flowing at 200 ml min-’. The satur- laboratory nitrogen. 752 J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 dibutyl sulfide and isoamyl acetate were provided by Firme- 6.0 nich SA. 5g 5.0 Preparation of Sensors 4.0 10 MHz (fundamental frequency) AT cut quartz crystals with u gold-plated electrodes (McKnight) were spray coated using an air brush charged with dilute solutions of the required Y-~~~~coating material in an appropriate solvent. The coatings were w 1.0 typically applied until the fundamental frequency was 0 100 200 300 400 500 600 depressed by ca. 10 kHz (in laboratory air environment) time/s which may be estimated to be equivalent to a coating thick- ness of a few hundred nanometres using eqn. (1) and the density of the coatings (assuming the coatings to be elastic). 2950 T Results and Discussion Fig.2 shows an example response from an ethyl cellulose coating piezoelectric crystal sensor when exposed to a toluene loaded vapour and then ‘purged’ with laboratory nitrogen. The difference frequency is defined throughout as a reference frequency (arbitrarily set at 10 MHz for convenience) minus the frequency of oscillation of the coated crystal. The frequency response is defined as the absolute fre- quency of the coated crystal, which decreases during the sample phase as the mass loading increases and conversely increases during the purge phase as the mass loading decreases. Initially a number of functions were fitted by hand to the ‘expose’ and ‘purge’ phases separately including single I and multiple exponentials and polynomials.The natural L logarithm of the response is shown in Fig. 3(a) in order to illustrate the poor fit obtained with a single exponential. Of the functions tried, the sum of two exponentials appears to give the best fit: 0 200 400 600 800 1000 1200 time/sR(t) = a, -a2 exp(-a,t) Fig. 3 (a) Natural logarithm of the purge phase of the response shown in Fig. 2 after removal of the dc offset. If the response consist- -a4 exp(-a,[); sample phase (2) ed of a single exponential, this plot should be a straight line. (b) The R(t)= a, -a2[1 -exp(-a,t)] example response shown in Fig. 2 (-) and the associated dual- exponential fit (offset by 10 Hz for clarity) (---). -a4[ 1 -exp(-a5t)] ; purge phase (3) An example of the fit obtained is shown in Fig.3(b). In order to ensure that the observed kinetics related to the are significantly altered by the coating used. Further tests vapour and coating properties rather those those of the showed that while addition of more coating increased the apparatus, a number of differently coated crystals were amplitude of the response the time constants were not signifi- exposed to the same vapour in the same apparatus. The cantly affected. results (see Fig. 4) clearly indicate that the response kinetics 2950 T 2650 f 2600 2550 L 2450 0 40 80 120 160 200 240 280 320 360 400 4402500t 0 200 400 600 800 1000 1200 percentage from final estimate ti me/s Fig. 4 Response of four differently coated crystal resonators to the Fig. 2 An example of the response of an ethyl cellulose coated same vapour in the experimental apparatus.The responses have been crystal on exposure to toluene vapour (1-600 s) and subsequently to expressed as a percentage of the steady-state amplitude in order to laboratory nitrogen (600-1200 s). The response is measured in terms illustrate the different rate constants observed with each coating of the difference in frequency between a fixed reference source and material. (a) AT1000, (b) OV101,(c) Carbowax 20 m, (d)ethyl cellu- the coated crystal. lose. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 In order to evaluate the ability of the dual-exponential function to fit the kinetics of the response of piezoelectric devices across a number of coatings and analytes, an auto- mated method of fitting is required.Unfortunately, the fitted function is non-linear with respect to the two rate constant parameters and no linearising transform (e.g. logarithms) is obvious. An iterative fitting process was therefore adopted based on the Levenburg-Marquadht (LM) alg~rithm.~ Initial work with synthetic data demonstrated that the fitting error was a unimodal function of the parameters (al-,), but that the gradient of the error surface could be shallow leading to slow convergence (see Fig. 5). The LM algorithm is well suited to such surfaces as it transforms from a simple gra- dient descent scheme into a quadratic root finding method as it approaches the minimum, thus reducing the convergence time.It was found that the iterative fitting process could fail if the sign of the estimate of one of the two rate constant parameters (a2,u4) went negative as this led the value of R(t) to increase exponentially with time and in some cases caused the calculation program to overflow. The algorithm was modified to reset the value of the rate constant parameters to a small positive value if they went negative. This modification removed the overflow problem and did not appear to prevent convergence. In order to generate statistics concerning the estimated parameters, it is necessary to know the noise associated with each measurement. The noise model used was based on known inaccuracies in the measurement process, i.e. the sam- pling (k0.5s) and gain time (k1 Hz).If only the first expo- nential is considered and the distribution of errors is assumed to be rectangular, the standard deviation associated with each measurement can be computed as : dt)= (C2.O + a2a3 exp(-a3 t)]2/12.0)1'2 (4) A plot of the estimate of a(t) for the example data shown in Fig. 2 is given in Fig. 6. If this noise model is taken as a good estimate then the fit shown in Fig. 3 is found to be significant at the 99.9% confidence level. This noise model is likely to be conservative as it does not include the second exponential or other noise sources (e.g. temperature variation). Inclusion of the noise model into the fitting process, rather than assuming a uniform value of a(t),weighted the different regions of mea- sured response and was found to speed up convergence con- siderably.Further work showed that the rate of convergence was also highly dependent on the quality of the initial estimate of the parameters. This initial estimate was calculated according to the heuristic process in Fig. 7. This makes a number of assumptions based on fitting several responses by hand. For example, the larger of the two exponentials is assumed to account for 90% of the steady-state response and to have the larger rate constant. The uniqueness of fit was tested on a number of experimental results in which the rate constant 45000 TI 40000 i! 35000 5 2 30000 25000 20000 15000 -50-40-30-20-10 0 10 20 30 40 50 percentage from final estimate Fig.5 Variation in 2' as a function of the value of one of the parameters of the dual-exponential equation. While the function is unimodal it is also shallow and gradient-based techniques may there- fore take some time to converge. =. 753 3000 T T 25 I 2900 20 128005 27001 2600 'c 2500 2400 , \z -o 2300 2200 ~ =m m....a.mm..m..."m==~==m==,a~e=ee.ee=n,~e ~ '~~'~0 ~'' 0 7.5 15.0 30.0 45.0 60.0 75.0 ti me/s Fig. 6 Estimate of ~(t)for the example data shown in Fig. 2: (0) difference frequency, (u)estimated standard deviation estimates (a3 and a,) were deliberately swapped. The result- ant fits yielded results for al-as which were within two stan- dard deviations of those obtained with the 'normal' method of estimation demonstrating the robustness of the final solu- tion.The incorporation of this initial heuristic estimate was found to improve the rate of convergence still further. In order to assess the reproducibility of the algorithm it was tested on six successive exposures to one vapour. The results of this are given in Table 1 and show that the stan- dard deviation of the parameter estimate was never more than 5% of the mean. The algorithm was also tested for tirne/s Diagram illustrating the heuristic method used to determine aninitial estimate of the parameter values of the fitting equation. The rate constant of the fast exponential (a3)is calculated from the time taken for the response to fall by half the steady-state amplitude, while the slow rate constant (as)is estimated from the time taken to com-plete the last 10%of the response's amplitude. Table 1 Estimated response parameters of six consecutive 'remove' phases following exposure to toluene vapour repeat number a1 a, a3 a4 a5 probability 248 7 430 0.110 36.2 0.018 1 .Ooo 2483 439 0.110 33.6 0.016 0.999 248 1 433 0.110 35.0 0.016 0.999 2480 429 0.111 35.3 0.016 1.Ooo 2480 447 0.113 38.1 0.017 1.Ooo 2479 444 0.110 35.8 0.016 1.Ooo mean 2482 431 0.111 35.7 0.017 1.Ooo standard 3 8 0.001 1.5 0.001 0.001 deviation 754 Table 2 Estimated response parameters from decreasing data lengths” ~ n um ber of samples a1 a2 a4 a5 42 1 2395 495 0.213 15.3 0.027 300 2385 503 0.218 17.1 0.031 200 2380 507 0.220 18.4 0.033 100 2381 505 0.219 18.0 0.032 50 2302 514 0.283 86.9’ 0.098’ 25 2303 511 0.283 88.6’ 0.100’ 10 2320 440’ 0.236’ 130.3’ 0.260’ ” Sampling interval, 1.5 s.’The parameters were insignificantly dif- ferent from zero at the 95% confidence level. robustness to short data lengths. The results of this are shown in Table 2. While the parameter estimates do change with data length, this is not entirely surprising as in the case with 50 samples an exponential with a half-time of ca. 30 s is being estimated in combination with an exponential whose amplitude is 25 times larger over a period of some 75 s. Further, note that the cases of significant parameter variation may be detected from the statistics generated by the pro- cedure.These results demonstrate that the parameters of the sensor response may be estimated from an initial portion of the response before steady state is reached, thereby poten- tially speeding up sensor operation. BAW devices are frequently referred to as ‘mass balance’ devices. A simple mass absorption model is likely to lead to responses to step changes in vapour concentrations which are well fitted by a single exponential. This model is supported by the general observation that increasing the amount of coating material deposited on the surface of the device (and hence the volume of coating material) leads to an increase in the sensitivity of piezoelectric devices. The results here suggest that a secondary process is occurring which typically accounts for 10% of the overall response.The nature of the second process has not yet been positively identified but can- didates include a separate surface adsorption phenomenon and changes in the viscoelastic properties of the coating as the concentration of vapour in the material builds up. Our lack of knowledge of the identity of the mechanisms underlying the response kinetics does not prevent us from exploiting them to provide additional information from the sensor to classify the atmosphere it is sensing. Fig. 8 shows the response kinetics of an ethyl cellulose coated crystal to three odorous compounds, while Table 3 gives the estimated value of the fast exponential’s rate constant (parameter a3) and the standard deviation of the estimate.These results demonstrate that it is possible to discriminate between these three compounds using a single sensor. This discrimination could be made irrespective of compound concentration or the amount of coating on the device as these factors do not Table 3 Estimated rate constant of the fast exponential part of the ‘remove’ phase of the response of an ethyl cellulose coated crystal resonator to three compounds, and the standard deviation of the estimate standard deviation compound rate constant, a, of estimate dibutyl sulfide 0.050 0.002 linalol 0.030 0.001 isoamyl acetate 0.09 1 0.009 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 1001 , i ” 0 50 100 150 200 250 300 350 400 450 500 time/s Fig.8 Response of an ethyl cellulose coated sensor to three differ- ent compounds. The responses have been expressed as a percentage of the steady-state amplitude in order to make the variation in the rate constants clear. (a)Dibutyl sulfide, (b)linalol, (c)isoamyl acetate. change the rate constant of the response, merely its ampli- tude, The characterisation of the response kinetics therefore offers more information for classification of the analyte than the steady-state response amplitude alone. Conclusions The response kinetics of coated piezoelectric crystal reson- ators to a variety of vapours appears to be well modelled by the sum of two exponentials. The parameters of these expo- nentials depend on the chemical nature of both the coating and the vapour.An automated method of estimating the parameters of the non-linear kinetics equation is presented which is relatively robust to short data lengths. This allows the response of piezoelectric sensors to be characterised before steady state is reached, potentially reducing sampling time. The accuracy of the dual-exponential fit suggests that two concurrent processes are occurring such as diffusion into the coating and changes in the coating’s viscoelastic proper- ties. Characterisation of the sensor’s response in this way has been shown to offer more information for the classification of the analyte than use of the steady-state response amplitude alone. The rs gratefully acknowledge support from Firmenich SA ould like to thank Dr. L. Wunsche and Dr. M. Kearney Ior useful discussions. References G. Sauerbrey, Z. Phys., 1959,155,206. W. H. King, Anal. Chem., 1964,36,1735. J. J. 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