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Physical interpretation of the influence of humidity on an SO2 sensor
6 CHEMICAL
ELSEVIER
Sensors and Actuators B 24-25 (1995) 552-554
Physical interpretation
of the influence of humidity on an SO2 sensor J. Pichlmaier
Universit~t der Bundeswehr
Miinchen, I&i&t
fiir Me& und Automatisienmgstechni~
Werner-Heiswber-Weg
39, D-85577 NeubibeG
Germany
Abstract SO2 concentrations can be measured by organically modified ceramics that change their dielectric permittivities when they adsorb SO,. The sensor considered here consists of a planar interdigital capacitor coated with this sensitive layer, whose capacity changes are proportional to the gas concentration in the ambient air. As a result of the sensor principle and the dipole moment of water molecules, the layer is also sensitive to humidity to a certain extent. All characteristic lines of the sensor, exposed to humidities ranging from 0 to 2 vol.% at temperatures between 20 and 50 “C, are BET shaped. The characteristic lines can be fitted by BET isotherms with restricted accuracy. However, three further models, one of them comprising the Langmuir isotherm, lead to a very good modelling. To include the effect of temperature in the model, a physical model based on a dynamic equilibrium of two-step adsorption and desorption is established. The temperature dependence of the characteristic lines is fully described by this physical model and it provides a value of the activation energy. Keywordx
Humidity effects; Sulfur dioxide sensors
1. Introduction
Many methods of measuring gas concentrations, particularly SO, concentrations, have to consider the interference of humidity with the measuring process. SO, sensors, which this paper is concerned with, work on the principle of adsorption. Tertiary amines in N,Ndimethyl-3-aminopropyltrimethoxysilane (NND) form reversible adducts with sulfur dioxide, and thereby alter the dielectric permittivity of the sensitive layer [l]. The layer has been proved to be insensitive to many gases [2]. Although the sensitivity to humidity has been reduced by cocondensing hydrophobic material, the layer is still strongly affected by humidity [3]. Mathematical models, e.g. the polynomial approximation, generally facilitate a microcontroller-based compensation of the unwanted influence of humidity. To understand the sensor’s operating principle thoroughly, an appropriate physical model of the influence of humidity has to bc found. An interpretation of the influence of humidity from a physical point of view is given here.
Teller (BET) isotherms. First four different physically motivated approaches, including the BET isotherm and one that contains the Langmuir isotherm (Fig. l), are applied to the characteristic lines at each temperature. The sensor signal n is proportional to the number 40 of H,O molecules adsorbed by two independent adsorption processes which can be superposed: n=a -?p+b
+c[exp(&)-l]
The first termof Eq. (1) represents the process according to Langmuir (a, b =model parameters); the second term is the solution of the differential equation
“5=d(n+c) acp
Eq. (2) expresses the assumption that the change of the number of adsorbed particles Wlqo is proportional
2. Model of humidity effect All measured characteristic lines (see Fig. 5) are qualitatively comparable to the Brunauer, Emmet and 092.5-4005/95/$09.50 8 1995 Elsevier Science S.A. All rights reserved SSDI 0925-4005(95)01742-E
(1)
Fig. 1. Model based on Langmuir isotherm.
J. Pichlmaier / Sensors and Acntaton
E 24-25
(1995) 552-554
553
60 BET model
500 400 300
modified
Langmulr
model humidity bmt.%
200
60
100 0 -100
Fig. 2. Residuals of BET model and modified Langmuir model for all temperatures.
‘b
%O
20.0 ‘C
Exampk data batto c&u!&e achtim
8
550 .a
energy
T, = 20.0 ‘C Tz= 25.0 ‘C
%
,” 40
VI = 1.I 174vol.l * = 1.5699v0l.K
B
number of adsorbed particles heI. units
/ 22.5 'C
20
10
0 -0
0.2
0.4
0.6 0.E
1.0
1.2
1.4
1.6
1.6
2.0
humidity /vol.%
Fig. 3. Calculations of the activation energy.
Fig. 5. Characteristic lines with temperature as parameter: top, change of capacitance vs. humidity; bottom, change of capacitance vs. number of adsorbed particles.
influence of humidity is found for every single temperature. If it were possible in addition to find a physical model for the influence of temperature on the model parameters, the work would be finished. However, the influence of temperature on the model parameters cannot be interpreted physically. Yet another approach leads to a description of the influence of temperature.
3. Model of temperature effect
0.6 activation energy
Fig. 4. Determination energy distribution.
0.7
/eV
of the activation energy by evaluating the
to the sum of the number of adsorbed particles n and nuclei c, i.e., d(n+c). After fitting the characteristic lines for all temperatures, the residuals of the two models are depicted in Fig. 2. Both models differ mainly because of the different numbers of parameters (BET, three parameters; modified Langmuir, four parameters). In any case, deviations are rather low and a model for the
Temperature effects (see Fig. 5 top) are described by a new model [4] based on a two-step process: in the first step water molecules are adsorbed on and desorbed from the surface. The adsorption rate is proportional to the impact rate of water molecules on the surface. The desorption rate depends on the activation energy. Either of the sorption processes, and hence the entire first step, depends on temperature. In the second step the particles are adduced to the layer. There is an equilibrium between the number of adsorbed particles according to the first step and the adduced particles governed by free sites on the layer. As a result an activation energy e, of desorption can be evaluated:
(3)
554
1. Pidhaier
I Sensors and Achutors B 24-25 (1995) 552-554
k contains the equilibrium constant of adsorption and desorption.
4. Determination of activation energy e, The sensor signal is assumed to be proportional to the number of adduced particles, thus for a fixed sensor signal (e.g., as indicated by the horizontal line in Fig. 3) the number of adduced particles is unique. By taking any two characteristic lines at temperatures TI and T,, with any common value of the sensor signal, and the corresponding humidities ‘pl and (pz, the activation energy ep of the desorption can be evaluated from Eq. (3). 1560 data sets have been evaluated in this way. The frequency, expectation value and standard deviation of the activation energy are given in Fig. 4. For the set of characteristic lines given in Fig. 5 an activation energy of 0.393 + 0.056 eV is determined.
5. Conclusions
The temperature dependence of the characteristic lines is fully described by this physical model. Without any consideration of the form of the characteristic lines, both an activation energy can be determined and the set of temperature-dependent characteristic lines (Fig. 5, top) is reduced to one line valid for all temperatures (Fig. 5, bottom).
The BET-type characteristic lines can be represented at a !ixed temperature by models based on physical considerations. Another physical model represents the temperature dependence of the humidity influence, leading to an activation energy. With the help of a physically interpretable activation energy, a more profound understanding of the working principle of these SO, sensors will be feasible.
Acknowledgement This work was supported by the Bundesministerium fiir Forschung und Technologie, project nos. 13 AS 01089 and 13 MV 0156.
References PI F. Hutter, Feldeffekttransistor-Gassensoren
mit Heteropolysiloxanschichten und auf heterogen-kataiytischer Basis, AbschZuJZwichtmm Forschungsvorfaben, Fraunhofer Institut fiir Silicatforschung, W&burg, 1990. I21 J. Lin, S. MSller and E. Obermeier, Thin-film gas sensor with organically modified silicates for the measurement of SO*, Serwn and Actuators B, 5 (1991) 219-221. PI J. Pichlmaier, Kalibrierung van Gassensoren in befeuchteter Atmosphtie and Modellierung des Feuchteeinflusses auf kapazitive SO&nsoren, Fwtschrift-Berichte, Series 15, No. 126, VDI, Diisseldorf,1994. I41 M. Horn, J. Pichhnaier and H.-R. TrZnkJer, Physical description for the sensor principle of a S02-sensor, Sensors and Actuators B, 24-25 (1995) 4001102.
ELSEVIER
Sensors and Actuators B 24-25 (1995) 552-554
Physical interpretation
of the influence of humidity on an SO2 sensor J. Pichlmaier
Universit~t der Bundeswehr
Miinchen, I&i&t
fiir Me& und Automatisienmgstechni~
Werner-Heiswber-Weg
39, D-85577 NeubibeG
Germany
Abstract SO2 concentrations can be measured by organically modified ceramics that change their dielectric permittivities when they adsorb SO,. The sensor considered here consists of a planar interdigital capacitor coated with this sensitive layer, whose capacity changes are proportional to the gas concentration in the ambient air. As a result of the sensor principle and the dipole moment of water molecules, the layer is also sensitive to humidity to a certain extent. All characteristic lines of the sensor, exposed to humidities ranging from 0 to 2 vol.% at temperatures between 20 and 50 “C, are BET shaped. The characteristic lines can be fitted by BET isotherms with restricted accuracy. However, three further models, one of them comprising the Langmuir isotherm, lead to a very good modelling. To include the effect of temperature in the model, a physical model based on a dynamic equilibrium of two-step adsorption and desorption is established. The temperature dependence of the characteristic lines is fully described by this physical model and it provides a value of the activation energy. Keywordx
Humidity effects; Sulfur dioxide sensors
1. Introduction
Many methods of measuring gas concentrations, particularly SO, concentrations, have to consider the interference of humidity with the measuring process. SO, sensors, which this paper is concerned with, work on the principle of adsorption. Tertiary amines in N,Ndimethyl-3-aminopropyltrimethoxysilane (NND) form reversible adducts with sulfur dioxide, and thereby alter the dielectric permittivity of the sensitive layer [l]. The layer has been proved to be insensitive to many gases [2]. Although the sensitivity to humidity has been reduced by cocondensing hydrophobic material, the layer is still strongly affected by humidity [3]. Mathematical models, e.g. the polynomial approximation, generally facilitate a microcontroller-based compensation of the unwanted influence of humidity. To understand the sensor’s operating principle thoroughly, an appropriate physical model of the influence of humidity has to bc found. An interpretation of the influence of humidity from a physical point of view is given here.
Teller (BET) isotherms. First four different physically motivated approaches, including the BET isotherm and one that contains the Langmuir isotherm (Fig. l), are applied to the characteristic lines at each temperature. The sensor signal n is proportional to the number 40 of H,O molecules adsorbed by two independent adsorption processes which can be superposed: n=a -?p+b
+c[exp(&)-l]
The first termof Eq. (1) represents the process according to Langmuir (a, b =model parameters); the second term is the solution of the differential equation
“5=d(n+c) acp
Eq. (2) expresses the assumption that the change of the number of adsorbed particles Wlqo is proportional
2. Model of humidity effect All measured characteristic lines (see Fig. 5) are qualitatively comparable to the Brunauer, Emmet and 092.5-4005/95/$09.50 8 1995 Elsevier Science S.A. All rights reserved SSDI 0925-4005(95)01742-E
(1)
Fig. 1. Model based on Langmuir isotherm.
J. Pichlmaier / Sensors and Acntaton
E 24-25
(1995) 552-554
553
60 BET model
500 400 300
modified
Langmulr
model humidity bmt.%
200
60
100 0 -100
Fig. 2. Residuals of BET model and modified Langmuir model for all temperatures.
‘b
%O
20.0 ‘C
Exampk data batto c&u!&e achtim
8
550 .a
energy
T, = 20.0 ‘C Tz= 25.0 ‘C
%
,” 40
VI = 1.I 174vol.l * = 1.5699v0l.K
B
number of adsorbed particles heI. units
/ 22.5 'C
20
10
0 -0
0.2
0.4
0.6 0.E
1.0
1.2
1.4
1.6
1.6
2.0
humidity /vol.%
Fig. 3. Calculations of the activation energy.
Fig. 5. Characteristic lines with temperature as parameter: top, change of capacitance vs. humidity; bottom, change of capacitance vs. number of adsorbed particles.
influence of humidity is found for every single temperature. If it were possible in addition to find a physical model for the influence of temperature on the model parameters, the work would be finished. However, the influence of temperature on the model parameters cannot be interpreted physically. Yet another approach leads to a description of the influence of temperature.
3. Model of temperature effect
0.6 activation energy
Fig. 4. Determination energy distribution.
0.7
/eV
of the activation energy by evaluating the
to the sum of the number of adsorbed particles n and nuclei c, i.e., d(n+c). After fitting the characteristic lines for all temperatures, the residuals of the two models are depicted in Fig. 2. Both models differ mainly because of the different numbers of parameters (BET, three parameters; modified Langmuir, four parameters). In any case, deviations are rather low and a model for the
Temperature effects (see Fig. 5 top) are described by a new model [4] based on a two-step process: in the first step water molecules are adsorbed on and desorbed from the surface. The adsorption rate is proportional to the impact rate of water molecules on the surface. The desorption rate depends on the activation energy. Either of the sorption processes, and hence the entire first step, depends on temperature. In the second step the particles are adduced to the layer. There is an equilibrium between the number of adsorbed particles according to the first step and the adduced particles governed by free sites on the layer. As a result an activation energy e, of desorption can be evaluated:
(3)
554
1. Pidhaier
I Sensors and Achutors B 24-25 (1995) 552-554
k contains the equilibrium constant of adsorption and desorption.
4. Determination of activation energy e, The sensor signal is assumed to be proportional to the number of adduced particles, thus for a fixed sensor signal (e.g., as indicated by the horizontal line in Fig. 3) the number of adduced particles is unique. By taking any two characteristic lines at temperatures TI and T,, with any common value of the sensor signal, and the corresponding humidities ‘pl and (pz, the activation energy ep of the desorption can be evaluated from Eq. (3). 1560 data sets have been evaluated in this way. The frequency, expectation value and standard deviation of the activation energy are given in Fig. 4. For the set of characteristic lines given in Fig. 5 an activation energy of 0.393 + 0.056 eV is determined.
5. Conclusions
The temperature dependence of the characteristic lines is fully described by this physical model. Without any consideration of the form of the characteristic lines, both an activation energy can be determined and the set of temperature-dependent characteristic lines (Fig. 5, top) is reduced to one line valid for all temperatures (Fig. 5, bottom).
The BET-type characteristic lines can be represented at a !ixed temperature by models based on physical considerations. Another physical model represents the temperature dependence of the humidity influence, leading to an activation energy. With the help of a physically interpretable activation energy, a more profound understanding of the working principle of these SO, sensors will be feasible.
Acknowledgement This work was supported by the Bundesministerium fiir Forschung und Technologie, project nos. 13 AS 01089 and 13 MV 0156.
References PI F. Hutter, Feldeffekttransistor-Gassensoren
mit Heteropolysiloxanschichten und auf heterogen-kataiytischer Basis, AbschZuJZwichtmm Forschungsvorfaben, Fraunhofer Institut fiir Silicatforschung, W&burg, 1990. I21 J. Lin, S. MSller and E. Obermeier, Thin-film gas sensor with organically modified silicates for the measurement of SO*, Serwn and Actuators B, 5 (1991) 219-221. PI J. Pichlmaier, Kalibrierung van Gassensoren in befeuchteter Atmosphtie and Modellierung des Feuchteeinflusses auf kapazitive SO&nsoren, Fwtschrift-Berichte, Series 15, No. 126, VDI, Diisseldorf,1994. I41 M. Horn, J. Pichhnaier and H.-R. TrZnkJer, Physical description for the sensor principle of a S02-sensor, Sensors and Actuators B, 24-25 (1995) 4001102.