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Effects of surface physical sorption on characteristic of coated quartz-crystal humidity sensor
*RS
mum B
Sensors
and Actuators
CHEMICAL
B 24-25 (1995) 62-64
Effects of surface physical sorption on characteristic quartz-crystal humidity sensor
of coated
Yonggui Dong, Guanping Feng Deportment of PrecisionInstrument and Mechanolqy, Tsinghua Univemity,Beijing 100084, China
Abstract A three-layer mechanical model, which consists of a quartz layer, a solid film layer and a fluid-phase film layer, is presented and a formula is deduced for calculating the relationship between the surface state and frequency shift of a quartz-crystal resonator. The theory has been used to analyse the characteristic of a resonant humidity sensor using a coated quartz-crystal resonator. Experiments prove that the new deduced formula gives better agreement with experimental results than Sauerbrey’s formula. Furthermore, the three-layer theory can be widely used in developing sensors constructed with quartz-crystal resonators. Keywords Humidity
sensor; Quartz-crystal
resonator;
Surface sorption
1. Introduction
After King constructed a ‘piezoelectric sorption detector’ [l], more and more humidity-gas sensors have been developed using AT-cut quartz-crystal resonators vibrating in the thickness-shear mode. The principle is mainly based upon Sauerbrey’s formula [2,3]:
where Am = mass of substances absorbed on the surface, Af= shift of frequency. When the sorbed layer can be regarded as a solid phase, no doubt Eq. (1) is appropriate. However, in the case of physical sorption, like that of water molecules, surface sorption of vapour is almost definitely multimolecular. When the sorbed amount reaches a certain extent, an ‘almost liquid’ layer will be formed. As shear vibration will be damped rapidly in this layer, Eq. (1) is no longer applicable. In this paper, a three-layer mechanical model is presented and a new formula is deduced for calculating the relationship between the state and frequency shift of a coated quartz-crystal resonator. This three-layer theory can not only be used in analysing and developing the characteristics of humidity sensors as mentioned in this paper, but can also be generally applied to those sensors constructed from AT-cut quartz-crystal resonators. 09254OOS/9S/$O9.50 8 1995 Elsevier Science S.A. All rights reserved S.SDI 0925-4005(94101316-A
2. Principles While a coated quartz-crystal resonator is vibrating in ambient air (assuming only one surface is in contact with the ambient air), it can be simplified as the threelayer model shown in Fig. 1, where layer I consists of the quartz crystal (including the lower electrode), layer II consists of the upper electrode and absorbentiabsorbate materials that can be regarded as solid phase and layer III is regarded as a pure fluid layer where shear vibration will be damped rapidly. When a bulk-shear acoustic wave has been generated by piczoelectricity inside the resonator, let u = particle displacement, v = particle displacement velocity (V = au/ at) and p, p, q represent density, shear modulus and generalized viscosity, respectively. The following equations can easily be found [4]: Layer I, wave equation:
Fig. 1. Three-layer
model.
63
X Dong, G. Feng / Sensors and Actuoton Ii 24-25 (1995) 6264
Considering Eqs. (1.3), (X3), (III.3) yields
particle displacement: u = [A expfjk,z) +B exp( - jk,z)] exp(j~8)
(1.2)
where k,-o(pqI&J1’2
(04zcIJ
(1.3)
Layer Ii, wave equation:
@z&z=
(II.l)
(~~/~~}~~~/~fZ)
particle displacement:
tat&l,)
u = [C cxp&z) +D exp( - jk,z)] exp(jwt)
=- 2
tan&Z,- 012)
(11.2)
where
(9)
kf = m(p&.#n
(Z,
(II.3)
Since
Layer III, wave equation:
(111.1))
a%W= (fi/71J(aZi/af)
Since shear vibration will be damped rapidly in the fluid layer, the reflected wave from z=l,f 1,-tIL can be neglected. Therefore, the particle displacement velocity can be expressed as v=au/at=E
exp(-i,z)
exp(jwt)
Af=-
where ~,_=(1tj)kL=(1+j)[w&(2~L)]1n (I,+f,
(111.3)
The bounds conditions are (1) at r=O, the shear stress is equal to zero; (2) at z=Z, and z=i,+&, the particle d~placement, velocity and shear stress are mathematically continuous. Then five equations containing five unknowns can be obtained as A=8 A expcjk,i,) 48
Using f instead of w,
(III.2)
(1)
exp( - jk,l,)
= C exp(jk&,)t D exp( - jk,Z,)
(2)
= CktFf exptjk&J --Dkaf exp( -jk&,)
(3)
Cjw expIjk& +I,)] f Djw exp[ -jk,(l, +&)I =E exp[-$(I,+&)]
(4)
explik& +4)1- Witr exp[-$#, +L>l = - LLqLEexp[ - jL& t IS]
(5)
Cj&
0
Eq. (11) represents the relationship between the surface situation and frequent shift of the qua~~~stal resonator. It can be found that Af consists of two factors
Af=Afm+Afi_
02)
where Afm is caused by the mass increment of solid layer II. Especially, AL = -2&.f0%,~Y2=
-
2~~~/[~(f~~~)'~l
It can easily be found that Afmis just the same as Eq. (1) (when n=l.), i.e., when the effect of q,_ can be neglected, Eq. (11) is just the same as Eq. (1). On the other hand, ML=
Ak,pq ewfI_ik,4)-~kq~q exp(-jk&
-M-f+%.)lnf~” (pqpq)l/2
112 -f~3~I~~~/~~~~~~~l
is mainly dependent upon the density pr and generalized viscosity Q_ of layer III. Since qL is related to many sophisticated factors, quantitative calculation of AfL is almost impossible. However, it is known that when the amount of surface sorption is large enough, AfL will be great enough to affect Af so that Eq. (1) will not be applicable.
From Eqs. (l)-(5), we get 3. ~x~rirn~n~s and analysis One quay-c~stal resonator is coated with different thicknesses of the same absorbant material. Its frequen~-humidi~ characters arc tested and listed in Table 1, where no absorbent material is coated in A,
y. Dong, G. Feng I Sensors and Actuators B 24-25 (1995) 62-64
64
Table 1 Frequency-humidity Relative
characteristics
(3) when the sorption further increases, the sensitivity will not increase, but decreases (curve D) and even ‘reverses’, reflecting that AfL has become the main factor of AJ
(Hz)
20
35
60
75
96
3582149 3581546 3581481 3580544 3579191
3582146 3581401 3581289 3580375 3578917
3.582140 3581256 3581110 3580232 3578938
3582144 3581006 3580842 3580095 3579080
3582140 3580617 3580484 3579900 3579182
humidity (RH %) A B C D E
0 A
I” .L
-200
;=r ._c v,
- 400
0” -600 : zi
4. Discussion and conclusions (1) A three-layer model theory is presented in this paper. It can be found that coated/uncoated quartzcrystal resonators can all be generalized by such a mechanical model. Thus this theory can be widely applied to sensors constructed with quartz-crystal resonators. (2) Since physical adsorption is usually multimolecular, speaking theoretically, the amount of absorbate (water vapour or other gases) absorbed on the surface has an optimum value. If this amount is dependent upon the thickness of coated absorbent material (as in the humidity sensor mentioned in this paper), the coated thickness has an optimum value that will lead to an optimum sensor characteristic.
-800
Acknowledgements g 2 -1000
-1200:
This work is financially supported by the Fund of National Natural Sciences ,of China. 0
I
20
I
I
40
60
I
80
1
RHw Fig. 2. Af-humidity
sensitivity curves.
and an increasing thickness of absorbent is coated in B, C, D and E. Taking RH = 20% as the basic frequencyf,, sensitivity curves are represented in Fig. 2. It can be found that: (1) when no absorbent is coated (curve A), Af is only slightly affected by humidity; (2) as the thickness of coated material increases, surface sorption increases and a high sensitivity is obtained (curves B and C).
References A. We&r, Humidiry and Moisture, Vol. 1, Reinhold, New York, 1965, pp. 578-583. PI G. Sauerbrey, Verwendung van Schwingquarzen zur Wagung diinner Schichten und zur Mikrowagung, Z. Phys., 155 (1959) 206-222. 131 M.R. Deakin and D.A. Buttry, Electrochemical applications of the quartz crystal microbalance, AnaL Chim. C/rem., 61 (1989) 1147-1154k [41 K.K. Kanazawa and J.G. Gordon, The oscillation frequency of a quartz resonator in contact with a liquid, Anal. Chim. Acta, 175 (1985) 99-105.
PI
mum B
Sensors
and Actuators
CHEMICAL
B 24-25 (1995) 62-64
Effects of surface physical sorption on characteristic quartz-crystal humidity sensor
of coated
Yonggui Dong, Guanping Feng Deportment of PrecisionInstrument and Mechanolqy, Tsinghua Univemity,Beijing 100084, China
Abstract A three-layer mechanical model, which consists of a quartz layer, a solid film layer and a fluid-phase film layer, is presented and a formula is deduced for calculating the relationship between the surface state and frequency shift of a quartz-crystal resonator. The theory has been used to analyse the characteristic of a resonant humidity sensor using a coated quartz-crystal resonator. Experiments prove that the new deduced formula gives better agreement with experimental results than Sauerbrey’s formula. Furthermore, the three-layer theory can be widely used in developing sensors constructed with quartz-crystal resonators. Keywords Humidity
sensor; Quartz-crystal
resonator;
Surface sorption
1. Introduction
After King constructed a ‘piezoelectric sorption detector’ [l], more and more humidity-gas sensors have been developed using AT-cut quartz-crystal resonators vibrating in the thickness-shear mode. The principle is mainly based upon Sauerbrey’s formula [2,3]:
where Am = mass of substances absorbed on the surface, Af= shift of frequency. When the sorbed layer can be regarded as a solid phase, no doubt Eq. (1) is appropriate. However, in the case of physical sorption, like that of water molecules, surface sorption of vapour is almost definitely multimolecular. When the sorbed amount reaches a certain extent, an ‘almost liquid’ layer will be formed. As shear vibration will be damped rapidly in this layer, Eq. (1) is no longer applicable. In this paper, a three-layer mechanical model is presented and a new formula is deduced for calculating the relationship between the state and frequency shift of a coated quartz-crystal resonator. This three-layer theory can not only be used in analysing and developing the characteristics of humidity sensors as mentioned in this paper, but can also be generally applied to those sensors constructed from AT-cut quartz-crystal resonators. 09254OOS/9S/$O9.50 8 1995 Elsevier Science S.A. All rights reserved S.SDI 0925-4005(94101316-A
2. Principles While a coated quartz-crystal resonator is vibrating in ambient air (assuming only one surface is in contact with the ambient air), it can be simplified as the threelayer model shown in Fig. 1, where layer I consists of the quartz crystal (including the lower electrode), layer II consists of the upper electrode and absorbentiabsorbate materials that can be regarded as solid phase and layer III is regarded as a pure fluid layer where shear vibration will be damped rapidly. When a bulk-shear acoustic wave has been generated by piczoelectricity inside the resonator, let u = particle displacement, v = particle displacement velocity (V = au/ at) and p, p, q represent density, shear modulus and generalized viscosity, respectively. The following equations can easily be found [4]: Layer I, wave equation:
Fig. 1. Three-layer
model.
63
X Dong, G. Feng / Sensors and Actuoton Ii 24-25 (1995) 6264
Considering Eqs. (1.3), (X3), (III.3) yields
particle displacement: u = [A expfjk,z) +B exp( - jk,z)] exp(j~8)
(1.2)
where k,-o(pqI&J1’2
(04zcIJ
(1.3)
Layer Ii, wave equation:
@z&z=
(II.l)
(~~/~~}~~~/~fZ)
particle displacement:
tat&l,)
u = [C cxp&z) +D exp( - jk,z)] exp(jwt)
=- 2
tan&Z,- 012)
(11.2)
where
(9)
kf = m(p&.#n
(Z,
(II.3)
Since
Layer III, wave equation:
(111.1))
a%W= (fi/71J(aZi/af)
Since shear vibration will be damped rapidly in the fluid layer, the reflected wave from z=l,f 1,-tIL can be neglected. Therefore, the particle displacement velocity can be expressed as v=au/at=E
exp(-i,z)
exp(jwt)
Af=-
where ~,_=(1tj)kL=(1+j)[w&(2~L)]1n (I,+f,
(111.3)
The bounds conditions are (1) at r=O, the shear stress is equal to zero; (2) at z=Z, and z=i,+&, the particle d~placement, velocity and shear stress are mathematically continuous. Then five equations containing five unknowns can be obtained as A=8 A expcjk,i,) 48
Using f instead of w,
(III.2)
(1)
exp( - jk,l,)
= C exp(jk&,)t D exp( - jk,Z,)
(2)
= CktFf exptjk&J --Dkaf exp( -jk&,)
(3)
Cjw expIjk& +I,)] f Djw exp[ -jk,(l, +&)I =E exp[-$(I,+&)]
(4)
explik& +4)1- Witr exp[-$#, +L>l = - LLqLEexp[ - jL& t IS]
(5)
Cj&
0
Eq. (11) represents the relationship between the surface situation and frequent shift of the qua~~~stal resonator. It can be found that Af consists of two factors
Af=Afm+Afi_
02)
where Afm is caused by the mass increment of solid layer II. Especially, AL = -2&.f0%,~Y2=
-
2~~~/[~(f~~~)'~l
It can easily be found that Afmis just the same as Eq. (1) (when n=l.), i.e., when the effect of q,_ can be neglected, Eq. (11) is just the same as Eq. (1). On the other hand, ML=
Ak,pq ewfI_ik,4)-~kq~q exp(-jk&
-M-f+%.)lnf~” (pqpq)l/2
112 -f~3~I~~~/~~~~~~~l
is mainly dependent upon the density pr and generalized viscosity Q_ of layer III. Since qL is related to many sophisticated factors, quantitative calculation of AfL is almost impossible. However, it is known that when the amount of surface sorption is large enough, AfL will be great enough to affect Af so that Eq. (1) will not be applicable.
From Eqs. (l)-(5), we get 3. ~x~rirn~n~s and analysis One quay-c~stal resonator is coated with different thicknesses of the same absorbant material. Its frequen~-humidi~ characters arc tested and listed in Table 1, where no absorbent material is coated in A,
y. Dong, G. Feng I Sensors and Actuators B 24-25 (1995) 62-64
64
Table 1 Frequency-humidity Relative
characteristics
(3) when the sorption further increases, the sensitivity will not increase, but decreases (curve D) and even ‘reverses’, reflecting that AfL has become the main factor of AJ
(Hz)
20
35
60
75
96
3582149 3581546 3581481 3580544 3579191
3582146 3581401 3581289 3580375 3578917
3.582140 3581256 3581110 3580232 3578938
3582144 3581006 3580842 3580095 3579080
3582140 3580617 3580484 3579900 3579182
humidity (RH %) A B C D E
0 A
I” .L
-200
;=r ._c v,
- 400
0” -600 : zi
4. Discussion and conclusions (1) A three-layer model theory is presented in this paper. It can be found that coated/uncoated quartzcrystal resonators can all be generalized by such a mechanical model. Thus this theory can be widely applied to sensors constructed with quartz-crystal resonators. (2) Since physical adsorption is usually multimolecular, speaking theoretically, the amount of absorbate (water vapour or other gases) absorbed on the surface has an optimum value. If this amount is dependent upon the thickness of coated absorbent material (as in the humidity sensor mentioned in this paper), the coated thickness has an optimum value that will lead to an optimum sensor characteristic.
-800
Acknowledgements g 2 -1000
-1200:
This work is financially supported by the Fund of National Natural Sciences ,of China. 0
I
20
I
I
40
60
I
80
1
RHw Fig. 2. Af-humidity
sensitivity curves.
and an increasing thickness of absorbent is coated in B, C, D and E. Taking RH = 20% as the basic frequencyf,, sensitivity curves are represented in Fig. 2. It can be found that: (1) when no absorbent is coated (curve A), Af is only slightly affected by humidity; (2) as the thickness of coated material increases, surface sorption increases and a high sensitivity is obtained (curves B and C).
References A. We&r, Humidiry and Moisture, Vol. 1, Reinhold, New York, 1965, pp. 578-583. PI G. Sauerbrey, Verwendung van Schwingquarzen zur Wagung diinner Schichten und zur Mikrowagung, Z. Phys., 155 (1959) 206-222. 131 M.R. Deakin and D.A. Buttry, Electrochemical applications of the quartz crystal microbalance, AnaL Chim. C/rem., 61 (1989) 1147-1154k [41 K.K. Kanazawa and J.G. Gordon, The oscillation frequency of a quartz resonator in contact with a liquid, Anal. Chim. Acta, 175 (1985) 99-105.
PI