Frequency-temperature coefficient of an electrode-separated piezoelectric sensor in the liquid phase

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Journal of Electroanalytical Chemistry 387 (1995) 23-28

Frequency-temperature coefficient of an electrode-separated piezoelectric sensor in the liquid phase Yuanjin Xu, Dazhong

Shen, Qingji Xie, Lihua Nie, Shouzhuo

Yao

*

Department of Chemistry and Chemical Engineering, Human UnicersiO,, Changsha, 410082, People's Republic of China Received 27 September 1994; in revised form 28 November 1994

Abstract

The frequency-temperature coefficient of an electrode-separated piezoelectric sensor (ESPS) was derived theoretically and verified experimentally over the temperature range 10-50°C. The frequency-temperature coefficient of an ESPS in an electrolyte solution is strongly dependent on the conductivity of the solution. A near-zero frequency-temperature coefficient can be obtained under certain solution conditions. In a non-electrolyte solution, the frequency-temperature coefficient of the ESPS is similar to that of a normal quartz crystal microbalance.

Keywords: Frequency-temperature coefficient; Piezoelectric sensor

1. Introduction Piezoelectric quartz crystal microbalances (QCMs) are widely used to respond to the mass loading on the electrode surface of a quartz crystal in a vacuum [1]. Since the beginning of the 1980's, increasing attention has been paid to the operation of QCMs in the liquid phase [2-8]. Piezoelectric sensors used in chemical applications usually consist of a thin vibrating AT-cut quartz wafer sandwiched between two metal excitation electrodes. However, a type of electrode-separated piezoelectric sensor (ESPS) has recently been described [9] in which the electrode is removed from the surface of the quartz crystal and the space is filled with liquid. The computation of the equivalent circuit parameters [10,11] and the oscillation frequency characteristic of the ESPS [12,13] have been discussed. Applications based on the mass effect of the ESPS have been reported [13-16]. To apply the ESPS efficiently, it is useful to investigate the f r e q u e n c y - t e m p e r a t u r e coefficient of the

* Corresponding author. 0022-0728/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved SSDI 0 0 2 2 - 0 7 2 8 ( 9 5 ) 0 3 8 5 6 - 2

ESPS systematically, as the properties of the liquid are temperature dependent. The influence of the solution temperature on the oscillation frequency of the ESPS has been reported for a 0.1 M KCI solution [13]. However, the effect has not been investigated in other solutions. In the work reported in this paper, the f r e q u e n c y - t e m p e r a t u r e coefficient of the ESPS was investigated systematically over the temperature range 10-50°C.

2. Experimental

2.1. Apparatus and chemicals An impedance analyser (Hewlett Packard model 4192A) was used to measure the resonant frequency of the ESPS. AT-cut 9 MHz piezoelectric crystals (diameter 12.5 ram) were obtained commercially. The configuration of the ESPS used in this work is shown in Fig. 1. The separated electrode was constructed by attaching a platinum disc of diameter 6 m m and thickness 1 m m to one end of a ground glass tube with silicone resin. The solution temperature was controlled to +0.1°C by a thermostatic water jacket.

Y Xu et al. /Journal of Electroanalytical Chemistry 387 (1995) 23-28

24

Analytical grade chemical reagents and double-distilled water were used throughout.

60 I

2.2. Procedure

30-

The test solution was introduced into the detection cell and the solution temperature was controlled by the water jacket. The lead wires of the piezoelectric sensor were connected to the impedance analyser by means of a high frequency test fixture. After temperature equilibrium had been achieved, the conductance of the ESPS was scanned as a function of frequency within the resonant frequency range of the quartz crystal. The measuring frequency corresponding to the maximum conductance was taken as the resonant frequency of the ESPS.

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3. Results and discussion

As discussed previously [10], the resonant frequency of the ESPS is given by

w2Cl(C ~ - GRICo) F=F o 1+ 2[G2+wZC~(C~+Co) ]

(1)

where w = 2~-Fo, F 0 = 1 / 2 % / L t C I , is the resonant frequency of the normal QCM, and L 1 = 10 mH, CI =

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3.1. Frequency-temperature coefficient in electrolyte solution

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Fig. 2. Theoretical relationship between the frequency temperature coefficient and the conductivity at 25°C: (l) aF0/fIT; (2) (aF/aCs)(dC ~/dT); (3) (aF/OG)(dG /dT); (4) d F/dT.

0.03 pF, R l = 1 0 2 - 1 0 3 ~Q depending on the density and viscosity of the liquid and C 0 = 10 pF are the motional inductance, motional capacitance, motional resistance and static capacitance of the crystal respectively. G = kK is the solution conductance, C~ = ke + Cp is the solution capacitance, K and • are the conductivity and permittivity of the solution respectively, k is the cell constant of the ESPS, which is related to the area of the separated electrode and the distance between the separated electrode and the crystal, and Cp is the parasitic capacitance between the lead wires. As can be seen in Eq. (1), the resonant frequency of the ESPS depends on the conductivity and permittivity of the solution. In addition, the value of R I is related to the density and viscosity of the solution. Therefore the resonant frequency also depends on the density and viscosity of the solution. According to the Eq. (1), the effect of the solution temperature on the resonant frequency, i.e. the f r e q u e n c y - t e m p e r a t u r e coefficient d F / d T , is given by

dF

OFo

dT

OT

OF dG

OF d Q

+ -OG dT 0C~ d T

(2)

where

13 Fig. 1. Configuration of the ESPS: A, water jacket; B, detection cell; C, piezoelectric quartz crystal; D, silver electrode of normal QCM and lead wire; E, separated electrode.

aF

2"n'2Fq~Cl[RlW2CsCo(Co + Cs)+ 2GC s G2RICo]

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(3)

OF

2rr2F~C, [G 2 + w2RtGCo(Co + 2C~) - w2C~]

ac,

[G 2 + wZc~(co + C~)] 2 (4)

Y. Xu et al. /Journal of Electroanalytical Chemistry 387 (1995) 23-28

and aFo/aT is the f r e q u e n c y - t e m p e r a t u r e coefficient of the the normal QCM. It is caused by changes in solution density and viscosity with t e m p e r a t u r e as well as the f r e q u e n c y - t e m p e r a t u r e coefficient of the quartz crystal itself [2]. The terms (aF/aG)(dG/dT) and (aF/aC~)(dCs/dT) are due to changes in solution conductivity and permittivity respectively with temperature. The theoretical correlation between the frequencytemperature coefficient of the ESPS and the solution

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Temperature/°C Fig. 4. Dependence of the frequency-temperature coefficient of the ESPS on the cell constants in 3 × 10 3 M KCI solution: (1) 0.0063 m; (2) 0.0104 m; (3) 0.0154 m; (4) 0.0356 m; (5) 0.0418 m. L

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Fig. 3. (a) Dependence of the resonant frequency shift of the ESPS on the temperature in KCI solutions (k = 0.0154 m): (1) no KCI; (2) 10 4 M KCI; (3) 5 × 10 -4 M KCI; (4) 10 .3 M KCI; (5) 2 × 10 3 KC1; (6) 3 × 1 0 3 KCI; (7) 5 × 1 0 .3 KCI; (8) 7.5×10 3 KCI; (9) 2 × 1 0 2 KC1; (10) 5 × 10 .2 KCI. (b) Plots of frequency-temperature coefficients of the ESPS versus the solution temperature for the data in (a).

conductivity given by Eq. (2) is illustrated in Fig. 2 for typical sensor parameters (at 25°C). It can be seen that aFo/aT is always positive and is almost independent of the conductivity, but (aF/aG)(dG/dT) and ('OF/aC~) (dC~/dT) are significantly related to the conductivity. In a poorly conducting solution (aF/aG)(dG/dT) is very small and (aF/aCs)(dCs/dT) is positive; hence the f r e q u e n c y - t e m p e r a t u r e coefficient is positive and is determined mainly by OF~/OTand (OF/OC~)(dCJdT). Therefore, the resonant frequency of the ESPS increases with an increase in temperature. As the conductivity increases, (aF/aG)(dG/dT) tends to a negative maximum at G =wC~, and then gradually approaches zero. The behaviour of (OF/aC~)(dCJdT) is similar but the extent of variation is much less than that of the (aF/aG)(dG/dT). Thus the frequencytemperature coefficient of the ESPS in a moderately conducting solution is negative and the resonant frequency decreases with increasing solution temperature. In a highly conducting solution, the (OF/aG)(dG/dT) and (aF/aCs)(dCs/dT) are close to zero. The freq u e n c y - t e m p e r a t u r e coefficient of the ESPS, like that of the normal QCM, depends mainly on aFo/aT. Therefore the resonant frequency of the ESPS increases with increasing solution temperature again. As shown in Fig. 2, the f r e q u e n c y - t e m p e r a t u r e coefficient of the ESPS depends strongly on the solution conductivity, particularly at moderate conductivities. The frequency-temperature coefficient in a highly conducting solution is less than that in a poorly conducting solu-

E Xu et al. /Journal of Electroanalytical Chemistry 387 (1995) 23-28

26

tion. It is w o r t h noting that t h e r e a r e two n a r r o w ranges w h e r e the f r e q u e n c y - t e m p e r a t u r e coefficient is close to zero. T h e e x p e r i m e n t a l results for the effect o f solution t e m p e r a t u r e on the r e s o n a n c e f r e q u e n c y and the freq u e n c y - t e m p e r a t u r e coefficient of the E S P S in KC1 solutions are shown in Fig. 3. T h e s e results are in a g r e e m e n t with the t h e o r e t i c a l p r e d i c t i o n . T h e f r e q u e n c y - t e m p e r a t u r e coefficient of the ESPS also d e p e n d s on the cell c o n s t a n t of the ESPS. T h e f r e q u e n c y shifts of the E S P S with d i f f e r e n t cell constants in 3 x 10 -3 M KCI solution a r e illustrated in Fig. 4. Obviously, the effect of conductivity on the f r e q u e n c y - t e m p e r a t u r e coefficient of the E S P S dec r e a s e s with increasing cell constant, i.e. a large elect r o d e a r e a or a small d i s t a n c e b e t w e e n the s e p a r a t e e l e c t r o d e a n d the crystal can result in a d e c r e a s e d influence of conductivity on the f r e q u e n c y - t e m p e r a ture coefficient o f the ESPS. In the critical case w h e n G = k n ~ ~, the E S P S t r a n s f o r m s to a n o r m a l Q C M a n d the f r e q u e n c y - t e m p e r a t u r e coefficient no l o n g e r d e p e n d s on the solution conductivity.

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3.2. Frequency-temperature coefficient in a non-electrolytic solution In a n o n - e l e c t r o l y t i c solution G << wC~ a n d h e n c e the influence of the conductivity can be ignored. T h e r e f o r e Eq. (2) can be simplified to

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(b) T e m p e r a t u r e / °C Fig. 6. (a) Dependence of the resonant frequency shift of the ESPS on temperature in water+ dioxane mixtures (k = 0.0154 m) with the following relative permittivities (at 20°C): (1) 2.2; (2) 21.7; (3) 41.1; (4) 60.5; (5) 80. (b) The difference between the temperature effects on the resonant frequencies of an ESPS and a normal QCM in a 50% water+ dioxane mixture.

where OF i

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Relative p e r m i t t i v i t y Fig. 5. Theoretical relationship between the frequency-temperature coefficient and the relative permittivity in a non-electrolyte solution at 25°C: (1) dF/dT; (2) aFo/aT; (3) (3F/aC~)(dC~/dT).

0Cs -

G)C1 2(C0 q- C s ) 2

(6)

T h e t h e o r e t i c a l c o r r e l a t i o n b e t w e e n the f r e q u e n c y t e m p e r a t u r e coefficient o f the E S P S a n d the relative permittivity o f solution given by Eq. (5) is i l l u s t r a t e d in Fig. 5 for typical sensor p a r a m e t e r s (at 25°C). It can be

E Xu et al./Journal of Electroanalytical Chemistry 387 (1995) 23 28 s e e n that (OF/aCs)(dCs/dT) is always positive, like aFo/aT, b u t it is s m a l l e r t h a n aFo/OT; h e n c e the freq u e n c y - t e m p e r a t u r e coefficient o f t h e E S P S in none l e c t r o l y t e solutions is always positive and d e p e n d s m a i n l y on OFo/OT.

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Fig. 8. Dependence of the frequency-temperature coefficient of an ESPS on the cell constants in a 50% water + dioxane mixture. Cell constant/m: (1) 0.0063; (2) 0.0104; (3) 0.0154; (4) 0.0356; (5) 0.0418.

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T h e effect of the solution t e m p e r a t u r e on the reson a n t f r e q u e n c y of E S P S in w a t e r + d i o x a n e m i x t u r e s a n d glycerin solutions a r e shown in Figs. 6(a) a n d 7(a) respectively. Figs. 6(b) a n d 7(b) show the d i f f e r e n c e b e t w e e n the t e m p e r a t u r e effects on the r e s o n a n t freq u e n c y of an E S P S a n d a n o r m a l Q C M in a 50% w a t e r + d i o x a n e mixture and a 50% glycerin + w a t e r solution, respectively. It can be seen that the effects of t e m p e r a t u r e on the r e s o n a n t f r e q u e n c y of the E S P S a n d the n o r m a l Q C M are similar in n o n - e l e c t r o l y t e solutions, as p r e d i c t e d above. Fig. 8 shows the f r e q u e n c y shift of the E S P S with d i f f e r e n t cell c o n s t a n t s in a 50% w a t e r + d i o x a n e mixture. Obviously, the cell c o n s t a n t also affects the freq u e n c y - t e m p e r a t u r e coefficient of the E S P S in none l e c t r o l y t e solutions, b u t the m a g n i t u d e o f the effect is less t h a n that in e l e c t r o l y t e solutions.

4. C o n c l u s i o n s

0 ~

10

20

30

40

50

60

(b) T e m p e r a t u r e / °C Fig. 7. (a) Dependence of the resonant frequency shift of the ESPS on the temperature in glycerin +water solutions (k = 0.0154 m) with the following glycerin concentrations: (1) 0; (2) 20 wt.%; (3) 30 wt.%; (4) 40 wt.%; (5) 50 wt.%; (6) 60 wt.%; (7) 65 wt.%. (b) The difference between the temperature effects on the resonant frequencies of an ESPS and a normal QCM in a 50% glycerin+water solution.

Both t h e o r e t i c a l analysis a n d e x p e r i m e n t a l results show that the f r e q u e n c y - t e m p e r a t u r e coefficient of the E S P S d e p e n d s significantly on the s o l u t i o n conductivity in e l e c t r o l y t e solutions. T h e influence o f conductivity on the f r e q u e n c y - t e m p e r a t u r e coefficient is d e c r e a s e d if the cell c o n s t a n t of t h e E S P S is i n c r e a s e d . A small f r e q u e n c y - t e m p e r a t u r e coefficient for t h e E S P S can b e o b t a i n e d by limiting t h e solution conductivity to a n a r r o w range. In n o n - e l e c t r o l y t e solutions, the fre-

28

Y Xu et al. /Journal of Eh'ctroanalytical Chemistry 387 (1995) 23 28

quency-temperature coefficients of the ESPS and the normal QCM are similar.

Acknowledgments This work was supported by the National Science Foundation and the Education Commission Foundation of China.

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