Maximum separation-distance for a separated-electrode piezoelectric sensor: application to the determination of cationic surfactant adsorbed onto quartz surface

Sensors and Actuators B 50 (1998) 253 – 258

Maximum separation-distance for a separated-electrode piezoelectric sensor: application to the determination of cationic surfactant adsorbed onto quartz surface Dazhong Shen a,*, Qi Kang b, Yanhui Xue b, Lingxin Chen a, Lizeng Wang a a

b

Chemistry College, Shandong Uni6ersity, 250100 Jinan, People’s Republic of China Shandong Institute of Mining and Technology, 270019 Taian, People’s Republic of China

Received 17 November 1997; received in revised form 15 June 1998; accepted 18 June 1998

Abstract In a separated-electrode piezoelectric sensor (SEPS), the two excitation electrodes are separated by solution layers. The oscillation ability of the SEPS depends obviously on the separation-distance between the two excitation electrodes. In a given solution, there is a maximum separation-distance (Dmax) for the SEPS. If the separation-distance is \ Dmax, operation of the SEPS is not stable or even ceases to oscillate. The dependence of Dmax value on conductivity of solution was investigated and explained. The SEPS was applied for the determination of the adsorption density of dicetyldimethyl-ammonium bromide onto quartz surface. © 1998 Elsevier Science S.A. All rights reserved. Keywords: Piezoelectric sensor; Quartz crystal; Adsorption; Surfactant

1. Introduction

2. Experimental

A normal piezoelectric sensor comprises a thin vibrating AT-cut quartz crystal disc with two excitation electrodes deposited on its surfaces. The electrodes provide an alternating electric field, which induces a shear vibration of the quartz crystal with resonant frequencies in the megahertz (MHz) region. Recently, a type of separated-electrode piezoelectric sensor (SEPS) was reported [1–5]. In this type of piezoelectric sensor, the excitation electrode is separated from the quartz disc by a liquid layer. This configuration offers the advantage of long lifetime of the sensor. As the high-frequency alternating electric field is applied to the quartz disc through the liquid layer, the oscillational ability of the SEPS depends greatly on the electric properties of the liquid layer. To use the SEPS more efficiently, its oscillational ability, described by the maximum separation-distance between the two separated-electrodes was investigated in this paper. The SEPS was applied to determine the amount of cationic surfactant adsorbed onto quartz surface.

2.1. Apparatus and reagents

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The configuration of the SEPS used in the oscillational ability experiment was described in Fig. 1. A 5 MHz AT-cut blank piezoelectric quartz crystal disc (diameter 12.5 mm, Beijing No 707 Manufactory) was fixed between two glass tubes (internal diameter 10 mm, external diameter 14 mm) with silicone resin. The solu-

Fig. 1. Schematic diagram of the SEPS system in oscillational ability experiment. A, oscillator amplifier; B, frequency counter; C, piezoelectric quartz crystal disc; D1, D2, detection cell; E, separatedelectrode.

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tions in the two detection cells were insulated for a direct current signal. Two platinum disc electrodes with diameter 8 mm were used as the separated-electrodes. The platinum electrodes are concentric with the quartz disc, and their leading wires were short as possible. The two leading wires were physically fixed with a parallel distance of :10 cm. A TTL oscillator designed and built at the Shandong Institute of Mining and Technology (by the author) was employed to drive the SEPS, its oscillating frequency being recorded by a frequency counter (Model 7200, Shijiazhuang No 4 Radio Factory). An impedance analyser (HP 4192A) was used to measure the equivalent circuit parameters of the solution and the quartz crystal. All the experiments were performed at room temperature of 25°C. Each experiment was carried out three times and the averaged value is reported. All chemicals were of analytical-reagent grade. Solutions were prepared in doubly quartz-distilled water. Dicetyldimethyammonium bromide (DCAB) was recrystallised from an acetone – ethanol mixture and its purity confirmed by surface tension measurement.

2.2. Adsorption of dicetyldimethyammonium bromide on quartz surface In the adsorption experiment, the detection cells of the SEPS were made of Teflon. Cell 1, volume : 2 ml, was filled by 1 mol l − 1 KCl solution. Cell 2, volume : 50 ml, was used for the adsorption measurement. The distance between the separated-electrode and the quartz disc was :2 mm. Before the determination of adsorption, the quartz crystal disc surface in cell 2 was cleaned carefully using chromic – sulfuric acid mixture, 1:1 (by volume) hot HCl for at least ten times, then rinsed repeatedly with water. Then 40 ml phosphate buffered saline (PBS, pH 7, 0.01 mol l − 1 phosphate, 0.15 mol l − 1 NaCl) was put into cell 2. The platinum grid electrode was put into the cells. Under the condition of mild stirring, the stable oscillating frequency, F1, was recorded. An accurate amount of DCAB stock solution (prepared with PBS and its conductivity was adjusted to be the same as that of the buffer by adding NaCl or water), was added to cell 2 with a microsyringe. The stable oscillation frequency, F2, was recorded again. The frequency shift, DF =F2 −F1, was used for the calculation of adsorption density.

3. Results and discussion

3.1. Maximum separation-distance for the SEPS The KCl test solution with known conductivity was introduced into the detection cells in the SEPS. The distance between the two separated-electrodes was in-

creased gradually. In low conductivity solutions, the SEPS ceases to oscillate suddenly when the separationdistance is greater than a critical value. This critical separation-distance is recorded as the maximum separation-distance (Dmax). If the separation-distance is larger than the Dmax value, the SEPS will cease to oscillate. In this case, the oscillating frequency of the oscillator is far beyond the fundamental frequency of the quartz crystal and the frequency stability is rather poor (DF \ 95 kHz). In fact, a parasitic oscillation of the oscillator was monitored by the frequency counter under such situation. As the Dmax is the sum of the maximum separationdistance in cell 1 (D1max) and in cell 2 (D2max), the maximum separation-distance in two cells is related to each other. The larger the D1max value, the smaller D2max can be. But the value of (Dmax = D1max +D2max) was nearly constant under our experimental conditions for a given solution. For example, the mean of ten Dmax values in water with D1max ranging from 0.5 to 2.5 cm is 3.08 cm. The relative S.D. for the ten Dmax values is 7.3%. In intermediate conductivity solutions, the frequency stability of the SEPS decreases as the separation-distance increases. To obtain a frequency stability desired, there is also a maximum separation-distance for the SEPS. In this paper, the separation-distance corresponding to the frequency stability of DF : 9 10 Hz is recorded as the Dmax value. As the Dmax value remains constant in a given solution condition, the value of Dmax is used to describe the oscillational ability of the SEPS in this paper. The greater the value of Dmax, the better the oscillational ability of the SEPS.

3.2. Dependence of Dmax on solution conducti6ity As shown in Fig. 2, the Dmax values depend obviously on the conductivity of the solution. With increasing conductivity in low conductivity solutions, the Dmax values increase slightly, the oscillational ability of the SEPS is improved. In an intermediate conductivity solution, however, there is a minimum for the Dmax value, the oscillation ability of the SEPS becomes the weakest. In high conductivity solutions, the Dmax values increases obviously with increasing conductivity, the oscillational ability of the SEPS increases. This result may be explained below.

3.3. Deri6ation of the oscillational condition for the SEPS As discussed previously [4], the electric behaviour of the SEPS in Fig. 1 can be described by the equivalent circuit model in Fig. 3. For simplicity of treatment, the equivalent circuit of the SEPS is shown in the reduced form of Fig. 4. The impedance of SEPS, Z, is given by

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Fig. 4. Equivalent circuit for the SEPS.

the phase of impedance, the following equation is obtained for the SEPS:



 

1 M CO Rq − =b + RS 2 2 2 vCO M + N CS M +N2

Fig. 2. Dependence of the maximum separation-distance and the corresponding effective quality factor of the SEPS on conductivity in KCl solutions.

Z = RS +





Rq j M C + −1 − O 2 2 2 2 vCO M +N M +N CS

(1) (2)

1 vC1 vC2 = 2 + 2 2 2 vCS G 1 +v C 1 G 2 +v 2C 22

(3)

where M = 1+ CO/Cq −v 2LqCO, N =RqvCO, j=

− 1. CO, Cq, Lq and Rq are the static capacitance, motional capacitance, motional inductance and motional resistance, respectively. G1 =1/R1 =A1k /D1, C1 =oA1/ D1, G2 = 1/R2 =A2k /D2, C2 = oA2/D2, v =2pF. F is the oscillation frequency of the SEPS, k and o are the conductivity and permittivity of the solution, respectively. In the oscillation frequency measurement, the SEPS is connected between the input and output of the amplifier used in the oscillator (see Fig. 1). The SEPS provides the positive feedback needed for the oscillator and determines its oscillation frequency. According to the phase shift condition of the oscillation, if the impedance of the amplifier has a phase of u, the phase of the impedance of the SEPS must be −u. According to the definition of

(4)

where b= tan u is a parameter related to the phase of oscillator, which depends on the type of oscillator and its operating conditions. The typical b value for the oscillator used in this paper is 1.18. Eq. (4) is rewritten as: PM 2 − M+PN 2 − bN = 0 P=1+

G G RS = 2 1 2 2 + 2 2 2 2 G 1 + v C 1 G 2 +v G 2



(5)

vCO(vC1 − bG1) vCO(vC2 − bG2) + G 21 + v 2C 21 G 22 + v 2C 22

(6)

In Eq. (4), M is the variable that determines the oscillating frequency of the SEPS. As M is a real number, the following condition must be satisfied in Eq. (5): 1+ 4bPN − 4P 2N 2 ] 0

(7)

Based on Eq. (7), we have: (b− 1 + b 2)52PN 5 (b+ 1 + b 2). Because of N\ 0, P\ 0, the oscillational condition for the SEPS is obtained. P5 (b+ 1 + b 2)/2N

(8)

With the same test solution filled in cell 1 and 2 in the SEPS, the oscillation condition can be expressed as: 1+



D1 D2 + A1 A2



n

vCO(vo− bk) b+ 1 +b 2 5 k 2 + v 2o 2 2N

(9)

Under our experimental conditions, A1 : A2 = A, Eq. (9) is rewritten as (D1 + D2)5





b+ 1 + b 2 −1 2N

n

A(k 2 + v 2o 2) vCO(vo− bk)

(10)

Eq. (10) reveals that there is a maximum separationdistance (D1max + D2max) for the SEPS. The maximum separation-distance is related to the conductivity of the solution. In low conductivity solution such as pure water, k vo, we may have Dmax = Ao(b+ 1 +b 2)/2vRqCO2

(11)

By using the values of A= 0.6 cm , o= 78oo, oo = 8.854× 10 − 14 F/cm, b= 1.18, F= 5×106 Hz, Rq =420 V, CO = 12.2× 10 − 12 F, the Dmax value in Eq. (11) is 2.69 cm, which is in good agreement to the experimentally measured value. 2

Fig. 3. Equivalent circuit for the SEPS. C1, C2, solution capacitance; R1, R2, solution resistance; CO, Lq, Rq, Cq, static capacitance, motional inductance, motional resistance and motional capacitance of the quartz crystal.

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As shown in Eq. (10), the Dmax value increases with increasing conductivity, which is supported by the experimental results in low conductivity solutions. However, as can be seen in Fig. 2, the Dmax value decreases as the conductivity increases when k \0.01 S m − 1. And there is a minimum value for Dmax in a solution with conductivity of :0.05 S.m − 1. Then Dmax value increases with increasing conductivity again. This contradictory result suggests that other oscillational condition except Eq. (7) should be taken into account to set up a stable oscillation for the SEPS in intermediate conductivity solutions. As discussed previously [4], the frequency stability of a piezoelectric sensor can be described by an effective quality factor (Qe). In this paper, the Qe value of the SEPS with Dmax was measured according to the impedance analysis method [4]. As can be seen in Fig. 2, the corresponding Qe value of the SEPS is fairly high in low conductivity solutions, it decreases to : 300 in intermediate conductivity solutions. Hence, the need in frequency stability for the SEPS is considered. It can be seen from Fig. 4 that the frequency stability of the SEPS is effected mainly by Rq and RS. Rq represents energy loss due to acoustic impedance by the oscillating quartz disc surface into liquid. RS represents the energy loss arising from the heat motion of ions in conducting the high-frequency alternating electric field through the solution layers. The larger the Rq or RS value, the poorer the frequency stability of the SEPS. As the Rq value is dependent on the viscosity and density of the liquid and it is nearly constant in aqueous solutions, the frequency stability of the SEPS is related mainly to RS value. With the same test solution filling the two cells, the RS values can be expressed as: RS =



D1 +D2 A





k k +v 2o 2 2

(12)

It can be seen that the RS value is proportional to the separation-distance. Hence, the frequency stability of the SEPS decreases as the separation-distance increases. As shown Eq. (12), the RS values depends significantly on the solution conductivity. For example, in low conductivity solutions, i.e. k vo, the RS value is small, the frequency stability of the SEPS is effected mainly by Rq. As the Qe values are fairly high, the Dmax values are determined by Eq. (8). However, as the conductivity increases, RS value increases, the Qe values and frequency stability of the SEPS decrease. When the Qe values decrease to : 300, which corresponds to a frequency stability of 9 10 Hz, the Dmax values are determined by the need for frequency stability. Because RS has its maximum in a solution with k = vo, there is a minimum for Dmax in an intermediate conductivity solution nearby. As the RS value decreases with increasing

conductivity if k\ vo, the Dmax value increases again. In highly conductive solutions, the solution acts approximately like a wire, the separation-distance can be much larger, thus the SEPS possess a strong oscillational ability. For example, the stable oscillation of the SEPS is still obtained even with the separation-distance between a two separated-electrodes being as far as 30 cm in 1 mol l − 1 KCl solution.

3.4. In situ determination of surfactant absorbed on quartz surface by the SEPS method One of the characteristic features of surfactants is their tendency to adsorb at interfaces in an oriented fashion. The adsorption of surfactant molecules at solid–liquid interfaces underpins their widespread use in various technologies [6]. Ellipsometry [7], surface plasmon resonance and quartz crystal microbalance [8], spectroscopic methods [9], neutron reflection technique [10] have all been used for the quantitative analysis of the adsorbed layers. In the SEPS, the quartz surface is in a direct contact with the solution. The ease of measuring the oscillating frequency of the SEPS with high precision has made it an extremely useful tool for monitoring minute change in mass associated with the deposition or loss of a foreign material from the quartz surface. According to Fuerstenau [11], the quartz surface is charged negatively and can adsorb cationic surfactants. Hence, the SEPS was employed to determine the adsorption amount of surfactant onto quartz surface. The principle of this method is simple. When surfactant is adsorbed onto the quartz surface, the mass load of the quartz crystal increases, which will cause a decrease in the frequency of the SEPS. Thus the adsorption amount can be in situ monitored by the frequency change of the SEPS. According to the Sauerbrey’s equation [12], we have G= DF/2.26× 10 − 6F 2o

(13)

where symbol G is the adsorption density in g cm , DF the frequency shift in Hz, Fo the fundamental frequency of the quartz crystal in Hz. As the frequency of the SEPS is also effected by the conductivity of the solution, it is very important to eliminate the influence of a variation in conductivity on the measurement of the frequency shift in the adsorption experiment. In this paper, the stock solution of DCAB has the same conductivity as the buffer, thus the conductivity in cell 2 is not effected by the addition of DCAB. In addition, buffer of high ion strength is used, as the frequency of a SEPS is insensitive to a variation in conductivity in solutions of high conductivity [5]. As mentioned above, the high conductivity is also helpful in improving the oscillational ability of the SEPS. As shown in Fig. 5, the frequency of SEPS decreases upon injection of DCAB. The decrease in the frequency is due to the adsorption of DCAB onto the surface of −2

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conductivity of solution. In low conductivity solutions, the oscillational ability of the SEPS increase slightly with conductivity. However, the oscillational ability becomes the weakest in an intermediate conductivity solutions. The SEPS has strong oscillational ability in highly conductive solutions. The adsorption process of DCAB on quartz surface from solution was monitored in situ by the SEPS method.

Acknowledgements This work is supported by funding from the National Science Foundation of China and the Go Beyond the Century Foundation of Shandong University. Fig. 5. Frequency changes as a function of time for the adsorption of DCAB onto quartz surface. [DCAB] = 8× 10 − 5 mol l − 1.

References

Fig. 6. Adsorption isotherms of DCAB onto quartz crystal surface.

the quartz crystal in the SEPS. The adsorption process is finished in 4 min for a DCAB solution of 8× 10 − 5 mol l − 1. The rate of the adsorption increases as DCAB concentration increases. Fig. 6 shows the adsorption isotherms of DCAB. With increasing DCAB concentration, the adsorption density increases rapidly in DCAB solution of low concentration. Exceeding a concentration of 2×10 − 5 mol l − 1, a slight increase in adsorption density is observed.

4. Conclusions The oscillational ability of the SEPS, described by the maximum separation-distance, is related to the

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Biographies Dazhong Shen received a B.Sc. in analytical chemistry from Chengdu Institute of Geology in 1983. After spending 5 years as a teaching assistant in Shandong Institute of Mining and Technology, he earned a Ph.D. in analytical chemistry from Hunan University in 1994. Since June 1994, he has been an associate professor in Chemistry College, Shandong University. His research interests include electroanalytical chemistry and chemical sensors, especially piezoelectric sensors. Qi Kang received a B.Sc. in analytical chemistry from Shandong University in 1984. Since July 1984, she works in Shandong Institute of Mining and Technology. She earned an M.Sc. in organic chemical engineering from China University of Mining and Technology in 1996. She became an associate professor in December 1996. Her research interests include organic and analytical chemistry.

.

Yanhui Xue received a B.Sc. in analytical chemistry from Chendgu Institute of Geology in 1983. After spending 12 years as engineer assistant and engineer in Team for Svlvite of Chemistry Industry Ministry, he became a lecturer in Shandong Institute of Mining and Technology in 1995. His research interest is analytical chemistry. Lingxin Chen received a B.Sc. in chemistry from Shandong Institute of Education in 1997. Now he is a graduate student in Chemistry College, Shandong University. Lizeng Wan received a B.Sc. in chemistry from Shandong University in 1964. Since then she works in Shandong University. She has been an associate professor in Chemistry College, Shandong University, since 1990. Her research interest is electroanalytical chemistry.