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Analyzing the response of a contactless conductivity detector in capillary electrophoresis by a resonant method
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Chinese Chemical Letters 23 (2012) 831–834 www.elsevier.com/locate/cclet
Analyzing the response of a contactless conductivity detector in capillary electrophoresis by a resonant method Qi Kang, Qing Zhang, Yao Long Li, Dong Dong Li, Da Zhong Shen * The Key Lab in Molecular and Nano-Materials Probes of the Ministry of Education of China, School of Chemistry, Chemical Engineering and Material Science, Shandong Normal University, Jinan 250014, China Received 15 February 2012 Available online 9 June 2012
Abstract We report a resonant method to measure the wall capacitance (Cw) and solution resistance (RS) in a capacitively coupled contactless conductivity detector (C4D). Under the typical operating conditions in capillary electrophoresis (I.D. 50 mm, O.D. 360 mm, electrode length of 4 mm, electrode gap of 1 mm, frequency of 200 kHz), the values of Cw measured in 1 and 20 mmol/L NaCl solutions are 2.8 and 32 fF, which are only 1.1% and 12% of prediction by the equation in references, respectively. The value of RS is less than the prediction in solutions with k < 0.02 S/m. The response current of C4D is due to the change in Cw because the total impedance of a C4D is composed mainly by the impedance from Cw. # 2012 Da Zhong Shen. Published by Elsevier B.V. on behalf of Chinese Chemical Society. All rights reserved. Keywords: Contactless conductivity detector; Equivalent circuit parameter; Quartz crystal resonator; Resonant method
Since the works of Zemann et al. [1] and da Silva and do Lago [2] in 1998, a capacitively coupled contactless conductivity detector (C4D) has received considerable attention as an alternative detection method in capillary and microchip electrophoresis [3–8]. Although the C4D conception seems simple, to understand how it works is important for the ones who use C4D or intend to implement such a system. Compared to comprehensive applications, theoretical aspects related to the response of C4D are rare [9–15]. In this work, we propose a resonant method to measure the impedance parameters of C4D. The increase of wall capacitance (Cw) with increasing solution conductivity is reported for the first time. 1. Experimental A schematic representation of the experimental setup is given in Fig. 1A. A C4D was placed outside of a fused silica capillary with 50 mm I.D. and 360 mm O.D. A home-made frequency function generator was used to apply an actuator voltage over the C4D and two piezoelectric quartz crystal (PQC) resonators of 200 kHz. The frequency of the actuator voltage was adjusted by a user program. The circuitry on the pick-up side comprises a current-to-voltage converter, followed by rectification, low-pass filtering, an offset stage for baseline suppression, and amplification. The current signal was calculated according to the response of the circuitry and its amplification. * Corresponding author. E-mail address: [email protected] (D.Z. Shen). 1001-8417/$ – see front matter # 2012 Da Zhong Shen. Published by Elsevier B.V. on behalf of Chinese Chemical Society. All rights reserved. http://dx.doi.org/10.1016/j.cclet.2012.05.011
832
Q. Kang et al. / Chinese Chemical Letters 23 (2012) 831–834
(B)
(A) 3
(C)
(D)
1
2
RS CW 4 RS
6
5
CL
CL ≈0
CW C4 D+ RS
PQC
CW Lq Rq
7
Fig. 1. Block diagram of the electronic circuitry in resonant method (A), equivalent circuit model of C4D (B) and simplified equivalent circuit model of C4D (C) and C4D + PQC (D). (1) function generator, (2) piezoelectric quartz crystal; (3) capillary; (4) shielded ground copper plate; (5) contactless electrode; (6) current detection circuitry; and (7) chromatographic working station.
2. Results and discussion Usually, a C4D is modeled by the equivalent circuit model in Fig. 1B [2,9,11,13,14]. Under well designed shielding conditions, the influence of CL is negligible. Thus, a C4D is equivalent to the series combination of wall capacitance (Cw) and solution resistance (RS) (Fig. 1C). When an actuator voltage was applied, the signal current (I) is given by: I ¼ UjYj ¼ UvCw ð1 þ R2S v2 Cw2 Þ
0:5
(1)
where jYj is the admittance magnitude of C4D, U is the amplitude of actuator voltage, v = 2pf, f is the working frequency, respectively. In references [11–15], the values of Cw and RS are estimated by: Cw ¼
pLe0 er lnðr 2 =r 1 Þ
(2)
RS ¼
4d pr12 k
(3)
where L is the electrode length, d the electrode gap, r2 and r1 the outer and inner diameters of the capillary, e0 = 8.854 1012 F/m, er the relative permittivity of quartz, k the conductivity of the solution in capillary, respectively. By using the typical dimensions of C4D in capillary electrophoresis (L = 10 mm, d = 1 mm, r1 = 50 mm, r2 = 360 mm), Cw = 0.66 pF is evaluated according to Eq. (2). As depicted in Fig. 2, the predicted admittance magnitude of C4D by Eq. (1), jYjpred., is close to the reciprocal of RS in Eq. (3), especially in solutions of low conductivity. Thus, the response of C4D seems to be similar to that of a contact conductivity detector. Such prediction may be the reason for rare theoretic investigation in the response of C4D. However, this prediction is not supported by our experimental results. As can be seen in Fig. 2, the experimental values (jYjexp.) are much less than the predictions. The large difference between jYjpred. and jYjexp. reveals that the response of C4D is rather complicated because the electrodes are arranged along the axis of the fluid channel from outside of the capillary. To analyze the response of C4D, it is essential to measure the values of Cw and RS. Because of the cabined dimension of capillary, it is difficult to measure the two parameters directly. In this work, a resonant method is proposed to measure Cw and RS. In this measurement approach, an inductive impedance from PQC is added in series combination with C4D (Fig. 1D). Accordingly, the jYj of the series combination of C4D + PQC is expressed by: 2
jYj ¼ ½ðvLq v1 Cw 1 Þ þ ðRS þ Rq Þ2
0:5
(4)
where Lq and Rq are the equivalent series inductance and resistance of the PQC, respectively. Under the condition of (vLq v1Cw1) = 0, the capacitive impedance from Cw is neutralized by the inductive impedance from PQC. Hence, the jYj value of the combination has a maximum, jYjmax=1/(RS + Rq), which is supported by the experimental
Q. Kang et al. / Chinese Chemical Letters 23 (2012) 831–834 720
833
ππ rr12κκ 2 1
4d
4d
|Y| (nS)
540
| Y|pred. pred.
360
|Y|exp.
55 180
0 0.0
0.1
0.2
0.3
0.4
Conductivity (S/m) Fig. 2. Comparison of the response of C4D experimentally measured with the predicted values. Conditions: L = 10 mm, d = 1 mm, f = 200 kHz, r1 = 50 mm, and r2 = 360 mm.
result in Fig. 3. Usually, the value of RS is much larger than Rq. Hence, the value of RS 1/jYjmax is estimated in the resonant method. On the other hand, the value of jYjmax is 5.6 times of the value of jYj in C4D itself. This result indicates that total impedance of a C4D is composed mainly by the impedance from wall capacitor. That is to say, the response of the C4D is due mainly to the change in wall capacitance. Based on Eq. (1), the value of Cw in C4D is evaluated by: jYj jYj jYj C w ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi v v 1 ðRS jYjÞ2 v 1 ðjYj=jYjmax Þ2
(5)
The influence of electrode length and solution conductivity on the values of Cw and RS of C4D is shown in Fig. 4. With increasing electrode length, the value of Cw increases non-linearly. When the capillary was filled with 1 mmol/L NaCl solution, the values of Cw measured at L = 1, 2, 4 and 10 mm are 1.31, 1.49, 2.78 and 3.1 fF, respectively. Moreover, the value of Cw is much less than the prediction in Eq. (2), especially in solutions of low conductivity. In C4D with L = 4 mm, for example, Cw = 264 fF is predicted. The values of Cw measured in 1 and 20 mmol/L NaCl 100
|Y|max |Y| max
|Y| (nS)
75
50
25
0 200.89
C
C4D +PQC
C4D
200.92
200.95
200.98
Frequency (kHz) Fig. 3. Influence of working frequency on the response of C4D + PQC combination and C4D. Condition: L = 10 mm, d = 1 mm, r1 = 50 mm, r2 = 360 mm, and k = 0.0528 S/m.
Q. Kang et al. / Chinese Chemical Letters 23 (2012) 831–834
834
100
48
L= 10 mm
L= 4 mm
L= 4 mm
L= 2 mm
L= 2 mm
L= 1 mm
L= 1 mm
RS (M Ω )
CW (f F)
36
L= 10 mm
24
10
12
R S ==
0
π4d r12κ
2 π r4d κ 1
1 0.00
0.12
0.24
0.36
0.005 0.01
Conductivity (S/m)
0.05
0.1
0.5
Conductivity (S/m)
Fig. 4. Dependence of wall capacitance and solution resistance of C4D with different electrode length on solution conductivity. d = 1 mm, f = 200 kHz, r1 = 50 mm, and r2 = 360 mm.
solutions are 2.8 and 32 fF, which are only 1.1% and 12% of the prediction, respectively. For a given electrode length, the value of Cw increases with increasing solution conductivity, which does not support the prediction of constant Cw in Eq. (2). The influence of solution conductivity on Cw may relate to the change in the distribution of electric lines in C4D. When mercury was filled the capillary, the value of Cw measured is close to the prediction. On the other hand, as can be seen in Fig. 4, the values of RS are related to electrode length, which does not support the prediction by Eq. (3). The value of RS is less than the predicted one in a low conductivity solutions but larger than the predicted one in a high conductivity solution. The response model for the impedance parameters of C4D is under investigation. The resonant method provides a simple and low cost way to measure the equivalent circuit parameters of C4D. It was shown that the value of Cw measured is much less than the prediction by the equation in references and increases with increasing solution conductivity in the capillary. The value of RS is less than the prediction in a low conductivity solution but larger slightly than the prediction in a high conductivity solution. The response current of C4D is due to the change in Cw because the total impedance of a C4D is composed mainly by the wall capacitor. On the other hand, the current signal of C4D is significantly increased in the combination of C4D + PQC under the condition of resonance, which is helpful to enhance the sensitivity of C4D in capillary electrophoresis. Acknowledgment This work is supported by the National Natural Science Foundation of China (nos. 20975062 and 21175084). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
A.J. Zemann, E. Schnell, D. Volgger, et al. Anal. Chem. 70 (1998) 563. J.A.F. da Silva, C.L. do Lago, Anal. Chem. 70 (1998) 4339. F. Shen, M. Yang, Y. Yu, et al. Chin. Chem. Lett. 19 (2008) 1333. X. Li, Y.L. Tong, C. Liu, et al. Chin. J. Anal. Chem. 37 (2009) 1547. A.A. Elbashir, H.Y. Aboul-Enein, Biomed. Chromatogr. 24 (2010) 1038. P. Kuban, P.C. Hauser, Electrophoresis 32 (2011) 30. L.B. Ma, Y. Xu, J. Liang, et al. Chin. J. Anal. Chem. 39 (2011) 1123. F. Opekar, K. Sˇtulik, Electrophoresis 32 (2011) 795. E. Baltussen, R.M. Guijt, S.G. van der, et al. Electrophoresis 23 (2002) 2888. P. Tuma, F. Opekar, K. Stulı´k, Electrophoresis 23 (2002) 3718. A.J. Zemann, Electrophoresis 24 (2003) 2125. P. Kuban, P.C. Hauser, Electrophoresis 25 (2004) 3387. J.G.A. Brito-Neto, J.A.F. da Silva, L. Blanes, et al. Electroanalysis 17 (2005) 1207. S.E. Johnston, K.E. Fadgen, L.T. Tolley, et al. J. Chromatogr. A 1094 (2005) 148. C.G. Chen, L.G. Li, Y.J. Si, et al. Electrochim. Acta 54 (2009) 6959.
Chinese Chemical Letters 23 (2012) 831–834 www.elsevier.com/locate/cclet
Analyzing the response of a contactless conductivity detector in capillary electrophoresis by a resonant method Qi Kang, Qing Zhang, Yao Long Li, Dong Dong Li, Da Zhong Shen * The Key Lab in Molecular and Nano-Materials Probes of the Ministry of Education of China, School of Chemistry, Chemical Engineering and Material Science, Shandong Normal University, Jinan 250014, China Received 15 February 2012 Available online 9 June 2012
Abstract We report a resonant method to measure the wall capacitance (Cw) and solution resistance (RS) in a capacitively coupled contactless conductivity detector (C4D). Under the typical operating conditions in capillary electrophoresis (I.D. 50 mm, O.D. 360 mm, electrode length of 4 mm, electrode gap of 1 mm, frequency of 200 kHz), the values of Cw measured in 1 and 20 mmol/L NaCl solutions are 2.8 and 32 fF, which are only 1.1% and 12% of prediction by the equation in references, respectively. The value of RS is less than the prediction in solutions with k < 0.02 S/m. The response current of C4D is due to the change in Cw because the total impedance of a C4D is composed mainly by the impedance from Cw. # 2012 Da Zhong Shen. Published by Elsevier B.V. on behalf of Chinese Chemical Society. All rights reserved. Keywords: Contactless conductivity detector; Equivalent circuit parameter; Quartz crystal resonator; Resonant method
Since the works of Zemann et al. [1] and da Silva and do Lago [2] in 1998, a capacitively coupled contactless conductivity detector (C4D) has received considerable attention as an alternative detection method in capillary and microchip electrophoresis [3–8]. Although the C4D conception seems simple, to understand how it works is important for the ones who use C4D or intend to implement such a system. Compared to comprehensive applications, theoretical aspects related to the response of C4D are rare [9–15]. In this work, we propose a resonant method to measure the impedance parameters of C4D. The increase of wall capacitance (Cw) with increasing solution conductivity is reported for the first time. 1. Experimental A schematic representation of the experimental setup is given in Fig. 1A. A C4D was placed outside of a fused silica capillary with 50 mm I.D. and 360 mm O.D. A home-made frequency function generator was used to apply an actuator voltage over the C4D and two piezoelectric quartz crystal (PQC) resonators of 200 kHz. The frequency of the actuator voltage was adjusted by a user program. The circuitry on the pick-up side comprises a current-to-voltage converter, followed by rectification, low-pass filtering, an offset stage for baseline suppression, and amplification. The current signal was calculated according to the response of the circuitry and its amplification. * Corresponding author. E-mail address: [email protected] (D.Z. Shen). 1001-8417/$ – see front matter # 2012 Da Zhong Shen. Published by Elsevier B.V. on behalf of Chinese Chemical Society. All rights reserved. http://dx.doi.org/10.1016/j.cclet.2012.05.011
832
Q. Kang et al. / Chinese Chemical Letters 23 (2012) 831–834
(B)
(A) 3
(C)
(D)
1
2
RS CW 4 RS
6
5
CL
CL ≈0
CW C4 D+ RS
PQC
CW Lq Rq
7
Fig. 1. Block diagram of the electronic circuitry in resonant method (A), equivalent circuit model of C4D (B) and simplified equivalent circuit model of C4D (C) and C4D + PQC (D). (1) function generator, (2) piezoelectric quartz crystal; (3) capillary; (4) shielded ground copper plate; (5) contactless electrode; (6) current detection circuitry; and (7) chromatographic working station.
2. Results and discussion Usually, a C4D is modeled by the equivalent circuit model in Fig. 1B [2,9,11,13,14]. Under well designed shielding conditions, the influence of CL is negligible. Thus, a C4D is equivalent to the series combination of wall capacitance (Cw) and solution resistance (RS) (Fig. 1C). When an actuator voltage was applied, the signal current (I) is given by: I ¼ UjYj ¼ UvCw ð1 þ R2S v2 Cw2 Þ
0:5
(1)
where jYj is the admittance magnitude of C4D, U is the amplitude of actuator voltage, v = 2pf, f is the working frequency, respectively. In references [11–15], the values of Cw and RS are estimated by: Cw ¼
pLe0 er lnðr 2 =r 1 Þ
(2)
RS ¼
4d pr12 k
(3)
where L is the electrode length, d the electrode gap, r2 and r1 the outer and inner diameters of the capillary, e0 = 8.854 1012 F/m, er the relative permittivity of quartz, k the conductivity of the solution in capillary, respectively. By using the typical dimensions of C4D in capillary electrophoresis (L = 10 mm, d = 1 mm, r1 = 50 mm, r2 = 360 mm), Cw = 0.66 pF is evaluated according to Eq. (2). As depicted in Fig. 2, the predicted admittance magnitude of C4D by Eq. (1), jYjpred., is close to the reciprocal of RS in Eq. (3), especially in solutions of low conductivity. Thus, the response of C4D seems to be similar to that of a contact conductivity detector. Such prediction may be the reason for rare theoretic investigation in the response of C4D. However, this prediction is not supported by our experimental results. As can be seen in Fig. 2, the experimental values (jYjexp.) are much less than the predictions. The large difference between jYjpred. and jYjexp. reveals that the response of C4D is rather complicated because the electrodes are arranged along the axis of the fluid channel from outside of the capillary. To analyze the response of C4D, it is essential to measure the values of Cw and RS. Because of the cabined dimension of capillary, it is difficult to measure the two parameters directly. In this work, a resonant method is proposed to measure Cw and RS. In this measurement approach, an inductive impedance from PQC is added in series combination with C4D (Fig. 1D). Accordingly, the jYj of the series combination of C4D + PQC is expressed by: 2
jYj ¼ ½ðvLq v1 Cw 1 Þ þ ðRS þ Rq Þ2
0:5
(4)
where Lq and Rq are the equivalent series inductance and resistance of the PQC, respectively. Under the condition of (vLq v1Cw1) = 0, the capacitive impedance from Cw is neutralized by the inductive impedance from PQC. Hence, the jYj value of the combination has a maximum, jYjmax=1/(RS + Rq), which is supported by the experimental
Q. Kang et al. / Chinese Chemical Letters 23 (2012) 831–834 720
833
ππ rr12κκ 2 1
4d
4d
|Y| (nS)
540
| Y|pred. pred.
360
|Y|exp.
55 180
0 0.0
0.1
0.2
0.3
0.4
Conductivity (S/m) Fig. 2. Comparison of the response of C4D experimentally measured with the predicted values. Conditions: L = 10 mm, d = 1 mm, f = 200 kHz, r1 = 50 mm, and r2 = 360 mm.
result in Fig. 3. Usually, the value of RS is much larger than Rq. Hence, the value of RS 1/jYjmax is estimated in the resonant method. On the other hand, the value of jYjmax is 5.6 times of the value of jYj in C4D itself. This result indicates that total impedance of a C4D is composed mainly by the impedance from wall capacitor. That is to say, the response of the C4D is due mainly to the change in wall capacitance. Based on Eq. (1), the value of Cw in C4D is evaluated by: jYj jYj jYj C w ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi v v 1 ðRS jYjÞ2 v 1 ðjYj=jYjmax Þ2
(5)
The influence of electrode length and solution conductivity on the values of Cw and RS of C4D is shown in Fig. 4. With increasing electrode length, the value of Cw increases non-linearly. When the capillary was filled with 1 mmol/L NaCl solution, the values of Cw measured at L = 1, 2, 4 and 10 mm are 1.31, 1.49, 2.78 and 3.1 fF, respectively. Moreover, the value of Cw is much less than the prediction in Eq. (2), especially in solutions of low conductivity. In C4D with L = 4 mm, for example, Cw = 264 fF is predicted. The values of Cw measured in 1 and 20 mmol/L NaCl 100
|Y|max |Y| max
|Y| (nS)
75
50
25
0 200.89
C
C4D +PQC
C4D
200.92
200.95
200.98
Frequency (kHz) Fig. 3. Influence of working frequency on the response of C4D + PQC combination and C4D. Condition: L = 10 mm, d = 1 mm, r1 = 50 mm, r2 = 360 mm, and k = 0.0528 S/m.
Q. Kang et al. / Chinese Chemical Letters 23 (2012) 831–834
834
100
48
L= 10 mm
L= 4 mm
L= 4 mm
L= 2 mm
L= 2 mm
L= 1 mm
L= 1 mm
RS (M Ω )
CW (f F)
36
L= 10 mm
24
10
12
R S ==
0
π4d r12κ
2 π r4d κ 1
1 0.00
0.12
0.24
0.36
0.005 0.01
Conductivity (S/m)
0.05
0.1
0.5
Conductivity (S/m)
Fig. 4. Dependence of wall capacitance and solution resistance of C4D with different electrode length on solution conductivity. d = 1 mm, f = 200 kHz, r1 = 50 mm, and r2 = 360 mm.
solutions are 2.8 and 32 fF, which are only 1.1% and 12% of the prediction, respectively. For a given electrode length, the value of Cw increases with increasing solution conductivity, which does not support the prediction of constant Cw in Eq. (2). The influence of solution conductivity on Cw may relate to the change in the distribution of electric lines in C4D. When mercury was filled the capillary, the value of Cw measured is close to the prediction. On the other hand, as can be seen in Fig. 4, the values of RS are related to electrode length, which does not support the prediction by Eq. (3). The value of RS is less than the predicted one in a low conductivity solutions but larger than the predicted one in a high conductivity solution. The response model for the impedance parameters of C4D is under investigation. The resonant method provides a simple and low cost way to measure the equivalent circuit parameters of C4D. It was shown that the value of Cw measured is much less than the prediction by the equation in references and increases with increasing solution conductivity in the capillary. The value of RS is less than the prediction in a low conductivity solution but larger slightly than the prediction in a high conductivity solution. The response current of C4D is due to the change in Cw because the total impedance of a C4D is composed mainly by the wall capacitor. On the other hand, the current signal of C4D is significantly increased in the combination of C4D + PQC under the condition of resonance, which is helpful to enhance the sensitivity of C4D in capillary electrophoresis. Acknowledgment This work is supported by the National Natural Science Foundation of China (nos. 20975062 and 21175084). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
A.J. Zemann, E. Schnell, D. Volgger, et al. Anal. Chem. 70 (1998) 563. J.A.F. da Silva, C.L. do Lago, Anal. Chem. 70 (1998) 4339. F. Shen, M. Yang, Y. Yu, et al. Chin. Chem. Lett. 19 (2008) 1333. X. Li, Y.L. Tong, C. Liu, et al. Chin. J. Anal. Chem. 37 (2009) 1547. A.A. Elbashir, H.Y. Aboul-Enein, Biomed. Chromatogr. 24 (2010) 1038. P. Kuban, P.C. Hauser, Electrophoresis 32 (2011) 30. L.B. Ma, Y. Xu, J. Liang, et al. Chin. J. Anal. Chem. 39 (2011) 1123. F. Opekar, K. Sˇtulik, Electrophoresis 32 (2011) 795. E. Baltussen, R.M. Guijt, S.G. van der, et al. Electrophoresis 23 (2002) 2888. P. Tuma, F. Opekar, K. Stulı´k, Electrophoresis 23 (2002) 3718. A.J. Zemann, Electrophoresis 24 (2003) 2125. P. Kuban, P.C. Hauser, Electrophoresis 25 (2004) 3387. J.G.A. Brito-Neto, J.A.F. da Silva, L. Blanes, et al. Electroanalysis 17 (2005) 1207. S.E. Johnston, K.E. Fadgen, L.T. Tolley, et al. J. Chromatogr. A 1094 (2005) 148. C.G. Chen, L.G. Li, Y.J. Si, et al. Electrochim. Acta 54 (2009) 6959.