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The application of spline wavelet transform to the determination of electroosmotic mobility in capillary electrophoresis
Talanta 57 (2002) 1093– 1100 www.elsevier.com/locate/talanta
The application of spline wavelet transform to the determination of electroosmotic mobility in capillary electrophoresis Xiong Jianhui, Xu Guowang *, Zhang Pudun, Zheng Yufang, Zhang Yukui National Chromatography R&A Center, Dalian Institute of Chemical Physics, The Chinese Academy of Science, ZhongShan Road 161, Dalian 116011, PR China Received 31 January 2002; received in revised form 4 April 2002; accepted 4 April 2002
Abstract The rule of current change was studied during capillary electrophoresis (CE) separation process while the conductivity of the sample solution was different from that of the buffer. Using a quadratic spline wavelet of compact support, the wavelet transforms (WTs) of capillary electrophoretic currents were performed. The time corresponding to the maximum of WT coefficients was chosen as the time of current inflection to calculate electroosmotic mobility. The proposed method was suitable for different CE modes, including capillary zone electrophoresis, nonaqueous CE and micellar electrokinetic chromatography. Compared with the neutral marker method, the relative errors of the developed method for the determination of electroosmotic mobility were all below 2.5%. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Capillary electrophoresis; Electroosmotic mobility; Spline wavelet transform
1. Introduction Capillary electrophoresis (CE) has been gaining more and more attentions as a separation and analytical technique. Unlike in high performance liquid chromatography (HPLC), the driving force in CE is electroosmotic flow (EOF), which is a basic phenomenon in all electrophoretic separation processes [1–3]. The variation of EOF not only influences the separation velocity, but also changes the separation selectivities [4,5]. So the * Corresponding author. Tel./fax: +86-411-3693403. E-mail address: [email protected] (Xu G.).
proper control and determination of EOF was an important task in CE separations [6–11]. The EOF mobility is often determined by the neutral marker method. The neural markers have to fulfill some requirements: the compound must be neutral over a wide pH range and should show high detection sensitivity. Additionally in micellar electrokinetic chromatography (MEKC), the EOF marker should not interact with the micelle. Methanol [8], formamide [9], thiourea [10] and benzyl alcohol [11] have been used as the EOF marker. Wavelet transform (WT) is a signal processing method developed on the basis of Fourier trans-
0039-9140/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 9 - 9 1 4 0 ( 0 2 ) 0 0 1 9 2 - 3
X. Jianhui et al. / Talanta 57 (2002) 1093–1100
1094
form and has been widely applied in analytical chemistry [12–15]. There are many wavelet basic functions, such as Haar, Daubechies and Mexican hat, which can be chosen to process different kinds of signals. Generally WT has smoothing and de-noising functions. Besides these, spline wavelet transform (SWT) has also derivative character, it could be used in the detection of the signal inflection points [15–17]. In this paper, the characteristic of current change during CE separation was investigated while the conductivity of the sample solution was different from that of the buffer. Using a quadratic spline wavelet of compact support, the WTs of CE separation currents were performed. The time corresponding to the maximum of WT was chosen as the current inflection time to calculate electroosmotic mobility. The result was in good accordance with that by the neutral marker method.
1 x dqs (x) s (x)= =s dx s s the following equation can be derived:
dq d (x)= s ( f *qs ), (x) dx dx
Ws f(x)=f s
( )= i
2. Theory [16,17]
&
q(x)dx = 1;
limq(x) =0 x
−
(1)
We suppose that (x) is the first derivative of q(x): (x) =
dq(x) dx
Because
&
sin( /4) /4
4
(7)
4
(8)
respectively. According to fast discrete dyadic WT algorithm in one dimension, with n decomposition of the signal S d1 f, we can get the discrete approximations S d21 f, S d22 f,…, S d2n f, and WT coefficients W d21 f, W d22 f,…, W d2n f, at different scales.
3.1. Reagents and solutions
(3)
the function (x) can be considered as a basic or mother wavelet. The WT of f(x) with respect to (x) is: 1 s
sin( /4) /4
3. Experimental
dq(x) (x)dx = dx =q(x) − =0 − − dx
Ws f(x)=
q ( )=
(2)
&
(6)
( f*qs ) is the smoothed result of f(x) with respect to q(x) at the scale s, while Ws f(x) is the first derivative of the function f(x) smoothed at the scale s. When the scale is small, the smoothed result of f(x) with respect to q(x) has little influence on the position and shape of f(x) sharp variation; when the scale s is large, the convolution with q(x) removes small signal fluctuations and only the sharp variations of large structures can be detected. Here we use a quadratic spline wavelet with compact support, which is the derivative of a cubic spline whose integral is equal to 1. Their Fourier transforms are
q(x) is supposed to be a smoothing function, and satisfies the following conditions:
(5)
&
−
x− t f(t)dt s
(4)
Based on the definition of (x), the dilated wavelet can be written:
Dipotassium hydrogen phosphate, ammonium acetate (Reagent Plant of Liaoning Medical Commercial Corporation, ShenYang, China), sodium acetate (Shanghai Chemical Regent IV Plant, ShangHai, China), 85% phosphoric acid (Changchun Chemical Regent Plant, Changchun, China), formamide (Shanghai Chemical Regent Company, Shanghai, China), sodium lauryl sulfate (SDS, Farco Chemical Supplies, HongKong) and thiourea (Beijing Chemical Plant, Beijing,
X. Jianhui et al. / Talanta 57 (2002) 1093–1100
China) were all of analytical grade. Sodium hydroxide (Experiment II Plant of ShangHai ShangHaiGongXueTuan, Shanghai, China) and disodium tetraborate decahydrate (YanLing Chemical Plant, Shanghai, China) and (Beijing Chemical Plant, Beijing, China) were all of RB grade. 3-[Cyclohexylamino]-1-propanesulfonic acid (CAPS) was from Sigma (St. Louis, MO). Acetonitrile (ACN) of HPLC grade were obtained from Tedia Company Inc. (FairField, CT). Ethanol (EtOH) of HPLC grade was purchased from Tianjin KeMiOu Technology Company (Tianjin, China). The distilled water was purified with a Milli-Q Purification System (Millipore, Milford, MA). Thiourea and formamide (20 mg ml − 1, dissolved in pure water) were chosen as the EOF marker in capillary zone electrophoresis and MEKC, respectively. The pH of buffer was adjusted by 0.1 M H3PO4 or 0.1 M NaOH. Prior to use, the buffer was filtered by 0.45 mm filter and ultrosonicated for 10 min.
1095
50 mm I.D., 375 mm O.D. fused silica capillary (Yongnian Optical Fiber Factory, Hebei, China), the total length was 50 cm and the distance between injection and detection was 40 cm. The detection wavelength was 214 nm. Unless indicated, the applied voltage was 15 kV (positive polarity); the capillary was controlled at 25 °C. The samples were injected by application of 0.5 psi of pressure. The used pH meter was Beckman f340 (Beckman-Coulter).
3.3. Methods The capillary was rinsed daily with 0.1 M sodium hydroxide, water, then with running buffer by application of 20 psi of pressure for 10 min, respectively. When a different buffer was used, the capillary was treated with the same procedure. Between injections the capillary was flushed only with buffer for 2 min. The program for WT was written in C language, and was performed on a Pentium 200 Hz microcomputer.
3.2. Apparatus 4. Results and discussion All experiments were performed on the Beckman P/ACE™ MDQ System (Beckman-Coulter, Fullerton, CA). Separations were carried out in a
4.1. The deri6ati6e characteristic of spline wa6elet In order to testify the derivative characteristic of spline wavelet, the WT of sine function y= sin x(00x0 2p) was performed and WT coefficients W d21 f, W d22 f, W d23 f and W d24 f were gotten. Taking W d21 f as an example, the phase difference between them was exactly p/2 (Fig. 1). It proved that spline wavelet had derivative characteristic. The maximum of the first derivative corresponds to the position where the signal has sharp variation, so the maximum point of WT coefficients at one scale could be chosen as the inflection point.
4.2. The rule of current change during CE Separation
Fig. 1. Sine function and its wavelet transform W d21 f.
During CE separations, if the ion strength of sample solution is equal to that of the buffer, there would be no change in separation current.
X. Jianhui et al. / Talanta 57 (2002) 1093–1100
1096
DI =I2 − I1 =
Ls(kb − ks) VSkb Ltotal Ls(kb − ks)+ Ltotalks
(11)
4.3. The detection of current cur6e inflection point and calculation of electroosmotic mobility When the neutral marker method was used to determine EOF, there was the following relationship between the migration time t1 of the marker and the EOF velocity weof: Fig. 2. Schematic representation of the abrupt change of current during CE separation process. (a) The sample solution was injected and electric field was applied; (b) the sample solvent passed through detection window; (c) the sample solvent just reached the capillary outlet end; (d) the sample solvent has just migrated out of the capillary; (e) the schematic current siganl in CE (the conductivity of the sample was lower than that of the buffer).
However, if there is a little difference between them, sudden change of current inside the capillary would be observed (Fig. 2). If the stacking or broadening of sample zone is assumed to be negligible before the sample solvent reaches the capillary outlet end, the current inside the capillary could be approximately expressed: I1 =
V V = Rtotal Ls Ltotal −Ls + Sks Skb
(9)
where V is the applied voltage, Rtotal is the average resistant of the solution through the capillary, ks, kb are the conductivities of sample zone and buffer solution, respectively, Ltotal and Ls are the total length of the capillary and the zone length of injected sample, and S is the section area of the capillary. When the sample solvent zone migrates from the capillary, the current through the capillary could be expressed as follows: I2 =
V Ltotal Skb
(10)
Subtracting Eq. (10) from Eq. (9), the degree of the current change can be expressed:
t1 =
Ldet weof
(12)
where Ldet is the length between the inlet end and the detection window, t1 was also the time that the sharp variation of the marker concentration occurred. Similarly, if the time t2 corresponding to the inflection point of current curve was obtained, it could be considered as the migration time that the sample solvent migrated through the total capillary: t2 =
Ltotal weof
(13)
Thus the electroosmotic mobility veof can be calculated: veof =
L 2total Vt2
(14)
Dividing Eq. (12) by Eq. (13), the relationship between t1and t2can be obtained as follows: t1 = t2
Ldet Ltotal
(15)
Fig. 3 gives the CE electropherogram of thiourea dissolved in water and its current curve. It could be observed that the current change occurred during the separation and the migration time of thiourea was prior to the inflection time of current, which was in accordance with our judgement. The SWT of the current signal with 4 decomposition was performed, as shown in Fig. 4. The time corresponding to the maxima of W d21 f, W d22 f, W d23 f and W d24 f were substituted into Eq. (15) to get t%1. Although there were a little
X. Jianhui et al. / Talanta 57 (2002) 1093–1100
difference among these t%1, compared with the migration time of thiourea, the relative errors were all below 1.5% (see Table 1). The difference was because that W d21 f, W d22 f, W d23 f and W d24 f were gotten at different scales and the width and height of derivative peak showed difference. In the following study, the time corresponding to the maximum of W d22f was chosen to calculate the electroosmotic mobility.
1097
4.4. The influence of injection length on detection of current inflection It can be informed from Eq. (11) that the current change increased with injection length. As shown in Fig. 5A, the current curves obtained at different injection time proved it. The WTs W d22f of these curves were also performed (see Fig. 5B). Compared with the neutral marker method, the
Fig. 3. Electropherogram of thiourea and the corresponding separation current curve. Buffer conditions: 30 mM K2HPO4 (pH 7.0), sample injection: 0.5 psi for 5 s, other conditions was shown in text.
Fig. 4. The wavelet transform of CE separation current signal at different scales, experiment conditions as Fig. 3.
X. Jianhui et al. / Talanta 57 (2002) 1093–1100
1098
Table 1 Comparison between the migration time of thiourea and those of EOF calculated by WT at different scales
t%1 (min) Relative error (%)
W d21 f
W d22 f
W d23 f
W d24 f
4.283 0.10
4.287 0.18
4.297 0.41
4.337 1.38
The migration time of thiourea: 4.279 min.
relative errors between them were all below 0.5% (see Table 2). Although at injection time of 3 s, the degree of current change was only 0.2 mA and the noise of current also reached 0.08 mA, the maximum point of W d22 f was still detected easily. It was testified that SWT not only could detect sharp variation, but also had strong de-noising ability.
Fig. 5. (A) The CE separation current curves at different injection times; (B) the corresponding wavelet transforms W d22 f; injection time: 1 – 3 s, 2 – 5 s, 3 – 10 s, 4–20 s; other conditions as Fig. 3.
X. Jianhui et al. / Talanta 57 (2002) 1093–1100
1099
Table 2 Comparison between the neutral marker method and the proposed method at different injection times Injection time (s)
3 5 10 20
EOF mobility (10−4 cm2 V−1 s−1) Neutral marker method
Wavelet transform method
Relative error (%)
5.184 5.193 5.198 5.409
5.156 5.184 5.221 5.433
−0.53 −0.18 0.43 0.44
Table 3 Comparison between the neutral marker method and the proposed method in different buffer systems Buffers
50 mM NaAc (pH 4.0) 40 mM Na2B4O7 (pH 9.0) 30 mM CAPS (pH 10.9) 25 mM Na2B4O7–30 mM SDS (pH 9.0) 30 mM NH4Ac (EtOH–ACN, 50:50, V/V)
EOF mobility (10−4 cm2 V−1 s−1) Neutral marker method
RSD (%) (n = 3)
Wavelet transform method
RSD (%) (n = 3)
Relative error (%)
2.241 4.633 6.004 5.046
1.05 0.19 0.13 0.24
2.216 4.618 6.050 4.927
1.00 0.20 0.16 0.35
−1.09 −0.32 0.76 −2.35
2.978
0.55
3.042
0.60
−2.10
4.5. The applications of the method de6eloped in different buffer systems Besides phosphate, the proposed method was also applied to the EOF determination in acetate, Borate, CAPS, ethanol– acetonotrile mixture buffers containing ammonium acetate and MEKC containing SDS. The repeatibilities were all better than 1.0%. Compared with the neutral marker method, the relative errors were all below 2.5% (see Table 3).
tral marker method in different running buffers were all below 2.5%.
Acknowledgements We are thankful to the National Natural Science Foundation of China for financial support (No.29975029).
References 5. Conclusions In this study, the current change during CE separation was studied when the ion strength of sample solution was different from that of the buffer. The time corresponding to sharp variation of current was detected using the derivative characteristic of SWT, and thus the EOF mobility was calculated. The relative errors compared with neu-
[1] J.W. Jorgenson, K.D. Lukas, J. Chromatogr. 218 (1981) 209. [2] J.W. Jorgenson, K.D. Lukas, Anal. Chem. 53 (1981) 1298. [3] J.W. Jorgenson, K.D. Lukas, Science 222 (1983) 266. [4] C. Schwer, E. Kenndler, Chromatographia 33 (1992) 331. [5] E. Kenndler, J. Microcol. Sep. 10 (1998) 273. [6] S.V. Ermakov, L. Capelli, P.G. Righetti, J. Chromatogr. A 744 (1996) 55. [7] B.A. Willams, G. Vigh, Anal. Chem. 68 (1996) 1174.
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[8] C.P. Ong, C.L. Ng, H.K. Lee, S.F.Y. Li, J. Chromatogr. 588 (1991) 335. [9] S.M. Masselter, A.J. Zemann, Anal. Chem. 67 (1995) 1047. [10] J. Tjfrnelund, S.H. Hansen, J. Chromatogr. A 792 (1997) 475. [11] M. Chen, R.M. Cassidy, J. Chromatogr. 602 (1992) 227. [12] M. Bos, E. Hoogendam, Anal. Chim. Acta 267 (1992) 73.
[13] L. Yan, J.Y. Mo, Chin. Sci. Bull. 40 (1995) 1567. [14] B.K. Alsberg, A.M. Woodword, D.B. Kell, Chemom. Intell. Lab. Syst. 37 (1997) 215. [15] H. Wang, Z.X. Pan, W. Liu, M.S. Zhang, S.Z. Si, L.P. Wang, Chem. J. Chin. Univ. 18 (1997) 1286. [16] S. Mallat, S. Zhong, IEEE Trans. Pattern Anal. Mach. Intelligence 14 (1992) 710. [17] S. Mallat, W.L. Hwang, IEEE Trans. Information Theory 38 (1992) 617.
The application of spline wavelet transform to the determination of electroosmotic mobility in capillary electrophoresis Xiong Jianhui, Xu Guowang *, Zhang Pudun, Zheng Yufang, Zhang Yukui National Chromatography R&A Center, Dalian Institute of Chemical Physics, The Chinese Academy of Science, ZhongShan Road 161, Dalian 116011, PR China Received 31 January 2002; received in revised form 4 April 2002; accepted 4 April 2002
Abstract The rule of current change was studied during capillary electrophoresis (CE) separation process while the conductivity of the sample solution was different from that of the buffer. Using a quadratic spline wavelet of compact support, the wavelet transforms (WTs) of capillary electrophoretic currents were performed. The time corresponding to the maximum of WT coefficients was chosen as the time of current inflection to calculate electroosmotic mobility. The proposed method was suitable for different CE modes, including capillary zone electrophoresis, nonaqueous CE and micellar electrokinetic chromatography. Compared with the neutral marker method, the relative errors of the developed method for the determination of electroosmotic mobility were all below 2.5%. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Capillary electrophoresis; Electroosmotic mobility; Spline wavelet transform
1. Introduction Capillary electrophoresis (CE) has been gaining more and more attentions as a separation and analytical technique. Unlike in high performance liquid chromatography (HPLC), the driving force in CE is electroosmotic flow (EOF), which is a basic phenomenon in all electrophoretic separation processes [1–3]. The variation of EOF not only influences the separation velocity, but also changes the separation selectivities [4,5]. So the * Corresponding author. Tel./fax: +86-411-3693403. E-mail address: [email protected] (Xu G.).
proper control and determination of EOF was an important task in CE separations [6–11]. The EOF mobility is often determined by the neutral marker method. The neural markers have to fulfill some requirements: the compound must be neutral over a wide pH range and should show high detection sensitivity. Additionally in micellar electrokinetic chromatography (MEKC), the EOF marker should not interact with the micelle. Methanol [8], formamide [9], thiourea [10] and benzyl alcohol [11] have been used as the EOF marker. Wavelet transform (WT) is a signal processing method developed on the basis of Fourier trans-
0039-9140/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 9 - 9 1 4 0 ( 0 2 ) 0 0 1 9 2 - 3
X. Jianhui et al. / Talanta 57 (2002) 1093–1100
1094
form and has been widely applied in analytical chemistry [12–15]. There are many wavelet basic functions, such as Haar, Daubechies and Mexican hat, which can be chosen to process different kinds of signals. Generally WT has smoothing and de-noising functions. Besides these, spline wavelet transform (SWT) has also derivative character, it could be used in the detection of the signal inflection points [15–17]. In this paper, the characteristic of current change during CE separation was investigated while the conductivity of the sample solution was different from that of the buffer. Using a quadratic spline wavelet of compact support, the WTs of CE separation currents were performed. The time corresponding to the maximum of WT was chosen as the current inflection time to calculate electroosmotic mobility. The result was in good accordance with that by the neutral marker method.
1 x dqs (x) s (x)= =s dx s s the following equation can be derived:
dq d (x)= s ( f *qs ), (x) dx dx
Ws f(x)=f s
( )= i
2. Theory [16,17]
&
q(x)dx = 1;
limq(x) =0 x
−
(1)
We suppose that (x) is the first derivative of q(x): (x) =
dq(x) dx
Because
&
sin( /4) /4
4
(7)
4
(8)
respectively. According to fast discrete dyadic WT algorithm in one dimension, with n decomposition of the signal S d1 f, we can get the discrete approximations S d21 f, S d22 f,…, S d2n f, and WT coefficients W d21 f, W d22 f,…, W d2n f, at different scales.
3.1. Reagents and solutions
(3)
the function (x) can be considered as a basic or mother wavelet. The WT of f(x) with respect to (x) is: 1 s
sin( /4) /4
3. Experimental
dq(x) (x)dx = dx =q(x) − =0 − − dx
Ws f(x)=
q ( )=
(2)
&
(6)
( f*qs ) is the smoothed result of f(x) with respect to q(x) at the scale s, while Ws f(x) is the first derivative of the function f(x) smoothed at the scale s. When the scale is small, the smoothed result of f(x) with respect to q(x) has little influence on the position and shape of f(x) sharp variation; when the scale s is large, the convolution with q(x) removes small signal fluctuations and only the sharp variations of large structures can be detected. Here we use a quadratic spline wavelet with compact support, which is the derivative of a cubic spline whose integral is equal to 1. Their Fourier transforms are
q(x) is supposed to be a smoothing function, and satisfies the following conditions:
(5)
&
−
x− t f(t)dt s
(4)
Based on the definition of (x), the dilated wavelet can be written:
Dipotassium hydrogen phosphate, ammonium acetate (Reagent Plant of Liaoning Medical Commercial Corporation, ShenYang, China), sodium acetate (Shanghai Chemical Regent IV Plant, ShangHai, China), 85% phosphoric acid (Changchun Chemical Regent Plant, Changchun, China), formamide (Shanghai Chemical Regent Company, Shanghai, China), sodium lauryl sulfate (SDS, Farco Chemical Supplies, HongKong) and thiourea (Beijing Chemical Plant, Beijing,
X. Jianhui et al. / Talanta 57 (2002) 1093–1100
China) were all of analytical grade. Sodium hydroxide (Experiment II Plant of ShangHai ShangHaiGongXueTuan, Shanghai, China) and disodium tetraborate decahydrate (YanLing Chemical Plant, Shanghai, China) and (Beijing Chemical Plant, Beijing, China) were all of RB grade. 3-[Cyclohexylamino]-1-propanesulfonic acid (CAPS) was from Sigma (St. Louis, MO). Acetonitrile (ACN) of HPLC grade were obtained from Tedia Company Inc. (FairField, CT). Ethanol (EtOH) of HPLC grade was purchased from Tianjin KeMiOu Technology Company (Tianjin, China). The distilled water was purified with a Milli-Q Purification System (Millipore, Milford, MA). Thiourea and formamide (20 mg ml − 1, dissolved in pure water) were chosen as the EOF marker in capillary zone electrophoresis and MEKC, respectively. The pH of buffer was adjusted by 0.1 M H3PO4 or 0.1 M NaOH. Prior to use, the buffer was filtered by 0.45 mm filter and ultrosonicated for 10 min.
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50 mm I.D., 375 mm O.D. fused silica capillary (Yongnian Optical Fiber Factory, Hebei, China), the total length was 50 cm and the distance between injection and detection was 40 cm. The detection wavelength was 214 nm. Unless indicated, the applied voltage was 15 kV (positive polarity); the capillary was controlled at 25 °C. The samples were injected by application of 0.5 psi of pressure. The used pH meter was Beckman f340 (Beckman-Coulter).
3.3. Methods The capillary was rinsed daily with 0.1 M sodium hydroxide, water, then with running buffer by application of 20 psi of pressure for 10 min, respectively. When a different buffer was used, the capillary was treated with the same procedure. Between injections the capillary was flushed only with buffer for 2 min. The program for WT was written in C language, and was performed on a Pentium 200 Hz microcomputer.
3.2. Apparatus 4. Results and discussion All experiments were performed on the Beckman P/ACE™ MDQ System (Beckman-Coulter, Fullerton, CA). Separations were carried out in a
4.1. The deri6ati6e characteristic of spline wa6elet In order to testify the derivative characteristic of spline wavelet, the WT of sine function y= sin x(00x0 2p) was performed and WT coefficients W d21 f, W d22 f, W d23 f and W d24 f were gotten. Taking W d21 f as an example, the phase difference between them was exactly p/2 (Fig. 1). It proved that spline wavelet had derivative characteristic. The maximum of the first derivative corresponds to the position where the signal has sharp variation, so the maximum point of WT coefficients at one scale could be chosen as the inflection point.
4.2. The rule of current change during CE Separation
Fig. 1. Sine function and its wavelet transform W d21 f.
During CE separations, if the ion strength of sample solution is equal to that of the buffer, there would be no change in separation current.
X. Jianhui et al. / Talanta 57 (2002) 1093–1100
1096
DI =I2 − I1 =
Ls(kb − ks) VSkb Ltotal Ls(kb − ks)+ Ltotalks
(11)
4.3. The detection of current cur6e inflection point and calculation of electroosmotic mobility When the neutral marker method was used to determine EOF, there was the following relationship between the migration time t1 of the marker and the EOF velocity weof: Fig. 2. Schematic representation of the abrupt change of current during CE separation process. (a) The sample solution was injected and electric field was applied; (b) the sample solvent passed through detection window; (c) the sample solvent just reached the capillary outlet end; (d) the sample solvent has just migrated out of the capillary; (e) the schematic current siganl in CE (the conductivity of the sample was lower than that of the buffer).
However, if there is a little difference between them, sudden change of current inside the capillary would be observed (Fig. 2). If the stacking or broadening of sample zone is assumed to be negligible before the sample solvent reaches the capillary outlet end, the current inside the capillary could be approximately expressed: I1 =
V V = Rtotal Ls Ltotal −Ls + Sks Skb
(9)
where V is the applied voltage, Rtotal is the average resistant of the solution through the capillary, ks, kb are the conductivities of sample zone and buffer solution, respectively, Ltotal and Ls are the total length of the capillary and the zone length of injected sample, and S is the section area of the capillary. When the sample solvent zone migrates from the capillary, the current through the capillary could be expressed as follows: I2 =
V Ltotal Skb
(10)
Subtracting Eq. (10) from Eq. (9), the degree of the current change can be expressed:
t1 =
Ldet weof
(12)
where Ldet is the length between the inlet end and the detection window, t1 was also the time that the sharp variation of the marker concentration occurred. Similarly, if the time t2 corresponding to the inflection point of current curve was obtained, it could be considered as the migration time that the sample solvent migrated through the total capillary: t2 =
Ltotal weof
(13)
Thus the electroosmotic mobility veof can be calculated: veof =
L 2total Vt2
(14)
Dividing Eq. (12) by Eq. (13), the relationship between t1and t2can be obtained as follows: t1 = t2
Ldet Ltotal
(15)
Fig. 3 gives the CE electropherogram of thiourea dissolved in water and its current curve. It could be observed that the current change occurred during the separation and the migration time of thiourea was prior to the inflection time of current, which was in accordance with our judgement. The SWT of the current signal with 4 decomposition was performed, as shown in Fig. 4. The time corresponding to the maxima of W d21 f, W d22 f, W d23 f and W d24 f were substituted into Eq. (15) to get t%1. Although there were a little
X. Jianhui et al. / Talanta 57 (2002) 1093–1100
difference among these t%1, compared with the migration time of thiourea, the relative errors were all below 1.5% (see Table 1). The difference was because that W d21 f, W d22 f, W d23 f and W d24 f were gotten at different scales and the width and height of derivative peak showed difference. In the following study, the time corresponding to the maximum of W d22f was chosen to calculate the electroosmotic mobility.
1097
4.4. The influence of injection length on detection of current inflection It can be informed from Eq. (11) that the current change increased with injection length. As shown in Fig. 5A, the current curves obtained at different injection time proved it. The WTs W d22f of these curves were also performed (see Fig. 5B). Compared with the neutral marker method, the
Fig. 3. Electropherogram of thiourea and the corresponding separation current curve. Buffer conditions: 30 mM K2HPO4 (pH 7.0), sample injection: 0.5 psi for 5 s, other conditions was shown in text.
Fig. 4. The wavelet transform of CE separation current signal at different scales, experiment conditions as Fig. 3.
X. Jianhui et al. / Talanta 57 (2002) 1093–1100
1098
Table 1 Comparison between the migration time of thiourea and those of EOF calculated by WT at different scales
t%1 (min) Relative error (%)
W d21 f
W d22 f
W d23 f
W d24 f
4.283 0.10
4.287 0.18
4.297 0.41
4.337 1.38
The migration time of thiourea: 4.279 min.
relative errors between them were all below 0.5% (see Table 2). Although at injection time of 3 s, the degree of current change was only 0.2 mA and the noise of current also reached 0.08 mA, the maximum point of W d22 f was still detected easily. It was testified that SWT not only could detect sharp variation, but also had strong de-noising ability.
Fig. 5. (A) The CE separation current curves at different injection times; (B) the corresponding wavelet transforms W d22 f; injection time: 1 – 3 s, 2 – 5 s, 3 – 10 s, 4–20 s; other conditions as Fig. 3.
X. Jianhui et al. / Talanta 57 (2002) 1093–1100
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Table 2 Comparison between the neutral marker method and the proposed method at different injection times Injection time (s)
3 5 10 20
EOF mobility (10−4 cm2 V−1 s−1) Neutral marker method
Wavelet transform method
Relative error (%)
5.184 5.193 5.198 5.409
5.156 5.184 5.221 5.433
−0.53 −0.18 0.43 0.44
Table 3 Comparison between the neutral marker method and the proposed method in different buffer systems Buffers
50 mM NaAc (pH 4.0) 40 mM Na2B4O7 (pH 9.0) 30 mM CAPS (pH 10.9) 25 mM Na2B4O7–30 mM SDS (pH 9.0) 30 mM NH4Ac (EtOH–ACN, 50:50, V/V)
EOF mobility (10−4 cm2 V−1 s−1) Neutral marker method
RSD (%) (n = 3)
Wavelet transform method
RSD (%) (n = 3)
Relative error (%)
2.241 4.633 6.004 5.046
1.05 0.19 0.13 0.24
2.216 4.618 6.050 4.927
1.00 0.20 0.16 0.35
−1.09 −0.32 0.76 −2.35
2.978
0.55
3.042
0.60
−2.10
4.5. The applications of the method de6eloped in different buffer systems Besides phosphate, the proposed method was also applied to the EOF determination in acetate, Borate, CAPS, ethanol– acetonotrile mixture buffers containing ammonium acetate and MEKC containing SDS. The repeatibilities were all better than 1.0%. Compared with the neutral marker method, the relative errors were all below 2.5% (see Table 3).
tral marker method in different running buffers were all below 2.5%.
Acknowledgements We are thankful to the National Natural Science Foundation of China for financial support (No.29975029).
References 5. Conclusions In this study, the current change during CE separation was studied when the ion strength of sample solution was different from that of the buffer. The time corresponding to sharp variation of current was detected using the derivative characteristic of SWT, and thus the EOF mobility was calculated. The relative errors compared with neu-
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