Journal of Chromatography A, 1216 (2009) 4913–4922

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Journal of Chromatography A

journa l homepage: www.e lsev ier .com/ locate /chroma

Computer simulation on a continuous moving chelation boundary inethylenediaminetetraacetic acid-based sample sweeping in capillaryelectrophoresis

Jie Jin, Jing Shao, Si Li, Wei Zhang, Liu-Yin Fan ∗∗, Cheng-Xi Cao ∗

Laboratory of Analytical Biochemistry & Bio-separation, Key Laboratory of Microbiology of Educational Ministry, School of Life Science and Biotechnology,Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China

a r t i c l e i n f o

Article history:Received 19 December 2008Received in revised form 19 March 2009Accepted 14 April 2009Available online 18 April 2009

Keywords:Capillary electrophoresisComputer simulationEDTA

a b s t r a c t

This paper introduces a mathematic mode of moving chelation boundary (MCB) for computer simulationof a continuous EDTA-based sample sweeping in capillary electrophoresis (CE). Besides the equationsof MCB used herein, the mode also includes electro-neutrality equation, constant current density, jumpboundary condition of MCB, Kohlrausch’ regulating function expressed in MCB formulation, product ofwater, ionic apparent mobility, ionic strength and conductivity of electrolyte as well as simple equilibriumreaction, etc. The simulation software is developed based on the mode. With the software the relevantsimulation is carried out, and the corresponding experiments on a MCB are performed. The results on thesimulation and experiments demonstrate that (1) the software can simulate a dynamic process, charac-teristic peak shape and relevant electrophoregram of a MCB; (2) the simulator can quantitatively computevelocities of MCB and complex boundary (CB), all of ionic concentrations (especially the concentration of

Moving reaction boundary

Sample sweeping complex) and sweeping efficiency; (3) these simulation results mentioned above are generally in accor-dance with the experiments. The simulation software holds evident significances for the study on a MCB

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. Introduction

Computer simulation has become a powerful tool to vividlyeveal the dynamical process of electrophoresis and to econom-cally optimize the conditions for an electrophoretic separation1]. Up to now, various computer simulators have been devel-ped for the simulation of different electrophoretic modes, suchs isoelectric focusing (IEF), isotachophoresis (ITP), capillary zonelectrophoresis (CZE) and sample stacking in capillary elec-rophoresis (CE).

Numerous studies on IEF simulation have been performed sincehe 1970s. In 1978, Park et al. [2] advanced a simulating approach tohe equilibrium of a rapidly dimerizing solute. In 1979, Murel et al.3] developed a model of pH gradient created by two ampholytesnd compiled the relevant program for explaining IEF instability. In

981–1983, Bier et al. [1,4,5] advanced a model of steady state IEFor the simulation on concentration structure, pH, conductivity andotential gradient in an IEF. Later, they [6,7] developed the relevantimulator for the dynamical study on a simple IEF. In 2000, Mao et

∗ Corresponding author. Tel.: +86 21 3420 5682; fax: +86 21 3420 5820.∗∗ Corresponding author. Fax: +86 21 3420 5820.

E-mail addresses: lyfan@sjtu.edu.cn (L.-Y. Fan), cxcao@sjtu.edu.cn (C.-X. Cao).

021-9673/$ – see front matter. Crown Copyright © 2009 Published by Elsevier B.V. All rioi:10.1016/j.chroma.2009.04.038

n such an EDTA-based sample sweeping of metal ion in CE.Crown Copyright © 2009 Published by Elsevier B.V. All rights reserved.

al. [8] developed a high resolution simulator for the dynamics of IEF.With the simulator, Mosher and Thormann [9] revisited the post-separation stable phase in IEF, and Thormann et al. [10–12] simu-lated the dynamics of protein IEF and the concurrent mobilizationof pH gradient. Shimao also performed a series of studies, includingthe numerical simulation of protein IEF [13], general procedure ofprotein IEF [14,15], and an IEF system without proteins [16].

Almost at the same time, a series of simulations were carriedout on an ITP. As early as in 1972, Beckers et al. [17,18] developeda computer program for the ITP separation of eight metal cations.The versatile simulator by Bier et al. [1,5] could also imitate thedynamics of ITP. In 1984, Hirokawa et al. [19] simulated an ITP of lan-thanoid ions. Next year, Radi and Schumacher [20] conducted thenumerical simulation for three ITP systems. In 1986, Shimao [21,22]advanced the numerical approach for the simulation of ITP bound-ary between protein and weak acid. In 1992, Heinrich and Wagner[23] described a versatile program for the high-speed simulation onan ITP, and Ermakov et al. [24] carried out the simulation on an ITPand a CZE as well. Next year, Caslavska et al. [25] developed a simula-

tor for the evaluation of an ITP. Two years later, Schafer-Nielsen [26]advanced a computer model for time-based simulation of ITP withfreely defined initial and boundary conditions. Schwer et al. [27] in1993 and Hruska et al. [28] in 2006 developed simul 4 and simul 5,respectively, for the numerical imitation on ITP and CZE as well.

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914 J. Jin et al. / J. Chromato

Besides the simulations above, CZE is the third important fieldor computer simulation. In 1994–1999, Reijenga et al. [29–31]eveloped a computer program for the simulation on migration,ispersion of samples and the influence of different injection inZE. Cifuentes and Poppe [32] in 1994 and Janini et al. [33] in 1999erformed the simulation of peptide separation and mobility. Gast al. [34] in 1995 simulated the peak dispersion, including walldsorption. Recently, they greatly developed the PeakMaster forhe optimization of electrophoretic conditions in a CZE [35–37].n 2001–2003, Erny et al. [38–40] discussed how to use Haarhoff-an der Linde (HVL) equation to simulate the peak in a CZE. Lastear, Hsu and Hung [41] conducted the simulation of charged ionigration in a CZE by using particle in cell method.Numerous computer programs have been developed for sam-

le stacking in CE. The first two are the software of simul 4 andimul 5 [27,28] that plainly simulate an ITP-induced sample stack-ng. The second is the one developed by Tsai et al. [42] that simulatesn electrokinetic injection technique in microchip. The third is theimulator by Srivastava et al. [43] that shows the simulation of DNAample preconcentration in microdevice. And the fourth is the oney Breadmore et al. [44] that uses pH boundary, a kind of mov-ng reaction boundaries (MRBs), to dynamically imitate the sampletacking in CE [45,46].

As a novel sample stacking, the sweeping technique has becomen important online treatment of sample. In 1998, Terabe and co-orkers [47–50] first proposed the concept of sample sweeping foreutral analytes and achieved as high as 5000-fold stacking effi-iency in MEKC. Recently, this method of sweeping is further usedn the areas of chip-based capillary electrophoresis [51,52]. Based

n the sweeping technique, Quirino et al. [53] and Isoo and Ter-be [54] in 2002–2003 advanced a highly efficient sweeping viaynamic complexation of EDTA and metal ions and successfullychieved up to 140 000-folds enhancement of sensitivity in termsf peak height. It was revealed later by Fan et al. [55] and Cao et

ig. 1. Model of a MCB formed with EDTA and Cu(II). (A) Initial electrolytes of EDTA and Cormation of new phase and boundary (viz., CB) between phase �′ and �. The symbols ‘+’ af MCB, complex and ions. For other symbols see the figure.

216 (2009) 4913–4922

al. [56] that there was a MRB, exactly a moving chelation boundary(MCB), in the EDTA-based sample sweeping.

Besides the two kinds of MRB mentioned above, the ionexchange boundary (IEB) and moving precipitate boundary (MPB)are also important forms of MRB [56–59]. In 1957, Schumacher[57] advanced the original mode of IEB between cations and com-plex anions (see Fig. 1 in Ref. [57]) and idealized a mode in whichthe cation is focused as a peak of complex with different valencesin a concentration gradient of anion (see Fig. 2 in Ref. [57]). In1970, Deman and Rigole [58,59] developed the idea of MPB andobserved stacking efficiency and IEB-induced separation of metalions. Based on the IEB and MRB (especially the sample sweepingmethod [53,54]), Fan et al. [55] developed the concept of mov-ing chelation boundary, and further quantitatively illuminated theEDTA-based sweeping by using the concept. However, there hasnot been any computer simulator for the EDTA-based sweeping ina MCB yet.

Therefore, the main purpose herein is to develop the MCB modefor the compilation of computer program simulating the dynamicprocess of EDTA-based sweeping. As shown below, the program can(1) imitate evolution of a MCB system, (2) compute boundary veloc-ities and sweeping efficiency (SE) and (3) calculate concentrationof all ions in different phases as well as the relevant ionic strengthand conductance. Below are the relevant results.

2. Theoretical

2.1. Model of MCB

The concept of a MCB has been discussed in detail in the previouswork [55,56]. Fig. 1 shows the brief model of a MCB. In Panel A, theleft side of the tube is filled with EDTA and the right side containsa metal ion, such as Cu(II). The pH value in the whole tube is set atpH 4.5. Under the given condition, more than 95% EDTA is existed

u(II); (B) initial MCB, complex, EDTA and Cu(II) migrating in opposite direction; (C)nd ‘−’ mean the anode and cathode, respectively. The arrows mean the movements

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s the subspecies of (EDTAH2)2− and Cu2+ has two positive charges60]. After the run, EDTA and Cu(II) move towards the anode andhe cathode, respectively. When meeting, the two ions create theollowing equilibrium reaction:

u(II) + [EDTAH2]2−K=18.80−→ [Cu − EDTA]2− + 2H+

The equilibrium reaction results in the formation of complexCu–EDTA]2− and the equilibrium constant K for Cu(II) and EDTA isery high (lg K = 18.80) [61]. This indicates that the side products areery tiny. This reaction results in the formation of the initial MCBnd the product of [Cu–EDTA]2− as shown in Panel B. The complexarries two negative charges and moves towards the anode. Theovement of the complex induces the formation of the complex

oundary (CB), as revealed in Panel C. Thus, the whole MCB systemn Panel C can be simply expressed as

DTA (−) ¦¦ [Cu–EDTA]2−, Cu(II) || Cu2+ (+)

DTA (−) || [Cu–EDTA]2−, EDTA ¦¦ Cu2+ (+)

he symbols of “¦¦” and “||” imply MCB and CB, respectively. The twooundaries isolate the whole system as the EDTA phase, the com-lex phase and the copper ion phase. In this paper, we will use phase, phase �′ and phase � to represent these three phases, respec-

ively. If the velocity of CB is faster than that of MCB, which takesp the most case, the complex phase is composed of [Cu–EDTA]2−

nd Cu(II). This condition is shown in Fig. 1. Conversely, the phaseontains [Cu–EDTA]2− and EDTA (not shown in Fig. 1).

The mode of MCB in Fig. 1 simulated herein is different fromhose of IEB and cation focusing advanced by Schumacher [57]. Theweeping in Fig. 1 is based on MCB and CB [55], and no IEB or noEB-induced separation occurs in such a MCB mode formed withsingle metal ion and chelant. However, in the IEB mode (see Fig.in Ref. [57]) there are a series of exchange boundaries and these

oundaries separate the cations as different complexes. In the modef cation focusing (see Fig. 2 in Ref. [57]), the ratio of the cationnd anion for reaction is always changing due to the concentrationradient of anion. Whereas, in the MCB mode, the reaction ratio ofu(II) and EDTA is 1:1 and the EDTA concentration is constant.

Two kinds of buffer solutions, one is 150 mmol L−1 pH 4.5 acetateuffer for Cu(II) and the other is 50 mmol L−1 pH 4.5 acetate bufferor EDTA (see Section 3.3), were used in our experiment system inrder to maintain the stable concentration of EDTA and Cu(II) inhase � and phase �, respectively. With the buffers, the concen-ration of [Cu–EDTA]2− and the velocities of two boundaries (MCBnd CB) were almost constant during the whole run. Please notehat the buffers used in Section 3.3 are not typical to that used inZE analysis of metals with EDTA.

It has been theoretically and experimentally demonstrated thathe velocity of MCB (VMCB) can be computed with

MCB = cEDTAVEDTA − cCu(II)VCu(II)

cCu(II) + cEDTA(1)

here C and V are the concentration and velocity of the ions, respec-ively [55,56]. As the quantity of produced [Cu–EDTA]2− is equal tohe consumption of Cu(II), the concentration of [Cu–EDTA]2− cane calculated with [55,56]

[Cu(II)−EDTA] = cCu(II)VCu(II) + VMCB∣∣VCB − VMCB

∣∣ (2)

In Eq. (2), VCB represents the velocity of the complexCu–EDTA]2−, which is considered as the same as the velocity ofomplex [Cu–EDTA]2−.

CB = V[Cu−EDTA]2− (3)

216 (2009) 4913–4922 4915

The sweeping efficiency (SE) of Cu(II) in a MCB system can bedefined as [55,56]

SE = c[Cu(II)−EDTA]

cCu(II)(4)

2.2. Mathematic principles for computer simulation

Besides Eqs. (1)–(4) used for the computer simulation, someother mathematic principles are applied for the compilation ofthe simulator developed herein. The first principle is the electro-neutrality equation for computation of each ion concentration inthe whole system of MCB [1]∣∣∣∑ c+z+

∣∣∣ =∣∣∣∑ c−z−

∣∣∣ (5)

In Eq. (5), z is the ionic charge(s), the subscripts of “+” and “−”indicate the positive and negative charges, respectively. Second,there exist three different phases in the MCB system (see Section2.1), and their conductivities are not equal to each other. However,they have the same current density at any time and any place dueto uniform capillary I.D. Namely there is∑n

i=1|zi|c�i

m�i

�� =∑n

i=1|zi|c�′i

m�′i

��′ =∑n

i=1|zi|c�i

m�i

��(6)

where � is the conductivity of zone, and m is the ionic mobility.Third, as the cation Na+ migrates from the anode to the cathode, inaddition, the whole capillary is filled with Cu(II) solution before theexperiment (see Section 3.3). Hence, according to the jump bound-ary conditions by Mosher et al. [1], we can express the equation ofMRB [56] as follows:

(c�′

Na+ − c�Na+

)VCB

i= c�′

Na+ m�′Na+

��′ − c�Na+ m�

Na+

��(7)

Fourth, Kohlrausch’s regulating function holds validity for a MCBunder the condition of nonzero boundary velocity, as has beendemonstrated in the previous work [62]. The function used for aMCB is expressed as [62]

∑∣∣za±,i

∣∣ ca±,i

ma∓,i

=∑∣∣za′

∓,i

∣∣ ca′∓,i

ma′∓,i

(8)

At 25 ◦C, the product (Kw) of water is 10−14

cH+cOH− = 10−14 (9)

where cH+ and cOH− are the concentrations of hydrogen andhydroxyl ions, respectively. In computer simulation, the velocityof an ion in the MCB system is computed with [55,56]

Vi = mii

�(10)

Owing to the existence of electroosmotic flow (EOF), the appar-ent velocity of the ion [63,64] is

Vi(app) = mii

�+ VEOF (11)

Owing for the influence of ionic strength on ionic mobility, theabsolute ionic mobility needs to be corrected with the empiricalequation [63,64]{ √

mact = m0 exp(−0.5 I) |z| = 1

m0 exp(−0.77√

zI)|z| ≥ 2(12)

where mact and m0 are the actual and absolute mobilities, respec-tively, I is the ionic strength, and z is the ionic valence. We have

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916 J. Jin et al. / J. Chromato

nother two equations for calculating the ionic strength and theonductivity of different zones or phases [1,28]:

= 12

(n∑

i=1

ciz2 + cOH− + cH+

)(13)

= F

(n∑

i=1

|zi|cimi + cOH−mOH− + cH+mH+

)(14)

In Eq. (14), F means the Faraday constant. And a set of acid dis-ociation constants is also used in the computation [28]

i,z = cH+ci,z

ci,zz = −1, −2, . . . k and i = 1, 2, . . . , n (15a)

i,z = cH+ci,z−1

ci,zz = 1, 2, . . . q and i = 1, 2, . . . , n (15b)

The complete mathematical model for a simulation on a contin-ous MCB is built by using all of these equations listed above. Underhe condition in which the velocity of MCB is faster than that of CBVMCB > VCB), the only difference is that the anion EDTA will replaceor the cation Cu(II), and the method of calculation is almost theame as those under the condition of VMCB < VCB.

With these equations listed above, one can not only computehe sweeping of metal ion in a continuous MCB system, but alsoalculate the ionic strength, conductance and concentrations ofll the ions (including pH and pOH values) in different phases orones, as well as the velocities of MCB, CB and SE. As the bound-ry velocities, the concentration of the chelating complexes andhe SE are the most important data in a MCB system, only theseata will be shown during the simulation while the remaining willot.

. Experimental

.1. Reagents

CuCl2·2H2O (analytical-reagent grade, AR) and ethylenedi-minetetraacetic acid disodium salt (EDTA, AR) were purchasedorm Sinopharm Chemical Reagent Co. (Shanghai, China). Sodiumhloride (guaranteed-reagent grade, GR), potassium chlorideguaranteed-reagent grade, GR), hydrochloric acid (AR) and agaroseel (biochemical-reagent grade, BR) with no EOF were purchasedrom the Shanghai Chemical Reagent Co. (Shanghai, China). Sodiumydroxide (GR) was bought from the Shanghai Zhuangong Reagentactory (Shanghai). Acetic acid (AR) is purchased from Guoyaohemical Reagent Co. (Shanghai, China).

.2. Instruments

The experiments in CE were performed with a P/ACETM MDQapillary electrophoresis system (Beckman Coulter, Fullerton, CA,SA). The system was equipped with 32 Golden Beckman Soft-are, a UV detector, up to 30 kV high-voltage supply with reversibleolarity. A fused-silica capillary (purchased from the Factory ofongnian Optical Fiber, Hebei, China) was used (total length 31.2 cm,1 cm effective length, I.D. 75 �m). At the first time of use, theapillary was rinsed with 1.0 mol L−1 NaOH for 10 min, ultra-ure water for 10 min, 1.0 mol L−1 HCl for 10 min and runninguffer for 20 min in order. The temperature in all runs was set at

5 ◦C.

The experiments in a large tube were performed with home-ade apparatus [55,56]. A glass tube with 200 mm × 3.11 mm I.D.as used for a run. The glass tube was divided into two halves,

he left and right ones were filled with the EDTA and Cu(II)

216 (2009) 4913–4922

gels (see Section 3.3), respectively. The EDTA and Cu(II) solu-tions were continuously flowed by two peristaltic pumps (HL-2,Shanghai Huxi Instrumental Factory, Shanghai, China). The electricfield was yielded by a power supply (DYY-2C, Beijing Lu-yi Scien-tific Instrument Factory, Beijing, China). A digital camera (6490,Kodak, Rochester, NY, USA) was fixed over the tube to monitorthe migration of MCB and color change. A pure water system (SGWasseraufbereitung und Regenerierstation, Fahrenberg, Barsübt-tel, Germany) was used to produce ultra-pure water with specificconductivity down to 0.055 �S cm−1.

3.3. Solutions and samples

In order to sweep the metal ion with EDTA in CE, two kinds ofbackground buffers (BGB) will be needed. One is the EDTA BGB con-taining 50.0 mmol L−1 pH 4.5 HAc–NaAc buffer and 25 mmol L−1

EDTA. And the other is Cu(II) BGB having 150 mmol L−1 pH 4.5HAc–NaAc buffer + 2.5/1.5/0.8/0.1/mmol L−1 Cu(II).

Two kinds of gels are prepared for the large tube exper-iment of MCB. The first is the EDTA gel prepared with theEDTA solution. The composition of the gel contains 2.0% agarosegel + 30.0 mmol L−1 EDTA + 5.40 mmol L−1 KCl, the pH of the solu-tion is adjusted to pH 5.0 with 1.00 mol L−1 NaOH. The second wasthe Cu(II) gel which is made up with 2.0% agarose gel + 2.0 mmol L−1

CuCl2 + 94.0 mmol L−1 KCl, the pH of the solution is also adjusted topH 5.0.

For the formation of calibration curve of [Cu–EDTA]2−, a stocksolution of 50 mmol L−1 [Cu–EDTA]2− was prepared at first. Withthis stock solution, a series of standard solutions of [Cu–EDTA]2−

can be made, which includes 0.1/0.5/1.0/2.5/5.0/10.0/15.0/20.0/25.0/30.0/40.0/50.0 mmol L−1 [Cu–EDTA]2− and 150 mmol L−1 pH4.5 acetate buffer. And 150 mmol L−1 pH 4.5 HAc–NaAc was alsoprepared as the BGB used in CZE.

3.4. Procedures of computer simulation

On the basis of the model described in Section 2, we compiled acomputer software with Delphi 7. The software includes two majorwindows. The first window is used for inputting and calculatingthe parameter of the experimental conditions (see Fig. 2). The sec-ond one is used to show the dynamic process and the result ofelectrophoregram (see Fig. 3).

In the first window (see Fig. 2), the component and concentra-tion of Cu(II) and EDTA BGB can be set in the anode column and thecathode column, respectively. The experimental conditions, includ-ing the total or effective length of capillary and the current densityetc, can be adjusted in the input column. Then the software cancalculate the velocity of MCB and CB as well as the concentra-tion of all the ions in both the new phase with newly producedcomplex and the original phases. And some important parameters,such as the concentration of [Cu–EDTA]2−, the SE, the VMCB and VCB(the effect of EOF has been considered), are shown in the outputcolumn.

There are two main columns in the second window, viz., the‘Result column’ and ‘In CE column’ (see Fig. 3). During a run ofsimulation, the ‘In CE column’ displays a real-time simulation ondynamic process of MCB in a capillary. The ‘Result column’ exhibitsa simulation on an electrophoregram of MCB, viz., the detectionof MCB passing through the detector. The simulation results in thetwo columns are displayed in accordance with the calculations inthe first window in Fig. 2.

In the simulation herein, the following physico-chemical param-eters are used for the computation. Acetic acid (Ac−): m0 = 42.4 ×10−9 m2 V−1 s−1, pKa = 4.76; sodium (Na+): m0 = 51.9 × 10−9 m2 V−1

s−1; [Cu–EDTA]2−: m0 = 43.0 × 10−9 m2 V−1 s−1; cuprum (Cu2+):m0 = 55.6 × 10−9 m2 V−1 s−1; (EDTAH2)2−: m0 = 44.1 × 10−9 m2 V−1

J. Jin et al. / J. Chromatogr. A 1216 (2009) 4913–4922 4917

t colu

smm[si

Fd

Fig. 2. Main window of the developed software concerning the inpu

−1; chlorine (Cl−): m0 = 67.0 × 10−9 m2 V−1 s−1; hydrogen (H+):0 = 362.0 × 10−9 m2 V−1 s−1; hydroxyl (OH−): m0 = 212.0 × 10−9

2 V−1 s−1. The data of the mobilities for simulation is used in Refs.35–37]. Total length of capillary is 31.2 cm. The voltage applied iset at −15, −10, −7.5 or −5 kV, the corresponding current intensitys −22 000, −15 000, −11 000 or −8000 A m−2.

ig. 3. Simulating window concerning the ‘In CE column’ displaying dynamic process ofetected by the detector in CE.

mn, the anode column, the cathode column and the output column.

3.5. Procedure of EDTA-based sweeping in CE

The experiments are conducted with two manners, viz., the con-stant voltage and constant Cu(II) concentration. In the first manner,the voltage is constant, while the concentration of Cu(II) in thebuffer is changed. In the second manner, the concentration of Cu(II)

a MCB and the ‘Result column’ showing the simulating electrophoregram of a MCB

4918 J. Jin et al. / J. Chromatogr. A 1216 (2009) 4913–4922

Table 1Comparisons of simulating and experimental results of SE under different concentration of copper ion in CE.

Cu (mmol L−1) Cu–EDTA (mmol L−1) (Sim) AU Cu–EDTA (mmol L−1) (Exp) SE (Sim) SE (Exp) Ratio (Sim/Exp)

2.5 22.14 0.401 20.63 8.86 8.25 1.071.5 18.07 0.393 18.35 12.00 12.23 0.980 610 47

A lating

ipw

3

(Cwittb

3

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V

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3

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TC

V

−−

A

.8 15.11 0.374 15.

.1 6.62 0.196 5.

U means UV absorption value; Exp implies experimental value, Sim indicates simu

s kept invariable, but different voltage is applied. And then the com-uter software is utilized to simulate the experiments performedith the two manners.

.5.1. The first mannerBefore each run, the capillary was rinsed by the Cu(II) buffer

holding 150 mmol L−1 pH 4.5 HAc–NaAc + 2.5/1.5/0.8/0.1 mmol L−1

u(II), respectively) for 5 min. After then the capillary was filledith the Cu(II) buffer. After that the right and left ends of the cap-

llary were dipped into the anode vial with the Cu(II) buffer andhe cathode vial with the EDTA buffer (see Section 3.3), respec-ively. Then, −15 kV voltage was applied and a MCB system coulde created.

.5.2. The second mannerThe capillary was first rinsed with the Cu(II) buffer (contain-

ng 150 mmol L−1 pH 4.5 HAc–NaAc + 1.5 mmol L−1 Cu(II)) for 5 min,hen the capillary was filled with the Cu(II) buffer. After then theight and left ends of the capillary were dipped into the anode vialith the Cu(II) buffer and the cathode vial with the EDTA buffer

see Section 3.3), respectively. After that, −15/−10/−7.5/−5 kV waspplied for the run of MCB.

In a run of MCB, the EOF mobility is approximately considered asconstant value because the same acetic buffer in high concentra-

ion, coupled with NaCl, is present in the EDTA and Cu(II) buffers.ith the treatment of constant EOF, the experimental velocity of a

oundary (including MCB and CB) is computed with

= S

t(16)

here S represents the effective length of the capillary (=21 cmerein), t means the migration time of a boundary. With Eq. (16),he velocities of MCB and CB in an experiment can be calculated.he simulating velocities of MCB and CB are calculated by Eqs. (1)nd (3), respectively, the results are displayed in the output columnf the software.

.6. Procedure for MCB in large tube

The relevant procedure has been described in detail in Refs.55,56]. First the right half side of the tube was filled with the Cu(II)el. After the coagulation of Cu(II) gel, the left half side of the tube

as filled with the EDTA gel. After that, the tube was fixed on anperating table, an initial boundary between the Cu(II) and EDTAels was marked immediately. When a voltage was applied, a seriesf photographs were taken at different times by a digital camera.he constant current was set at 10 mA in all of the runs.

able 2omparisons of simulating and experimental results of SE in a MCB system under differen

oltage (kV) Current density (A m−2) AU Cu–EDTA (m

15 −22 000 0.393 18.3510 −15 000 0.399 19.33−7.5 −11 000 0.393 18.35−5 −8 000 0.395 19.00

U means UV absorption value; Exp implies experimental value, Sim indicates simulating

18.89 19.51 0.9766.40 54.70 1.21

value.

3.7. Determination of [Cu(II)–EDTA] in CE

The relevant procedure has been described in detail in Ref. [55].The capillary was first rinsed by 150 mmol L−1 HAc–NaAc buffer for5 min. Then the sample solution of [Cu–EDTA]2− (see Section 3.3)was introduced into the capillary with 0.5 psi pressure for 10 s. Afterthat, a CZE was conducted at −15 kV and a saturated/flat-toppedpeak could be obtained due to large volume sample injection. Thecalibration curve of [Cu–EDTA]2− would be finally established whenall the samples of [Cu–EDTA]2− solutions were done.

4. Results and discussion

4.1. Numeral computation of SE

SE is an important parameter in sample preconcentration in CE.The software can perform the numeral computation of SE, shownin Fig. 2. Table 1 shows the result of numeral computation on SEin a MCB system formed with 25 mmol L−1 EDTA and 2.5, 1.5, 0.80or 0.10 mmol L−1 Cu(II). It is evident in Table 1 that the complexconcentration decreases from 22.14 to 6.64 mmol L−1 while the SEincreases from 8.86 to 66.4, as the [Cu(II)] is diluted from 2.5 to0.1 mmol L−1.

The relevant experiments were also performed with the gel-filled tube procedure to test the validity of numeral computation.Table 1 also gives the experiments. The experiments in Table 1 showthat complex concentration reduces from 20.63 to 5.47 mmol L−1

but the SE is enhanced from 8.25- to 54.7-fold when the metal ionconcentration is decreased from 2.5 to 0.1 mmol L−1.

Both the experimental and simulation results in Table 1 indicatethat when the concentration of Cu(II) becomes lower, the corre-sponding concentration of [Cu–EDTA]2− also turns down while theSE rises up. The ratios between the simulating and experimentalresults change from 0.97 to 1.21, indicating a quite good agree-ment between the simulation and experiments. The comparisonsin Table 2 further demonstrate the similar agreement between thenumeral computation of SE and the relevant experiments in a con-tinuous MCB system in CE.

4.2. Numeral computation of boundary velocity

Boundary velocities, including MCB and complex boundary, are

the most important parameters affecting the SE in a continuoussystem [55]. Fig. 2 shows that the software can estimate both a MCBvelocity and a CB velocity. Table 3 gives the numeral computationon MCB and CB velocities. It is revealed in Table 3 that simulatingvelocity of a MCB increases from 1.17 to 1.62 mm s−1 and that of

t voltages in CE.

mol L−1) (Exp) Cu–EDTA (mmol L−1) (Sim) Ratio (Sim/Exp)

17.98 0.9817.98 0.9317.98 0.9817.98 0.95

value.

J. Jin et al. / J. Chromatogr. A 1216 (2009) 4913–4922 4919

Table 3Comparisons of simulating and experimental results of boundary velocities in a MCB system under different concentrations of copper ion in CE.

Cu (mmol L−1) VMCB (mm s−1) (Sim) VMCB (mm s−1) (Exp) Ratio VCB (mm s−1) (Sim) VCB (mm s−1) (Exp) Ratio

2.5 1.17 1.25 0.94 1.76 1.48 1.191.5 1.31 1.30 1.01 1.87 1.50 1.250 0.88 1.97 1.75 1.130 0.98 2.06 1.80 1.14

E

ac

dtcTsaca

4

Ma‘oiapabkmttb

3tstc

Fig. 4. Formations of MCB, CB and new phase as well as boundary movements in aMCB formed by 2.00 mmol L−1 CuCl2 + 94.0 mmol L−1 KCl solution and 30.0 mmol L−1

EDTA + 5.4 mmol L−1 KCl solution at (A) 3.0, (B) 9.0, (C) 15.0 and (D) 20.0 min. Con-ditions: 10 mA electric current, 2.0% agarose gel in the tube, I.D. of tube = 3.11 mm;

−1

Fp3

.8 1.43 1.59

.1 1.62 1.66

xp means experimental value, Sim means simulating value.

CB is slightly enhanced from 1.76 to 2.06 mm s−1 as the copperoncentration is decreased from 2.5 to 0.1 mmol L−1.

The relevant experiments are also given in Table 3. It isetected in CE that the relevant MCB velocity changes from 1.25o 1.66 mm s−1 and the CB varies from 1.48 to 1.80 mm s−1. Theomparisons between the simulating and experimental results inable 3 demonstrate that the ratios of a MCB velocity between theimulating and the experimental drift from 0.88 to 1.01 and those ofCB velocity change from 1.13 to 1.25. These ratios imply a fair coin-idence of boundary velocity between the numeral computationnd the experiments in a continuous MCB.

.3. Dynamic simulation of complex profile

The simulator can imitate the dynamic process of a continuousCB in a capillary, including the initial MCB, the evolution of MCB

nd CB, and the concentration profile of complex [Cu–EDTA]2−. TheIn CE column’ in Fig. 3 shows the dynamic process of a MCB systemriginally formed with 25 mmol L−1 EDTA and 0.1 mmol L−1 copperon. The dynamic process shows that (1) the initial MCB and CB arelmost uprightness and the width of sweeping peak, viz., the com-lex of [Cu–EDTA]2−, is much sharp; (2) both a MCB and a CB movelmost as a constant velocity; (3) after a while the sweeping peakecomes wider as a function of run time, while the height of peakeeps almost constant; (4) hence the value of SE is initially decidedainly by the starting conditions of EDTA and metal ion concentra-

ions, and the increase of sweeping time has no new contribution tohe SE value. The simulating results are proved by the experimentselow.

Fig. 4 shows the experiments of a MCB formed with

0.0 mmol L−1 EDTA and 2.0 mmol L−1 copper ion in a gel-filledube. It is clearly shown in Fig. 4 that (1) the initial boundary is veryharp; (2) both a MCB and a CB migrate as a constant velocity; (3)he complex zone turns wider gradually while the color intensity ofomplex has no evident change. The results in Section 4.6 will fur-

ig. 5. Computer simulation of sweeping efficiency of metal ion by a MCB system formed wH 4.5 HAc–NaAc buffer + (A) 2.5 mmol L−1, (B) 1.5 mmol L−1, (C) 0.80 mmol L−1 and (D) 0.101.2 cm (effective length 21 cm to the detector), 25 ◦C.

length of tube = 200 mm; flow rate of the anolyte and catholyte = 0.35 mL min ;“Start position” means the initial boundary between Cu(II) and EDTA gels beforeelectric field. In the experiment system, the cathode is set at the left side of the tubewhile the anode is set at the right side. Other symbols see the figure.

ther prove that the SE is constant if the concentrations of EDTA andmetal ion are kept invariable, and the prolonging of sweeping timehas no obvious influence on the SE. Evidently, the results in Fig. 4and Section 4.6 qualitatively manifest the dynamic simulations ofa continuous MCB in Fig. 3.

4.4. Simulation of electrophoregram

The software can imitate an electrophoregram for a continuousMCB system in CE. In Fig. 3, as the dynamic process of a MCB isvividly simulated, an electrophoregram is automatically producedin the ‘Result column’ because of the detector set. Initially, a baseline

ith 50.0 mmol L−1 pH 4.5 HAc–NaAc buffer + 25.0 mmol L−1 EDTA and 150 mmol L−1

mmol L−1 Cu(II). Simulation conditions: EOF = 8.0 × 10−9 m2 V−1 s−1, −22 000 A m−2,

4920 J. Jin et al. / J. Chromatogr. A 1216 (2009) 4913–4922

F 0.0 mH 0 mm(

itcsd‘gi

4

s0bbAt

tV(Cir

FHE

ig. 6. Sweeping efficiency of metal ion by a MCB system initially formed with 5Ac–NaAc buffer + (A) 2.5 mmol L−1, (B) 1.5 mmol L−1, (C) 0.80 mmol L−1 and (D) 0.1

effective length 21 cm to the detector), 25 ◦C.

s shown. When the swept complex passes through the detec-or, a peak is detected. The peak is correspondent with the sweptomplex. After that, a baseline is represented again. Evidently, theimulating result is similar to a normal electrophoregram in CE. Theifference is that a complex concentration is directly given in the

Result column’ while a UV value is shown in a normal electrophore-ram in a CE run. The simulating results will be systemically provedn Sections 4.5 and 4.6.

.5. Effect of concentration of Cu(II)

Fig. 5 shows the simulating results of the EDTA-basedweeping under different copper(II) concentrations (from 2.5 to.1 mmol L−1). The relevant experiments are given in Fig. 6. It cane observed in Figs. 5 and 6 that the velocities of MCB and CB willecome faster when the concentration of copper ion is decreased.nd the lower the concentration the closer the distance between

he MCB and the CB.According to the physico-chemical model of Fig. 1, the concen-

ration of Cu(II) plays an important role in VMCB (see Eq. (1)), while

CB is mainly determined on the ionic strength and conductancesee Eq. (3)). Hence, the MCB velocity can vary greatly, while theB velocity cannot change a lot because of the existence of approx-

mately uniform background buffer. In other words, the fluctuationange of VMCB is much greater than that of VCB. Clearly, a narrow

ig. 7. The simulation of metal ion sweeping by a MCB system initially formed with 50.0Ac–NaAc buffer + 1.5 mmol L−1 Cu(II). The current density applied is (A) −22 000 A m−2,OF = (A) 8.0 × 10−9 m2 V−1 s−1, (B) 10.0 × 10−9 m2 V−1 s−1, (C) 14.0 × 10−9 m2 V−1 s−1 and (

mol L−1 pH 4.5 HAc–NaAc buffer + 25.0 mmol L−1 EDTA and 150 mmol L−1 pH 4.5ol L−1 Cu(II). Experimental conditions: EOF = 8.0 × 10−9 m2 V−1 s−1, −15 kV, 31.2 cm

complex peak can be achieved by adjusting the copper ion concen-tration and the MCB velocity.

4.6. Effect of voltage

Fig. 7 shows the simulating results of the EDTA-based sweepingwith a same concentration Cu(II) under different current densitiesor voltages. The simulations in Fig. 7 indicate that (1) the concentra-tion of [Cu–EDTA]2− is always constant while the migration timeschange a lot; (2) the concentration of [Cu–EDTA]2− has no relationwith the voltage. The simulations are proved by the correspondingexperiments in Fig. 8.

Fig. 9 further displays the velocities of MCB and CB formed withEDTA and Cu(II) under different voltages/current densities. Both thesimulation and the experiment indicated that with the decrease ofthe current density/voltage the velocities of MCB and CB drop downand the corresponding peak becomes wider. According to Eqs. (1)and (3), the velocity is in proportion to the voltage/current density.This is the main reason why VMCB and VCB have approximate linearrelation with the voltage as shown in Fig. 9.

4.7. Deviation analysis for computer simulation

Some deviations are always present in calculating the ionicstrength and the conductance. In addition, the current density and

mmol L−1 pH 4.5 HAc–NaAc buffer + 25.0 mmol L−1 EDTA and 150 mmol L−1 pH 4.5(B) −15 000 A m−2, (C) −11 000 A m−2 and (D) −8000 A m−2. Simulating conditions:D) 18.0 × 10−9 m2 V−1 s−1, 31.2 cm (effective length 21 cm to the detector), 25 ◦C.

J. Jin et al. / J. Chromatogr. A 1216 (2009) 4913–4922 4921

Fig. 8. Metal ion sweeping by a MCB system initially formed with 50.0 mmol L−1 pH 4.5 HAc–NaAc buffer + 25.0 mmol L−1 EDTA and 150 mmol L−1 pH 4.5 HAc–NaAcbuffer + 1.5 mmol L−1 Cu(II). The voltage applied is (A) −15 kV, (B) −10 kV, (C) −7.5 kV, (D) −5 kV. Experimental conditions: EOF = (A) 8.0 × 10−9 m2 V−1 s−1, (B)10.0 × 10−9 m2 V−1 s−1, (C) 14.0 × 10−9 m2 V−1 s−1 and (D) 18.0 × 10−9 m2 V−1 s−1, 31.2 cm (effective length 21 cm to the detector), 25 ◦C.

of the

ttitmp

tietpcced

fpsssoe

are conducted. Though there are some deviations between the sim-

Fig. 9. The relationship between the voltage and velocities

he EOF are not easy to determine due to the incessant formation ofhe new phase in capillary. Therefore, the deviation of simulations evidently unavoidable, especially for calculating the velocities ofhe two boundaries. In the simulation of EDTA-based sweeping, the

igration times are determined by VMCB and VCB. Thus, the complexeak in the simulation is broader than that in the experiment.

From the comparison in Table 3 and Fig. 9, it also can be foundhat the deviation of VCB between the simulation and experiments slightly higher than those of VMCB. According to Eq. (1) and thexperiment, the velocity of MCB depends on two aspects: one ishe actual mobility and concentration of Cu(II) in the new formedhase, and the other is that of EDTA in the cathode BGB. Since theondition of EDTA BGB is constant during a run, VMCB can be cal-ulated with minor error. In addition, the diffusion has a greaterffect on the velocity of CB than that of MCB, which led to a highereviation for the simulation of VCB.

If two or more metal ions (e.g., Cu(II) and Co(II) etc.) were usedor the experiment, an interesting result was observed in the com-lex MCB system. We found that the two ions can be not only

wept but also well separated as two complexes in the manner ofhoulder-to-shoulder. It is proved with analyses of ICP–AES and UVpectrophotometer that the separation of two complexes is basedn a chelation exchange boundary, which is similar to the ion-xchange reaction boundaries [56–59]. Obviously, the simulation

two boundaries. (A) VCB and voltage; (B) VMCB and voltage.

software developed herein cannot be used to illuminate the mech-anism of separation in an exchange boundary at present time dueto different physico-chemical modes.

5. Conclusions

From the results mentioned above, it is evident that a math-ematical mode of MCB is developed for computer simulation ofa continuous EDTA-based sample sweeping in CE as well as ingel-filled tube. The mode concerns the boundary velocity equa-tions of MCB and CB, the expression of SE, the electro-neutralityconditional equation, the constant current density in a capillaryor tube, the jump boundary condition for a MRB equation, theKohlrausch’ regulating function, the product of water, the ionicapparent mobility, the ionic strength, the conductivities of elec-trolytes and the acid-base equilibrium, etc. The simulation softwareof MCB is developed from the mode and the relevant experiments

ulation and experiments on the complex concentration, sweepingefficiency and boundary (including MCB and CB) velocities, the sim-ulating results are in general consistent with the experiments onMCB formed with EDTA and single copper ion. All of these indicatethat the software developed can simulate a MCB system with com-

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922 J. Jin et al. / J. Chromato

arative accuracy and optimize the experimental conditions for anDTA-based sweeping.

cknowledgements

The project was supplied by the Natural Science Foundationf China (Approved nos. 20675051, 20821005 and 20805031),he National Basic Research Program of China (973 Program, no.009CB118906), the Shanghai Leading Academic Discipline ProjectApproved no. B203) and Shanghai Jiao Tong University.

ppendix A. Supplementary data

Supplementary data associated with this article can be found, inhe online version, at doi:10.1016/j.chroma.2009.04.038.

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