Moving boundary system (MBS),an important concept in electrophoresis and physico-chemistry,was gradually developed for isotachophoresis (ITP). From 1910s to 1950s,this kind of MBS created with strong electrolytes was broadly studied by numerous scientists ^[1-3]. Svensson ^[4],Alberty et al. ^[5-6] and Nichol ^[7] investigated the MBS formed with weak electrolytes. Furthermore,Nichol et al. ^[8] showed the similarity between weak-electrolyte-created MBS and electrophoresis of proteins,and utilized the series solutions of Dole’s equations for electrophoretic analysis. The MBS has laid the foundation for both classic ITP theory and technique ^[9-10]. At the same time,moving reaction boundary (MRB) in a MBS or ITP had been recognized. Bo ek et al. ^[10] performed systemic investigations on the MRB formed with weak acidic or alkaline buffers in the classic ITP.

A novel kind of MRB,which was different from that in the MBS or the classic ITP ^{[4-7, 10]},was also unveiled. As early as in 1970,Deman and Rigole ^[11-12] advanced the novel idea of “precipitate reactive front (PRF)”,developed the Deman-Rigole’s equations showing the movement and separation efficiency of PRF,performed the experiments of PRF in U-shape tube with agar gel,and observed the separation of metal ions during the runs of PRF. Deman and Rigole’s work is important,since it implied a new kind of MRB system,which had not been explored before.

Relied on the important work mentioned above,Cao et al. ^[13-16] developed the concept of MRB,and formulated the equations of MRB for both strong and weak reactive electrolytes,which were in form similar to,but actually different from those of MBS. In order to illuminate the mechanism of IEF(isoelectric focusing electrophoresis),Cao et al. ^[13-14] unveiled the relations between IEF and MRB. Recently,they developed the theoretical and experimental procedures for the preparation of colloidal materials in gel by using MRB ^[13]. The experiments of MRB formed with strong reactive electrolytes quantitatively demonstrate the validity of MRB theory ^[13].

Numerous reaction boundaries have been used for the sample stacking in capillary electrophoresis (CE). For example,the MRB has been used for the quantitative design of experimental conditions of sample stacking ^[17]. Grochocki et al. ^[18] advanced the sweeping technique for the analyte stacking by field-enhanced sample injection and micelle in CE. Kong et al. ^[19] described the assay of melamine in milk products with a pH-mediated sample stacking technique in CE. Li et al. ^[20] developed an analogous method called as “dynamic pH junction stacking” for the monitoring of cerebroside sulfotransferase in CE. We also developed the MRB-induced sample stacking for the enhancement of column efficiency and online stacking of analytes in the high salt content matrixes. At the same time,we performed quantitative studies to illuminate the MRB-induced stacking mechanism ^[21-26].

However,when creating an anodic-moving MRB formed with weak acidic buffer and strong alkali of NaOH and applying the MRB for the stacking of insulin,we found there was an evident difference between the experiment and theoretical computation relied on the original MRB model ^[13]. The in-depth theoretical analyses show the invalidity of MRB model is not induced by the theory itself but by the formations of a new phase and derivation of MRB after the use of electric field. Herein we report the new theoretical model of derived MRB,the findings of the new phase and derivatized MRB and the demonstration to the new phase and derivatized MRB as well as some new procedures. Compared with traditional CE,the derivatized MRB proposed by us is more efficient in sample separation and sample stacking. In addition,it can avoid the influence of electroosmotic flow,and then improve the experimental efficiency. Furthermore,the proposed derivatized MRB can be used to measure parameters quickly and efficiently,such as the quantitative protein analysis.

1 Theoretical

1.1 Original MRB

Original MRB is:

5.0-80 mmol/L pH 3.0 formic buffer+20 mmol/L NaCl (α,+)‖4.0 mmol/L NaOH+10 mmol/L NaCl (γ,-)

where,the symbols “α” and “γ” imply phases α and γ respectively,“+” and “-” mean the anodic and cathodic sides respectively,and the symbol of “‖” indicates a boundary created between phases α and γ. The boundary is designed to move towards the anode,thus the velocity of original boundary should be computed with the following equation (Eq.) (1) in accordance with the original model of MRB ^[13],

${{v}^{\alpha \gamma }}_{ori}=\left( \frac{{{{\bar{m}}}^{a}}_{H+}{{{\bar{c}}}^{a}}_{H+}}{{{k}^{a}}}-\frac{{{m}^{{{\gamma }_{O{{H}^{-}}}}}}{{c}^{{{\gamma }_{O{{H}^{-}}}}}}}{{{k}^{\gamma }}} \right)\frac{i}{{{{\bar{c}}}^{{{\alpha }_{{{H}^{+}}}}-}}{{c}^{{{\gamma }_{OH}}}}}$

(1)

The meanings of symbols in Eq. (1) are given below. c: the concentration. The bar “-” over c means the constituent concentration. The subscripts H⁺ and OH^- indicate the hydrogen and hydroxyl ions respectively and the superscripts α and γ imply phases α and γ,respectively. Signed quantity,it’s positive if the ion carries net positive charge(s) and it’s negative if net negative charge(s),as has been treated by numerous scientists ^{[1-9, 13]}. i: the current intensity (A/m²) in tube,here it is set at 589.5 A/m² (the experimental value). m: the mobility (m²/(V\5s)). The bar “-” over m indicates the constituent mobility. Other symbols are the same as those for c. Signed quantity is like c. v^αγ and v^αβ: the velocities (m/s) of the original and derivatized MRBs. Signed quantity is similar to c. κ: the specific conductivity of electrolyte in a phase (S/m).

As pointed out by Alberty ^[6] and Tiselius ^[27],a substance consisting of several forms with different mobilities in equilibrium with each other will generally migrate as a uniform substance. Thus,the constitutent mobility and concentration are respectively defined as:

$\bar{m}=\sum {{a}_{i}}{{m}_{i}}$

(2)

$\bar{c}=\sum {{c}_{i}}$

(3)

where,m_i is the mobility of subspecies i,a_i is the fraction of subspecies i with mobility m_i,viz.,

${{a}_{i}}=\frac{{{c}_{i}}}{{\bar{c}}}=\frac{{{c}_{i}}}{\sum {{c}_{i}}}$

(4)

1.2 Model of derivatized MRB

After the electric field is applied,the pH 3.0 formic buffer in phase α will be continuously neutralized by the hydroxyl ion migrated from phase γ,which contains 20 mmol/L NaCl and 4 mmol/L NaOH. With the reaction,a new phase,defined as phase β,is formed.

It is analyzed that the conductivity in phase β is higher than that in phase γ and the high conductivity leads the electromigration of hydroxyl ion and chlorine ion in phase β are lower than that in phase γ. As a result,the electromigration of OH^- and Cl^- from phases γ to β increases the concentrations of OH^- and Cl^- in phase β. The concentrations of OH^- and Cl^- in phase β can be well computed by means of computer simulation described in Section 1.3.

The new formation of phase β results in a derivatized MRB formed between phases α and β. At the same time,another boundary is formed between phases β and γ since they contain different concentrations of OH^- and Cl^-. From the corresponding experiment,it could be found the moving velocity of this boundary is very slow,and it could be considered as a stationary boundary. Thus,the whole MRB system can be written as follows:

Formic buffer+NaCl (α,+)‖Sodium formate+NaCl+NaOH (β)‖NaOH+NaCl (γ,-)

The velocity of the derivatized MRB,viz.,boundary αβ,should be computed with Eq. (5),

${{v}^{\alpha \beta }}=\left( \frac{{{{\bar{m}}}^{a}}_{H+}{{{\bar{c}}}^{a}}_{H+}}{{{k}^{a}}}-\frac{{{m}^{{{\beta }_{O{{H}^{-}}}}}}{{c}^{{{\beta }_{O{{H}^{-}}}}}}}{{{k}^{\gamma }}} \right)\frac{i}{{{{\bar{c}}}^{{{\alpha }_{{{H}^{+}}}}-}}{{c}^{{{\beta }_{OH}}-}}}$

(5)

rather than Eq. (1) used for the computation of boundary αγ in accordance with the corrections ^{[13, 17]}. The meanings of symbols in Eq. (5) are similar to those in Eq. (1).

1.3 Theoretical computation

In order to calculate the concentrations of all the ions in phase β,various mathematical principles are needed. The first principle is the electro-neutrality equation for computation of each ion concentration in the whole system ^[28],

$\left| \sum {{c}^{+}}{{z}^{+}} \right|=\left| \sum {{c}^{-}}{{z}^{-}} \right|$

(6)

In Eq. (6),z is the ionic charge(s),the subscripts “+” and “-” indicate the positive and negative charges,respectively. Second,as there is always the following constant equation during a run of MRB at any time ^[22],

${{i}^{a}}={{i}^{\beta }}={{i}^{\gamma }}$

(7)

hence,one gets the following expression from Eq. (7),

$\frac{\sum\limits_{i=1}^{n}{{{c}^{a}}_{i}{{m}^{a}}_{i}}}{{{k}^{a}}}=\frac{\sum\limits_{i=1}^{n}{{{c}^{\beta }}_{i}{{m}^{\beta }}_{i}}}{{{k}^{\beta }}}=\frac{\sum\limits_{i=1}^{n}{{{c}^{\gamma }}_{i}{{m}^{\gamma }}_{i}}}{{{k}^{\gamma }}}$

(8)

Third,the Cl^- migrates from the cathode to the anode,and the boundary between phases β and γ is almost stationary. Hence,according to the jump boundary conditions by Mosher et al ^[28],the flux of Cl^- between these two phases is equal:

${{c}^{\beta }}_{Cl}-{{v}^{\beta }}_{Cl-}={{c}^{\gamma }}_{Cl}-{{v}^{\gamma }}_{Cl-}$

(9)

Fourth,the total flux of the OH^- migrates from phase γ is equal to the sum of the quantity of the OH^- contained in phase β and the consumption of OH^- for the neutralization within a certain time (t).

${{c}^{\gamma }}_{OH-}-{{v}^{\gamma }}_{OH-}t={{c}^{\beta }}_{OH-}-{{v}^{a\beta }}t+{{c}^{\beta }}_{OH-}\left( {{v}^{\beta }}_{OH-}-{{v}^{a\beta }} \right)t$

(10)

Fifth,Kohlrausch’s regulating function holds validity for the derivatized MRB system under the condition of nonzero boundary velocity ^[28],which could be expressed as:

$\sum \left( \frac{1}{{{m}^{a}}_{i}}-\frac{{{z}^{a}}_{i}}{{{m}^{a}}_{H+}} \right){{{\bar{c}}}_{i}}^{a}=\sum \left( \frac{1}{{{m}^{\beta }}_{i}}-\frac{{{z}^{\beta }}_{i}}{{{m}^{\beta }}_{OH+}} \right){{{\bar{c}}}_{i}}^{\beta }$

(11)

At 25 ℃,the ionic product of water (K_w) is 10^{-14 [29]}:

${{c}_{H}}+{{c}_{OH}}={{10}^{-14}}$

(12)

The velocity of an ion in the MRB system is computed with Eq. (13):

${{v}_{i}}={{m}_{i}}i/\kappa $

(13)

Owing for the influence of ionic strength on ionic mobility,the absolute ionic mobility needs to be corrected with the empirical Eq. (14):

${{m}_{act}}={{m}_{0}}\exp \left( -\eta \sqrt{zI} \right)\left( \eta =0.77,ifz\ge 2;\eta =0.50,ifz=1 \right)$

(14)

$I=0.5\underset{i}{\mathop{\sum }}\,{{c}_{i}}{{z}^{2}}_{i}$

(15)

where,m_act and m₀ are the actual and absolute mo-bilities,respectively,I is the ionic strength,z is the ionic valence,and η is the coefficient. The ionic strength should be well controlled within 100 mmol/L,or Eq. (14) cannot well predict ionic mo-bility.

To calculate the conductivities of different phases,another equation (16) will be used ^[30]:

$k=F\left( \sum\limits_{i=1}^{n}{\left| {{z}_{i}} \right.}\left| {{c}_{i}}{{m}_{i}}+ \right.{{c}_{OH-}}{{m}_{OH-}}+{{c}_{H+}}{{m}_{H+}} \right)$

(16)

In Eq. (16),F means the Faraday constant. On the basis of the equations listed above,a mathematical model can be established. Then a computer program can be further developed to calculate the concentrations of different ions in phase β and the velocity of the derivatized MRB.

2 Experimental

2.1 Chemicals

Formic acid,NaCl were bought from Shanghai Chemical Reagents Co. (Shanghai,China),and both of them were AR (analytical reagent) grade. Sodium formate was purchased from Shanghai LinFeng Chemical Factory (Shanghai,China),and it was also AR grade. NaOH was bought from Shanghai Reagents Co.,and the grade was GR (guarantee reagent). The thymol blue used as an indicator was purchased from Shanghai Science Reagents (Shanghai,China). The agarose used as the anti-convection medium was a biochemical reagent (Shanghai Chemical Reagents Co.,Shanghai,China). Note here,the agarose gel is better in contrast to the agar gel,since there is an absence of electroosmostic flow (EOF) in agarose gel. L-phenylalanine (Phe) was purchased from Shanghai Chemical Reagent Co.

2.2 Apparatus

A high performance capillary electrophoresis (ACS 2000,Beijing Cailu Instrumental Co.,Beijing,China) was used,which was equipped with a power supply (up to a constant voltage of 30 kV),an HW-2000 Chromatography Workstation and a UV-VIS (ultraviolet-visible) detector (double beam,λ=190-720 nm,set at 210 nm). A fused-silica capillary was used (Factory of Yongnian Optical Fiber,Hebei,China),which is one with a total length 50 cm,effective length 40.5 cm and i. d. 75 μm. The runs were carried out with an air-cooled capillary at 20 ℃. The new capillary was conditioned by rinsing with 1.0 mol/L NaOH for 20 min,ultra-pure water for 10 min,1.0 mol/L HCl for 20 min and running buffer for 30 min,in order. A pure water system (Ultra Clear Basic,SG Wasseraufbereitung und Regenerierstation Gmbh,Germany) was used to produce the ultra pure water with the specific conductivity down to 0.055 μS/cm.

A home-made apparatus was developed from our previous apparatus ^[31]. A glass tube is filled with 20 g/L agarose gel containing the alkali NaOH,20 mmol/L NaCl and 1 g/L thymol blue. The tube,together with the ruler,was fixed on a small operating-table,over which an adjustable digital camera (Model DX6490,Kodak Co. Ltd.,US) was fixed. The camera was used to record the movement of the MRB with the time. With the two rubber-tubes,the two ends of the glass tube were connected to two three-way-pipes,which were joined with two peristaltic pumps (viz.,pumps 1 and 2,Model HL-2,Shanghai Huxi Analytical Instrument Factory,Shanghai,China) and two platinum electrodes (viz.,the anode and cathode). The flows of anolyte and catholyte were pushed by the two pumps. A power supply (Model DYY-12C,constant voltage 20-5 000 V,constant current 2-200 mA,Beijing Liuyi Instrument Factory,Beijing,China) was used to yield the direct current. The apparatus is very efficient and convenient for the experimental studies on MRB created with either strong or weak reactive electrolytes of acid and alkali.

2.3 Procedures

2.3.1 Derivatized MRB and its stacking in CE

Mark and stacking of derivatized MRB: the capillary as well as cathodic vial was filled with Phe. The anodic vial has 10-40 mmol/L pH 3.0 formic buffer. The derivatized MRB was between phases α and β. Because Phe can be stacked by the MRB if the proper concentration of formic buffer is used,the stacked Phe can dynamically tag the derivatized MRB.

Marks of initial MRB,MB (moving boundary) and derivative MRB: before the run,0.01% (v/v) DMSO (dimethylsufoxide) sample is injected at 1.5 kPa for 10 s. The DMSO marks the initial MRB and MB,and the stacked Phe marks the derivative MRB.

2.3.2 Procedure for observation from original to derivatized MRBs in tube

The run of MRB in tube with gel is performed in accordance with the “electrolytic-continuous-flow moving reaction boundary method”. The preparation of gel is according to the method described in Refs. (references) ^[11-12]. The original MRB in this paper is carried out as follows: (1) the agarose gel in the glass tube contains 5.0-80.0 mmol/L pH 3.0 fomic buffer+20 mmol/L NaCl+1 g/L thymol blue. (2) The anolyte holds the same formic buffer used in the glass tube,while the catholyte comprises 4.0 mmol/L NaOH+20 mmol/L NaCl+1 g/L thymol blue. (3) The power supply is turn on,with 6 mA constant current,and an original MRB is created between the pH 3.0 formic buffer in phase α and the alkaline buffer in phase γ just at the use of electric field. But after a while,a derivatized MRB is created between phases α and β,as shown in Fig. 1b. (4) Thanks to the existence of thymol blue in the whole MRB system,the right side of derivatized MRB in tube (including phases β and γ) turns blue,while the left side becomes light yellow. (5) By using a digital camera with high resolution,we can easily position the original and derivatized MRBs,further determine the displacement of derivatized MRB under a given time,finally calculate the experimental velocity of derivatized MRB with Eq. (17) under the given constant current 6.0 mA.

${{v}^{\alpha \beta }}_{exp,der}={{L}^{\alpha \beta }}_{der}/{{t}_{der}}$

(17)

where,v_exp,der^αβ is the experimental velocity of derivatized MRB,L^αβ_der is the length of movement of dervied boundary αβ within its given time t_der.

Fig. 1

Fig. 1 Model of derived MRB in boundary system initially formed with 5.0-80 mmol/L pH 3.0 formic buffer and 4.0 mmol/L NaOH a. original MRB formed between phase α (5.0-80 mmol/L pH 3.0 formic buffer) and phase β (4.0 mmol/L NaOH); b. derivatized MRB formed between phase α and phase β and stationary boundary formed between phases β and γ. “+” and “-” indicate the anode and cathode,respectively.

2.3.3 Procedure for computer simulation

On the basis of the model described in Section 1.3 and Eq. (5),we compiled a computer software with Delphi 7. The component and concentration of pH 3.0 formic buffer and NaOH buffer solution can be set in α phase and γ phase column,respectively. Then according to the input current density,the software can calculate the concentration of all the components,the ionic strength and conductance of the new formed phase as well as the velocity of the derivatized MRB with Eq. (5). And the results will be shown in β phase column. In the simulation herein,the following physico-chemical parameters are used for the computation. Formic acid (For^-): m₀=56.6×10^-9m²/(V\5s); pK_a=3.75; sodium (Na⁺): m₀=51.9×10^-9m²/(V\5s); (Cl^-): m₀=67.0×10^-9m²/(V\5s); hydrogen (H⁺): m₀=362.0×10^-9m²/(V\5s); hydroxyl (OH^-): m₀=205.0×10^-9m²/(V\5s). The data of the mobilities for simulation were used in Refs. ^[29-30]. The current intensity applied for simulation is 589.5 A/m².

3 Results and discussion

3.1 Stacking predicted by original MRB

If there is analyte in the boundary system of Fig. 1,the MRB may stack the analyte. According to the previous work ^[17],the stacking condition in Fig. 1a is

$\left| {{v}^{\gamma }}_{z-} \right|＞\left| {{v}^{a\gamma }}_{orig} \right|$

(18)

which indicates a stacking of zwitterion can be achieved if the velocity of zwitterion in phase γ $\left( {{v}^{\gamma }}_{z-} \right)$ should be higher than that of original MRB formed by phase α and γ$\left( {{v}^{a\gamma }}_{orig} \right)$. Otherwise the zwitterion in phase β cannot follow the original MRB moving toward the anode,consequently cannot be stacked by the MRB. According to the previous work ^[17],the velocity of original MRB in Fig. 1a should be computed with Eq. (1). The computation is given in Fig. 2. The velocity of Phe should be calculated with

${{v}^{\gamma }}_{z-}={{m}^{\gamma }}_{z-}i/{{k}^{\gamma }}$

(19)

where,i is the electric current intensity. The subscript of z^- indicates the zwitterionic ions carried negative charge(s) due to higher pH value of phase γ than pI of zwitterion. The velocity of Phe in phase γ is shown in Fig. 2.

Fig. 2

Fig. 2 Comparison between initial MRB velocity in Fig. 1a and Phe velocity in phase γ with 4.0 mmol/L NaOH+20 mmol/L NaCl

The comparisons of MRB and zwitterion velocities can be used for stacking prediction as shown in Ref. ^[17]. Fig. 2 shows the velocity of Phe and MRB of Fig. 1a,and implies such a prediction: if less than 7.2 mmol/L pH 3.0 formic buffer is used in phase α,the velocity of MRB towards the anode is greater than or equal to that of Phe moving towards the anode. So the Phe in phase γ cannot catch up with the MRB. As a result,no Phe stacking is induced by the fast MRB. However,if the higher than 7.2 mmol/L formic buffer is used,the velocity of MRB is less than that of Phe. The Phe can catch up with the MRB and be stacked by the slow MRB in line with Eq. (18).

3.2 Disaccord between experiments and original MRB theory

Fig. 3 shows the Phe stacking by MRB created with 10-40 mmol/L pH 3.0 formic buffer and 4 mmol/L NaOH. Fig. 3a displays that no stacking occurs,if 10 mmol/L pH 3.0 formic buffer is used to form the MRB. Fig. 3b verifies that the sharp stacking of Phe is achieved,if 20 mmol/L formic buffer is used. Fig. 3c or 3d manifests the powerful stacking of Phe,if 30 or 40 mmol/L formic buffer is used in phase α. Evidently,prediction fits the stacking of Panel b,c and d,while Panel a does not fit.

Fig. 3

Fig. 3 Phe stacking and boundary marks by MRB created with phase α with (a) 10,(b) 20,(c) 30 and (d) 40 mmol/L pH 3.0 formic buffer+20 mmol/L NaCl and phase γ with 4.0 mmol/L NaOH+20 mmol/L NaCl+10 ng/ml Phe Conditions: 52 cm in length (effective length 43 cm) and 75 μm i. d. capillary,210 nm,15 mbar 20 s sample injection,the voltage was 10 kV,and current was 10-20 mA,with 20 ℃ cooling air. DMSO: dimethylsufoxide.

According to the method of Fig. 1a,the MRB experiments in large tube were carried out,with which one can directly observe the boundary velocity. Fig. 4 shows the experiments of derived MRB originally created with 5.0-80 mmol/L pH 3.0 formic buffer+20 mmol/L NaCl and 4.0 mmol/L NaOH+20 mmol/L NaCl,as well as 1 g/L thymol blue in the whole system. Panel a displays the original MRB just before the use of electric field. Panels b to j reveal the 9.0 min anodic movements of the derived MRBs formed with phase β and α having 5.0,10,20,30,40,50,60,70 and 80 mmol/L pH 3.0 formic buffers+20 mmol/L NaCl,respectively. The results of Panels b to j unveil that the anodic movement of derived MRB become slower,if higher concentration pH 3.0 formic buffer is used to create the boundary. The qualitative results in Fig. 4 are in accordance with the prediction of Eq. (1),but there are evident differences between the quantitative analyses of experiments and computation with Eq. (1).

Fig. 4

Fig. 4 Nine min anodic movements of the MRB created with NaOH and HCOOH under the existence of 20 mmol/L background electrolyte NaCl in 20 g/L agarose gel a. original MRB; b-j: derivatized MRB. Conditions: phase α contains 20 mmol/L NaCl+1 g/L thymol blue+(b) 5.0,(c) 10,(d) 20,(e) 30,(f) 40,(g) 50,(h) 60,(i) 70 and (j) 80 mmol/L pH 3.0 formic buffer; phase β contains 20 mmol/L NaCl,4.0 mmol/L NaOH+1 g/L thymol blue; 20 g/L agarose gel. Current intensity: 589.5 A/m2; run time: 9 min; i. d. of the tube: 3.6 mm; length of the tube: 90 mm; flow rate of anolyte and catholyte: 0.6 mL/min. The anode is on the left and the cathode is on the right.

The experimental velocity of derivatized MRB in Fig. 4 can be computed with Eq. (17),the velocity of original boundary can be computed with Eq. (1). Fig. 5a shows the comparisons between the computation of original MRB velocity with Eq. (1) and the experimental velocity of derivatized MRB in Fig. 4. As shown in Fig. 5a,there are fair agreements between the theoretical results and experiments in Fig. 4,if high concentration (e. g.,70 and 80 mmol/L) pH 3.0 formic buffer is used as phase α. Whereas,there were great disaccords between the computation and the experiments,and there existed serious systemic errors between the experiments and calculations with Eq. (1),if low concentration (e. g.,5.0-60 mmol/L) pH 3.0 formic buffer is used. The reason why there are the disaccords is the formation of derivatized MRB,as will be shown in Sections 3.3 and 3.4.

Fig. 5

Fig. 5 Velocity comparison between (a) the experiments and computer simulating of derived MRB and (b) the experiments and theoretical computation with Eq. (1) The experiments and conditions are the same as those in Fig. 4.

The fair agreement between the computation and experiment with 60-80 mmol/L pH 3.0 formic buffer used as phase α may be caused by the following reasons. If high concentration formic buffer is used in phase α,the velocity of boundary becomes very slow. The limitation of the ruler is just 1 mm,so it is hard to distinguish boundary movement exactly. The small error of determination can be omitted if the boundary moves very fast (see Panels b-e in Fig. 4) under the conditions of low concentration pH 3.0 formic buffer,but result would have evident deviation if the boundary moves very slow under the conditions of high concentration formic buffer.

3.3 Existences of phase β and derivatized MRB

Fig. 3c shows the electropherogram of boundary initially formed with 30 mmol/L pH 3.0 formic buffer+20 mmol/L NaCl in phase α and 4.0 mmol/L NaOH+20 mmol/L NaCl+10 ng/mL Phe in the capillary and cathodic vial,viz.,phase γ. The initial MRB is marked with 1.5 kPa 10 s DMSO (0.6％,v/v) in 4.0 mmol/L NaOH+20 mmol/L NaCl. The low plateau indicates phase γ while the high plateau implies phase α and phase β since UV absorbance of the formate. DMSO is a neutral material with strong UV absorbance,hence the DMSO used herein can detect the initial boundary. The DMSO peak is nearly combined with the steep,viz.,the MB. This means the very slow movement of MB.

The Phe dissolved in phase γ can be used to mark the derivatized MRB because its velocity moving towards the anode is faster than that of derivatized MRB ^[17]. The left and right high plateaus are respectively phase β and phase α. The stacking peak of Phe indicates the position of derived MRB just passing through the detector.

Evidently,the experiments in Fig. 3c manifests that there are two boundaries in the reaction system. First is the derivatized MRB formed between phases α and β,and the second is a stationary boundary created with phases β and γ. Between the two boundaries,a new phase,viz.,phase β is formed. The experimental results prove the existence of phase β and derivatized MRB.

3.4 Numerical computation of component concentration in phase β

By the means of the developed numerical computation software described in Sections 1.3 and 2.3,we can calculate the concentration of all the components in phase β of Fig. 4. Table 1 shows the simulating results,which unveils the concentration of hydroxyl and chlorine ion in phase β are manifestly higher than that in phase γ containing 4.0 mmol/L NaOH+20 mmol/L NaCl. And the concentration of OH^- and Cl^- turns up (the concentration of OH^- raised from 3.97 to 12.22 mmol/L,while the concentration of Cl^- raised from 19.85 to 61.08 mmol/L) with the increase of the formic buffer concentration (from 5 to 80 mmol/L) in phase α. In the results of numerical computation,it could also be found that the concentration of sodium formic is from 0.01 to 0.49 mmol/L in phase β. In addition,there is no formic ion in the phase γ.

表 1 (Table 1)

Table 1 Computer simulation of ionic strength,conductance and concentration of components in phase β of the derivatized MRB of Fig. 4 c(Formic Hα)/(mmol/L) c(Iβ)/(mmol/L) κβ/(S/m) c(OH-β)/(mmol/L) c(Cl-β)/(mmol/L) c(Sodium formic-β)/(mmol/L) c(Na+β)/(mmol/L) 5 23.9 0.302 3.97 19.9 0.29 24.11 10 27.3 0.344 4.55 22.8 0.01 27.32 20 34.1 0.425 5.68 28.4 0.06 34.13 30 40.7 0.504 6.78 33.9 0.15 40.83 40 47.3 0.580 7.86 39.3 0.49 47.68 50 53.9 0.657 8.98 44.9 0.15 54.03 60 60.5 0.731 10.1 50.3 0.23 60.62 70 66.9 0.804 11.1 55.7 0.32 66.94 80 73.4 0.877 12.2 61.1 0.41 73.70

Table 1 Computer simulation of ionic strength,conductance and concentration of components in phase β of the derivatized MRB of Fig. 4

3.5 Agreement of experiments and simulations

According to the results of numerical computation in phase β as shown in Table 1,the software can calculate the velocity of the derivatized MRB with Eq. (5). The corresponding calculation data are given in Fig. 5a.

Fig. 5a shows the comparisons between the velocities of experimental and simulating derived MRB. There are high agreements between the experiments and numerical computations. The ratio between the experimental and numerical computing results changes from 0.93 to 1.12. While the ratio between the experimental and original academic results changes from 1.08 to 1.27. It is obvious that the computation is far more accurate and the serious systemic errors in Fig. 5b are evidently corrected by the derived MRB model and Eq. (5). The results in Fig. 5a demonstrate the validity of derived MRB model of Fig. 1 and Eq. (5) as well as the mathematical model for numerical computation described in Section 1.3.

With Eq. (5) and the calculation program achieved above,one can also compute the theoretical velocity of derivative MRB in Fig. 3. The velocity of Phe in phase β should be calculated with:

${{v}^{\beta }}_{z-}={{m}^{\beta }}_{z-}i/{{k}^{\beta }}$

(20)

rather than Eq. (19). Fig. 6 displays the velocity comparisons of derivative MRB with Eq. (5) and the analyte with Eq. (20). Panel a indicates such a prediction: if less than 10.3 mmol/L pH 3.0 formic buffer is used to create the boundary,the velocity of derivative MRB is higher than or equal to that of Phe,the Phe in phase β cannot catch up with the boundary,and cannot be stacked. Whereas,if greater than 10.3 mmol/L formic buffer is used,the velocity of MRB is less than that of Phe. Hence,the Phe can be stacked by the slow derivative MRB.

Fig. 6

Fig. 6 Velocity comparison between derivatized MRB and Phe

Evidently,such a prediction above is all proved by the experimental results in Fig. 3.

4 Conclusions

From the above results and discussion,one can conclude that (1) a new phase containing (0.01-0.49) mmol/L sodium formate+(3.97-12.22) mmol/L NaOH+(19.85-61.08) mmol/L NaCl derivatized from an original MRB formed with (5.0-80) mmol/L pH 3.0 formic buffer+20 mmol/L NaCl and 4.0 mmol/L NaOH+20 mmol/L NaCl; (2) the derivatization of the new phase leads to the formations of derivatized MRB (created between phase α and phase β) and stationary boundary (formed between phase β and phase α); (3) the new phase and derivatized MRB can be quantitatively investigated with CE,a home-made apparatus and numerical computation based on the developed MRB theory.

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