MEASURING THE LENGTH OF HYDRODYNAMICALLY INJECTED PLUGS IN CAPILLARY ELECTROPHORESIS USING THE ELECTRICAL CURRENT MONITORING.
Guillaume L. Erny and Alejandro Cifuentes*
Institute of Industrial Fermentation (CSIC), Juan de la Cierva 3, 28006 Madrid, Spain
*Corresponding author. Tel.: +34-91-562-2900; fax: +34-91-564-4853. E-mail address:
Abbreviations:CM, Current monitoring; IS, Internal standard
Keywords: Current monitoring, quantitative analysis, reproducibility
Abstract
Although Capillary Electrophoresis (CE) is nowadays a worldwide separation technique, it is generally recognized that one of its main limitations is its poor robustness for quantitative analysis. Although this limitation can partially be surpassed using internal standards, it is well known that to find adequate standards is a very difficult task when too complex mixtures have to be analyzed. In this work, an alternative method to improve quantitation by CE is presented using the electrical current profile monitored during any CE run. Thus, an abrupt step in the current monitoring is observed when a hydrodynamically injected plug of conductivity different from the background electrolyte leaves the capillary under the influence of the electroosmotic flow. It is demonstrated that under these conditions, the relative amplitude of this step can be used to experimentally measure the injection length. This measure can not only be used for calibration, but also to correct variations of the length injected what is demonstrated to significantly improve the quantitative accuracy and reproducibility of CE. Thus, RSD values for inter-day quantification (5 experiments a day for 5 days) were improved from 10.5 % to 4.2 %. Moreover, it is also demonstrated that accuracy of quantitative determinations by CE can greatly be improved by using this procedure. The method can also be implemented in other separation techniques where the electroosmotic flow is used as driving force (e.g., capillary electrochromatography, micellar electrokinetic chromatography or chip based separations). Advantages and limitations of this approach in comparison to the use of internal standards are also discussed.
1. Introduction
Although Capillary Electrophoresis (CE) can be considered a well-established analytical technique, CE still shows low precision and accuracy for quantitative analysis. It is usually accepted than this is mainly due to the poor reproducibility of the volume of sample injected[1], but also due to the detector (e.g. low signal to noise ratio and data-sampling rate)[2,3], the integration software[4], and other physical effects that might occur during the separation[5,6]. The poor reproducibility of the injected sample is due to various causes (variation of pressure and viscosity, capillary diameter, evaporation, etc)[1], and they are usually responsible for 1 to 3% of the relative standard deviation (RSD) observed [7].
Internal standards (IS) have successfully been used to correct the poor reproducibility of the injection mode in CE, and together with adequate separation conditions (high signal/noise ratios, high sampling-rate, etc) can provide RSD values as low as 1%[8,9]. However, the choice of a given internal standard is not straightforward. The internal standard should not be present in the original sample, be resolved from the target analytes and have physico-chemical properties (e.g., mobility, solubility, extinction coefficient, etc) close to that of the target analytes[9]. Other requirements for IS are: they have to be stable in solution, commercially available, with high purity and they should provide a high signal under the detection conditions [1].
In this paper we present an alternative procedure to measure the hydrodynamically injected volume in CE based on the electrical current signal or current monitoring (CM) recorded (together with the electropherogram) by any commercial CE apparatus. The first application of CM was proposed by Huang et al. to measure the electroosmotic flow (eof) rate[10]. In that method, the capillary and outlet vial were filled with a solution of a given conductivity, whereas the inlet vial was filled with the same solution but at a different concentration. When the voltage was turn on, under the influence of the eof, the solution in the inlet vial replaced the solution in the capillary. The recording of the current showed a change in the intensity of the current, which allowed determining the eof. This method is now often used to measure and study the eof in microfabricated devices[11-14].
The goal of this work is to demonstrate that when working with an hydrodynamically injected zone of different conductivity to that of the background electrolyte, the recording of the electrical current signal allows determination of the length of the injection plug, and thus to correct the poor reproducibility of the injection in CE. The initial background theory is similar from the work of Chien and Helmer [15] in which they studied eof and peak broadening in field-amplified capillary electrophoresis; however, the last steps of our theory and its application are totally different from that work (vide infra).
2. Theoretical section.
In a conductor with a non-uniform conductivity or cross sectional area, the resistance R is obtained from the Ohm’s law:
(1)
where L is the total length of the conductor, κ(x) is the electrical conductivity at point x and A(x) is the cross sectional area at this position. Applying this equation to the case of a capillary filled with a background electrolyte (BGE) of conductivity κ with the presence of an injection plug of length l0, and conductivity κ0 = ακ (being α a proportionality factor < 1 that can be easily calculated as described under Experimental), and assuming no interaction between the two zones of different conductivity, the resistance is
(2)
where x = (l0/L). The current, Ib, measured when applying a voltage V in the presence of the injection plug (see Figure 1) will be
(3)
This last equation is the one already proposed by Chien and Helmer[15]. In our case, Equation 3 is rearranged to
(4)
where Ia is the current measured after the injection plug has left the capillary (x = 0) and As is the relative amplitude of the step in the CM due to injection plug leaving the capillary (see Figure 1). However, in equation 4, it has been assumed that there is no interaction between the two zones; therefore, this equation 4 will only be accurate at time zero. As a function of time, diffusion will decrease the concentration in the injection plug, and increase the length of the plug.
The electrical conductivity of an electrolyte is given by
(5)
where F is the Faraday constant. When the injection plug has totally diffused, the concentration of the specie i will be constant and equal to ci, = (1-x) ci,0 + xαci,0, where ci, is the concentration after the injection plug has totally diffused, and ci,0 is the initial concentration in the BGE. Using equations 2 and 5 it can easily be shown that the resistance will tend to
(6)
In this case the current Ibis given by
(7)
and the relative amplitude in the current by
(8)
Therefore, when an injection plug is present, the electrical current will increase from the value given in equation 3 to the value given in equation 7, and with this, the relative amplitude of the step. The speed in which the electrical current can vary will depend on the diffusion constant of the species in the injection plug, D, and the length of the injection plug. To study this process a simulation will be performed in the following section.
The step in the electrical current monitoring due to the injection plug leaving the capillary has previously been used to measure the electroosmotic mobility in CE[16-18]. However, to our knowledge, its application to determine the injection length has not been reported yet. Thus, the application of equations 4 and 8 to measure the length injected in CE will be discussed in the following sections, comparing this procedure with that more common based on the use of internal standards (IS). The fact that the sample has to be injected in a diluted BGE is not detrimental to the interest of this new method. This will induce a stacking effect[19], which might increase the efficiency and resolution of the separation. Moreover, it is already well known in CE that if the sample is in a high conductive medium, defocusing will occur.
2. Experimental section.
2.1 Chemicals.
Sodium hydroxide, boric acid and m-hydroxybenzoic acid were from Merck (Darmstad, Germany). Water was deionized with a Milli-Q system (Millipore, Bedford, MA, USA).
2.2 Buffers preparation.
Two sodium borate buffers were used in this work. They were constituted of 50 mM boric acid with 25 mM NaOH (25 mM sodium borate buffer at pH 9.1), and 100 mM boric acid with 50 mM NaOH (50 mM sodium borate buffer at pH 9.1).Buffers were sonicated before use.
2.3 Separation conditions.
CE experiments were performed on a P/ACE MDQ CE instrument from Beckman (Fullerton, CA, USA). The capillaries used were bare fused silica with 50 μm i.d. and 363 μm o.d. (Composite Metals, Worcester, UK.), with 500 mm of total length (400 mm detection length). Sample injections were performed using a pressure of 0.5 psi. Before first use, capillaries were conditioned in the following way: a 20 min rinse with 0.1 M NaOH was followed by a 20 min water rinse. Between injections, the capillary was flushed with 0.1 M NaOH for 1 min and BGE solutions for 2 min. The wavelength was set at 214 nm. The ramp time of the voltage (time to go from zero to the marked value) was set at 10 s. The capillary was thermostated at 22 or 25C.
2.4 Samples preparation.
m-hydroxybenzoic acid (m-HBA) was dissolved at the indicated concentrations in different BGE:water dissolutions.
2.5 Measuring of value.
In order to experimentally determine the value (see Equation 2), the CE instrument was used as a conductimeter[20-21]. Namely, the electrical current of each sample (or BGE) was measured by filling the capillary with the sample (or BGE). The electrical current was measured applying a voltage of 5 kV. The value was determined dividing the electrical current obtained with the sample by that obtained with the BGE.
3. Results and discussion
3.1. Determination of the injection length.
Equations 4 and 8 have been proposed in the theoretical part to correlate the relative amplitude of the electrical current step (see Figure 1) to the difference of conductivity between the BGE and injection plug, and the length of the injection plug. Equation 4 should be accurate at time zero, while equation 8 should give an accurate value at infinite time. To validate this model, a simple dynamic simulation of the changes in concentration of the co- and counter-ions as a function of time has been performed. The numerical scheme used was the following central difference scheme[22]
(9)
where C is the concentration, D is the diffusion constant, is the electrophoretic velocity and t and z correspond to small intervals of time and distance, respectively. To study the diffusion in the injection plug, simulations were performed assuming that the electrophoretic velocity was zero. From the concentration distribution obtained, the conductivity was calculated (using 4.6 and 5.2×10-8 m2 V-1 s-1 for the mobility of the co and counter-ion respectively) at all points in the capillary and time of the separation, and the theoretical current ratio Ib/Ia as a function of time by summing the local conductivities over the capillary length. Simulated parameters where L = 0.5 m, Δx = 2.5·10-4 m, Δt = 5s, D = 5·10-9 m2 s-1 (diffusion coefficient) and C = 50 mM. The simulation, performed using an injection length of 2.5 mm and α = 0.2 (a), together with the theoretical ratio of current obtained using equation 3 (b) and 7 (c) is shown in Figure 2. As predicted the ratio of current will start at the value predicted by equation 3, then increases and tends to the values predicted by equation 7. In this Figure 2 the time at which the injection plug leaves the capillary has been arbitrarily selected at 9 min. To study the effects on the injection length, the relative standard error (RSE), using either equation 3 (RSE3) or equation 7 (RSE7), obtained during the current prediction has been calculated for different injection lengths (. The current was measured after 5 min of simulation time. The RSE was calculated using
(10)
where is the electrical current when the injection plug is present and obtained by the simulation after 5 min. It could observed that better RSE values were obtained using equation 7 than equation 3 for short injections (namely, for x = 0.002 values were RSE7 = 0.02% and RSE3= -0.4%; for x = 0.01 values were RSE7 = 0.76% and RSE3= -1.43%). On the other hand, better RSE values were obtained using equation 3 compared to equation 7 for long injections (namely, for x = 0.04 values were RSE3= -1.43% and RSE7 = 7.08%; for x = 0.06 values were RSE3= -1.36% and RSE7 = 11.2%). Whereas for short injections (1% or less of the total capillary length) equations 7 and 8 will give a good estimation of the electrical current and of the relative amplitude of the step, for long plugs (5% or more that the total capillary length) equations 3 and 4 will be more suitable.
Figure 3 shows that the limit of quantification of the amplitude of the step in the CM is around 0.05 µA. Moreover, both the electrical current curvature and its step are visible in this Figure 3 in good agreement with our model. However, inspecting carefully the data it is observed that the noise is not due to the inherent limit of this approach, but to the limited performance of the device used for monitoring the electrical current signal. This can be observed if Figure 3 by the discretisation of the data.
To corroborate the proposed model different experiments were performed using a 25 mM sodium borate buffer at pH 9.1. The injection plug was constituted of different ratios of BGE:water (50:50, 25:75 and 10:90), and injected for different time (3, 5, 7, 10 and 20 seconds) at a pressure of 0.5 psi. The separation was carried at 20 kV, and the capillary was thermostated at 22°C. With hydrodynamic injection, the relation between injection time (tinj) and l0 can be determined using the Poiseuille equation[23]
(11)
where ΔP is the pressure difference across the capillary, dc is the capillary internal diameter, and η is the viscosity. Since a deviation of around 4% in the internal diameter can be expected with any capillary manufacturer[24], this will give a deviation around 8% in the determination of l0. Adding to this the uncertainty in the viscosity (and sometimes in L), a deviation higher than 10% can be expected in l0 using equation 11.
In order to obtain a more precise empirical expression for our CE conditions, the following experiment was carried out. First, both the capillary and the sample were thermostated at 22C; the coating was removed over 2 mm at the inlet of the capillary to reduce sample carryover[5], and the capillary shape at the injection end was checked using a microscope. The outlet vial during the sample injection was filled with water to avoid any siphoning effects. Under these conditions, the sample was pushed through the capillary by applying a pressure of 0.5 psi until reaching the detection window; knowing l0 (in this case the detection length) and determining tinj (the time required to fill the detection length), the equation l0 = 0.53(± 0.01)·tinj (n = 3) was then experimentally obtained, showing a reasonable agreement with the theoretical expression of 0.56·tinj obtained using the Poiseuille equation.
In Figure 4, AS as a function of l0, calculated using l0 = 0.53(± 0.01)·tinj, is plotted for α = 0.10. Each experiment has been performed in triplicate. The experimental values are compared with the theoretical values obtained using equation 8 (straight line). A good agreement can be observed between the theoretical and experimental values until l0 6 mm. Similar results were obtained with α = 0.50 and α = 0.75 (data not shown). These results are in good agreement with the behavior expected at different injection lengths as already predicted and discussed above.
In order to further corroborate the suitability of this new approach, the following experiment was carried out. Thus, according to equation 8 and postulating k = l0/tinj, the plot of As as a function of tinj should give a straight line, with an origin at zero and a slope equal to k/L(1- α). In order to probe this, a sample plug with α = 0.25 was injected for tinj = 3, 4, 5, 6 and 7 s in a capillary thermostated at 25°C. Under these conditions, the linear regression gave an r2 of 0.947 with an origin at 0.07 ± 0.21 and a slope equal to 0.92 ± 0.06 s-1. The experimental k value was found equal to 0.62 ± 0.04 mm s-1. This value compares well with the theoretical k of 0.60 mm s-1 obtained using the Poiseuille equation, and the measured value, determined as previously, of 0.65 ± 0.01 mm s-1. These results demonstrate that the CM approach can be used to experimentally determine the length of the injected plug with good accuracy and precision.
3.2. Precision and accuracy of the quantitative analysis after correction of the injection length using the current monitoring.
To demonstrate that this approach can improve the precision and accuracy in CE, two series of experiments were performed (see below). For each experiment, the peak area was corrected in two different ways: using AreaN (i.e., the typical normalized area used in CE, that is, peak area divided by migration time) and AreaCM (i.e., the CM-corrected normalized area, that is, the AreaN value multiplied by the theoretical injection length in each case l0the and divided by the injection length determined experimentally using the CM, l0CM). RSDN and RSDCM are the relative standard deviations of AreaN and AreaCM, respectively.
For the first series of experiments, the RSD value was determined for the peak area of a test analyte injected five times per day for five consecutive days. In this experiment all injections were directly considered without using any injection to stabilize the instrument at the beginning of the day. Results are summarized in Table 1. For each day, peak area was measured using the two procedures mentioned above obtaining AreaN, AreaCM, RSDN and RSDCM. As can be seen in Table 1, the intra-day RSDN shows huge variations from day to day; 15.6 % the first day, around 5 % the second and third day, and around 9 % the last two days. Whereas, 5 % is an acceptable RSD when quantifying without internal standard, 9 and 15.6% are quite poor. This can be due to a temporally plugged capillary or not stabilized CE conditions. Interestingly, after correcting for l0 using the CM, the RSD is always lower with values ranging from 3.3% to 4.3%. This clearly indicates that the CM approach can be used to correct variations of the injection length. This is confirmed by the low inter-day RSD obtained after CM correction. Using CM, the inter-day RSD value (five days) has been improved by a factor of 2.5, namely, RSDN = 10.5% and RSDCM = 4.2% were obtained in each case.