Effect of non-thermostated capillary inlet in affinity capillary electrophoresis: Uranyl-selenate system at variable temperatures

Journal of Chromatography A, 1263 (2012) 189–193

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Effect of non-thermostated capillary inlet in affinity capillary electrophoresis: Uranyl-selenate system at variable temperatures Vladimir Sladkov a,b,∗ a b

CNRS, Institut de Physique Nucléaire (IPN), UMR 8608, Orsay F-91406, France Univ Paris-Sud, Orsay F-91405, France

a r t i c l e

i n f o

Article history: Received 14 June 2012 Received in revised form 27 August 2012 Accepted 13 September 2012 Available online 19 September 2012 Keywords: Affinity capillary electrophoresis Complexation Uranyl Selenate Temperature effect Non-thermostated capillary inlet

a b s t r a c t The influence of non-thermostated capillary inlet on accuracy of data obtained by affinity capillary electrophoresis is examined in the case of kinetically labile systems (with fast kinetics of equilibrium) at different temperatures. The system uranyl-selenate is studied in aqueous perchloric acid solutions (pH 2.5, ionic strength 0.05 mol l−1 ) in the temperature range from 15 ◦ C to 55 ◦ C. Moving of the sample through the non-thermostated inlet into the thermostated region of the capillary is used in order to avoid the influence of non efficiently thermostated short capillary inlet. The data on mobility values of uranyl and the values of stability constants obtained by this mode are compared with the data obtained in a traditionally used mode (injection in non-thermostated inlet region). The uranyl mobility values obtained by the two methods are different at temperature higher than 35 ◦ C. However, the difference between stability constants obtained by the two methods is not significant (ambient temperature is 20 ◦ C). © 2012 Elsevier B.V. All rights reserved.

1. Introduction Affinity capillary electrophoresis (ACE) is widely used for the determination of stability constants of complex species between metal ion and inorganic or organic ligands in the last years [1–13]. The recent achievements in this field are reviewed [14–19]. In the past decade kinetic capillary electrophoresis (KCE) as a conceptual platform for development of kinetic homogenous affinity methods is proposed for studying kinetics and thermodynamics of molecular interactions [20,21]. In KCE, differential mobility of target (substrate) and ligand is used to create conditions for measuring rate and equilibrium constants of their interactions. A number of methods are developed for systems with different types of kinetics [22–29]. These methods are widely applied for the study of biomolecular interactions. However, in papers [30,31] it was demonstrated, that the short non-cooled capillary inlet can lead to large systematic errors in quantitative CE-based affinity analyses. The temperature increase due to Joule heating in short non-cooled capillary inlet is a main source of these errors. One of the kinetic capillary electrophoresis methods, nonequilibrium capillary electrophoresis of equilibrium mixtures (NECEEM) [22–24,26], is used to demonstrate it. In this method the sample is pre-incubated to reach equilibrium before

the injection into the capillary (“pre-equilibrated mode”). Background electrolyte (BGE) does not contain any species of the sample mixture. Preliminary formed complex species dissociate during the electrophoretic run at these non equilibrium conditions. In this case the equilibrium constants can be found from the measured peak areas [22]. Based on the kinetics of the equilibrium, these systems can be classified as the systems with intermediate kinetics [15,32]. From the point of view of capillary electrophoresis time scale, the time required for dissociation of preliminary formed complex species is comparable with the migration time of these complex species. The systems of non-covalent complexes studied by affinity capillary electrophoresis, particularly “mobility shift assay”, have to be kinetically labile [15]. In this case the equilibrium is sufficiently fast and the time required for equilibrium is negligible compared with the migration time of species. In our paper we are interested in such systems with fast kinetics to understand if the short non-thermostated capillary inlet can lead to significant systematic errors in the determination of stability constants and ion mobility values. Uranyl-selenate system, which is a kinetically labile system [7], is chosen for this study. The different temperatures (from 15 ◦ C to 55 ◦ C) are tested. 2. Experimental 2.1. Chemicals and solutions

∗ Correspondence address: CNRS, Institut de Physique Nucléaire (IPN), UMR 8608, Orsay F-91406, France. Tel.: +33 0169156406; fax: +33 0169157150. E-mail address: [email protected] 0021-9673/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.chroma.2012.09.041

All chemicals used were of analytical reagent grade. The stock UO2 (ClO4 )2 solution (0.1 M in 0.63 M HClO4 ) was obtained by

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V. Sladkov / J. Chromatogr. A 1263 (2012) 189–193

dissolving UO2 (NO3 )2 ·6H2 O (>99% Fluka Puriss) in 12 M HClO4 (Merck Suprapur) and evaporating the resulting solution to almost dryness on a sand bath. The residue was dissolved in concentrated HClO4 and evaporated again. This last operation was repeated three times. Sodium selenate (Na2 SeO4 , Sigma ultra grade) was provided by Sigma–Aldrich. The aqueous solutions obtained from these products were checked by the capillary electrophoresis method described elsewhere [33]. Concentrated perchloric acid (60% solution from Sigma–Aldrich) is diluted in water to the requested concentration. The exact concentration is determined by acid–base titration with certified NaOH solution. Sodium perchlorate (99%, Fluka) was provided by Merck. The exact concentration of the diluted solution was determined by gravimetric method. Dimethyl sulfoxide (DMSO) (≥99.9%) was provided by Sigma–Aldrich. All solutions were prepared with deionised water (Millipore direct Q, R = 18 M). 2.2. Apparatus and software 2.2.1. Capillary electrophoresis measurements P/ACE system MDQ capillary electrophoresis instrument (Beckman Coulter, France) was used. The system is comprised of 0–30 kV high-voltage built-in power supply, equipped with a diode array detector. UV direct detection at 200 nm and at 230 nm was used in this work. A capillary (50 ␮m I.D., 363 ␮m O.D.) made from fused silica was obtained from Beckman Instruments and had a total length (L) of 31.2 cm and an effective separation length (l) of 21 cm. The capillary was housed in an interchangeable cartridge with circulating liquid coolant. The length of non-thermostated capillary inlet was about 4.2 cm (about 20% of the effective separation length). The ambient temperature was about 20 ◦ C. Every measurement was repeated at least three times. Data acquisition and processing were carried out with Karat 32 software (Beckman Coulter, France). All concentration and constant calculations were done with the EXCEL® and ORIGIN® software programs. The solver module was used for fitting experimental points by least squares curve fitting. 2.2.2. pH measurements A pH-meter GLP-21 (Crison, France) and a combination electrode were used for pH measurements after calibration against NIST standards (4.01 and 7.00). An aliquot of solution was used for each measurement. The pH value of solutions was 2.50 ± 0.05. 2.3. Procedure The capillary was conditioned prior to use by successive washes with 0.1 M sodium hydroxide, deionised water and the buffer solution under study. It was rinsed for 2 min (at a pressure of 103.4 kPa) with the buffer between two runs and kept filled with deionised water overnight. In order to avoid hydrolysis and/or polymerisation of the uranyl ion, that could potentially lead to the formation of additional species and/or to the modification of uranyl mobility values, we used the perchloric acid–sodium perchlorate aqueous solutions at pH value 2.5 as BGE. At such value and uranyl concentration of 1 × 10−4 M, the contribution of hydrolysed and polymeric species to U(VI) (VI is an oxidation number) is negligible [34]. The ionic strength (I) of BGE was 0.05 mol l−1 . The normal polarity mode was applied (injection is performed at the positive end). The sample, containing only uranyl ions and the neutral marker, was injected in the capillary. The capillary contained BGE (perchloric aqueous solution at pH 2.5 with ionic strength 0.05 mol l−1 ) with fixed concentrations of selenate ions. Sets of runs were then made for different concentrations of selenate (from 0 to 0.01 mol l−1 ) in BGE. The potential applied was 5 kV and the injection time (by a pressure of 3.45 kPa) was 4 s. This value

of applied voltage was chosen to respect the Ohm’s law. The current was about 30 ␮A and the input power was about 0.15 W. In these conditions we can estimate that the effect of Joule heating is insignificant in the thermostated part of capillary and the deviation from the desired temperature is a maximum of 1 ◦ C [3,35]. The separations were performed at constant forward pressure of 1.4 kPa. 2.4. Data treatments 2.4.1. Electrophoretic mobility determination The electrophoretic mobility  (m2 s−1 V−1 ) can be calculated by using a following expression: =

Ll(1/t − 1/teof ) V

(1)

where L (m) is the total capillary length, l (m) is the length between capillary inlet and the detection window, V is applied voltage in V, t (s) is the migration time of the studied species and teof (s) is the migration time of dimethylsulfoxide (DMSO), used as a neutral marker for electro-osmotic flow mobility determination. 2.4.2. Complex species mobility estimation at different temperatures In order to estimate the complex species mobility values we used the expression proposed in the paper [36], based on the relationship between the limiting conductivity 0 of an ion and the Stokes radius and a postulate that the volume of a hydrated complex ion is, to a first approximation, equal to the sum of the hydrated volumes of the constituent simple ions. 0complex =

|zcomplex |



3 (zi /0i )

1/3

(2)

0complex and zcomplex refers to the limiting conductivity and the charge of the complex, 0i and zi refers to the limiting conductivities and the charges of the species i, constitutive of the complex. By applying the relation between the limiting conductivity and the electrophoretic mobility, given by 0 =

0 F

(3)

where F is the Faraday constant, estimation of complex species mobility is possible [3]. An uncertainty of ±25% is considered for the calculation of complex species mobility [3]. The values of individual ion mobilities used for the calculation of the complex species mobilities with the expression (2) and (3) were taken from papers [37–41]. The values of limiting conductivities for uranyl at various temperatures have not been found in the literature. They are estimated with aid of Walden’s rule [42]. For extrapolation to needed ionic strength the equation based on Debye–Huckel–Onsager (DHO) limiting law and Pitts’ equation were used [43,44]. 3. Results and discussion On the electropherograms of 1 × 10−4 M U(VI) with increasing Se(VI) concentrations (from 0 to 0.01 mol l−1 ) in BGE at pH 2.5 only one peak is observed, whose mobility is diminished with the increase of ligand concentration in BGE [7]. We deal with kinetically labile complex system [6,15]. The equilibrium is sufficiently fast and the time required for equilibrium is negligible compared with the separation time [6,7,15]. The mobility observed corresponds to the sum of mobilities of coexisting different charged species of U(VI). U(VI) is presented as uranyl (aquacomplex UO2 (H2 O)5 )2+ ), whose mobility is positive, in the absence of selenate in BGE. In our

V. Sladkov / J. Chromatogr. A 1263 (2012) 189–193

case the mobility of U(VI) is diminished, as the mobility of the complex species formed is zero (UO2 SeO4 ) or negative (UO2 (SeO4 )2 2− ). The mobility of U(VI) can be calculated from the weighted average of the mobilities of the respective species [45]: U(VI) =



i ˛i

(4)

where i is the mobility of the respective U(VI) species and ˛i is its mole fraction. In the case of Se(VI) we can assume the following complexation equilibriums: UO2 2+ + SeO4 2−  UO2 SeO4

(5)

UO2 2+ + 2SeO4 2−  UO2 (SeO4 )2 2−

(6)

The stability constants are ˇ1 =

ˇ2 =

[UO2 SeO4 ]

(7)

[UO2 2+ ][SeO4 2− ] [UO2 (SeO4 )2 2− ] [UO2 2+ ][SeO4 2− ]

2

(8)

The expression for mobility values observed (derived from (4)) is U(VI) = ˛0 UO2 2+ + ˛2 UO2 (SeO4 )2 2−

(9)

where ˛0 = [UO2 2+ ]/CU(VI) = 1/(1 + ˇ1 [SeO4 2− ] + ˇ2 [SeO4 2− ]2 ) and ˛2 = [UO2 (SeO4 )2 2− ]/CU(VI) = ˇ2 [SeO4 2− ]2 ˛0 . (CU(VI) is the total concentration of U(VI) species). The expression (9) is used for fitting of the U(VI) mobility experimental points, obtained with different selenate concentrations at different temperatures. The values of stability constants ˇ1 and ˇ2 are obtained from this fitting. The electrophoretic mobility for complex species UO2 (SeO4 )2 2− is estimated with expressions (2) and (3). The selenate concentrations are calculated taking into account the dissociation constants of selenic acids at given ionic strength and at given temperature. The dissociation constant values for selenic acid at different temperature are taken from paper [46]. 3.1. Effect of non-thermostated capillary inlet To study the influence of non-thermostated capillary inlet on data obtained by ACE at various temperatures two modes of experimental design are applied: (I) the “traditional” mode (injection in non-thermostated capillary inlet) and (II) moving the sample through the non-thermostated inlet into the capillary thermostated region [2,30]. 3.1.1. Mobility determination in the case of moving the sample into the thermostated zone of capillary To calculate the ion mobility for the second mode, expression (1) needs to be modified. In this case l is no longer the length between the capillary inlet and the detection window, but is now the length between the position of the sample in the capillary thermostated zone and the detection window (l ). To find l we measure the retention time of marker (DMSO), using only forward pressure. In this case we can write p =

d2 l , 4tm

(10)

where p is the volumetric flow rate (generated by forward pressure, m3 /s), d is the capillary diameter (m2 ) and tm is the retention time of marker (s). The l can be calculated with aid of Poiseuille

191

equation for laminar viscous and incompressible flow and the expression (10): l =

Pd2 tm , 32L

(11)

where P is the applied pressure (Pa),  is the dynamic viscosity (Pa s) and L is the total capillary length (m). Knowing the water viscosity at the given temperature [47], we can calculate l with expression (11). It should be noted that here we use the aqueous BGE, consisting mainly of sodium perchlorate electrolyte with an ionic strength of 0.05 mol l−1 . Such concentrations of sodium perchlorate do not modify the viscosity of water [47,48] and we can suppose that the viscosity of the BGE is the same as that of the water. l is calculated as the average value from the 10 measurements for each temperature. The time chosen for the moving the sample through the non-thermostated inlet is 30 s (under the pressure of 6.9 kPa). With these parameters, as it has been found, we can be sure that the sample is present in the thermostated part of capillary at all temperatures studied (i.e. l < l − linlet ). 3.1.2. Comparison of two modes The mobility values of uranyl obtained in this manner are compared with the values obtained in a traditionally used mode, when sample is not moved in the capillary thermostated region. The results are presented in Fig. 1. The electrophoretic mobility of U(VI) increases with increasing temperature, as the mobility value is inversely proportional to the media viscosity: =

q 6r

(12)

where q is the charge of the ionised solute and r is the solute radius. The water viscosity decreases as temperature increases. The mobility values obtained by two modes are plotted versus 1/ at different temperatures (Fig. 1A). From this figure we can see, that the mobility values in the temperature range from 15 ◦ C to 35 ◦ C are only slightly different (almost in the limit of experimental errors), but with a temperature increase from 35 ◦ C to 55 ◦ C the difference becomes more important. According to the expression (12) the plot of mobilitiy values from 1/ should pass through zero ( → ∞,  → 0). It is a case, when the mode of the sample moving in the capillary thermostated region is used. If we compare the Walden products (products of mobility and viscosity) calculated for two cases (Fig. 1B), we observe that it is practically constant in the studied temperature range in the second case. It is characteristic for hydrated uranyl ions. As noted in [42], the ions for which Walden product is most nearly constant are those of large size, wherever this large size is due to their being polyatomic or to extensive hydration. Thus, the mobility values obtained with the use of the second mode seem to be more accurate at elevated temperature (from 35 ◦ C). The impact of the capillary non-thermostated part becomes more important at elevated temperature, as the temperature difference between thermostated and non-thermostated zones of capillary increases with the temperature increase of the capillary thermostated part. The values of stability constants are determined at various temperatures with the use of these two modes. The experimental points and fitting curves (with expression (9)) obtained at different temperatures for uranyl-selenate system are presented in Fig. 2. The electrophoretic mobility of U(VI) increases with increasing temperature since, as already noted, the mobility value is inversely proportional to the media viscosity (expression (12)). The stability constant values ˇ1 and ˇ2 obtained at different temperatures are presented in the table. For the first stability constants we do not find the difference between values obtained by two modes at all temperatures studied. In the case of the second stability constant,

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V. Sladkov / J. Chromatogr. A 1263 (2012) 189–193 Table 1 Values of stability constants obtained at various temperatures by two modes: traditionally used (I) and moving the sample into the capillary thermostated region (II). I = 0.05 mol l−1 , pH 2.5. Temperature (◦ C)

Log ˇ1

Log ˇ2

I 15 25 35 45 55

2.19 2.24 2.32 2.41 2.48

II ± ± ± ± ±

0.03 0.02 0.02 0.03 0.02

2.15 2.27 2.33 2.44 2.51

I ± ± ± ± ±

0.03 0.03 0.02 0.02 0.02

2.97 3.24 3.32 3.42 3.69

II ± ± ± ± ±

0.07 0.06 0.08 0.10 0.11

3.07 3.23 3.39 3.51 3.64

± ± ± ± ±

0.08 0.08 0.09 0.09 0.10

the values obtained by two modes are slightly different at the temperature other than 25 ◦ C. However, because of uncertainty of estimated complex species mobility values (25%), this difference is not significant, as the confidence intervals for the values of the second constants overlap (Table 1). 4. Conclusion

Fig. 1. (A) Mobilities of 1 × 10−4 M uranyl, as a function of viscosity, measured by two methods: traditionally used (I) and moving the sample into the capillary thermostated region (II). Straight lines are the trend curves. I = 0.05 mol l−1 , pH 2.5. (B) Walden product, as a function of temperature, obtained with two methods.

Acknowledgements

7 6

4

8

I am grateful to Dr. Jean Aupiais for fruitful discussions. I also thank Dr. Marion Mac Cormick for English language corrections.

55 °C 45 °C

References

35 °C 25 °C

2

µ ×10 , m V s

-1 -1

5

3 15 °C

2 1 0 1E-6

The impact of non-thermostated capillary inlet on experimental data accuracy is examined in the case of affinity capillary electrophoresis. The kinetically labile uranyl-selenate system is chosen for this aim. The results obtained demonstrate, that the nonthermostated capillary inlet does not have a significant impact on the values of the stability constants determined, although we could expect to have some significant difference due to the temperature change in the non-themostated zone. It seems that the contribution of error because of the presence of the short non-thermostated part of capillary is not significant in the overall experimental error. We can consider that the values of the stability constants obtained by ACE at ambient temperature in a traditionally used mode are accurate. Thus the influence of non-thermostated capillary is much less important in the case of ACE, where the systems with fast kinetics are used, than in the case of the method of nonequilibrium capillary electrophoresis of equilibrium mixtures (NECEEM) for systems with intermediate kinetics. At eleveted temperature it seems that moving the sample through the non-thermostated inlet into the thermostated region of the capillary is preferable, as more accurate results are expected. But the presicion, especially in the case of the second constant, is not enough to conclude it with certanity.

1E-5

1E-4

1E-3

0,01

0,1

2-

[SeO4 ], M Fig. 2. Experimental points (solid symbols) for U(VI) mobilities and fitting curves (dashed lines) as a function of [SeO4 2− ] concentration at different temperatures. Method II. pH 2.5, I = 0.05 mol l−1 (NaClO4 –HClO4 ).

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