Subscriber access provided by UB + Fachbibliothek Chemie | (FU-Bibliothekssystem)
Article
7 Approaches to Elimination of the Inherent Systematic Errors in Determination of Electrophoretic Mobility by Capillary Electrophoresis Pawe# Mateusz Nowak, Micha# Wo#niakiewicz, and Pawel Koscielniak Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.6b05036 • Publication Date (Web): 16 Feb 2017 Downloaded from http://pubs.acs.org on February 22, 2017
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
Analytical Chemistry is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
Page 1 of 22
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Analytical Chemistry
Article
7 Approaches to Elimination of the Inherent Systematic Errors in Determination of Electrophoretic Mobility by Capillary Electrophoresis Paweł Mateusz Nowak*, Michał Woźniakiewicz, Paweł Kościelniak Jagiellonian University in Kraków, Faculty of Chemistry, Department of Analytical Chemistry, Ingardena St. 3, 30-060 Kraków, Poland Author information. Corresponding author: Dr Paweł Mateusz Nowak, e-mail:
[email protected]; tel./fax +48 12 663 2257 Keywords: Capillary electrophoresis; Capillary cooling, Electrophoretic mobility; Electroosmotic flow, Joule heating, Voltage ramping
Abstract. Electrophoretic mobility is a basic parameter describing the electromigration of an ionized particle, which is used in many fields of analytical and physicochemical science. Its determination by capillary electrophoresis (CE) using a routine method is intrinsically affected by the generation of Joule heating, entailing a drop in viscosity and possible alteration of the degree of ionization, and also by other commonly overlooked effects: axial electric field distortion and voltage ramping. The aim of this work was to provide the first theoretical overview and experimental comparison of all accessible methods that could be used to prevent these sources of inaccuracy. We have discussed 7 independent approaches: (i) extrapolation of mobility to the zero power, (ii) initial buffer resistance-based correction, (iii) rational cooling adjustment, (iv) elimination of the non-thermostated capillary part, (v) inter-/extrapolation to the nominal temperature, (vi) internal standard-based correction, and (vii) simple recalculation based on the temperature rise. Two methodologies (v and vi) have been proposed for the first time. Furthermore we have shown how some approaches can be further developed, obtaining several novel and more sophisticated methods, which are also included in the comparison. Our investigation will help researchers to choose the optimal approach. We have also demonstrated for the first time how to measure the independent impact of four different effects. The outcomes reveal the compensatory character of some phenomena, and explain the highly diverse and unpredictable magnitude of the total errors. The use of a correction method seems crucial for ensuring the high reliability of CE-based analyses.
1 ACS Paragon Plus Environment
Analytical Chemistry
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 2 of 22
Introduction Electrophoretic mobility is a basic physicochemical parameter describing the migration of an ionized particle in an electric field. It is routinely determined by the capillary electrophoresis (CE) technique, using a simple equation:
∙
(1)
where µep is the electrophoretic mobility, Ltot and Leff are the total and effective capillary lengths (m), Unom is the nominal (programmed) separation voltage (kV); ttot is the total (observed) migration time of the analyte (min); while teof is the time measured for the neutral marker of electroosmotic flow (EOF). In CE electrophoretic mobility is an important analytical parameter. Due to its intrinsic independence from EOF, it is often a better criterion of peak identification than migration time and relative migration time.1,2 Electrophoretic mobility also does not depend on capillary dimensions and separation potential, enabling a transfer of methods between different experimental setups. Moreover, the transformation of an electropherogram from a traditional time scale into an alternative electrophoretic mobility scale may improve the reliability of the quantitative analysis.1-6 An accurate determination of electrophoretic mobility is also crucial in physicochemical analysis, in determination of the acid-base dissociation constant,7-11 the affinity/binding constant,12-14 and their thermal dependencies.15,16 Despite the fact that Eq.1 is broadly used in the literature, it yields a parameter value that is inherently affected by several different systematic errors. The first effect, widely studied in the past, is a rise in the actual temperature inside the capillary (see Fig.1A).17-19 This is due to Joule heating generation and inefficient heat dissipation. It is enhanced by the presence of two non-thermostated capillary parts,20,21 the inlet and outlet sections, although it also occurs in the thermostated part since temperature control is never ideal. It results in a drop in viscosity and in a consequent deviation of the mobility value from the nominal (assumed) experimental conditions. In the case of partially ionized compounds, the temperature rise may also alter their ionization degree because of a temperature-dependent shift of pKa.19,22 In some buffer systems the pKa value of the buffer component may also noticeably change upon temperature increase, e.g. in Tris-based solutions, leading to a shift in pH and thereby in the ionization degree of the analyte.19 Other effects are much more rarely considered, and in some cases probably simply overlooked. They are a ramping effect and an axial electric field distortion effect.
Fig.1 Schematic illustration of: (A) the profile of actual temperature along the capillary, with an indication of the average temperatures for two injection modes (long-end and short-end): Tlong-end and Tshort-end, respectively, and nominal temperature set using software – Tnominal; (B) ramping effect, with an indication of the average and nominal electric field strength, Eaverage and Enominal, respectively; (C) axial electric field distortion, with an indication of the nominal and average electric field strengths for two injection modes: Enominal, Elong-end and Eshort-end, respectively.
2 ACS Paragon Plus Environment
Page 3 of 22
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Analytical Chemistry
It is routine practice that the separation voltage is assumed to be constant during the whole analysis time. Nevertheless, it is generally advised to allow the electric field strength to grow to the nominal value for at least 0.1 min, and this prevents many undesirable effects related to a sudden generation of heat. 23,24 Therefore, the profile of the electric field as a function of analysis time resembles the one presented in Fig.1B. Despite the fact that normally used ramp times are relatively short and constitute only a minor part of the total migration times, the accuracy of electrophoretic mobility may be affected, especially in a fast analysis. It is also to be noted that the nominal electric field strength, defined by the nominal separation voltage and total capillary length, almost always differs from its average (effective) value for another reason. As follows from the profiles presented in Fig.1A and C, the higher is the local temperature (and the is higher conductivity), the lower is the local electric field necessary to preserve continuity of current.25-27 Average electric field strength is strictly dependent on the contribution of the non-thermostated section, which is normally different for the effective and total capillary lengths. Thus, the nominal value which is valid only for the whole capillary length is used in place of the average value, which is unknown, and this is another source of systematic error in electrophoretic mobility determination. Elimination of these effects has already been attempted in the literature using several distinct approaches,25-40 which are discussed in detail in the next part of the manuscript. These strategies are theoretically effective in regard to all or only to some inaccuracy sources. They have never been compared experimentally, and furthermore, they are not the sole strategies that could be used to tackle this general problem. The aim of this work was to present the first critical overview of all potentially applicable methods, including hitherto unreported approaches and novel variants of known correction strategies, combined with their experimental verification. To this end, we used a model sample containing several chemically different compounds and simple evaluation criteria. We studied the variation of electrophoretic mobility caused by different separation voltages and differences between the long-end and short-end injection modes, i.e. two independent runs performed with sample injection from opposite capillary ends, using the longer or shorter distance to the detector, respectively.37 We also demonstrated how to quantitatively assess the impacts of the individual effects, which enables a better understanding and prediction of errors.
Experimental section Sample material. The sample ingredients: 10-hydroxywarfarin (W10), amitriptyline (AMI), coumatetralyl (CT), and dimethyl sulfoxide (DMSO) were supplied by Sigma-Aldrich (St. Louis, MO, USA). All other chemicals were supplied by Avantor Performance Materials Poland. S. A. (Gliwice, Poland). All solutions were prepared in deionized water (MilliQ, Merck-Millipore Billerica, MA, USA) and filtered through the 0.45 µm regenerated cellulose membrane, then degassed by centrifugation. AMI was used as an entirely ionized base, CT as an entirely ionized acid, W10 as a partially ionized acid (pKa=5.95)9, and DMSO as the EOF marker to calculate electrophoretic mobility and as the analyte to calculate electroosmotic mobility. All compounds were dissolved in a background electrolyte (BGE), the concentration of AMI, CT and W10 was 0.20 mg/mL, whereas that of DMSO 0.1% (v/v). Instrumentation. The experiments were performed with a PA 800 plus CE System (Beckman Coulter, Brea, CA, USA) equipped with a diode array detector (DAD). A bare fused-silica capillary was applied, it had a total length of 31.1 cm, 21.1 cm effective length for the long-end injection and 10.0 cm for the shortend injection, 4.0 cm long inlet/outlet non-thermostated parts, 50 µm inner diameter and 375 µm outer diameter (Beckman Coulter). Sample injection was conducted using a low forward pressure of 2.0 kPa (0.3 3 ACS Paragon Plus Environment
Analytical Chemistry
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 4 of 22
psi) for 3 s, to minimize the length of the sample zone. Several different separation voltages were applied: 10.0, 14.0, 18.0, 22.0, 26.0 and 30.0 kV (normal polarity, anode at inlet). The measured current was between 20 – 75 µA. The voltage ramp time was set to 0.2 min. The capillary was conditioned at two temperatures (15 and 25°C) using a liquid cooling system. BGE was composed of the phosphate buffer (Na2HPO4/NaH2PO4) of 50 mM ionic strength and pH 6.0. All measurements were done in triplicate. See the Supporting Information for more details.
Theory General remarks. All methods described in this section may be used to correct both electrophoretic and electroosmotic mobilities. This issue and the potential contributions of minor effects other than those mentioned in the Introduction are discussed in the Supporting Information. Extrapolation of electrophoretic mobility to the zero power, Ia. This approach was proposed as an effective method for correcting electroosmotic28-30 and electrophoretic31 mobilities affected by excessive Joule heating. It was thoroughly discussed by Evenhuis et al.31 It requires several electrophoretic runs performed at different separation voltages to enable extrapolation of mobility, obtained using Eq.1, to the zero power where Joule heating does not occur (see Fig.2A). It assumes a linear correlation between mobility (µ) and electric power (P), i.e. the product of current (I) and voltage (U). This relationship derives from a direct proportionality between the temperature rise (∆T) inside the capillary and power per unit length applied.31
Fig.2 Various extrapolations used in the correction methods (real experimental data): (A) extrapolation of electroosmotic mobility obtained for DMSO at various average powers (Pav) – method Ia; (B) extrapolation of the ramping-corrected electroosmotic mobility obtained for DMSO at various average powers – method Ib; (C) extrapolation of resistance measured during the ramp time – method IIa; (D) extrapolation of resistance measured at various separation voltages – method IIb. Note that the application of the method Ib to determine electrophoretic mobility requires two extrapolations, independently for the analyte and the EOF marker.
Ib. Due to the ramping effect the average power values are different for the analyte and the EOF marker. To enable correction of this effect we propose another variant of this approach (Ib). It assumes the mathematical correction of mobility errors due to the ramping effect before mobility extrapolation and utilization of a more adequate model (Fig.2B). Accordingly, two independent extrapolations are required, for the apparent (observed) ramping-corrected electrophoretic mobility – µapp(ramp), and the ramping-corrected 4 ACS Paragon Plus Environment
Page 5 of 22
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Analytical Chemistry
electroosmotic mobility – µeo(ramp), respectively, performed with different values of average power, see the Supporting Information for more details. The corrected electrophoretic mobility value (in this method denoted as µep(Ib)) equals: () () ()
(2)
where µapp(ext) and µeo(ext) are the apparent and electroosmotic mobilities obtained by two independent extrapolations.Initial buffer resistance-based correction, IIa. Petersen and Hansen proposed another correction strategy, which was much faster because it required no additional measurements.32,33 In this approach the separation voltage is represented as a product of the average current (Iav) and the initial buffer resistance (R0). The use of average current eliminates any influence of voltage ramp time and current drift. R0 is the resistance of the buffer at zero electric power when Joule heating does not occur. Assuming that the mobility of all the ions shows the same dependence on viscosity, and that the temperature only modifies the conductance of the buffer by the change in viscosity, the use of R0 eliminates the viscosity effect.32 Taking into account the fact that Iav differs for the analyte and EOF marker, the corrected electrophoretic mobility can be calculated as: ()
()
( )
(3)
where µep(II) is the value of electrophoretic mobility corrected using approach II, and Iav(tot) and Iav(eof) are the average currents corresponding to the analyte and EOF marker. In the method proposed by Petersen and Hansen – (IIa), R0 may be obtained very easily, by using the increasing current values acquired during the voltage ramp time. Based on these values the actual resistance (R = U/I) is calculated, and presented on a plot versus voltage squared (U2).32 Then the linear model: R=aU2+R0 is extrapolated to U2=0, to obtain R0 (see Fig.2C). IIb. The inherent drawback of this method is the random uncertainty of a model built based on rapidly changing values measured during a very short period (ramp time). It is illustrated in Fig.2C as poor linearity of the extrapolative plot. This effect is enhanced in CE instruments equipped with an efficient liquid cooling system, as in this study, because the change in resistance upon voltage application is small. We assumed that a better model can be obtained by performing several electrophoretic runs at various separation voltages, see Fig.2D. In this method, denoted as IIb, the current is measured after the ramp time, when it is stable, and afterwards extrapolation is performed analogously. It requires the application of several voltages, but the additional measurements may be very short, each one
