CHAPTER 1 Fundamentals of Capillary Electrophoresis Theory Kevin D. Altria 1. Introduction This section will describe the fundamental theory, equations, and defi- nitions necessary to comprehend the concepts involved in capillary elec- trophoresis (CE). This is not an exhaustive treatment, but is considered sufficient to comprehend and appreciate the principles of CE. More detailed theoretical background can be obtained from a number of refer- ence books (I-6). Developments in the field of CE are reviewed in detail annually in the journal Analytical Chemistry. For example, the 80 1 papers published in 1992-l 993 were recently reviewed (7). CE can be broadly described as high-efficiency separations of sample ions in a narrow bore (25-100 pm) capillary tube that is filled with an electrolyte solution. A typical schematic of an instrument setup is shown in Fig. 1. The principal components are a high-voltage power supply, a capil- lary that passes through the optical center of a detection system con- nected to a data acquisition device, a sample introduction system, and an autosampler. Typically, the CE instrument is controlled by a personal computer. The capillary is first filled with the required buffer solution. Sample solution (typically l-20 nL) is then introduced at the end of the capillary away from the detector (usually the anode). The capillary ends are then dipped into reservoirs containing high-voltage electrodes and the required buffer solution. One electrode is connected to a cable leading to From Methods m Molecular Bology, Vol 52 Capdary Electrophoresrs Ed&d by K Altrla CopyrIght Humana Press Inc , Totowa, NJ 3 4 Altria n High voltage supply 0 Empty vial Fig. 1. Typical instrumental setup. the high-voltage output, whereast he other (situated at the detector end of the capillary) is connectedt o an earthing cable. Electrodesa re composed of an inert material, such as platinum. Application of a voltage (for example, 10-30 kV) across the capillary causes electrophoretic and electroendosmoticm ovements( discussedl ater in this chapter) resulting in the ionic speciesi n the samplem oving along the capillary and passing through the on-line detector. A plot of detector response (usually UV absorbancew) ith time is generatedw, hich is termeda n electropherogram. 1.1. Electrophoresis This processi s the movemento f samplei ons under the influence of an applied voltage. The ion will move toward the appropriate electrode and pass through the detector. The migration rate, or mobility, of the solute ion is governed largely by its size and number of ionic charges. For instance, a smaller ion will move faster than a larger ion with the same number of charges. Similarly, an ion with two chargesw ill move faster than an ion with only one charge and similar size. The ionic mobility (pE) is therefore related to the charge/massr atio (Eq. [ 11). (1) Fundamentals of CE Theory 5 Detector response Fig. 2. Theoretical separation of a range of catrons. where PE = electrophoretic mobility, CJ= number of charges, IJ = solu- tion viscosity, and r = radius of the ion. Therefore, when we separate a hypothetical mixture of ions havmg different charges and sizes, the smaller, more highly charged ions will be detected first (Fig. 2). The actual electrophoretic velocity, or speedo f the solute ions, is related to their mobilities and the magnitude of the applied voltage (Eq. [2]). v=pEE (2) where v = velocity of the ion and E = applied voltage (volts/cm). 1.2. Electra-Osmotic Flow (EOF) Application of voltage across a capillary filled with electrolyte causes a flow of solution along the capillary. This flow effectively pumps solute ions along the capillary toward the detector. This flow occurs because of ionization of the acidic silanol groups on the inside of the capillary when m contact with the buffer solution. At high pH, these groups are dissociated resulting in a negative charged surface. To maintain electro- neutrality, cations build up near the surface. When a voltage is applied, these cations migrate to the cathode (Fig. 3). The water molecules sol- vating the cations also move, causing a net solution flow along the capil- lary (Fig. 3). This effect could be considered an “electric pump.” The extent of the flow is related (Eq. [3]) to the charge on the capil- lary, the buffer viscosity, and dielectric constant of the buffer: pEOF=(&&/q) (3) where pEOF = “EOF mobility,” IJ = viscosity, and 6 = Zeta potential (charge on capillary surface). 6 Altria Ftg. 3. Schematico f electroendosmoticf low. The level of EOF is highly dependent on electrolyte pH, since the &, potential is largely governed by the ionization of the acidic silanols. Below pH 4, the ionization is small (8), and the EOF flow rate is there- fore not significant. Above -pH 9, the silanols are fully ionized and EOF is strong. The pH dependence of EOF is shown in Fig. 4. The level of EOF decreases with increased electrolyte concentration as the 6 poten- tial is reduced. The presence of EOF allows the separation and detection of both cations and anions within a single analysis, smce EOF is sufficiently strong at pH 7, and above, to sweep anions to the cathode regardless of their charge. Analysis of a mixture of cations, neutral compounds, and anions would result in the electropherogram shown in Fig. 5. The migra- tion times correspond to the time the individual peaks pass through the detector. The smaller anions fight more strongly against the EOF and are there- fore detected later than anions with a lower mobility. Multiply charged anions will migrate more strongly against the EOF and will be detected later. Therefore, pH is clearly identified as the major operating param- eter affecting the separation of ionic species, smce it governs both the solute charged state and the level of EOF. The overall migration time of a solute is therefore related to both the mobility of the solute and EOF. The term apparent mobility @A) is measured from the migration time, and is a sum of both yE and pEOF: PA = pE + JJEOF= (ZL/ tV) (4) where I= length along the capillary (cm) to detector, V = Voltage, and L = total length (cm) of the capillary. Fundamentals of CE Theory 7 15 1 05 0 3 4 5 6 I 9 PH Fig. 4. Varlatron of EOF with pH. Mobility values can be calculated from migration times when both ionic and neutral components are measured. For instance, in the separa- tion of a five-component mixture shown in Fig. 5, the mobility values for the peaks are calculated and given in Table 1. Example peak 2 = IA = (1L/ Vt) = (50 x 57 / 30,000 x 500) = 1.9 x lOA vEOF (from peak 3) = (IL / Vt) = (50 x 57 / 30,000 x 600) = 1.58 x 10q j~E=pA-pEOF=0.32x IO4 The negative values of PE for peaks 4 and 5 indicate that they are anions. The separation of ions is the simplest form of CE and is often termed Free Solution Capillary Electrophoresrs (FSCE). The separations rely 8 Altria Frg. 5 Theoretical separation of a range of ionic and neutral solutes. Table 1 Calculated Mobility Values for the Peaks m Fig. 5 Peak no Mlgratlon time, s PA cm2/Vs PE 1 400 2.38 x lo” 080x lOA 2 500 190x1@ 0 32 x lOA 3 600 1.58 x 1W’ 0 4 750 1.27 x lo” -031 x lOA 5 900 1.06 x lti -052 x 10“ I = 50 cm, L = 57 cm, and V = 30,000 V principally on the pH-controlled dissociation of acidic groups on the sol- ute or the protonation of basic functions on the solute. In FSCE, all neutral compounds are swept, unresolved, through the detector together (Fig. 5). Separation of neutrals is generally achieved by incorporation of anionic surfactant, at sufficient concentration to form micelles. These anionic micelles migrate against the EOF and can chro- matographically interact with neutral solutes. Solutes having a large interaction will migrate later than those having little or no interaction. Use of micellar solutions is known as micellar electrokinetic capillary chromatography (also called micellar electrokinetic chromatography) and is covered in depth in Chapter 12, which is coauthored by the origi- nator of the technique. When dealing with large biomolecules, such as nucleic acids, their electrophoretic mobilities may be very similar, and FSCE is often insuf- ficient for adequate resolution. In this case, separations are performed in Fundamentals of CE Theory capillaries filled with gel solutions. In Capillary Gel Electrophoresis (CGE), a sieving effect occurs as solutes of various sizes migrate through the gel filled capillary toward the detector. Chapter 13 describes the excep- tional, efficient separations that can be obtained in gel filled capillaries. The separation and quantitation of chiral samples are an important area in many industries. Highly efficient chiral CE separations (Chapter 14) can be obtained by the addition of chirally selective substances, such as cyclodextrins, into the electrolyte. Capillary electrochromatography (CEC), which is a hybrid between CE and HPLC, has been developed. In this technique, CE equipment is used to generate HPLC-type separations. Capillaries are filled with HPLC packing material, and the application of a voltage results in the EOF pumping the mobile phase through the capillary. The full details of this technology and some applications are given in Chapter 15, which is written by one of the initial developers of the technique. 1.3. Sample Introduction Sample can be introduced into the capillary by three techniques, all of which involve immersing the capillary end into the sample solution and exerting a force to inject sample into the capillary. The three mecha- nisms for introduction of sample solution into the capillary are hydrody- namic, gravity, and electrokinetic. All these methods are quantitative, and equations describing the volumes injected have been derived. Figure 6 shows the principles of operation for the three methods. 1.3.1. Pressure Differential In this method, the sampling end of the capillary is immersed in the sample solution and a pressure difference applied (positive pressure or vacuum). The volume of sample solution injected onto the column can be calculated: Volume = AP d411t / 128 q L (5) where AP = pressure difference (mbar), q = buffer viscosity, L = total capillary length, and d = capillary diameter (pm). Table 2 gives injection volumes (9) for l-s injections using 65-cm capillaries of varying bore, TJ= 1, and various AP values. These volumes generally correspond to sample plug lengths of <l mm in the capillary. It should be noted that there is a viscosity term in Eq. (5). Therefore, it is important to match the viscosities of the samples and standards. Tem- perature, therefore, has a large influence on injection volume, since vis- 10 Al tria Hydrodynamic Pre Siphoning Electrokinetic Fig. 6. Diagram of the three sample mtroduction methods. Table 2 Inlectlon Volumes / s for Various Capillary Bores AP 50 pm 75 pm 100 pm 50 mbar 1 OnL 5 2 nL 164nL 75 mbar 1 5 nL 7 8 nL 246nL 100 mbar 2.0 nL 104nL 32.8 nL cosity is inversely proportional to temperature. For example, raising the temperature from 20 to 25°C causest he viscosity of water to change from 1.00 to 0.89 (IO). Therefore, it is essential to employ a constant tempera- ture during routine operation to ensure reproducible injection volumes. The sampling pressure or vacuum setting is generally instrument-spe- cific with the sampling variable being time. Lists are available from Fundamentals of CE Theory instrument suppliers that equate a sampling time to the respective vol- ume of sample (on the order of l-20 nL) introduced into the capillary. 1.3.2. Gravity Injection In this method (II), the capillary, while dipping into the sample vial, is mechanically raised above the height of the detector electrolyte vial. Typically, the sample vial may be raised 5 cm for 10 s. The volume injected (12) may be calculated: Volume = (pgAH d41Yt I/ 128 q 15) (6) where AH = height difference (cm), g = gravitational constant, and p = density of the liquid. An injection volume of 6.35 nL can be calculated for a 10-s injection at 5 cm using a capillary length of 67 cm and capillary diameter of 75 urn. The following values are employed in this calculation assuming water as the buffer at 20°C density is 0.99707g/mL, viscosity is 0.8904 x 1O-2 g/cm/s, g is 980 cm/s2. The sampling variables with this technique are time and the height the sample is raised. 1.3.3. Electrokinetic In this method, the sampling end of the capillary and the high-voltage electrode are inserted into the sample solution. A voltage is then applied, causing solute ions to enter the capillary by electrophoretic migration and EOF. A greater number of more mobile ions enter the capillary, which can lead to sample bias effects. This effect can be turned to advantage (1.3), especially when attempting to quantify trace levels of small ions. The amount introduced during electrokinetic sampling is related to a variety of factors (Eq. [6]). Q=[(~E+uEOF)VlY-Ir*Ct/L] (7) where Q = amount injected, C = concentration of sample, and r = capil- lary radius. The sampling variables are the level and polarity of voltage, and sam- pling time. Various modifications to these sample introductory procedures can be used to increase the volume of sample solution introduced onto the cap- illary dramatically. This has considerable benefit in terms of increased sensitivity. The various schemes reported are reviewed in Chapter 16 by the two most active developers of these techniques. 12 Altria 1.4. Peak EfCciency The capillary format employed in CE minimizes most sources of band broadening that occur in conventional electrophoresis or m HPLC. Joule heating-the heat generated within the capillary during the voltage l appllcatlon IS effectively dlsslpated through the capillary walls, which reduces convection-related band broadening encountered m conventional electrophoresrs; On-column detection-a portion of the capillary is used as the detector, which l ehmmates postseparation broadening effects owing to connections, and EOF flow dynamics-the flow profile of EOF is plug-like m nature, l which mmlmlzes sample dispersion during solute transport along the cap- illary, compared to the lammar flow encountered m pumped systems, such as HPLC. The major dispersive effect remaimng in CE is that of molecular dif- fusion of the solute as it passesa long the capillary. This diffusion IS low- est for large molecules, such as proteins, which have small diffusion coefficients. Therefore, it is possible to obtain theoretical plate counts (N) of several million for biomolecules, such as nucleotldes and proteins (Chapters 17 and 19, respectively). The theoretical plate count can be calculated: N= pEV/2D (8) where D = diffusion coefficient. References 1 Ll, S F. Y , ed (1992) Capillary Electrophoresls, Prmclples, Practice and Apple- catzons Elsevler. 2 Kuhn, R and Hoffstetter-Kuhn, eds. (1993) Capillary Electrophoresls Prznclples and Practzce. Springer-Verlag, Berlin. 3. Wernberger, R , ed ( 1993) Practical Capdlary Electrophorew. Acadermc, London 4. Grossman, P. D. and Colburn, J C., eds. (1992) Capillary Electrophoreszs’ Theory and Practice Academic, London 5 Vmdevogel, J. and Sandra, P., eds, (1992) Introduction to Mlcellar Electrobnetrc Chromatography Huthlg, Heidelberg 6. Camllleri, P., ed. (1993) m Capillary Electrophoresls Theory and Practrce CRC, Boca Raton, FL 7. Monmg, C A. and Kennedy, R T. (1994) Capillary electrophoresls Anal Chem 66,28OR-3 14R 8 Altna, K. D. and Simpson,C . F (1987) High voltage capillary zonee lectrophore- sis: operating parameter effects upon electroendosmotlc flows and electrophoretic mobllities. Chromatographla, 24, 527-530