2010 A&. Chem. 1993, 65, 2010-2013

Electroosmotic Flow Control and Surface Conductance in Capillary Zone Electrophoresis Mark A. Hayes, Indu Kheterpal, and Andrew G. Ewing' Department of Chemistry, The Pennsylvania State University, 152 Davey Laboratory, University Park, Pennsylvania 16802

Electroosmotic flow within capillary zone elec- trophoresis can be altered electronically through a mechanism modeled as surface conductance. Experimentally, a small zone of conductive silver on the outer surface of the capillary is shown to permit good control of electroosmotic flow with an applied external voltage. This control is mod- eled as capacitance across the capillary wall and conductance along the double layer on the inner surface. Experimental results presented agree with theory developed from this model. Surface conductance in capillary zone electrophoresis may significantly simplify electronic control of elec- troosmotic flow and lead to a better understanding of the effects of chemical modifications to the inner surface of the capillary.

INTRODUCTION

Capillary zone electrophoresis (CE) is an important emerging analytical technique.13 Within this technique, we have examined the effect of an external voltage applied across the capillary wall on electroosmotic flow where this field was created by a conductive sheath covering only a small portion of the capillary. This is in contrast to former experimental apparatuses in which a radial voltage is applied over a maximum available outer surface area.4-6 We can relate these experiments to the double layer on the inner surface and surface conductance within this double layer.

One of the most important electrokinetic phenomena for reprodicibility in CE is electroosmotic flow. This flow can be altered by chemical modification of the capillary wall,1v7~8 adjustment of buffer pH9-l1 or ~ o n c e n t r a t i o n 2 J ~ ~ ~ the ad- dition of surface-active species (surfactants, glycerol,

(1) Jorgemon, J. W.; Lukaca, K. D. Science 1983,222,266-272. (2) Gordon, M. J.; Huang, X.; Pentoney, S. L.; b e , R. N. Science

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0003-27001 93/036!S2~10$04.00IO

Radially Applied Conductive Silver Paint

Flgwe 1. Schematic of the apparatus used to control electr"otic flow. A radial voltage is applied via a small portion of silver paint on the outsMe of the capillary or a tangential steel plate. The apparatus is similar to that in ref 28 wtth a conducting sheath that covers from 4 to 61 % of the length of the outer surface of the capillary.

etc.)lJJ5 or organic modifiers to the buffer,16 and the application of applied radial voltage to the capillary Experimental techniques developed for the electronic control of electroosmotic flow have utilized a radial voltage field over the majority of the length of the capillary. This has led to effective and practical experimental schemes. Theory de- veloped to data has assumed that the radial voltage affects the ( potential (hence flow) only in those portions of the capillary directly inward of the external voltage field.f+J7 In the experiments presented here, a relatively small portion of the outside center of the capillary has been covered with a conductive silver paint or a tangential-contact flat steel plate and attached to a 0-30-kV power supply (Figure 1). In this configuration, electroosmotic flow may still be controlled to a similar extent as with the other published systems. These results apparently defy previous theories on the electronic and molecular mechanism of electroosmotic flow control. Electroosmotic flow is not the only electrokinetic action to appear upon the application of the high-voltage separation field; electrophoresis and surface conductance also occur simultaneously.18 Theory and experiments are presented in this paper to strongly suggest that surface conductance along the inside surface of the capillary leads to a spreading of the external field-induced double-layer potential to sections of the capillary outside the area of direct external voltage field coverage. Surface conductance is a well-studied phenomenon at the glass-solution interface of electrolyte in water. Smoluchowski introduced the concept in 1910,19*20 and many experimental and theoretical reports appeared in the 1920s and 1 9 3 0 ~ . ~ l - ~ These reports were summarized in 1952 by Kruyt.27 Thus, the addition of this well-studied effect to the

(16) Van Oman, B. B.; Liversidge, G. G.; McIntire, G. C.; Olefirowicz, T. M.; Ewing, A. G. J. Microcol. Sep. 1990,2,176.

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(19) Sheludko, A. Colloid Chemistry; Elsevier: Amsterdam, 1966. (20) Smoluchowski, M. v. ElektTische Endosmose und Stromu-

ngsstrome; J. A. Barth Leipzig, 1914.

0 1993 American Chemical Society

ANALYTICAL CHEMISTRY, VOL. 65, NO. 15, AUQUST 1, 1993 2011

i C

a

3R.6 min

Flgwo 2. Three electropherograms representing (a) no conductlve external sheath, (b) 4%, and (c) 60% of the wtslde of the capHlary covered by conductlve silver paint sheath and held at -10 kV. The relative control of the electroosmotic flow is much greater at the 4% coverage than would be predicted by prlor thew. Experimental conditions: separatlon potential field, 123 Vlcm; caplllary, 57 cm (50 cm to the detector) X 20 pm 1.d. X 145 pm 0.d.; buffer, 10 mM phosphate, pH 3.9; detectlon, absorbance at 200 nm; neutral marker, phenol.

model and concept of electroosmotic flow control by an applied external field allows the effective control of this flow when applied over a small percentage of the capillary.

EXPERIMENTAL SECTION Apparatus. The basic experimental apparatus has been

described elsewhere.= Briefly, this system consisted of the apparatus shown schematically in Figure 1. This consisted of two Plexiglas interlock boxes. one box contained the separation power supply (Spellman, Plainview, NY) electrode and the injection end of the capillary, and the other box contained the center section of the capillary with the external voltage power supply electrode in contact with either a conductive sheath or a steel plate. The conductive sheath or steel plate is in direct contact with the outer surface of the separation capillary. The conductive sheath of varying length was applied as silver paint (Ernest F. Fullham, Lathum, NY; P/N 14810) and left to dry. The steel plate covered 5.4 cm of the capillary (57 cm total length, 9.5 % coverage). Capillaries for the steel plate experiments were 50 pm i.d., 370 pm o.d., and 57 cm long DB-1 columns (J&W Scientific, Folsom, CA). Buffers for the DB-1 columns contained 5% 2-propanol. Detection was by absorbance (Linear 200, Reno, NE). Other capillaries used in this study were 20 pm i.d., 144 pm o.d., and 52.6 cm in length (Polymicro Phoenix, AZ).

Chemicals. Solutions were made from HSO, (Baker, Phil- lipsburg, NJ) and NaHzPO, (Sigma, St. Louis, MO) and adjusted to the desired pH with NaOH. Phenol solutions were made from 'phenol liquefied" (Fisher, Fairlawn, NJ). Mesityl oxide was obtained from Aldrich Chemical Co., Milwaukee, WI. All chemicals were used as received without further purification. Twice-distilled (Megapure-Corning, Corning, NY) water was used for all buffers and solutions.

RESULTS AND DISCUSSION The radial voltage field created by a conductive sheath can

be used to modify the t potential on the inner surface of the capillary.6 This t potential is related to electroosmotic flow

(21) McBain, J. W.; Peaker, C. R.; King, A. M. J. Am. Chem. SOC. 1929,

(22) Urban,F.;Feldman,S.;White, H.L. J.Phys. Chem. 1935,39,606. (23) Urban, F.; White, H. L.; Strassner, E. A. J. Phys. Chem. 1935,39,

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(26) Fricke, H.; Curtis, H. J. J. Phys. Chem. 1936,40, 715. (27) Overbeek, J. Th. G. In Colloid Science; K ~ y t , H. R.; Ed.;

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61, 3294.

311.

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Eleevier: Amsterdam, 1952; Vol. I, pp 197-237.

27-31.

(u-) by vBo = tD,,EaPP/~,,, where Do is the permittivity of the buffer, qo is the viscosity, and Eapp is the separation potential fie1d.a In the present experiment, varied lengths of the center portion of the capillary have been coated with a conductive sheath followed by experimental evaluation of the electroos- motic flow. Under these conditions, according to current theory, a zone of high flow rate a t the inner wall along this coated region would be generated, effectively forming a pump in the middle of the capillary. Application of this model lea& to a prediction of varied flow rates along the capillary when electroosmotic flow is increased (or decreased) in the region of the applied radial voltage. The slower (or faster) moving buffer in unsheathed portions of the capillary is expected to lessen the effectiveness of the radial voltage control. In such a model, the bulk flow across the capillary is the weighted average of the sheathed and unsheathed flow zones. This results in the following re1ationship:M

(1) where vb is the bulk electroosmotic flow, x is the portion of the capillary covered by the sheath, us is the flow extrapolated to 100% sheath coverage, and u, is the flow without any sheath. An example of this type of experiment is shown in Figure 2. This figure shows three electropherograms, one for no sheath coverage (or the conventional CE system setup) and two showing the capillary with a conductive sheath of varying length with -10 kV applied to this sheath. The large degree of control for a 4 % coverage compared to 60 % appears to disagree with the theory outlined above. A plot of flow versus sheath coverage according to eq 1 is compared to experimental data obtained a t various sheath coverages and is shown in Figure 3. In this experiment, the effect of electroosmotic flow expected to be generated in the un- sheathed portions of the capillary on the overall flow is significantly smaller than that predicted by these assumptions, in both magnitude and slope of the resulting plot.

An explanation for the deviation from accepted theory is that the charge induced by the radial voltage in only a small percent of the inner surface of the capillary is dispersed over the entire double layer on the inner surface of the Capillary. Thus, the { potential varies less than might otherwise be predicted between the sheathed and unsheathed regions. Modification of existing theory to include a surface resistance

Vb = xu, + (1 - x)u,

~ ~~

(29) Rice, C. L.; Whitehead, R. J. J. Phys. Chem. 1965,69,4017-4024. (30) Chien, R.-L.; Helmer, J. C. Anal. Chem. 1991,63,1354-1361.

2012 ANALYTICAL CHEMISTRY, VOL. 65, NO. 15, AUGUST 1, 1993

.... ....V -

--.-

-87-

- 5 x- ....

i

C 20 40 60

Percent Coverage by Conductive Sheath

Flguro 3. Plot showing mlgratlon rate versus percent coverage of COndUctlve sheath for both eqs 1 (V) and 2 (A) and experimental data (0). Slopes for each are 0.026, 0.013, and 0.0075 for eq 1, eq 2, and experimental values, respectively. A potential of -10 kV has been applied to the conductive sheath for aH plots. Experimental conditions: caplllary, 52.5 cm (46.6 to detector) X 20 pm i.d. X 144 pm 0.d.; buffer, 25 mM phosphate, pH 2.0; probe, histidyl-phenylalanln, 8 X

M; detection, absorbance 200 nm (n = 3 for all experimental data sets, SD = 0.1-0.7%).

PO,

small arbitrary length - 9t-j- along capillary

- - PS

Flguro 4. Schematic representation of the equivalent electrical clrcult of a CE system under external field electroosmotic flow control. Both seperatlonpotential(P~andoutersheethpotentlal(P~are1ndependently adjustabk (from f 30 kV In our apparatus). The fused s i b capacitance (CQ), the resistance along the double layer (Re), the surface potential generated by the lonizatkn of swface silanol groups (PJ, the capacitance of the double layer (Ca), and the bulk buffer resistance are discussed In the text.

(or conductance) may better describe the capillary system under external voltage flow control. A circuit describing the proposed new model is shown in Figure 4. This new model includes the separation potential (Pa), bulk buffer resistance (Rb), outer sheath potential (P& and fused silica capacitance ( C Q ) ~ with the addition of a resistor along the inner surface, R,, and Pt, the potential generated by the ionized silanol groups (which occurs a t all points along the capillary). In this figure, ( is a consistent portion of the potential measured from R, across Pt and C,g to Rb. This modification to the theory is strongly supported by previous experimental data concerning thesilica-aolution interface. A surface conductance (Rd along the double-layer interface has been documentedl"27 and has been estimated31 at the glass-water interface to be lOl"lO13 Q/m. In addition, the potential caused by the ionization of the surface silanol groups may be calculated and is a complex

_ _ _ _ _ ~ ~

(31) Hunter, R. J. Zeta Potential in Colloid Science Principles and Applications; Academic Prees: London, 1981.

function of buffer pH and other physical properties of the buffer-inner surface interface (see eq 3 in ref 6). This model indicates that the additional surface charge from the radial voltage is effectively spread along the inner surface of the capillary through R, and directly effects the f potential over the entire capillary length.

This effect on flow may also be quantitated by assuming a linear gradient for the ( potential forms through R, from t8 (100% sheathed, u,) in the center to lw (unsheathed, uw) at the ends, across the unsheathed portions of the capillary. In the sheathed sections, the ( potential is equal to 5;. The value of (B used here is the average value for the sheathed section and was calculated as a fraction of the extrapolated flow velocity at 100% sheath coverage. In the unsheathed portions, the flow at the wall is modeled as a linear gradient from the flow corresponding to t8 (v,) to the flow corresponding to S, (vw). Since this is a linear gradient, the average flow, Y,, is (us + uw)/2. This average velocity may be substituted into eq 1 to give a new relationship for the fraction of capillary covered by the conducting sheath, x , versus bulk electroos- motic flow, VI,:

(2)

The plot of eq 2 in Figure 3 more closely reflects the experimental values than the plot of eq 1. However, the slope of the experimental data is even smaller than that predicted by this theory. This could be explained qualitatively if the spreading of the (potential due to surface conductance is not linear, but in fact hyperbolic. In addition, conductivity along the unsheathed but polyimide-coated region of the capillary might account for this small difference. However, this resistance would be in parallel to the surface conductance resistance, and the lesser of the two resistances would dominate the circuit. Since the polyimide has a resistance in the order of 1022 Q/m (assuming a 15 pm thick layer and volume resistivity of 1016 m)32 and the surface conductance is approximately lOl"lO13 Wm, the effect should be negligible. So the outer surface may have some effect, but most likely a very small one.

In addition to the experiments based on varying the degree of sheath coverage, a flat steel plate was employed to provide the external field. This plate merely had a tangential contact with the external surface at the center of the capillary. Under conditions where approximately 9.5% of the length of the capillary was in contact with the steel plate and a -15 kV potential was applied, the flow increased from 2.6 to 4.8 cm/ min (7-kV separation potential across a 50 pm i.d., 370 pm o.d., and 57 cm long capillary). It appears that the surface conductance is not only distributing the charge longitudinally down the capillary but also around the inner circumference. This is illustrated schematically in Figure 5a.

The model shown in Figure 4 predicts that, in some experimental configurations, a significant portion of the current across the capillary may be due to surface conductance rather than exclusively from the bulk buffer conductivity. Surface conductance attains a higher ratio of the total conductivity as the capillary diameter decreases (at extremes, this phenomenon has been termed 'capillary superconduc- t i v i t ~ ' ) . ~ ~ In addition, since R. is electrically connected to the separation potential, P,, the surface potential is largely defined by the separation potential. This potential also defines the calculated bulk buffer potential along the length of the capillary; relative to which the radial voltage is measured. The bulk buffer potential and the surface potential

Ub = xu, + (1 - x)V,,

(32) Anderson, H. L., JM. A Physicist's Desk Reference, 2nd ed.;

(33) Zhukov, I. I.; Fridrikhsberg, D. A. Kolloid Zhur. 1949, 11, 163- American Institute of Physics, New York, 1989.

171, cited from Chem. Abstr. 1949,43,7290.

ANALYTICAL CHEMISTRY, VOL. 65, NO. 15, AUGUST 1, 1993 2013

capillary. This includes the effects from the surface silanol groups, the separation potential, and the radial voltage capacitive effects. I t may be seen that this illustration matches the expected behavior by the proposed model circuit de- scribing the entire CE system.

Surface conductance plays a critical role in determining the rpotential along the inner wall of the capillary. This has enormous practical utility in designing capillary electro- phoresis experiments with control of the electroosmotic flow. In addition, the presence of surface conductance also may explain the presence of electroosmotic flow in commercial capillaries coated with hydrophobic stationary phases. Any surface charge in small holes in the stationary phase might effectively spread over a substantial segment of the capillary via surface conductance along the stationary phase and, thereby, result in greater than expected flow rates. This indicates that efforts to prevent or alter adsorption of analytes to the capillary wall may be carried out while retaining a significant amount of electroosmotic flow. A capillary which will not support any chemically generated surface charge might still generate electroosmotic flow through an applied external field.

In conclusion, the experiments reported in this paper have led to a model for electronic control of electroosmotic flow that involves surface conductance along the capillary. The design presented here requires application of only a small section of silver paint to the center of the capillary and only one power supply without any of the previously predicted reduced effectiveness for the control of flow. The theory presented here combined with the capillary electrophoresis experimental format should provide a better understanding of the double layer and the effects of electronically and chemically modifying the inner surface of the capillary.

a

Steel Plate

Fused Silica Capillary 1 b Conductive Sheath

Fused Silica Capillary I

Potential

Radial Voltage Induced

Separation Field Included

< Potential Only

Length Along Capillary

Flguro 5. (a) Proposed model for the distribution of charge around the inner radius of a fused silica capillary through surface conductance under the infuence of a charged steel plate. (b) Proposed model for the potentlal at the inner surface of the CE capillary. Line BB represents the potential within the bulk buffer. Line SP represents the surface potential. This surface potential is offset across the entire length of the capillary from the potential in the bulk buffer by Pt (see Figure 4) at the capillary surface. The addltional potential added to the surface by the external field (negative applied voltage in this case) is represented by the shaded area. The schematic at the bottom of the graph represents the resulting { potential over the length of the capillary where ZP Is the potential Induced by Pt and ZPRV Is the additional potential Induced by the applied external voltage.

are only offset byPt, the potential caused by the surface silanol groups and any contributions from the applied radial voltage. This radial voltage effect may also be modeled as having a resistor in parrallel with C Q . ~ However, the resistivity of fused silica is 10'6 R, hence this would not change the resulting f potential spread within the double layer as it is modeled here. The distribution of the additional charge may be more easily visualized by examining Figure 5b. This figure shows the expected surface potential as a function of position along the

ACHNO WLEDGMENT

This work was supported, in part, by the National Institutes of Health, the National Science Foundation, and Beckman Instruments, Inc. A.G.E. is a National Science Foundation Presidential Young Investigator (NSF CHE-8657193) and a Camille and Henry Dreyfus Teacher-Scholar. M.A.H. is a Shell Doctoral Fellow and a Wheeler P. Davey Fellow. Special thanks to Steve Herrick (Beckman) for his idea to use the steel plate and for discussions concerning the theory of electroosmotic flow control.

RECEIVED for review February 12, 1993. Accepted May 4, 1993.