1676 Anal. Chem. 1002, 64, 1676-1681

Effects of Capillary Temperature Control and Electrophoretic Heterogeneity on Parameters Characterizing Separations of Particles by Capillary Zone Electrophoresis Steven L. Petersen and Nathan E. Ballou' Chemical Sciences Department, Pacific Northwest Laboratory, Richland, Washington 99352

The effects of system parameters and partlcle propertles on separatlons by caplllary zone electrophoresls have been detennlned for mlxtures of charged polystyrene latex partlcles. Maintenance of constant caplllary temperature by a thermo- stated system dgnlflcantly reduced the large dependencles on voltage of mobllltles, selectlvlty, eff Ickncy, and resolution whlch were observed on a nonthermostated system. Elec- trophoretlc heterogenelty (Le., mlcroheterogenelty) In the parllcle samples was determlned to be the major source of zone broadenlng on the thermostated system. Slnce zone broadenlng due to electrophoretic heterogeneity Is Independent of voltage, the observed efflclencles were Independent of voltage. Resolutlon was also found to be Independent of voltage. The observed Independence of eff lclency on voltage Indlcated that partlclcwall lnteractlons were negllglble and that the separailons were electrophoretlc In nature. The relatlve standard devlatlon of the mobllHy dlstrlbutlon for a 0.07-pm carboxylate-modlkd latex was determlned to be 1.5%, whlch led to an efflclency of only 4400 theoretical plates. The large efflclency losses resultlng from electro- phoretic heterogenelty decrease restrlctlons on other broad- enlng sources. Thus, when zone broadenlng Is domlnated by electrophoretlc heterogenelty, larger InJectlon and detectlon volumes, caplllary Inner dlameters, and operatlng powers can be employed wlthout any slgnllcant further loss of efflclency or resolutlon.

INTRODUCTION

Several articles describing the separation of charged latex particle mixtures by capillary zone electrophoresis (CZE) have recently been published.'-3 Results obtained in our studies on a nonthermostated system revealed that mobilities, selectivity, efficiency, and resolution were all dependent on the applied potential gradient.' These dependencies were thought to be the result of significant temperature increases due to Joule heating of the buffer solution in the capillary. The effects of capillary temperature control on the above parameters have thus been determined with a thermostated system and are reported herein. The number of theoretical plates (efficiency) in CZE is determined in part by the zone variance of the sample. Factors contributing to zone variance in CZE separations of particulate samples have been iden- tified and their dependencies on the applied potential field are described theoretically. One such factor, electrophoretic

(1) Jones, H. K.; Ballou, N. E. Anal. Chem. 1990,62, 2484-2490. (2) VanOrman, B. B.; McIntire, G. L. J. Microcol. Sep. 1989,1,289-

( 3 ) VanOrman, B. B.; McIntire, G. L. Am. Lab. 1990, November, 66- 293.

67.

heterogeneity: is of special importance to particle separations and has unique properties. Based on theory and the experimental data from charged latex particles, the relative contributions of the factors to zone broadening have been determined. The implications of these results to CZE optimization strategies for particle separations are identified and discussed.

THEORY The dependence of various CZE parameters on the applied

potential field can be predicted by examining equations describing net mobility, selectivity, efficiency, resolution, and zone variance. The net mobility, p, of a sample zone can be described by any of the following equalities:

(la)

where p,, and pp are the electroosmotic and electrophoretic mobilities, respectively, v is the zone velocity, E is the applied potential gradient, x is the axial displacement relative to the point of injection, t is the migration time required for the zone to reach point x , and td is the migration time for the zone to reach the detector at xd.' For constant temperature and solution composition and in the absence of relaxation effects," po and pp (and thus p) are independent of E.6 Note that t is inversely proportional to E and v is directly proportional to E.5

To account for the possibility of particle-wall interactions, a distinction must be made between quantities correspond- ing to free particles and the apparent quantities that are observed. The mobilities, velocity, and time in eq l a correspond to the free quantities. If the fraction of particles that are free, 6, is less than unity, the free quantities will differ from the observed, apparent quantities. For example, the relationships between the apparent zone velocity, d , the apparent net mobility, p', and the apparent migration time, t', and their corresponding free quantities are v' = 6v, p' = 6p, and t = Bt'. Equation l a can then be restated in terms of the apparent (primed) quantities as

x d pf = 6(pa + pLp) = rrl = x = - E Et' Et,'

Assuming that 6 is independent of E , p' is independent of E when p is independent of E.

The selectivity between two zones in electrophoresis is defined as the relative difference of the apparent zone velocities, Av'Ivm', where Av' is the absolute difference of the apparent zone velocities and vm' is the mean apparent zone

(4) Wieme, R. J. In Chromatography: A Laboratory Handbook of Chromatographic and Electrophoretic Methods, 3rd ed.; Heftmann, E., Ed.; Van Nostrand Reinhold Co.: New York, 1975; Chapter 10, Section 6.

(5 ) Jorgenson, J. W.; Lukacs, K. D. Anal. Chem. 1981,53,1298-1302. ( 6 ) Hunter, R. J. Zeta Potential in Colloid Science; Academic Press:

London, 1981; Chapter 3.

0003-2700/92/0364-1676$03.00/0 0 1992 American Chemical Society

ANALYTICAL CHEMISTRY, VOL. 64, NO. 15, AUGUST 1, 1992 1677

velocity.' From eq lb, selectivity can be described as

(2a)

where p[ is the apparent net mobility of the ith zone. Thus selectivity is independent of E when free mobilities and 0s are independent of E. In the absence of particle-wall interactions or when 61 = 62 , eq 2areduces to the conventional form given by Jorgenson and Lukacss as

A d p 1 - k = APP

_- AV' pL11-p; - 61Cc1- 82Pz - Y,' ( P i + CLi)/2 - (61P1+ 62&)/2

(2b)

where pi is the free net mobility of the ith zone, App is the absolute electrophoretic mobility difference, and pp,, is the mean electrophoretic m ~ b i l i t y . ~

Efficiency in terms of number of theoretical plates, N, and resolution, R, in electrophoresis are defined according to Gid- dings as

_- - vm' (pi + &/2 pp,m + po

and

(3)

(4)

where ax2 and ad2 are the spatial zone variances a t x and x d , respectively, and N , is the mean efficiency.' Thus the E dependence of N is governed by the E dependence of ad2. When selectivity is independent of E, the E dependence of R is also determined by the E dependence of Ud2.

A number of studies on the various sources of zone broadening in the CZE of molecular ions have recently been published.611 For particles the total spatial zone variance is given by

where the terms on the right-hand side represent variance contributions from injection, detection, axial diffusion, the radial temperature profile caused by Joule heating, wall interactions, and electrophoretic heterogeneity, respectively. The first four sources of zone variance have been discussed in detail in the CZE literature.*ll The last term is from classical electrophoresis and representa zone broadening due to heterogeneity (variability in charge, size, and shape) in the particle ample.^ Zone variance due to heterogeneity, which has the unusual property of being E-reversible, has been theoretically studied by Sharp et al.,12 Alberty,13 and Brown and Cann.14 Equation 5 assumes the conductivity of the sample zone is equivalent to that of the buffer a t all times.

Substitution of variance terms presented e l s e ~ h e r e ~ ~ ~ ~ ~ . ~ into eq 5 leads to

(u,,Etl2 (6) where D is the diffusion coefficient of the particles, K is the

(7) Giddings, J. C. Sep. Sci. 1969,4, 181-189. (8) Huang, X.; Coleman, W. F.; Zare, R. N. J. Chromatogr. 1989,480,

95-110.

61, 241-246. (9) Grushka, E.; McCormick, R. M.; Kirkland, J. J. Anal. Chem. 1989,

(IO) Foret, F.; Deml, M.; BoEek, P. J. Chromatogr. 1988,452,601-613. (11) H j e d n , S. Electrophoresis 1990,11,665-690. (12) Sharp, D. G.; Hebb, M. H.; Taylor, A. R.; Beard, J. W. J. Biol.

(13) Uberty, R. A. J. Am. Chem. SOC. 1948, 70, 1675-1682. (14) Brown, R. A.; Cann, J. R. J. Phys. Chem. 1950,54, 364-369.

Chem. 1942,142,217-231.

electrical conductivity of the buffer, B is the exponential coefficient relating viscosityto temperature? a is the capillary inner radius, Ab is the thermal conductivity of the buffer, T, is the temperature at the inner wall of the capillary, kl-1 is the mean free lifetime of the particles, and a,, is the standard deviation of the distribution of net mobilities for the particle sample. The U D ~ term is from the Einstein equation5 The UT^ term is from Grushka et al. with the simplifying assumption that 8XbTa2 >> KBaZE2, which applies for the work reported here.9 The use of this form of CTT~ also assumes that exclusion effects (i.e., finite-size particles are sterically excluded from the slowest streamlines along the walls) are negligible.16 For the work reported here, this assumption leads to UT^ being overestimated by 10.80%. The uwd2 term is from Wieme4 and has ita origin in Giddings' nonequilib- rium chromatography theory.16 The ah2 term is from Al- b e r t ~ . ~ ~

To determine the E dependence of ax2, eqs l a and 1b are used to eliminate the E-dependent variables Y, t, and t' from eq 6. Then for t = t d and x = x d , the total spatial zone variance at the detector is

(a,/P)2x: (7) Note that ah2 is independent of E. For particle samples, winj2 and ah2 will often be the dominant variance terms under normal CZE running conditions. Under such conditions, ad2 and thus N and R will be independent of E. This is in contrast to CZE of molecular ions, where Ud2 and U D ~ are often the dominant variance contributors,8 so that ad2 decreases with increasing E until UT^ becomes significant.

EXPERIMENTAL SECTION Nonthermostated System. Detailed experimental conditions

for the data collected on the nonthermostated system have been given previously.' Capillaries were cut from the same stock as those used on the thermostated system. Runs were performed at 24 "C and cooling was by natural convection on1y.l

Thermostated System. Apparatus. Separations were per- formed on a P/ACE 2000 automated capillary electrophoresis system, which employs a liquid-cooled capillary cartridge (Beck- man Instruments, Palo Alto, CA). All runs were performed on the same capillary, a 75-pm-i.d., 190-pm-0.d. fused silica capillary that measured 39.4 cm from injection end to the detector window and 46.1 cm in total length (Polymicro Technologies, Inc., Phoenix, AZ). The capillary was thermostated at 25.0 * 0.2 O C .

The UV absorbance detector had a 200-pm-wide aperture and was set to 254 nm. Data were collected with the P/ACE control software at an acquisition rate of 10 Hz.

In the P/ACE system's cartridge, several sections of the capillary are not in contact with the cooling fluid. These nonther- mostated sections are comprised of 4.9 cm at each end of the capillary and 1.7 cm at the detector window. For the work reported here, 14 % of the 39.4-cm effective length of the capillary was nonthermostated. The data reported below indicate that the overall capillary temperature was held constant and that this small nonthermostated portion of the capillary did not signif- icantly influence the results.

Particle Standards and Buffer. Reagent-grade NaOH (Al- drich) and NazHPOl (Mallinckrodt) and Milli-Q deionized water (Millipore Corp., Bedford, MA) were used to prepare pH 10.7 phosphate buffer (5.00 mM total phosphate) as described previously.' The buffer was filtered daily at a filter pore size of 0.2 pm.

(15) Silebi, C. A.; DosRamos, J. G. AZChE J. 1989, 35, 1351-1364. (16) Giddings, J. C. In Chromatography: A Laboratory Handbook of

Chromatographic and Electrophoretic Methods, 3rd ed.; Heftmann, E., Ed.; Van Nostrand Reinhold Co.: New York, 1975; Chapter 3.

1878 ANALYTICAL CHEMISTRY, VOL. 84, NO. 15, AUGUST 1, 1992

Commercially available carboxylate-modified (Polysciences, Inc., Warrington, PA) and sulfate-modified (Interfacial Dynamics Corp., Portland, OR) latex dispersions were diluted with buffer to prepare latex standards as previously described.' The final concentrations in the mixture of 0.07- and 0.10-pm carboxylate- modified latexes were 1.0 X 10l2 and 9.1 X 1Olo particles/mL (0.020 and 0.0050 wt %), respectively. This mixture was a true dispersion with no sedimentation occurring over a period of at least 13 days. Dynamic light scattering experiments performed on individual standards of the 0.07- and 0.10-pm latexes indicated that neither latex formed aggregates in the phosphate buffer.

Procedure. The capillary was conditioned by rinsing it at 20 psi with 0.1 M NaOH, deionized water, and buffer for 15 min each. Following conditioning, the capillary was allowed to contact buffer only. Hydrodynamic injections were performed for 3.0 s at ca. 0.5 psi. Constant voltage runs were performed at applied voltages of 5.0-30.0 kV. Between runs, the capillary was given a 20-psi, 4.0-min buffer rinse. At the start of a separation, the P/ACE 2000 takes 0.17 min to ramp to the programmed voltage. Since the equations given above assume the programmed voltage is reached instantaneously, migration times were corrected by subtracting 0.085 min from the observed times. Electrophero- grams were analyzed interactively with the P/ACE control software. Gaussian peak shapes were assumed for the deter- mination of zone variance, which was taken as the spatial full- width-at-half-maximum squared divided by 5.545.

RESULTS AND DISCUSSION Mobilities and Selectivity. The following discussion

assumes a constant buffer composition and a constant &+ In addition, all data points in plots presented herein correspond to the means of 3-4 runs and contain f l standard deviation error bars, which are smaller than the symbols for many points. The average current I monitored during the course of an E- controlled CZE run is a good indicator of the extent of tem- perature rise within the ~apillary.1~ An I-E plot has a slope of 1ra2K, which will increase with temperature since K increases with temperature. Figure 1A shows I-E plots for both CZE Systems. The large I and high nonlinearity for the nonther- mostated system are indicative of significant capillary solution temperature increases with increasing E. Conversely, the I values for the thermostated system show only a slight deviation from linearity at large E , indicating efficient removal of Joule heat from the capillary. The operating power ranges for the data in Figure 1A were 0.0294-1.11 and 0.46-2.5 W for the thermostated and nonthermostated systems, respec- tively . As discussed above, mobilities should be independent of

E as long as the capillary temperature is held constant. Significant increases in capillary temperature with increasing E will result in increasing mobilities.6 Figure 1B shows po-E plots for injections of 1 % (v/v) acetone on the two systems. The p, values were calculated according to eq l a with pp = 0 and the assumption that 8 = 1 for acetone. The p, values for the thermostated system increase slightly with increasing E . On the other hand, the p, values for the nonthermostated system increase considerably with increasing E and are larger than the p, values for the thermostated system. These results are consistent with the I-E data and indicate small temper- ature increases for the thermostated system and large tem- perature increases for the nonthermostated system with increasing E.

Figure 2 shows typical electropherograms obtained with the thermostated system for a seven-component latex mixture at five different E . To allow comparison of the electrophero- grams, the x-axis was normalized by converting from td' to p' units according to eq Ib. The composition of the mixture, which contains both carboxylate-modified (CML) and sulfate-

n 50 4 W 3 40

+ 30

20

10

(17) Nelson, R. J.; Paulus, A.; Cohen, A. s.; Guttman, A,; Karger, B. L. J . Chromatogr. 1989, 480, 111-127.

-

-

-

-

-

80

7 0 ! A 60

0 ' 0 100 200 300 400 500 600 70C

E (V/cm>

I '

0

10

:o l 2 1 8 1 0 100 200 300 400 500 600 700

Flgurr 1. Average current vs potentlabgradlent (A) and electroos- motlc moblllty vs potentlabgradient (B) plots for the thermostated (A) and nonthermostated (B) systems. Nonthermostated data from ref 1.

modified (SML) latexes, has been given previously.1 The peaks correspond to (a) 0.030-pm SML; (b, c) unresolved 0.07-pm CML and 0.079-pm SML; (d) 0.10-pm CML; (e) 0.20- pm CML; (0 0.51-pm CML; and (9) 1.16-pm CML. The increases in p' with increasing E observed on the thermo- stated system are much smaller than those previously observed on the nonthermostated system.' For example, for peak d the increase in p' from E = 434 to E = 651 V/cm was 9.8% for the thermostated system, whereas it was 43% for the nonthermostated system.'

The dependence of p' on E was studied more thoroughly with two-component latex mixtures. Figure 3 is a typical electropherogram for the mixture of 0.07- and 0.10-pm CML particles separated on the thermostated system. The qual- itative features of the electropherogram did not vary with E. Figure 4A shows p'-E plots for the two-component mixture separated on the thermostated system along with data for a different two-component mixture previously separated on the nonthermostated system.' Again, the p' values obtained with the nonthermostated system show a strong dependence on E due to increasing capillary temperature with increasing E, while the p' acquired with the thermostated system show only a slight dependence on E . Since po (Figure 1B) and p'

k 0 4 0 a, 4 a, n

9

8 -

n

\ cu E 7 - 0

1 6 -- 0

5 -- 4 W

a 4 -

6 --

0 -'

-.

6

0 -

--

6 5 4 3 2 1

Figure 2. Electropherograms at five different voltages for the seven- component latex mixture separated on the thermostated system. The x-axis was normalized by convertlng unRs from apparent migration tlme to apparent net mobility. See text for peak assignments.

3 n 5 -4

4 2

(d d M .- 1 u1 k 0 4 0 a, a,

m I 0

W

4

r O

n 2.0 2.5 3.0 3.5 4.0

t,' (min) Figure 3. Typical electropherogram for the two-component latex mlxture separated on the thermostated system. Peaks correspond to 0.07-pm (a) and 0.10-pm (b) carboxylatamodlfled latex particles. The applied voltage gradlent was 542 Vlcm.

(Figure 4A) show only a slight dependence on E and 0 is assumed to be E-independent, pup must also be nearly independent of E for the thermostated system (eq lb).

Figure 4B shows selectivity vs E plots calculated from the p' data in Figure 4A according to eq 2a. For the thermo- stated system, selectivity is nearly independent of E, con- sistent with eq 2a and the small dependencies of p' on E in Figure 4A. The drop in selectivity at 542 Vlcm is due to an anomalous drop in Ap' at that voltage. For the nonthermo- stated system, selectivity increases sharply at the two largest E due to large increases in Ap' at these E.

ANALYTICAL CHEMISTRY, VOL. 64, NO. 15, AUGUST 1, 1992 1679

10

0.30

0.25

h

3

0 a, a) VI

5 z 0.20

r+

0.15

0.10

0 100 200 300 400 500 600 700

E (V/cm>

B ,i 1-5

0 100 200 300 400 500 600 700

E (v/cm> Figure 4. Apparent net mobility vs potentiaCgradlent (A) and selectivity vs potentlabgradlent (B) plots for the thermostated (open symbols) and nonthermostated (filled symbols) systems. Apparent net mobillties correspond to 0.07-pm carboxylate (A), 0.10-pm carboxylate- (0, m), and 0.079-pm sulfate (V) modified latex partlclea. Nontherm stated data from ref 1.

Zone Variance, Efficiency, and Resolution. The mea- sured Ud2 for each particle zone of the two-component mixture separated on the thermostated system are presented in Table I; the values in parentheses are standard deviations. There is no evident dependence of zone variance on E for this mixture. Because of the various orders of E dependence predicted by eq 7 for the different variance sources, it is useful to compare the values of the terms in order to establish their contribution to the total variance. Variance due to the finite width of the detector aperture can be calculated as Ude? = wdet2/12, where wdet is the aperture width.18 This equation gives a U&t2 of 3.3 X cm2, which is 10.0087% of the ad2 for the particles given in Table I. Values for m2 and UT^ calculated according to eq 7 are included in Table I for comparison. For both terms, 0 was assumed to equal unity (Le., p = p') so the u~~ are maximum values and the are

(18) Sternberg, J. C. In Aduances in Chromatography; Giddinga, J. C., Keller, R. A., Ede.; Marcel Dekker: New York, 1966; Volume 2, Chapter 6.

1680 ANALYTICAL CHEMISTRY, VOL. 64, NO. 15, AUGUST 1, 1992

Table I. Zone Variances for the Two-Component Mixture Separated on the Thermostated System at Six Electric Field Strengths

u 2 4000 a A

d

3000 .ri 3 u k ; 2000

0.07-pm CML 0.10-pm CML E (V/cm) 5". ( O C ) Ud2 (10-4 cm2) u$ (10"' cm2) UT^ (lo-* cm2) Ud2 (lo4 cm2) m2 (lo4 cm2) m2 (1W cm2)

-

-

-

108 25.11 (0.00)

217 25.43 (0.00)

325 26.00 (0.00)

434 26.79 (0.01)

542 27.81 (0.03)

651 29.21 (0.06)

0.60 (0.00) 0.30

(0.00) 0.19

(0.00) 0.14

(0.00) 0.11

(0.00) 0.090

(0.002)

minimum values with respect to the extent of wall interactions. The Stokes-Einstein equation was used to estimate D of 3.5 X 10-8 and 2.4 X 1W cm2/s for the 0.07- and 0.10-pm CML particles, respectively. The values for UT^ were calculated using B = 2400 K? Ab = 0.605 W/mK? and T, calculated from the equation and thermal conductivities given by Grushka et alS9 and the heat transfer coefficient for the P/ACE 2000 of 1052 W/m2K reported in ref 19. The resulting u ~ 2 and UT^ are 10.016% and 10.95 5% , respectively, of the corresponding Ud2 in Table I. An estimate of uhj2 can be obtained from data from the acetone runs, which used the same hydrodynamic injection conditions as the particle mixture runs. The Ud2 for acetone decreased with increasing E until reaching a limiting value at E 1 325 V/cm. Then according to eq 7, Ud2 uhj2 for acetone at E 1 325 V/cm, since Udet2 was negligible compared to Ud2 and Uh2 = 0 for acetone. Consequently, the average Ud2 observed for acetone at E 1 325 V/cm provides a good estimate of uhj2 for the latex particles. This value is 0.0328 f O.OOO9 om2 which is 18.6% of the Ud2 observed for the particles. Therefore, uhj2 is the only one of the first four variance terms in eq 5 that is significant in the present study, and ,9096 of the variance observed for the particles must be accounted for by uWd2 and uh2. The absence of E dependence in Ud2 (Table I) suggests that uwd2 is also negligible and that

0.0040 4437 (O.oooo) (519) 0.12 4236

(0.00) (69) 0.99 4662

(0.00) (117) 4.3 4201

(0.1) (222) 13 4351 (0) (390) 37 6199 (2) (353)

0.55 0.0043 (0.00) (O.oo00) 0.27 0.13

(0.00) (0.00) 0.18 1.1 (0.00) (0.0) 0.13 4.6

(0.00) (0.1) 0.10 14 (0.00) (0) 0.082 41

(0.002) (2)

With respect to the assumption of Gaussian peak (zone) shapes, it is apparent from Figure 3 that the assumption is a reasonably good one for the 0.07-pm CML. On the other hand, the peaks for theO.10-pm CML exhibit significant front- ing and second moment analysis would have been more exact for the determination of their Ud2,18 However, when the observed peaks at the various E for the 0.10-pm CML were plotted as detector signal vs axial displacement: they were found to be superposable. Since peak height, area, and shape were thus seen to be independent of E, the calculated second central moments would also have been independent of E. Therefore, if second central momenta (rather than half widths) had been used to determine Ud2, all discussion related to the E independence of Ud2 would have been unchanged. As discussed above, the E dependence of zone variance

determines the E dependence of efficiency and, when selectivity is independent of E, also determines the E de- pendence of resolution. Figure 5, parts A and B, shows N-E and R-E plots, respectively, for the two-component mixtures. For the thermostated system, N and R are essentially independent of E, except a t the largest E, consistent with eq 3,4, and 8 and the E independence of selectivity. N for the

(19) Vinther, A.; Soeberg, H. Poster PM-2, Presented at the Third International S y m p i u m on Capillary Electrophoresis, San Diego, CA, February 4-6, 1991.

VI 5000 r------

I

0 100 200 300 400 500 600 700

E (V/cm>

0

Q) e= v, 'i 0 4 0 100 200 300 400 500 600 700

E (v/cm> Flgwr 5. Number of theoretical plates vs potentialgradlent (A) and resolution vs potentiel-gradlent (B) plots for the thermostated (open symbols) and nonthermostated (filled symbols) systems. Theoretical plates correspond to 0.07-pm carboxylate- (A), 0.10-pm carboxylate- (0, .), and 0.079-pm sulfate- (V) modlfied latex particles. Nonther- mostated data from ref 1.

0.10-pm CML and R for the mixture vary significantly for the nonthermostated system, with R essentially following the E dependence of selectivity.1 For the thermostated system, R largely follows the E dependence of selectivity (Figure 4B),

ANALYTICAL CHEMISTRY, VOL. 64, NO. 15, AUGUST 1, 1992 1681

except at E = 325 and 651 V/cm, where the influence of N for the 0.10-pm CML is evident.

The independence of Ud2 on E (and thus on v and td)

indicates that wall interactions are insignificant in the present study and that the separations are electrophoretic in nature, as previously suggested.' This is in contrast to other reports, in which latex particles were separated under different experimental conditions and in which wall interactions were suggested to be the dominant separation mechanism.2~3 In another paper we describe the application of modified CZE methods to the determination of the contributions of wall interactions and electrophoretic heterogeneity to zone broad- ening in particle CZEa20

Optimization of Particle Separations. From the above discussion, it is clear that the presence of electrophoretic heterogeneity will lead to CZE optimization strategies that differ considerably from those previously developed for mo- lecular CZE, where an optimal E that minimizes both U D ~ and UT^ is often sought.&11 Electrophoretic heterogeneity makes an E-independent contribution to Udz, and its contributions to N and R are independent of both E and Xd. UT^ is of negligible magnitude here and for most molecular CZE. However, in consideration of the small D of submicrometer and micrometer size particles, UT^ may be significant in other particle CZE separations where larger operating powers are employed. Since u ~ 2 will always be negligible in typical particle CZE experiments, E can be decreased until UT^ is negligible. For cases where uwdZ is significant, E can again be decreased to mimimize uwd2, albeit with the sacrifice of longer run times.

When eq 8 applies, which should often be the case for particle samples, and Av'lv,' is E-independent, E has no effect on N and R. Then (for constant a$), selectivity, efficiency, and resolution are solely dependent on the properties of the particle sample when dispersed in the running buffer. Consequently, optimization strategies must attempt to in- crease selectivity and/or decrease u J p via chemical modifi- cation of the particle/buffer system. By subtracting the calculated values of uinj2, Udet2, U D ~ , and UT^ from Ud2 for each run (assuming u W ~ 2 = 0), average Uh2 values of 0.3629 f 0.0140 and 0.4377 f 0.0787 cmz are obtained for the 0.07- and 0.10- pm CML particles, respectively. These Uh2 lead to uJp of (1.53 f 0.03) 5% and (1.68 f 0.15) 9% for the 0.07- and 0.10-pm CML samples, respectively. These apparently small relative standard deviations for the p distributions cause large efficiency losses. If Uh2 could be minimized such that Ud2 = uiaj2, N would increase to 47 000 in Figure 5A. On the other hand, if uinj2 could be reduced to a negligible value so that Ud2

= Uh2, a uJp of 0.32% would be necessary for an N of 100 000. Finally, Figure 4B suggests that running at higher tem-

peratures may be a practical approach to optimizing particle CZE separations, providing the particle dispersions are stable at the higher temperatures. Since the heat transfer coefficient

for the nonthermostated system is not known, the equation of ref 9 cannot be used to calculate T,. However, T, can be estimated from electroosmotic mobility data using the proportionalitypo a €17, where e and 7 are the buffer's dielectric constant and viscosity, respectively, both of which are tem- perature d e ~ e n d e n t . ~ The ratio of po at two temperatures is equal to the ratio of €17 a t those two temperatures

where the subscripts u and r refer to unknown and reference temperatures, respectively. Tabulated values of e and 7 for water a t various temperaturesz1 were used to determine a second-order equation describing the right-hand side of eq 9 for T, = 25 "C. The resulting equation

*- - 0.5405 + 0.01924Tu - (2.107 X lO")T,2 (10) 10,25OC

was used to estimate Tu based on the measured po and the assumption that the temperature dependence of €17 for water reasonably approximates that for the buffer. The value of po at 108 V/cm for the thermostated system (Figure 1B) was assumed to equal p0,250c. The resulting Tu for the thermo- stated system were up to 9% larger than the corresponding T, calculated according to ref 9 (Table I). For the nonther- mostated system, the Tu a t E = 364,454,545, and 636 Vtcm were calculated from eq 10 to be 39, 50, 66, and 89 OC, respectively. Although these values are approximate, they reflect the large capillary temperature increases that were responsible for the dramatic increase in selectivity at large E for the nonthermostated system (Figure 4B).

CONCLUSIONS When the major source of zone broadening in CZE

separations of particles is electrophoretic heterogeneity in the particle samples and the capillary is efficiently thermo- stated, efficiency and resolution are largely independent of the applied voltage. Unfortunately, electrophoretic heter- ogeneity can also result in a large loss of efficiency. However, such conditions lessen the usual limitations on other broad- ening sources, most of which limit the practical application of CZE. Consequently, injection and detection volumes, capillary inner diameter, and power level can all be increased to enhance detectability and throughput without any sig- nificant additional loss of efficiency or resolution.

ACKNOWLEDGMENT This research was supported by the U.S. Department of

Energyunder Contract DE-AC06-76RLO 1830. PacificNorth- west Laboratory is operated for the US. Department of Energy by Battelle Memorial Institute under Contract DE- AC06-76RLO 1830.

(20) Petersen, S. L.; Ballou, N. E., unpublished work. (21) CRC Handbook of Chemistry and Physics, 60th ed.; Weast, R. C.,

Ed.; CRC Press: Boca Raton, 1980; pp E-61 and F-51. RECEIVED for Review December 16, 1991. Revised manu- script received May 8,1992. Accepted May 13, 1992.